Physics, Pharmacology and Physiology for Anaesthetists: Key Concepts for the FRCA

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Physics, Pharmacology and Physiology for Anaesthetists

Key concepts for the FRCA

Second edition

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Physics, Pharmacology andPhysiology for AnaesthetistsKey concepts for the FRCA

Second edition

Matthew E. Cross MB ChB MA(Ed) MRCP FRCA

Consultant Anaesthetist, Queen Alexandra Hospital, Portsmouth, UK

Emma V. E. Plunkett MBBS MA MRCP FRCA

Specialist Registrar in Anaesthetics, Birmingham School of Anaesthesia, UK

Foreword by

Professor Peter Hutton PhD FRCA FRCP FIMechE

Consultant Anaesthetist, University Hospital Birmingham and Honorary Professor ofAnaesthesia, University of Birmingham, Birmingham, UK

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University Printing House, Cambridge CB2 8BS, United Kingdom

Published in the United States of America by Cambridge University Press, New York

Cambridge University Press is part of the University of Cambridge.

It furthers the University’s mission by disseminating knowledge in the pursuit ofeducation, learning, and research at the highest international levels of excellence.

www.cambridge.orgInformation on this title: www.cambridge.org/9781107615885

© M. Cross and E. Plunkett 2008, 2014

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

Second edition first published 2014

Printed and bound in the United Kingdom by the MPG Books Group

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ISBN 978-1-107-61588-5 Paperback

Additional resources for this publication at www.cambridge.org/9781107615885

Cambridge University Press has no responsibility for the persistence or accuracy ofURLs for external or third-party internet websites referred to in this publication,and does not guarantee that any content on such websites is, or will remain,accurate or appropriate.

..............................................................................................Every effort has been made in preparing this book to provide accurate andup-to-date information which is in accord with accepted standards and practiceat the time of publication. Although case histories are drawn from actual cases,every effort has been made to disguise the identities of the individuals involved.Nevertheless, the authors, editors and publishers canmake nowarranties that theinformation contained herein is totally free from error, not least because clinicalstandards are constantly changing through research and regulation. The authors,editors and publishers therefore disclaim all liability for direct or consequentialdamages resulting from the use of material contained in this book. Readersare strongly advised to pay careful attention to information provided by themanufacturer of any drugs or equipment that they plan to use.

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http://www.cambridge.org/9781107615885

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It was with great sadness that we learned of the death of

Dr Mark duBoulay shortly after the first edition of this book

had gone to print. He is missed by many.

MC & EP

For Anna, Harvey and Fraser,

a wonderful family

MC

For Mum and Dad. Thank you for everything.

EP

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Contents

Acknowledgements page xiiPreface xiiiForeword to the second editionProfessor Peter Hutton xvForeword to the first editionTom E. Peck xvii

Introduction 1

Section 1 * Mathematical principles 5Mathematical relationships 7Exponential relationships and logarithms 9Integration and differentiation 16Physical measurement and calibration 19The SI units 23Non-SI units and conversion factors 26

Section 2 * Physical principles 29Simple mechanics 31The gas laws 34Laminar flow 36Turbulent flow 37Bernoulli, Venturi and Coanda 38Heat and temperature 40Humidity 43Latent heat 46Isotherms 48Mechanisms of heat loss 50Solubility and diffusion 53Osmosis and colligative properties 55Principles of surface tension 57Resistors and resistance 59Capacitors and capacitance 60Inductors and inductance 63Wheatstone bridge 65Resonance and damping 66Cleaning, disinfection and sterilization 70

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Section 3 * Principles of special equipment 73Magnetic resonance imaging 75Refraction and fibre-optics 79Laser principles 81Surgical diathermy 84Medical ultrasound 87The Doppler effect 89Oesophageal doppler 90Cardiac output measurement 92Goal directed fluid therapy 97Defibrillators 98Breathing systems 100Ventilator profiles 103Pulse oximetry 109Capnography 112Absorption of carbon dioxide 117Neuromuscular blockade monitoring 119Thromboelastography 124

Section 4 * Pharmacological principles 127Atomic structure 129Oxidation and reduction 131Chemical bonds 132Inorganic and organic chemistry 135Isomerism 138Enzyme kinetics 141G-proteins and second messengers 144The Meyer–Overton hypothesis 146The concentration and second gas effects 148Drug interactions 150Adverse drug reactions 151Pharmacogenetics 153

Section 5 * Pharmacodynamics 155Drug–receptor interaction 157Affinity, efficacy and potency 160Agonism and antagonism 164Hysteresis 170Tachyphylaxis and tolerance 171Drug dependance 173

viii Contents

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Section 6 * Pharmacokinetics 175Absorption, distribution and redistribution 177First pass metabolism and bioavailability 179Volume of distribution 181Clearance 183Time constant and half life 185Non-compartmental modelling 187Compartmental modelling 188Physiological modelling 193Context-sensitive half time 194Target controlled infusions 196

Section 7 * Respiratory physiology 201Lung volumes 203Spirometry 205Flow–volume loops 207The alveolar gas equation 211The shunt equation 212Pulmonary vascular resistance 214Distribution of pulmonary blood flow 216Ventilation/perfusion mismatch 218Dead space 219Fowler’s method 220The Bohr equation 221Oxygen delivery and transport 223Classification of hypoxia 226The oxyhaemoglobin dissociation curve 228Carriage of carbon dioxide 230Work of breathing 232Control and effects of ventilation 233Compliance and resistance 236

Section 8 * Cardiovascular physiology 239Einthoven’s triangle and axis 241Cardiac action potentials 244The cardiac cycle 246Electrocardiographic changes 249Pressure and flow calculations 254Central venous pressure 257Pulmonary capillary wedge pressure 258The Frank–Starling relationship 260Venous return and capillary dynamics 262

Contents ix

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Ventricular pressure–volume relationship 267Systemic and pulmonary vascular resistance 272The Valsalva manoeuvre 274Control of heart rate 276Materno-fetal and neonatal circulations 278Shock 280

Section 9 * Renal physiology 281Acid–base balance 283Buffers and the anion gap 285Glomerular filtration rate and tubulo–glomerular feedback 289Autoregulation and renal vascular resistance 291The loop of Henle 293Glucose handling 295Sodium handling 296Potassium handling 297

Section 10 * Neurophysiology 299Action potentials 301Muscle structure and function 305Muscle reflexes 308The Monro–Kelly doctrine 310Cerebral blood flow 313Flow-metabolism coupling 316Formation and circulation of cerebrospinal fluid 319Pain 320

Section 11 * Applied sciences 323The stress response 325Cardiopulmonary exercise testing 328Pregnancy 331Paediatrics 337Ageing 340Obesity 344

Section 12 * Statistical principles 347Types of data 349Indices of central tendency and variability 351Types of distribution 355Methods of data analysis 357Error and outcome prediction 366Receiver operating characteristic curve 369

x Contents

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Clinical trials 370Evidence-based medicine 374Kaplan Meier curves 376

Appendix 377Index 402

Contents xi

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Acknowledgements

We are grateful to the following individuals for their invaluable help in bringingthis book to publication

Surg Lt Cdr Bentley Waller BSc(Hons) MB ChB FRCA RNAnaesthetics Department, Queen Alexandra Hospital, Portsmouth, UK

For his thorough proof reading of the first edition and his extraordinary yetdiplomatic ability to suggest areas for improvement. Much appreciated.

Professor Peter Hutton PhD FRCA FRCP FIMechEAnaesthetics Department, University Hospital Birmingham, Birmingham, UK

In addition we are grateful for permission to reprint the illustrations on pages 183and 184 from International Thomson Publishing Services Ltd.

Cheriton House, North Way, Andover, UK

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Preface

In the years since the first edition of this book was published much has changed inthe world of anaesthesia. Some of these changes relate to the way we practice asprofessionals and the way in which the evidence is shaping our knowledge in newareas. Other changes relate to the way in which anaesthetists in the UnitedKingdom progress through their training programmes. It is natural for the worldaround us to change in this way but, of course, it means that we have to continuallyreassess our practice, our knowledge and how that knowledge may best be applied.

Fortunately, the fundamental basic science principles that underpin much ofanaesthesia have not changed to such an extent and so it is unlikely that you willsuddenly be faced with the challenge of revising a newly discovered law of physicsfor the examination.

Where practice has changed, and where these changes have been incorporatedinto the syllabus of the Royal College, we have tried to reflect this in the latestedition. The second edition introduces applied physiology, more physical princi-ples, fundamental biochemistry and many additional pages of information both inthe body of the book and in the larger appendix. The layout and principles remainthe same in that we hope you can use this book as a useful companion to explainsome principles in a different way or to remind you of things that you will haveread elsewhere. One thing that remains constant is that the FRCA examination ishard but fair. If you dedicate yourself to learning, absorbing and using all theinformation you need to be successful in the examination then you will emergewith the skills required to flourish in your profession. It is worth it and we hope thisbook can help you along the way.

Good luck in the examinations, by the time you read this the end is already insight!

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Foreword to the second edition

Anunderstanding of physics, pharmacology and physiology is central to high qualitypatient care. Grasping the key concepts is not optional: it is an essential cornerstoneunderpinning the frequent judgements that have to be made in everyday clinicalpractice.

Today, information is available from many sources: books, journals, the internet,and podcasts. However, some of this is not written for the postgraduate student anda proportion is unfiltered and of uncertain provenance. Sorting the wheat from thechaff can be both time-consuming and frustrating, and not infrequently leaves theexplorer less, rather than more, focused in their awareness of what really counts.

This book, written by two enthusiasts whose own experiences of postgraduateexaminations is still within recent memory, is a considerable contribution to theresources of those preparing for postgraduate examinations in anaesthesia andintensive care. In terms of key subject areas, I cannot find anything included withinit that is not essential and I can think of nothing excluded which is.

The text is clear and concise: the diagrams are immediately comprehensible butdo not lack detail; the general presentation reflects good examination technique.The authors themselves recognize the need for more detailed companion textswhere deeper study is necessary and have not tried to misrepresent their book’splace in the wider armamentarium of the examinee.

What all examinees need as they study for, and approach, postgraduate exami-nations is a single reliable source of pre-prepared essential information that theycan both carry with them and refer to with confidence. This book meets these twoneeds admirably. In addition, the text style demonstrates the way to conveyinformation quickly but without unnecessary embellishment – the ideal methodfor a candidate to adopt.

In summary, I think this is a valuable second edition of a text that has alreadyreceived a considerable following. The authors have done an excellent job; postgrad-uate trainees have available a book that ‘does what it says on the can’; and examinerscan look forward to future answers with that frequently elusive ‘high signal to noiseratio’.

All I can do now is to wish both the authors and the readers the very best in theirpersonal efforts to provide high quality care for patients. This after all, is whatmedicine is all about.

Professor Peter Hutton PhD FRCA FRCP FIMechEConsultant Anaesthetist, University Hospital BirminghamHonorary Professor, University of Birmingham

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Foreword to the first edition

Many things are currently in a state of flux within the world of medical educationand training, and the way in which candidates approach examinations is noexception. Gone are the days when large weighty works are the first port of callfrom which to start the learning experience. Trainees know that there are moreefficient ways to get their heads around the concepts that are required in order tomake sense of the facts.

It is said that a picture says a thousand words and this extends to diagrams aswell. However, diagrams can be a double-edged sword for trainees unless they areaccompanied by the relevant level of detail. Failure to label the axis, or to get thescale so wrong that the curve becomes contradictory is at best confusing.

This book will give back the edge to the examination candidate if they digest itscontents. It is crammed full of precise, clear and well-labelled diagrams. Inaddition, the explanations are well structured and leave the reader with a clearunderstanding of the main point of the diagram and any additional informationwhere required. It is also crammed full of definitions and derivations that are veryaccessible.

It has been pitched at those studying for the primary FRCA examination and Ihave no doubt that they will find it a useful resource. Due to its size, it is nevergoing to have the last word, but it is not trying to achieve that. I am sure that it willalso be a useful resource for those preparing for the final FRCA and also for thosepreparing teaching material for these groups.

Doctors Cross and Plunkett are to be congratulated on preparing such a clearand useful book – I shall be recommending it to others.

Dr Tom E. Peck MBBS BSc FRCAConsultant Anaesthetist, Royal Hampshire County Hospital, Winchester, UK

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Introduction

This book is aimed primarily at providing a reference point for the common graphs,definitions and equations that are part of the FRCA syllabus. In certain situations,for example the viva sections of the examinations, a clear structure to your answerwill help you to appear more confident and ordered in your response. To enable youto do this, you should have a list of rules to hand which you can apply to anysituation.

Graphs

Any graph should be constructed in a logical fashion. Often it is the best-knowncurves that candidates draw most poorly in their rush to put the relationshipdown on paper. The oxyhaemoglobin dissociation curve is a good example. Inthe rush to prove what they know about the subject as a whole, candidates oftensupply a poorly thought out sigmoid-type curve that passes through none of thetraditional reference points when considered in more detail. Such an approachwill not impress the examiner, despite a sound knowledge of the topic as awhole. Remembering the following order may help you to get off to a betterstart.

Size

It is important to draw a large diagram to avoid getting it cluttered. There willalways be plenty of paper supplied so don’t be afraid to use it all. It will make theexaminer’s job that much easier as well as yours.

Axes

Draw straight, perpendicular axes and label them with the name of the variableand its units before doing anything else. If common values are known for theparticular variable then mark on a sensible range, for example 0–300 mmHg forblood pressure. Remember that logarithmic scales do not extend to zero as zerois an impossible result of a logarithmic function. In addition, if there areimportant reference points they should be marked both on the axis and wheretwo variables intersect on the plot area, for example 75% saturation correspond-ing to 5.3 kPa for the venous point on the oxyhaemoglobin dissociation curve.Do all of this before considering a curve and do not be afraid to talk out loud asyou do so – it avoids uncomfortable silences, focuses your thoughts and showslogic.


Beginning of a curve

Consider where a curve actually starts on the graph you are drawing. Does it beginat the origin or does it cross the y axis at some other point? If so, is there a specificvalue at which it crosses the y axis and why is that the case? Some curves do notcome into contact with either axis, for example exponentials and some physio-logical autoregulation curves. If this is the case, then you should demonstrate thisfact and be ready to explain why it is so. Consider what happens to the slope of acurve at its extremes. It is not uncommon for a curve to flatten out at high or lowvalues, and you should indicate this if it is the case.

Middle section

The middle section of a curve may cross some important points as previouslymarked on the graph. Make sure that the curve does, in fact, cross these pointsrather than just come close to them or you lose the purpose of marking them on inthe first place. Always try to think what the relationship between the two variablesis. Is it a straight line, an exponential or otherwise and is your curve representingthis accurately?

End of a curve

If the end of a curve crosses one of the axes then draw this on as accurately aspossible. If it does not reach an axis then say so and consider what the curve willlook like at this extreme.

Other points

Avoid the temptation to overly annotate your graphs but do mark on any impor-tant points or regions, for example segments representing zero and first-orderkinetics on the Michaelis–Menten graph.

Definitions

When giving a definition, the aim is to accurately describe the principle in questionin as few a words as possible. The neatness with which your definition appears willaffect how well considered your answer as a whole comes across. Definitions mayor may not include units.

Definitions containing units

Always think about what units, if any, are associated with the item you are trying todescribe. For example, you know that the units for clearance are ml.min−1 and soyour definition must include a statement about both volume (ml) and time (min).

2 Introduction


When you are clear about what you are describing, it should be presented assuccinctly as possible in a format such as

‘x’ is the volume of plasma . . .

‘y’ is the pressure found when . . .

‘z’ is the time taken for . . .Clearance (ml.min−1) is the volume (ml) of plasma from which a drug iscompletely removed per unit time (min)Pressure (N.m−2) describes the result of a force (N) being applied over agiven area (m2).

You can always finish your definition by offering the units to the examiner if youare sure of them.

Definitions without units

If there are no units involved, think about what process you are being asked todefine. It may be a ratio, an effect, a phenomenon, etc.

Reynold’s number is a dimensionless number . . .The blood:gas partition coefficient is the ratio of . . .The second gas effect is the phenomenon by which . . .

Conditions

Think about any conditions that must apply. Are themeasurements taken at standardtemperature and pressure (STP) or at the prevailing temperature and pressure?

The triple point of water is the temperature at which all three phases are inequilibrium at 611.73 Pa. It occurs at 0.01 °C.

There is no need to mention a condition if it does not affect the calculation. Forexample, there is no need to mention ambient pressure when defining saturatedvapour pressure (SVP) as only temperature will alter the SVP of a volatile.

Those definitions with clearly associated units will need to be given in a clearand specific way; those without units can often be ‘padded’ a little if you are notentirely sure.

Equations

Most equations need only be learned well enough to understand the componentswhich make up the formula such as in

V = IR

where V is voltage, I is current and R is resistance.

Introduction 3


There are, however, some equations that deserve a greater understanding of theirderivation. These include,

The Bohr equationThe Shunt equationThe Henderson–Hasselbach equation

These equations are fully derived in this book with step by step explanations of themathematics involved. It is unlikely that the result of your examination will hingeon whether or not you can successfully derive these equations from first principles,but a knowledge of how to do it will make things clearer in your own mind.

If you are asked to derive an equation, remember four things.

1. Don’t panic!2. Write the end equation down first so that the examiners know you

know it.3. State the first principles, for example the Bohr equation considers a

single tidal exhalation comprising both dead space and alveolar gas.4. Attempt to derive the equation.

If you find yourself going blank or taking a wrong turn midway through then donot be afraid to tell the examiners that you cannot remember and would they mindmoving on. No one will mark you down for this as you have already supplied themwith the equation and the viva will move on in a different direction.

4 Introduction

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Section 1Mathematical principles



Mathematical relationships

Mathematical relationships tend not to be tested as stand-alone topics but anunderstanding of them will enable you to answer other topics with more authority.

Linear relationships

y = x

Draw and label the axes as shown. Plot the line so that it passes through theorigin (the point at which both x and y are zero) and the value of y is equal tothe value of x at every point. The slope when drawn correctly should be at 45° ifthe scales on both axes are the same.

y = ax + b

This line should cross the y axis at a value of b because when x is 0, ymust be0 + b. The slope of the graph is given by the multiplier a. For example, whenthe equation states that y = 2x, then y will be 4 when x is 2, and 8 when x is 4,etc. The slope of the line will, therefore, be twice as steep as that of the linegiven by y = 1x.


Hyperbolic relationships (y = k/x)

This curve describes any inverse relationship. The commonest value for theconstant, k, in anaesthetics is 1, which gives rise to a curve known as arectangular hyperbola. The line never crosses the x or the y axis and is describedas asymptotic to them (see definition below). Boyle’s law is a good example(volume = 1/pressure). This curve looks very similar to an exponential declinebut they are entirely different inmathematical terms so be sure about which oneyou are describing.

Asymptote

A curve that continually approaches a given line but does notmeet it at anydistance.

Parabolic relationships (y = kx2)

These curves describe the relationship y = x2 and so there can be no negativevalue for y. The value for a constant ‘k’ alters the slope of the curve in the sameway as ‘a’ does in the equation y = ax + b. The curve crosses the y axis at zerounless the equation is written y = kx2 + b, in which case the whole curve isshifted upwards and it crosses at the value of ‘b’.

8 Section 1 � Mathematical principles


Exponential relationships and logarithms

Exponential

A condition where the rate of change of a variable at any point in time isproportional to the value of the variable at that time.orA function whereby the x variable becomes the exponent of the equationy = ex.

Weare normally used to x being represented in equations as the base unit (i.e. y = x2).In the exponential function, it becomes the exponent (y = ex), which conveys somevery particular properties.

Euler’s number

Represents the numerical value 2.71828 and is the base of natural loga-rithms. Represented by the symbol ‘e’.

Logarithms

The power (x) to which a base must be raised in order to produce thenumber given as for the equation x = logbase(number).

The base can be any number, common numbers are 10, 2 and e (2.71828).Log10(100) is, therefore, the power to which 10 must be raised to produce thenumber 100; for 102 = 100, therefore, the answer is x = 2. Log10 is usually written aslog whereas loge is usually written ln.

Rules of logarithms

Multiplication becomes addition

log(xy) = log(x) + log(y)

Division becomes subtraction

log(x/y) = log(x) – log(y)

Reciprocal becomes negative

log(1/x) = −log(x)


Power becomes multiplication

log(xn) = n. log(x)

Any log of its own base is one

log10(10) = 1 and ln(e) = 1

Any log of 1 is zero because n0 always equals 1

log10(1) = 0 and ln(1) = 0

Basic positive exponential (y = ex)

The curve is asymptotic to the x axis. At negative values of x, the slope is shallowbut the gradient increases sharply when x is positive. The curve intercepts they axis at 1 because any number to the power 0 (as in e0) equals 1. Mostimportantly, the value of y at any point equals the slope of the graph at that point.

Basic negative exponential (y = e−x)

The x axis is again an asymptote and the line crosses the y axis at 1. This timethe curve climbs to infinity as x becomes more negative. This is because −x isnow becoming more positive. The curve is simply a mirror image, around they axis, of the positive exponential curve seen above.



Clinical tear away positive exponential (y = a.ekt)

The curve crosses y axis at value of a. It tends towards infinity as value of tincreases. This is clearly not a sustainable physiological process but could be seenin the early stages of bacterial replication where y equals number of bacteria.

Physiological negative exponential (y = a.e−kt)

The curve crosses the y axis at a value of a. It declines exponentially as tincreases. The line is asymptotic to the x axis. This curve is seen in physiologicalprocesses such as drug elimination and lung volume during passive expiration.

Physiological build-up negative exponential (y = a − b.e−kt)

Exponential relationships and logarithms 11


The curve passes through the origin and is asymptotic to a line that would cross they axis at a value of a. Although y increases with time, the curve is actually a negativeexponential. This is because the rate of increase in y is decreasing exponentially as tincreases. This curve may be seen clinically as a wash-in curve or that of lungvolume during positive pressure ventilation using pressure-controlled ventilation.

Half life

The time taken for the value of an exponential function to decrease by halfis the half life and is represented by the symbol t1/2orthe time equivalent of 0.693τ τ = time constant

An exponential process is said to be complete after five half lives. At this point,96.875% of the process has occurred.

Graphical representation of half life

This curve needs to be drawn accurately in order to demonstrate the principle.After drawing and labelling the axes, mark the key values on the y axis asshown. Your curve must pass through each value at an equal time interval onthe x axis. To ensure this, plot equal time periods on the x axis as shown, beforedrawing the curve. Join the points with a smooth curve that is asymptotic to thex axis. This will enable you to describe the nature of an exponential declineaccurately as well as to demonstrate easily the meaning of half life.

Time constant

The time it would have taken for a negative exponential process to com-plete, were the initial rate of change to be maintained throughout. Giventhe symbol τ.or



The time taken for the value of an exponential to fall to 37%of its previousvalue.orThe time taken for the value of an exponential function change by a factorof e1.orThe reciprocal of the rate constant.

An exponential process is said to be complete after three time constants. At thispoint 94.9% of the process has occurred.

Graphical representation of the time constant

This curve should be a graphical representation of the first and second defi-nitions of the time constant as given above. After drawing and labelling theaxes, mark the key points on the y axis as shown. Draw a straight line fallingfrom 100 to baseline at a time interval of your choosing. Label this time intervalτ. Mark a point on the graph where a vertical line from this point crosses 37%on the y axis. Finally draw the curve starting as a tangent to your originalstraight line and falling away smoothly as shown. Make sure it passes throughthe 37% point accurately. A well-drawn curve will demonstrate the timeconstant principle clearly.

Rate constant

The reciprocal of the time constant (k).orA marker of the rate of change of an exponential process.

The rate constant acts as a modifier to the exponent as in the equation y = ekt (e.g.in a savings account, k would be the interest rate; as k increases, more money isearned in the same period of time and the exponential curve is steeper).



Graphical representation of k (y = ekt)

k = 1 Draw a standard exponential tear-away curve. To move from y = et toy = et + 1 takes time t1.

k = 2 This curve should be twice as steep as the first as ‘k’ acts as a2 × multiplier to the exponent ‘t’. As ‘k’ has doubled, for the same changein y the time taken has halved and this can be shown as t2 where t2 is halfthe value of t1. The values t1 and t2 are also the time constants for theequation because they are, by definition, the reciprocal of the rateconstant.

Transforming to a straight line graph

Start with the general equation as follows

y = ekt

take natural logarithms of both sides

ln y = ln(ekt)

power functions become multipliers when taking logs, giving

ln y = kt. ln(e)

the natural log of e is 1, giving

ln y = kt.1 or ln y = kt

You may be expected to perform this simple transformation, or at least to describethe maths behind it, as it demonstrates how logarithmic transformation can makethe interpretation of exponential curves much easier by allowing them to beplotted as straight lines ln y = kt.



k = 1 Draw a curve passing through the origin and rising as a straight line atapproximately 45°.

k = 2 Draw a curve passing through the origin and rising twice as steeply asthe k = 1 line. The time constant is half that for the k = 1 line.



Integration and differentiation

There is no part of the FRCA examination that requires an in-depth understandingof integration or differentiation, however an understanding of these principles mayhelp with the explanation of other concepts, such as drug metabolism of cardiacoutput monitoring.

Integration

Integration is the process of calculating the multiplication sum of twovariables where one variable is changing. It may be described as findingthe area under the curve.

The description of integration is often described as calculating ‘the area under thecurve’. If we wish to calculate the multiplication sum of two fixed variables x and ythen we use simple multiplication:

y = 3

x = 4

xy = 12

However if y is changing as a function of x then integration becomes thesubstitute for multiplication. The process of integration divides x up intomany small samples. They are small enough so that the value of y does notchange appreciably between the beginning of the sample range and the end. Thiscreates, in effect, many tiny rectangles for which the area can be calculated bymultiplication and the results of these many calculations added together to givethe area as a whole.


ðbaf ðxÞdx

f ðxÞ ¼ equationof curve

The general equation for an integral simply describes that the solution is found bysumming (∫) the results of all the small sample areas underneath the curve ( f(x),where this represents the equation of the curve forming the upper border of thearea) as x changes (dx). The letters a and b show the range of x values over whichthe integration is to be applied.

In the example above we are integrating between 0 and 4 so if the upper curvehad the function y = 3x3 + 2x2 + x, the equation would read:ð4

03x3 þ 2x2 þ x :dx

Solving the equation is beyond the scope of the syllabus and you would not beexpected to do so in the examination.

Differentiation

Differentiation refers to the mathematical process by which the rate ofchange of one variable with respect to another may be calculated.

It is most unlikely that you would be asked to actually calculate any rate of change inthe exam setting, although, if asked, a common way to estimate this would be asbelow.

Integration and differentiation 17


Draw a curve and label the segment at which you wish to find the rate of changeA. Draw a straight line tangent to the main curve (dotted). The rate of change atpoint A on the main curve will approximate to a/b.

Mathematical methods of differentiation are beyond the scope of the syllabus andyou will not be expected to know them for the examination.



Physical measurement and calibration

This topic tests your understanding of the ways in which a measurement devicemay not accurately reflect the actual physiological situation.

Accuracy

The ability of a measurement device to match the actual value of thequantity being measured.

Precision

The reproducibility of repeatedmeasurements and ameasure of their likelyspread.

In the analogy of firing arrows at a target, the accuracy would represent how closethe arrow was to the bullseye, whereas the precision would be a measure of howtightly packed together a cluster of arrows were once they had all been fired.

Drift

A fixed deviation from the true value at all points in the measured range.Drift can be corrected by the process of zeroing.

Hysteresis

The phenomenon by which a measurement varies from the input value bydifferent degrees depending onwhether the input variable is increasing ordecreasing in magnitude at that moment in time.

Non-linearity

The absence of a true linear relationship between the input value and themeasured value.

Zeroing and calibration

Zeroing a display removes any fixed drift and allows the accuracy of the measuringsystem to be improved. If all points are offset by ‘+ x’, zeroing simply subtracts ‘x’from all the display values to bring them back to the input value. Calibration isused to check for linearity over a given range by taking known set points andchecking that they all display a measured value that lies on the ideal straight line.


The more points that fit the line, the more certain one can be that the line is indeedstraight. One point calibration reveals nothing about linearity, two point calibra-tion is better but the line may not necessarily be straight outside your twocalibration points (even a circle will cross the straight line at two points). Threepoint calibration is ideal as, if all three points are on a straight line, the likelihoodthat the relationship is linear over the whole range is high.

Accurate and precise measurement

Draw a straight line passing through the origin so that every input value isexactly matched by the measured value. In mathematical terms it is the same asthe curve for y = x.

Accurate imprecise measurement

Draw the line of perfect fit as described above. Each point on the graph isplotted so that it lies away from this line (imprecision) but so that the line ofbest fit matches the perfect line (accuracy).



Precise inaccurate measurement

Draw the line of perfect fit (dotted line) as described above. Next plot a series ofmeasured values that lie on a parallel (solid) line. Each point lies exactly on aline and so is precise. However, the separation of the measured value from theactual input value means that the line is inaccurate.

Drift

The technique is the same as for drawing the graph above. Demonstrate thatthe readings can be made accurate by the process of zeroing – altering eachmeasured value by a set amount in order to bring the line back to its idealposition. The term ‘drift’ implies that accuracy is lost over time whereas aninaccurate implies that the error is fixed.

Physical measurement and calibration 21


Hysteresis

The curves should show that the measured value will be different depending onwhether the input value is increasing (bottom curve) or decreasing (top curve).Often seen clinically with lung pressure–volume curves.

Non-linearity

The curve can be any non-linear shape to demonstrate the effect. The curvehelps to explain the importance and limitations of calibration. Points A and Brepresent a calibration range of input values between which linearity is likely.The curve demonstrates how linearity cannot be assured outside this range.The DINAMAP monitor behaves in a similar way. It tends to overestimate atlow blood pressure (BP) and underestimate at high BP while retaining accuracybetween the calibration limits.



The SI units

There are seven basic SI (Système International) units from which all other unitscan be derived. These seven are assumed to be independent of each other and havevarious specific definitions that you should know for the examination. The acro-nym is SMMACKK.

The base SI units

Unit Symbol Measure of Definition

second s Time The duration of a given number ofoscillations of the caesium-133atom

metre m Distance The length of the path travelled by light invacuum during a certain fraction of asecond

mole mol Amount The amount of substance whichcontains as many elementary particlesas there are atoms in 0.012 kg ofcarbon-12

ampere A Current The current in two parallel conductorsof infinite length and placed 1 metreapart in vacuum, which wouldproduce between them a force of2 × 10−7 N.m−1

candela cd Luminous intensity Luminous intensity, in a given direction,of a source that emits monochromaticlight at a specific frequency

kilogram kg Mass The mass of the internationalprototype of the kilogram held inSèvres, France

kelvin K Temperature 1/273.16 of the thermodynamictemperature of the triple point ofwater

From these seven base SI units, many others are derived. For example,speed can be denoted as distance per unit time (m.s−1) and acceleration asspeed change per unit time (m.s−2). Some common derived units are givenbelow.


Derived SI units

Measure of Definition Units

Area Square metre m2

Volume Cubic metre m3

Speed Metre per second m.s−1

Velocity Metre per second in a given direction m.s−1

Acceleration Metre per second squared m.s−2

Wave number Reciprocal metre m−1

Current density Ampere per square metre A.m2

Concentration Mole per cubic metre mol.m−3

These derived units may have special symbols of their own to simplify them. Forinstance, it is easier to use the symbol Ω than m2.kg.s−3.A−2.

Derived SI units with special symbols

Measure of Name Symbol Units

Frequency hertz Hz s−1

Force newton N kg.m.s−2

Pressure pascal Pa N.m−2

Energy/work joule J N.mPower watt W J.s−1

Electrical charge coulomb C A.sPotential difference volt V W/ACapacitance farad F C/VResistance ohm Ω V/A

Some everyday units are recognized by the system although they themselves arenot true SI units. Examples include the litre (10−3 m3), the minute (60 s), and thebar (105 Pa). One litre is the volume occupied by 1 kg of water but was redefined inthe 1960s as being equal to 1000 cm3.

Prefixes to the SI units

In reality, many of the SI units are of the wrong order of magnitude to be useful.For example, a pascal is a tiny amount of force (imagine 1 newton – about100 g – acting on an area of 1 m2 and you get the idea). We, therefore, often usekilopascals (kPa) to make the numbers more manageable. The word kilo- isone of a series of prefixes that are used to denote a change in the order ofmagnitude of a unit. The following prefixes are used to produce multiples orsubmultiples of all SI units.



Prefixes

Prefix 10n Symbol Decimal equivalent

yotta 1024 Y 1 000 000 000 000 000 000 000 000zetta 1021 Z 1 000 000 000 000 000 000 000exa 1018 E 1 000 000 000 000 000 000peta 1015 P 1 000 000 000 000 000tera 1012 T 1 000 000 000 000giga 109 G 1 000 000 000mega 106 M 1 000 000kilo 103 k 1000hecto 102 h 100deca 101 da 10

100 1deci 10−1 d 0.1centi 10−2 c 0.01milli 10−3 m 0.001micro 10−6 μ 0.000 001nano 10−9 n 0.000 000 001pico 10−12 p 0.000 000 000 001femto 10−15 f 0.000 000 000 000 001atto 10−18 a 0.000 000 000 000 000 001zepto 10−21 z 0.000 000 000 000 000 000 001yocto 10−24 y 0.000 000 000 000 000 000 000 001

The prefix 10100 is known as a googol, which was the basis for the name of theinternet search engine Google after a misspelling occurred.

The SI units 25


Non-SI units and conversion factors

Some everyday units are recognized by the système international (SI) althoughthey themselves are not true SI units. An understanding of the interrelationbetween SI and non-SI units is vital for understanding calculations which invar-iably require the candidate to describe all values in SI units regardless of theirinitial form.

Non-SI units

Measure of Definition Units

Time minute minTime hour hVolume litre lPressure bar barPressure pounds per square inch (PSI) lb.inch−2

Pressure atmosphere atmTemperature centigrade °C

In order to manipulate these units, conversion to SI is required.

Conversion factors

Non-SI term Non-SI unit Conversion SI unit

minute min x 60 shour h x 3600 slitre l x 10–3 m3

bar bar x 100 kPaPSI lb.inch−2 x 6.895 kPaatmosphere atm x 101.325 kPacentigrade °C +273.15 K

Using the above conversions, atmospheric (standard) pressure is:

101.325 kPa1.013 bar14.696 psi1 atm


Signal to noise ratio

Definition

The ratio of themagnitude of the desiredmeasurement (the signal) to thatof the undesirable information of the same type (the noise).

Signal to noise ratio (SNR) is often encountered when considering the function ofmeasuring systems, particularly where amplification is involved. A ratio greaterthan 1:1 means that there is more signal than noise being measured and a highSNR shows that the desired signal is being measured with high fidelity. SNR maybe static or dynamic in nature. A normal ECG trace on a monitor may initiallyshow a high SNR that is reduced when diathermy is being used.

Low signal to noise ratio

High signal to noise ratio



Section 2Physical principles



Simple mechanics

Although there is muchmore to mechanics as a topic, an understanding of some ofits simple components (force, pressure, work and power) is all that will be tested inthe examination.

Force

Force is that influence which tends to change the state of motion of anobject. (newtons, N)or

F = ma

where F is force, m is mass and a is acceleration.

Newton

That force which will give a mass of one kilogram an acceleration of onemetre per second per secondor

N = kg.m.s−2

When we talk about weight, we are really discussing the force that we sense whenholding a mass which is subject to acceleration by gravity. The earth’s gravita-tional field will accelerate an object at 9.81 m.s−2 and is, therefore, equal to9.81 N. If we hold a 1 kg mass in our hands we sense a 1 kg weight, which isactually 9.81 N:

F = maF = 1 kg × 9.81 m.s−2

F = 9.81 N

If 1 kg generates 9.81 N then 1 Nmust be the force generated by 1/9.81 kg (or 102 g).Putting it another way, a mass of 1 kg will not weigh 1 kg on the moon as theacceleration owing to gravity is only one-sixth of that on the earth, 1.63 m.s−2. The1 kg mass will weigh only 163 g.


Pressure

Pressure is force applied over a unit area. (pascals, P)

P = F/A

where P is pressure, F is force and A is area.

Pascal

One pascal is equal to a force of one newton applied over an area of onesquare metre. (N.m−2)

The pascal is a tiny amount when you consider that 1 N is equal to just 102 gweight. For this reason kilopascals (kPa) are used as standard.

Energy

The capacity to do work. (joules, J)

Work

Work is the result of a force acting upon an object to cause its displacementin the direction of the force applied. (joules, J)or

J = FD

where J is work, F is force and D is distance travelled in the direction of theforce.

Joule

The work done when a force of one newton moves one metre in thedirection of the force is one joule.

More physiologically, it can be shown that work is given by pressure × volume.This enables indices such as work of breathing to be calculated simply by studyingthe pressure–volume curve.

P = F/A or F = PA

and

V = DA or D = V/A

so

J = FD

32 Section 2 � Physical principles


becomes

J = (PA).(V/A)

or

J = PV

where P is pressure, F is force, A is area, V is volume, D is distance and J iswork.

Power

The rate at which work is done. (watts, W)or

W = J/s

whereW is the power in watts, J is the work done in joules and s is the timein seconds.

Watt

The power expended when one joule of energy is consumed in one secondis one watt.

The power required to sustain physiological processes can be calculated by usingthe above equation. If a pressure–volume loop for a respiratory cycle is plotted, thework of breathing may be found. If the respiratory rate is now measured then thepower may be calculated. The power required for respiration is only approximately700–1000mW, compared with approximately 80W needed at basal metabolic rate.

Simple mechanics 33


The gas laws

Boyle’s law

At a constant temperature, the volume of a fixed amount of a perfect gasvaries inversely with its pressure.

PV = K or V ∝ 1/P

Charles’ law

At a constant pressure, the volume of a fixed amount of a perfect gas variesin proportion to its absolute temperature.

V/T = K or V ∝ T

Gay–Lussac’s law (The third gas law)

At a constant volume, the pressure of a fixed amount of a perfect gas variesin proportion to its absolute temperature.

P/T = K or P ∝ T

Remember that water Boyle’s at a constant temperature and that Prince Charles isunder constant pressure to be king.

Perfect gas

A gas that completely obeys all three gas laws.orAgas that containsmolecules of infinitely small size,which, therefore, occupyno volume themselves, andwhich have no force of attraction between them.

It is important to realize that this is a theoretical concept and no such gas actuallyexists. Hydrogen comes the closest to being a perfect gas as it has the lowestmolecular weight. In practice, most commonly used anaesthetic gases obey the gaslaws reasonably well.

Avogadro’s hypothesis

Equal volumes of gases at the same temperature and pressure containequal numbers of molecules.


The universal gas equation

The universal gas equation combines the three gas laws within a single equation

If PV = K1, P/T = K2 and V/T = K3, then all can be combined to give

PV/T = K

For 1 mole of a gas, K is named the universal gas constant and given thesymbol R.

PV/T = R

for n moles of gas

PV/T = nR

so

PV = nRT

The equation may be used in anaesthetics when calculating the contents of anoxygen cylinder. The cylinder is at a constant (room) temperature and has a fixedinternal volume. As R is a constant in itself, the only variables now become P and nso that

P ∝ n

Therefore, the pressure gauge can be used as a measure of the amount of oxygenleft in the cylinder. The reason we cannot use a nitrous oxide cylinder pressuregauge in the same way is that these cylinders contain both vapour and liquid and sothe gas laws do not apply.

To calculate the available volume of gas from a compressed cylinder, adapt theuniversal gas equation as follows:

(P1 . V1)T1 = (P2 . V2)T2 = K

At a constant temperature, T1 and T2 can be deleted and the equationrearranged so

V2 = (P1 . V1) / P2

where P1 is the cylinder pressure, V1 is the cylinder volume, P2 is atmosphericpressure and V2 is the volume of gas at atmospheric pressure.

For example, for a cylinder with an internal volume of 5 l and a pressure of 137bar, the calculation is as follows:

V2 = (137 x 5)/1 = 685.

Remember that 5 l will remain in the cylinder and so there will be 680 l available.

The gas laws 35


Laminar flow

Laminar flow describes the situation when any fluid (either gas or liquid) passessmoothly and steadily along a given path, this is is described by the Hagen–Poiseuille equation.

Hagen–Poiseuille equation

Flow ¼ ppr4

8�l

where p is pressure drop along the tube (p1 − p2), r is radius of tube, l islength of tube and η is viscosity of fluid.

The most important aspect of the equation is that flow is proportional to the 4thpower of the radius. If the radius doubles, the flow through the tube will increase by16 times (24).

Note that some texts describe the equation as

Flow ¼ ppd4

128�l

where d is the diameter of tube.

This form uses the diameter rather than the radius of the tube. As the diameter istwice the radius, the value of d4 is 16 times (24) that of r4. Therefore, the constant(8) on the bottom of the equation must also be multiplied 16 times to ensure theequation remains balanced (8 × 16 = 128).

Viewed from the side as it is passing through a tube, the leading edge of acolumn of fluid undergoing laminar flow appears parabolic. The fluid flowing inthe centre of this column moves at twice the average speed of the fluid column asa whole. The fluid flowing near the edge of the tube approaches zero velocity.This phenomenon is particular to laminar flow and gives rise to this particularshape of flow.


Turbulent flow

Turbulent flow describes the situation in which fluid flows unpredictably withmultiple eddy currents and is not parallel to the sides of the tube through which itis flowing.

As flow is, by definition, unpredictable, there is no single equation that definesthe rate of turbulent flow as there is with laminar flow. However, there is a numberthat can be calculated in order to identify whether fluid flow is likely to be laminaror turbulent and this is called Reynold’s number (Re).

Reynold’s number

Re ¼ �vd�

where Re is Reynold’s number, ρ is density of fluid, v is velocity of fluid, d isdiameter of tube and η is viscosity of fluid.

If one were to calculate the units of all the variables in this equation, you would findthat they all cancel each other out. As such, Reynold’s number is dimensionless (ithas no units) and it is simply taken that

when Re < 2000 flow is likely to be laminar and when Re > 2000 flow is likely tobe turbulent.

Given what we now know about laminar and turbulent flow, the main points toremember are that

viscosity is the important property for laminar flowdensity is the important property for turbulent flowReynold’s number of 2000 delineates laminar from turbulent flow.


Bernoulli, Venturi and Coanda

The Bernoulli principle

An increase in the flow velocity of an ideal fluid will be accompanied by asimultaneous reduction in its pressure.

The Venturi effect

The Venturi effect is an extension of the Bernoulli principle that describes thecircumstances under which an increase in flow velocity may occur in a system. It isstated to be:

The effect by which the introduction of a constriction to fluid flowwithin atube causes the velocity of thefluid to increase and, therefore, the pressureof the fluid to fall.

These definitions are both based on the law of conservation of energy (also knownas the ‘first law of thermodynamics’). It is important to note that the Venturi effectdoes not describe the entrainment of air or any other fluid, this is a practicalapplication of the venturi effect rather than the effect itself. The reduced pressurecaused by the venturi effect can be used to pull (entrain) fluids or gases into thesystem in a predictable fashion.

The law of conservation of energy

Energy cannot be created or destroyed but can only change from one formto another.

Put simply, this means that the total energy contained within the fluid systemmustalways be constant. Therefore, as the kinetic energy (velocity) of the fluid increases,the potential energy (pressure) must reduce by an equal amount in order to ensurethat the total energy content remains the same.

The increase in velocity seen as part of the Venturi effect simply demonstratesthat a given number of fluid particles have to move faster through a narrowersection of tube in order to keep the total flow the same. This means an increase invelocity and, as predicted, a reduction in pressure. The resultant drop in pressurecan be used to entrain gases or liquids, which allows for applications such asnebulizers and Venturi masks.


The Coanda effect

The tendency of a stream of fluid flowing in proximity to a convex surfaceto follow the line of the surface rather than its original course.

The effect is thought to occur because a moving column of fluid entrains moleculeslying close to the curved surface, creating a relatively low pressure, contact point.As the pressure further away from the curved surface is relatively higher, thecolumn of fluid is preferentially ‘pushed’ towards the surface rather than continu-ing its straight course. The effect means that fluid will preferentially flow down onelimb of a Y-junction rather than being equally distributed.

Bernoulli, Venturi and Coanda 39


Heat and temperature

Heat

The form of energy that passes between two samples owing to the differ-ence in their temperatures. (joules, J)

Temperature

A measure of the mean kinetic energy of the molecules of a substance.andThe property of matter that determines in which direction heat energy willflow when an object is in contact with another of a different temperature.

Heat energy will flow from an object of a high temperature to an object of a lowertemperature. As heat energy is supplied to an object it acts to increase the kineticenergy of the molecules within it and hence the temperature. The opposite is truewhen heat energy leaves an object. An object with a high temperature does notnecessarily contain more heat energy than one with a lower temperature as thetemperature change per unit of heat energy supplied will depend upon the specificheat capacity of the object in question.

Triple point

The temperature at which all three phases of water – solid, liquid and gas –are in equilibrium at 611.73 Pa. It occurs at 0.01 °C.

Kelvin

One kelvin is equal to 1/273.16 of the thermodynamic triple point of water.A change in temperature of 1 K is equal in magnitude to that of 1 °C.

Kelvinmust be used when performing calculations with temperature. For example,the volume of gas at 20 °C is not double that at 10 °C: 10 °C is 283.15 K so thetemperature must rise to 566.30 K (293.15 °C) before the volume of gas will double.

Celsius/centigrade

Celsius (formerly called the degree centigrade) is a common measure oftemperature in which a change of 1 °C is equal in magnitude to a change of1 K. To convert absolute temperatures given in degrees celsius to kelvin,you must add 273.15. For example 20 °C = 293.15 K.


Resistance wire

The underlying principle of this method of measuring temperature is that the resist-ance of a thin piece of metal increases as the temperature increases. This makes anextremely sensitive thermometer yet it is fragile and has a slow response time.

Draw a curve that does not pass through the origin. Over commonly measuredranges, the relationship is essentially linear. The slope of the graph is very slightlypositive and a Wheatstone bridge needs to be used to increase sensitivity.

Thermistor

A thermistor can be made cheaply and relies on the fact that the resistance ofcertain semiconductor metals falls as temperature increases. Thermistors are fastresponding but suffer from calibration error and deteriorate over time.

Draw a smooth curve that falls as temperature increases. The curve will nevercross the x axis. Although non-linear, this can be overcome by mathematicalmanipulation.

Heat and temperature 41


The Seebeck effect

At the junction of two dissimilar metals, a voltage will be produced, themagnitude of which will be in proportion to the temperature differencebetween two such junctions.

Thermocouple

The thermocouple utilizes the Seebeck effect. Copper and constantan are the twometals most commonly used and produce an essentially linear curve of voltageagainst temperature. One of the junctions must either be kept at a constanttemperature or have its temperature measured separately (by using a sensitivethermistor) so that the temperature at the sensing junction can be calculatedaccording to the potential produced. Each metal can be made into fine wires thatcome into contact at their ends so that a very small device can be made.

This curve passes through the origin because if there is no temperature differ-ence between the junctions there is no potential generated. It rises as a nearlinear curve over the range of commonly measured values. The output voltageis small (0.04–0.06 mV. °C−1) and so signal amplification is often needed.



Humidity

The term humidity refers to the amount of water vapour present in the atmosphereand is subdivided into two types:

Absolute humidity

The totalmass ofwater vapour present in the air per unit volume. (AH, kg.m−3

or g.m−3)

Relative humidity

The ratio of theamountofwater vapour in the air comparedwith theamountthat would be present at the same temperature if the air was fully saturated.(RH, %)orThe ratio of the vapour pressure of water in the air compared with thesaturated vapour pressure of water at that temperature. (RH, %)

Dew point

The temperature at which the relative humidity of the air exceeds 100%and water condenses out of the vapour phase to form liquid (dew).

Hygrometer

An instrument used for measuring the humidity of a gas.

Non-electrical hygrometers consist of the hair hygrometer, wet and dry bulbhygrometer and Regnault’s hygrometer. Electrical hygrometers consist of trans-ducers and mass spectrometry. An understanding of the modes of actions of eachwill be required for the examination.

Hygroscopic material

One that attracts moisture from the atmosphere.

The main location of hygroscopic mediums is inside heat and moisture exchange(HME) filters.

Humidity graph

The humidity graph is attempting to demonstrate how a fixed amount of watervapour in the atmosphere will lead to a variable relative humidity depending on


the prevailing temperature. It also highlights the importance of the upper airwaysin a room fully humidifying by the addition of 27 g.m−3 of water vapour. You willbe expected to know the absolute humidity of air at body temperature.

100% RH After drawing and labelling the axes, plot the key y values asshown. The 100% line crosses the y axis at 8 g.m−3 and rises as a parabolacrossing the points shown. These points must be accurate.

50%RH This curve crosses each point on the x axis at a y value half that of the100% RH line. Air at 50% RH cannot contain 44 g.m−3 water until over 50 °C.The graph demonstrates that a fixed quantity of water vapour can result invarying RH depending on the temperature concerned.

Clinical relevance

If cold or dry anaesthetic gasses are delivered to a patient, heating and humid-ification will occur as the gas passes down the respiratory tract. This processremoves both heat and moisture from the patient’s airway. Drying of the airwayis the more relevant of these two effects as heat loss is minimal – although it may becalculated simply.

Heat loss from warming cold inspired air

E = VE ρ c ΔTE = 6 l.min−1 x 0.0012 kg.l−1 x 1010 J.kg−1.°C -1 x 17°CE = 123.6 J.min−1

E = 7.4 kJ.hour−1 (≈ 2 Watts.hour−1)



where E is energy, VE is minute ventilation, ρ is density of air, c is specificheat capacity of air and ΔT is temperature change from 20 °C to 37 °C.

Heat loss from humidifying dry air

E = VE AH cE = 6 l.min−1 x 44 g.m−3 x 2260 kJ.kg−1

E = 0.006 m3.min−1 x 0.044 kg.m−3 x 2260 kJ.kg−1

E = 0.59 kJ.min−1

E = 35.8 kJ.hour−1 (≈ 8 Watts.hour−1)

where AH is absolute humidity at 37 °C

The body’s power output under sleep conditions is approximately 80–100 W.hour−1. In the worst case scenario, heat loss from warming and humidifyingcompletely dry anaesthetic gases at room temperature utilizes only 10–12% ofthis yet this is easily minimized by the use of appropriate breathing systems andfilters.

Efficiency of inhaled gas humidifiers

Device Absolute humidity (g.m−3)

Cold water bath 10HME 25Hot water bath 40Nebulizer 60Ultrasonic nebulizer 90

Note that fully saturated air at 37 °C contains 44g.m−3 water. Therefore any deviceproducing more than this amount carries the risk of causing pulmonary fluidaccumulation when it is connected directly to the airway.

Humidity 45


Latent heat

Not all heat energy results in a temperature change. In order for a material tochange phase (solid, liquid, gas) some energy must be supplied to it to enable itscomponent atoms to alter their arrangement. This is the concept of latent heat.

Latent heat

The heat energy that is required for a material to undergo a change ofphase. (J)

Specific latent heat of fusion

The amount of heat required, at a specified temperature, to convert a unitmass of solid to liquid without temperature change. (J.kg−1)

Specific latent heat of vaporization

The amount of heat energy required, at a specified temperature, to converta unit mass of liquid into the vapour without temperature change. (J.kg−1)

Note that these same amounts of energy will be released into the surroundingswhen the change of phase is in the reverse direction.

Heat capacity

The heat energy required to raise the temperature of a given object by onedegree. (J.K−1 or J.°C−1)

Specific heat capacity

The heat energy required to raise the temperature of one kilogram of asubstance by one degree. (J.kg−1.K−1 or J.kg−1.°C−1)


Specific heat capacity is a different concept to latent heat as it relates to an actualtemperature change.

There is an important graph associated with the concept of latent heat. It isdescribed as a heating curve and shows the temperature of a substance in relationto time. A constant amount of heat is being supplied per unit time and the mainobjective is to demonstrate the plateaus where phase change is occurring. At thesepoints, the substance does not change its temperature despite continuing to absorbheat energy from the surroundings.

Heating curve for water

The curve crosses the y axis at a negative value of your choosing. Between theplateaus, the slope is approximately linear. The plateaus are crucial as theyare the visual representation of the definition of latent heat. The first plateau isat 0 °C and is short in duration as only 334 kJ.kg−1 is absorbed in this time(specific latent heat of fusion). The next plateau is at 100 °C and is longer induration as 2260 kJ.kg−1 is absorbed (specific latent heat of vaporization).

Latent heat 47


Isotherms

An isotherm is a line of constant temperature and it forms part of a diagram thatshows the relationship between temperature, pressure and volume. The graph isgas specific and usually relates to nitrous oxide. Three lines are chosen to illustratethe volume–pressure relationship above, at and below the critical temperature.

Nitrous oxide isotherm

Liquid and vapour Draw this outline on the diagram first in order that yourother lines will pass through it at the correct points.

20 °C From right to left, the line curves up initially and then becomeshorizontal as it crosses the ‘liquid/vapour’ curve. Once all vapour has beenliquidized, the line climbs almost vertically as liquid is incompressible,leading to a rapid increase in pressure for a small decrease in volume.

36.5 °C The critical temperature line. This climbs from right to left as arectangular hyperbola with a small flattened section at its midpoint. This isthe first point where liquefaction occurs as the pressure continues to rise. Itclimbs rapidly after this section as before.

40 °C A true rectangular hyperbola representing Boyle’s law. The pressuredoubles as the volume halves. As it is above the critical temperature, it is a gasand obeys the gas laws.

72 bar A horizontal line drawn from the flattened section of the criticaltemperature line should cross the y axis at this point. This is described asthe critical pressure of nitrous oxide


Critical temperature

The temperature above which a gas cannot be liquefied regardless of theamount of pressure applied. (K/°C)

Critical pressure

The minimum pressure required to cause liquefaction of a gas at its criticaltemperature. (kPa/Bar)

Isotherms 49


Mechanisms of heat loss

Heat may be lost from a patient in five main ways during anaesthesia and surgery.

Radiation

The loss of heat energy from the body via transfer of infrared radiationfrom it to a second system that is not in direct contact with it and that hasa lower temperature. It is proportional to the fourth power of the tem-perature difference between the body and its surroundings. (40–60%heat loss)

Convection

The loss of heat energy from the body via air movement across an exposedarea acting to remove previously warmed air and bring un-warmed air intocontact with it. The effect is proportional to both the exposed body surfacearea and the degree of air movement. (25–30% heat loss)

Conduction

The loss of heat energy from the body by direct transfer of that energy toan adjacent system that is in direct contact with it and that has a lowertemperature. (5% heat loss)

Evaporation

The loss of heat energy from the body via the latent heat of vaporizationthat is required to be taken from it as liquids in contact with the bodymoveto the vapour phase. (15–50% heat loss)

Respiration

The loss of heat energy from the body caused by the humidification (8%)and warming (2%) of inspired air. (5–10% heat loss)

The processes at work in heat loss through respiration are really evaporative andconductive losses happening within the airway, although they are often consideredseparately because to minimize these losses requires different treatment – HMEF,warming and humidifying inspired gasses – than other types of heat loss fromthe body.


Heat loss from convection is treated by passive insulation, for example ablanket, to trap warm air close to the patient. Loss from radiation is achieved byminimizing the temperature gradient between patient and surroundings, eitherby increasing the theatre temperature or by forced air warming. Evaporativeloss may be major, for example during laparotomy, and is often difficult tocompensate for.

Heat loss during surgery

Immediately post induction there is a loss of the ability of the body tomaintain a core-periphery temperature gradient due, primarily, to anaes-thesia induced vasodilatation. The ‘average’ temperature of these two com-partments is the new temperature attained and this process occurs over thefirst hour. The only real way to mitigate this fall in temperature is to pre-warm the periphery prior to induction, by forced air heating for example,until the core and periphery are at the same temperature. Warming theperiphery to 37 °C may, however, be uncomfortable for the patient and israrely done.

All the methods of heat loss described on the previous page affect the secondphase of the process and it is here that blankets, warm fluids, warm air heating,HMEF use etc can make a difference. Passive measures will reduce the slope ofphase 2 whereas active heating will cause a rise in the temperature back towards37 °C.

Anaesthesia widens the thermoregulatory range so that protective mecha-nisms against heat loss will not begin until the core temperature falls by3–4 °C. Left untreated, a patient’s temperature would begin to plateau at thisstage.

Time (hours)

Mechanisms of heat loss 51


Draw and label the axes as shown, the time is taken as time post induction. Thecurve is composed of three linear phases.

Phase 1. Drawn passing between 37 °C and 35.5 °C over the course of 1 hour.Reduction in core body temperature during this phase is due to the loss of thecore-periphery temperature gradient leading to redistrubution of body heat.

Phase 2. Drawn as a line with a shallower gradient over a further 2.5 hoursrepresenting actual heat losses from the body during surgery as listed on theprevious page. The slope of this phase may be altered by passive or activewarming and this can be drawn as a warming line as shown.

Phase 3. The final plateau line is at a temperature of around 34 °C, thisrepresents the point at which altered thermoregulatory mechanisms begin toact to stabilize temperature.

.



Solubility and diffusion

Henry’s law

The amount of gas dissolved in a liquid is directly proportional to the partialpressure of the gas in equilibrium with the liquid.

Graham’s law

The rate of diffusion of a gas is inversely proportional to the square root ofits molecular weight.

Rate ∝ 1/√MW

Fick’s law of diffusion

The rate of diffusion of a gas across a membrane is proportional to themembrane area (A) and the concentration gradient (C1 − C2) across themembrane and inversely proportional to its thickness (D).

Rate of diffusion / A C1 � C2½ �D

Blood: gas solubility coefficient

The ratio of the amount of substance present in equal volume phases ofblood and gas in a closed system at equilibrium and at standard temper-ature and pressure.

Oil: gas solubility coefficient

The ratio of the amount of substance present in equal volume phases of oiland gas in a closed system at equilibrium and at standard temperature andpressure.

Bunsen solubility coefficient

The volume of gas, corrected to standard temperature and pressure, thatdissolves in one unit volume of liquid at the temperature concerned wherethe partial pressure of the gas above the liquid is one atmosphere.


Ostwald solubility coefficient

The volume of gas that dissolves in one unit volume of liquid at the temper-ature concerned.

The Ostwald solubility coefficient is, therefore, independent of the partialpressure.



Osmosis and colligative properties

Osmole

One osmole is an amount of particles equal to Avogadro’s number.(6.02 × 1023)

Osmolarity

The amount of osmotically active particles present per litre of solution.(mmol.l−1)

Osmolality

The amount of osmotically active particles present per kilogram of solvent.(mmol.kg−1)

Osmotic pressure

The pressure exerted within a sealed system of solution in response to thepresence of osmotically active particles on one side of a semi-permeablemembrane. (kPa)

One osmole of solute exerts a pressure of 101.325 kPa when dissolved in 22.4 L ofsolvent at 0 °C.

Colligative properties

Those properties of a solution that vary according to the osmolarity of thesolution. These are:

depression of freezing point. The freezing point of a solution is depressedby 1.86 °C per osmole of solute per kilogram of solvent

reduction of vapour pressureelevation of boiling pointincrease in osmotic pressure.

Raoult’s law

The depression of freezing point or reduction of the vapour pressure of asolvent is proportional to the molar concentration of the solute.


Osmometer

An osmometer is a device used for measuring the osmolality of a solution. Devicescommonly utilize either the reduction of vapour pressure or depression of freezingpoint phenomena. In clinical laboratories, the depression of freezing point appa-ratus is most commonly used as it avoids the problems that arise when solutionscontain multiple substances that may exert a vapour pressure of their own (such asalcohol in blood). In the clinical osmometer, the solution is placed in the appara-tus, which cools it rapidly to 0 °C and then super-cools it more slowly to −7 °C.This cooling is achieved by the Peltier effect (absorption of heat at the junction oftwo dissimilar metals as a voltage is applied), which is the reverse of the Seebeckeffect. The solution remains a liquid until a mechanical stimulus is applied, whichinitiates freezing. This is a peculiar property of the super-cooling process. Thelatent heat of fusion is released during the phase change from liquid to solid sowarming the solution until its natural freezing point is attained. Because a plateautemperature is reached, there is sufficient time for a very sensitive thermometer(usually of the thermistor type) to measure the freezing point. This can then becompared to the expected freezing point of the sample and the osmolaritycalculated.

Graph

Plot a smooth curve falling rapidly from room temperature to 0 °C. After thisthe curve flattens out until the temperature reaches −7 °C. Cooling is thenstopped and a mechanical stirrer induces a pulse. The curve rises quickly toachieve a plateau temperature (freezing point).



Principles of surface tension

Surface tension

The intermolecular force developed at the surface of a liquid that tends toresist the action of external force upon the surface. (N.m−1)orThe force acting upon a line of unit length across a surface in a directionparallel to the surface and perpendicular to the line. (N.m−1)

The concept of surface tension is familiar yet often misunderstood. The phe-nomenon arises because of the difference in the vectors (directions) of inter-molecular forces acting upon molecules at a surface when compared withmolecules in the body of liquid itself. Molecules in the body of liquid haveforces acting on them in all directions that essentially net to zero and hencecancel each other out. At the surface, there are no molecules above the surfacemolecules, only below and to the side. The net vector is therefore inwards asshown.

Diagram

Intermolecular forces between molecules in the substance of a liquid tend tocancel each other out. At the surface, tension develops as a result of longitudinalforces along the surface and unopposed inwards forces resulting in the netvector shown by the black arrows.

LaPlace’s law (sphere)

T = Pr/2


or

P = 2T/r

where P is pressure, T is wall tension and r is radius.

LaPlace’s law (tube)

P = T/r

For a given wall tension, a sphere of smaller radius will have a greater pressuredrop across its wall than a sphere of larger radius. This means that a higherinflation pressure will be required to keep a small sphere inflated than will berequired for a large sphere, the reason why a balloon is difficult to inflate at first butbecomes easier as the balloon fills. A small alveolus will therefore collapse as itempties into an adjacent larger alveolus along its pressure gradient. Pulmonarysurfactant reduces surface tension preferentially in smaller alveoli thus reducingthis undesirable effect.



Resistors and resistance

Electrical resistance is a broad term given to the opposition of flow of currentwithin an electrical circuit. However, when considering components such ascapacitors or inductors, or when speaking about resistance to alternating current(AC) flow, certain other terminology is used.

Resistance

The opposition to flow of direct current. (ohms, Ω)

Reactance

The opposition to flow of alternating current. (ohms, Ω)

Impedance

The total of the resistive and reactive components of opposition to elec-trical flow. (ohms, Ω)

All three of these terms have units of ohms as they are all measures of some form ofresistance to electrical flow. The reactance of an inductor is high and comesspecifically from the back electromotive force (EMF; p. 46) that is generated withinthe coil. It is, therefore, difficult for AC to pass. The reactance of a capacitor isrelatively low but its resistance can be high; therefore, direct current (DC) does notpass easily. Reactance does not usually exist by itself as each component in a circuitwill generate some resistance to electrical flow. The choice of terms to define totalresistance in a circuit is, therefore, resistance or impedance.

Ohm’s law

The strength of an electric current varies directly with the electromotiveforce (voltage) and inversely with the resistance.

I = V/R

or

V = IR

where V is voltage, I is current and R is resistance.The equation can be used to calculate any of the above values when theother two are known. When R is calculated, it may represent resistance orimpedance depending on the type of circuit being used (AC/DC).


Capacitors and capacitance

Capacitor

A device that stores electrical charge.

A capacitor consists of two conducting plates separated by a non-conductingmaterial called the dielectric.

Capacitance

The ability of a capacitor to store electrical charge (farads, F).

Farad

A capacitor with a capacitance of one farad will store one coulomb ofcharge when one volt is applied to it.

F = C/V

where F is the capacitance in farads, C is the charge in coulombs and V is thepotential difference in volts.

One farad is a large value andmost capacitors will measure inmicro- or picofarads.

Principle of capacitors

Electrical current is the flow of electrons. When electrons flow onto a plate of acapacitor it becomes negatively charged and this charge tends to drive electrons offthe adjacent plate through repulsive forces. When the first plate becomes full ofelectrons, no further flow of current can occur and so current flow in the circuitceases. The rate of decay of current is exponential. Current can only continue toflow if the polarity is reversed so that electrons are now attracted to the positiveplate and flow off the negative plate.

The important point is that capacitors will, therefore, allow the flow of AC inpreference to DC. Because there is less time for current to decay in a high-frequency AC circuit before the polarity reverses, the mean current flow is greater.The acronym CLiFFmay help to remind you that capacitors act as low-frequencyfilters in that they tend to oppose the flow of low frequency or DC.

Graphs show how capacitors alter current flow within a circuit. The points todemonstrate are that DC decays rapidly to zero and that the mean current flow isless in a low-frequency AC circuit than in a high-frequency one.


Capacitor in DC circuit

These curves would occur when current and charge were measured in acircuit containing a capacitor at the moment when the switch was closed toallow the flow of DC. Current undergoes an exponential decline, demonstrat-ing that the majority of current flow occurs through a capacitor when thecurrent is rapidly changing. The reverse is true of charge that undergoesexponential build up.

Capacitor in low-frequency AC circuit

Base this curve on the previous diagram and imagine a slowly cycling ACwaveform in the circuit. When current flow is positive, the capacitor acts as itdid in the DC circuit. When the current flow reverses polarity the capacitorgenerates a curve that is inverted in relation to the first. The mean currentflow is low as current dies away exponentially when passing through thecapacitor.

Capacitors and capacitance 61


Capacitor in high-frequency AC circuit

When the current in a circuit is alternating rapidly, there is less time forexponential decay to occur before the polarity changes. This diagram shoulddemonstrate that the mean positive and negative current flows are greater in ahigh-frequency AC circuit.



Inductors and inductance

Inductor

An inductor is an electrical component that opposes changes in currentflow by the generation of an electromotive force.

An inductor consists of a coil of wire, which may or may not have a core offerromagnetic metal inside it. A metal core will increase its inductance.

Inductance

Inductance is the measure of the ability to generate a resistive electro-motive force under the influence of changing current. (henry, H)

Henry

Onehenry is the inductancewhen one ampereflowing in the coil generatesa magnetic field strength of one weber.

H = Wb/A

where H is the inductance in henrys, Wb is the magnetic field strength inwebers and A is the current in amperes.

Electromotive force (EMF)

An analogous term to voltage when considering electrical circuits andcomponents. (volts, E)

Principle of inductors

A current flowing through any conductor will generate a magnetic field around theconductor. If any conductor is moved through a magnetic field, a current will begenerated within it. As current flow through an inductor coil changes, it generatesa changing magnetic field around the coil. This changing magnetic field, in turn,induces a force that acts to oppose the original current flow. This opposing force isknown as the back EMF.

In contrast to a capacitor, an inductor will allow the passage of DC and low-frequency AC much more freely than high-frequency AC. This is because theamount of back EMF generated is proportional to the rate of change of the currentthrough the inductor. It, therefore, acts as a high-frequency filter in that it tends tooppose the flow of high-frequency current through it.


Graphs

A graph of current flow versus time aims to show how an inductor affects currentflow in a circuit. It is difficult to draw a graph for an AC circuit, so a DC example isoften used. The key point is to demonstrate that the back EMF is always greatestwhen there is greatest change in current flow and so the amount of currentsuccessfully passing through the inductor at these points in time is minimal.

Current Draw a build-up exponential curve (solid line) to show how currentflows when an inductor is connected to a DC source. On connection, the rateof change of current is great and so a high back EMF is produced. Whatwould have been an instantaneous ‘jump’ in current is blunted by this effect.As the back EMF dies down, a steady state current flow is reached.

Back EMF Draw an exponential decay curve (dotted) to show how back EMFis highest when rate of change of current flow is highest. This explains howinductors are used to filter out rapidly alternating current in clinical use.



Wheatstone bridge

Definition

A Wheatstone bridge is an electrical circuit designed to measure anunknown resistance by balancing two limbs of a bridge circuit so that thevoltage between the limbs is zero.

To understand the circuit, consider the four points a, b, c and d. The voltage dropbetween points a-b in this example is 10V because it must be equal to the voltagecreated by the battery. If R1 and R2 both have equal resistance then there must bean equal voltage drop across each, i.e. 5V between a-c and 5V across c-b. If RVar

and RX also have equal resistances then the same will apply across a-d and d-beven if the actual resistances of Rx and RVar are vastly different to R2 and R1.

Therefore, if the ratio of resistances in each limb is the same then no voltage (orcurrent for that matter) flows between points c-d as they are isoelectric. This meansthat the same voltage drop has occurred across R1 on one limb and RVar on the other.Therefore if the two limbs are connected at this point (V) they both share the samepotential difference and so there is no voltage drop between them to be measured.

Equation

R2 / R1 = Rx / RVar

so

Rx = RVar . (R2 / R1)

RVar can be altered until there is a zero reading across c-d and the resultant valueused to calculate Rx. Because a zero measurement is a very precise point, aWheatstone bridge is able to measure small changes in Rx. This makes it ideal incomponents such as strain gauges or resistance thermometers or for measuringother small physiological signals.


Resonance and damping

Both resonance and damping can cause some confusion and the explanations ofthe underlying physics can become muddled in a viva situation. Although thedeeper mathematics of the topic are complex, a basic understanding of the under-lying principles is all the examiners will want to see.

Resonance

The condition in which an object or system is subjected to an oscillatingforce having a frequency close to its own natural frequency.

Natural frequency

The frequency of oscillation that an object or systemwill adopt freely whenset in motion or supplied with energy. (hertz, Hz)

We become aware of resonance when the right frequency of sound from a passingvehicle’s engine begins to make the window pane vibrate. The window pane ishaving energy supplied to it by the sound waves emanating from the vehicle andthe amplitude of the resulting oscillation is maximal at the natural frequency of thepane. The principle is best represented diagrammatically.

The curve shows the amplitude of oscillation of an object or system as thefrequency of the input oscillation is steadily increased. Start by drawing a normalsine wave whose wavelength decreases as the input frequency increases.Demonstrate a particular frequency at which the amplitude rises to a peak. Byno means does this have to occur at a high frequency; it depends on what thenatural frequency of the system is. Label the peak amplitude frequency as the


resonant frequency. Make sure that, after the peak, the amplitude dies away againtowards the baseline.

This subject is most commonly discussed in the context of invasive arterialpressure monitoring.

Damping

A decrease in the amplitude of an oscillation as a result of energy loss froma system owing to frictional or other resistive forces.

A degree of damping is desirable and necessary for accurate measurement, but toomuch damping is problematic. The terminology should be considered in the contextof a measuring system that is attempting to respond to an instantaneous change inthemeasured value. This is akin to the situation in which you suddenly stop flushingan arterial line while watching the arterial trace on the theatre monitor.

Damping coefficient

A value between 0 (no damping) and 1 (critical damping) that quantifiesthe level of damping present in a system.

Zero damping

A theoretical situation in which the system oscillates in response to a stepchange in the input value and the amplitude of the oscillations does notdiminish with time; the damping coefficient is 0.

The step change in input value from positive down to baseline initiates a changein the output reading. The system is un-damped because the output valuecontinues to oscillate around the baseline after the input value has changed.The amplitude of these oscillations would remain constant, as shown, if noenergy was lost to the surroundings. This situation is therefore theoretical, asenergy is inevitably lost even in optimal conditions such as a vacuum.

Resonance and damping 67


Under-damped

The system is unable to prevent oscillations in response to a step change inthe input value. The damping coefficient is 0–0.3.

The step change in input value from positive to baseline initiates a change in theoutput reading. The system is under-damped because the output value con-tinues to oscillate around the baseline for some time after the input value haschanged. It does eventually settle at the new value, showing that at least somedamping is occurring.

Over-damped

The system response is overly blunted in response to a step change in theinput value, leading to inaccuracy. The damping coefficient is > 1.

This time the curve falls extremely slowly towards the new value. Given enoughtime, it will reach the baseline with no overshoot but clearly this type of response isunsuitable for measurement of a rapidly changing variable such as blood pressure.



Critical damping

That degree of damping which allows the most rapid attainment of a newinput value combined with no overshoot in the measured response. Thedamping coefficient is 1.

The response is still blunted but any faster response would involve overshoot ofthe baseline. Critical damping is still too much for a rapidly respondingmeasurement device.

Optimal damping

The most suitable combination of rapid response to change in the inputvalue with minimal overshoot. The damping coefficient is 0.64.

Draw this curve so that the response is fairly rapid with no more than twooscillations around the baseline before attaining the new value. This is the levelof damping that is desirable in modern measuring systems.

Resonance and damping 69


Cleaning, disinfection and sterilization

Maintaining cleanliness and sterility is involved in everyday practice but, for themost part, is not under the direct control of anaesthetists. Nevertheless, a familiar-ity will be expected with the main definitions and methods of achieving adequatecleanliness.

Cleaning

The process of physically removing foreignmaterial from an object withoutnecessarily destroying any infective material.

Disinfection

The process of rendering an object free from all pathogenic organismsexcept bacterial spores.

Sterilization

The process of rendering an object completely free of all viable infectiousagents including bacterial spores.

Decontamination

The process of removing contaminants such that they are unable to reach asite in sufficient quantities to initiate an infection or other harmful reaction.

The process of decontamination always starts with cleaning and is followed byeither disinfection or sterilization.


Methods

Technique Process

Cleaning Manual WashingAutomated Ultrasonic bathAutomated Low-temperature steam

Disinfection Chemical Gluteraldehyde 2%Chemical Alcohol 60–80%Chemical Chlorhexidine 0.5–5%Chemical Hydrogen peroxideHeat Pasteurization

Sterilization Chemical Ethylene oxideChemical Gluteraldehyde 2%Heat AutoclaveRadiation Gamma irradiationOther Gas plasma

Cleaning, disinfection and sterilization 71



Section 3Principles of special equipment



Magnetic resonance imaging

Magnetic resonance imaging (MRI) is a daunting subject for many candidates, inpart because of the seemingly complex physics involved with its use. In reality, thelevel of knowledge required for the FRCA examination is relatively straightforwardand, more often than not, a question will progress rapidly to the clinical concernssurrounding the induction of anaesthesia in the MRI suite.

Basic principles

The fundamental component of an MRI is the magnet and its ability to produce astrong yet stable magnetic field in the order of 0.5–3 tesla. Magnetic field strengthnomenclature can be confusing so it is best to concentrate only on the frequentlyused terms. To begin with it is important to realize that the terms magnetic fieldstrength and magnetic flux density are used interchangeably.

Tesla

The SI unit of magnetic flux density. (T)

T = Wb/m2

where Wb is weber.

Weber

Themagnetic flux that would generate a potential difference of one voltin a coil of one turn if it were allowed to decay uniformly over onesecond. (Wb)

Gauss

The Gaussian unit of magnetic flux density. (G)

Although the Gaussian system of units has been long superseded by the SI systemthe gauss is still in common use.

T = 10,000G

The earth’s magnetic field strength is approximately 0.5 gauss, which highlightsjust how strong the magnetic field of a modern MRI is.


Principle

and

The MRI utilizes the fact that virtually all tissues of the body contain anabundance of water and therefore hydrogen atoms (protons). All protonsspin upon an axis and in the normal state these axes point in completelyrandom directions (A). However, when exposed to a strong magnetic field,the magnetic moments of these protons (the direction of the axis about whichthe proton is spinning) become aligned (B).

76 Section 3 � Principles of special equipment


If you were to look closely at an individual proton you would see that rather thanpoint in a single direction the magnetic moment itself actually rotates around acentral axis in a motion that is known as precession.

Precession

A change in the direction of the rotational axis of a rotating body.

The central axis (A) is aligned in a north-south direction along the core ofthe MRI, however the magnetic moment that each proton is spinningaround (B) also spins around this axis (B) as shown by the arrow. Thisprecession is much like the movement of a spinning top and occurs at aparticular frequency called the Larmor frequency. The Larmor frequency isdependant upon the magnetic field strength of the MRI and the atomconcerned – in this case hydrogen.

If a radiofrequency (RF) pulse is now applied to the area of the body beingimaged at a frequency matching the Larmor frequency then the rotation of axisB around axis A will be forced to oscillate (B’).

When the radiofrequency pulse is switched off, the protons rapidly fall backinto their original precession around the external magnetic field and in doingso give out a quantity of radiofrequency energy that can be picked up bysensor coils within the MRI and analyzed. This interaction between the RFpulse and the precession of protons is where the term resonance comesinto MRI.

Magnetic resonance imaging 77


The other magnets involved with imaging are the gradient magnets that alter theshape of the main magnetic field and therefore allow for images to be created inslices. During the scan, the huge amount of interaction between the gradientmagnets (which are pulsed on and off) and the coil magnet (which is always on)creates physical vibrations and, in turn, noise that can exceed 100dB.



Refraction and fibre-optics

Fibre optic cables are commonplace in medical practice. A good example of theiruse in anaesthetics is to guide light from a source to a distant target in instrumentssuch as laryngoscopes or bronchoscopes. Rather than being just a hollow tube,fibre optic cables have specific properties that make use of the phenomenon ofrefraction in order to achieve their effect.

Refraction

The phenomenon by which the direction of a wave will alter when itreaches a boundary of two different transition media.

To demonstrate refraction, consider two joined substances through which awave, in this case light, is passing (n1 and n2). Perpendicular to the junctionof these substances is an imaginary line (dotted) called the normal line. Iflight travels in the direction of the normal line it will pass unaltered throughboth n1 and n2. As the angle between the incident light and the normal lineincreases (θa,b,c) so does the angle of the emergent light at the junction of n1and n2. At the critical angle (θb in the example above) the emergent lightruns parallel to the junction of n1 and n2 and above the critical angle (θc)light is actually reflected back into n1 – so called total internal reflection. Thecritical angle will change depending on the properties (refractive indices) ofn1 and n2.

In physics the critical angle is measured with reference to the normal line, whereasin fibre optic terminology it is measured with reference to the direction of thejunction between n1 and n2, i.e. at 90 degrees to the normal line.

Total internal reflection

The phenomenon by which a wave is entirely reflected at the junction oftwo differing media because the angle of incidence exceeds the criticalangle.


In order to enable these phenomena to occur, fibre optic cables have an extremelypure transparent core with a high refractive index, usually glass, surrounded by atransparent cladding substance with a low refractive index. Many of these fibresare bundled together and, in turn, coated in a protective sheath. Because no light isabsorbed into the cladding layer it maintains its intensity very effectively.



Laser principles

Lasers are used in many types of surgery and the examinations will test bothyour understanding of their underlying principles and aspects related to lasersafety.

Definition

LASER is an acronym that stands for Light Amplification by StimulatedEmission of Radiation.

Principle

The definition of the word laser also gives a very succinct description of itsmode of action. A lasing medium describes the type of laser, for example a‘CO2’ laser contains CO2 as the lasing medium. The medium is pulsed withenergy from an external source, typically an intense light or electrical dis-charge. The application of external energy raises the electrons in the lasingmedium to a higher orbit or energy state around their host atom. When thepulsed external energy is off, the excited electrons return to a lower energyorbit and, in doing so, release photons (light). The wavelength of this light isdependant upon the nature of the lasing medium and the energy differencebetween the high energy and low energy orbits. Photons travel in randomdirections although some will travel parallel to the walls of the container thatholds the lasing medium. This container has mirrors at both ends that reflectthe photons back and forth through the medium. As each photon hits anelectron in the excited state it stimulates it to release its own photon and, indoing so, to return to a lower energy orbit. The phenomenon of this stimu-lated release of photons is that they share the same wavelength and phase asthe photon causing the release. The mirror at one end of the container ispartially mirrored in that it reflects a proportion of the photons that hit it butalso allows a proportion of them out of the container as laser light. Threeimportant properties of laser light produced by this process are that it ismonochromatic, collimated and coherent.

Monochromatic

Each photon of laser light shares the same wavelength and thereforecolour.


Collimated

The wave paths of laser light photons are tightly packed and parallel toeach other producing a non-divergent beam.

Coherent

Each photon of laser light describes a wave that is exactly in phase withevery other photon.

Pulsed energy is transmitted from the energy source (grey bar) to the lasingmedium and acts to raise electrons to a higher energy state around their respec-tive atoms. This is the priming stage.

The energy pulse is switched off and some orbiting electrons return to theirlower energy state. In doing so, they give off photons that travel in randomdirections within the lasing medium. Only those photons travelling parallel tothe walls of the container strike themirrors at either end at the angle required tobe reflected back into the medium whilst remaining parallel to the walls of thecontainer.



When a photon collides with an electron that has been primed and is in a highenergy state, it forces the electron to return to a low energy state and release aquantum of energy in the form of a photon. This process is called stimulatedemission. The second photon has the same wavelength, direction of travel andphase relationship as the first. When this process is repeated within the tube alaser beam is produced. A further input of energy is now required from theenergy source in order to re-prime those electrons that have assumed a lowenergy orbit around their atom.

Laser principles 83


Surgical diathermy

The principle behind the use of surgical diathermy is that of current density.Whena current is applied over a small area, the current density is high and heating mayoccur. If the same current is applied over a suitably large area then the currentdensity is low and no heating occurs. For monopolar diathermy, the apparatusutilizes a small surface area at the instrument end and a large area on the diathermyplate to allow current to flow but to confine heating to the instrument alone.Bipolar diathermy does not utilize a plate as current flows directly between twopoints on the instrument.

Frequency

The safety of diathermy is enhanced by the use of high frequency (1 MHz) current,as explained by the graph below.

Note that the x axis is logarithmic to allow a wide range of frequencies to beshown. The y axis is the current threshold at which adverse physiological events(dysrhythmias etc.) may occur. The highest risk of an adverse event occurs atcurrent frequencies of around 50 Hz, which is the UK mains frequency. Atdiathermy frequencies, the threshold for an adverse event is massively raised.

Cutting diathermy

This type of diathermy is used to cut tissues and is high energy. It differs fromcoagulation and blended mode diathermy by its waveform.


When activated, the instrument delivers a sustained high-frequency AC wave-form. Current density at the implement is higher with this mode than any otherbecause the average power is higher. Local heating causes tissue destructionwhich is limited to the tip of the implement allowing for effective cutting in theabsence of widespread thermal tissue damage. The sine wave continues untilthe switch is released.

Coagulation diathermy

When activated, the instrument delivers bursts of high-frequency AC inter-rupted by periods of no current flow. The percentage duration of current flow isset by the manufacturer and is often in the region of 10% current 90% nocurrent. Local tissue heating occurs and is more widespread than that seen in acutting mode leading to extensive local tissue destruction.

Surgical diathermy 85


Blended diathermy

When activated, the instrument delivers bursts of high-frequency AC inter-rupted by periods of no current flow. The ratio of current:no current is decidedby the manufacturer but 50:50 is commonly used. The mode is used primarilyto allow for ‘haemostasis as you cut’ and causes more thermal destruction thancutting alone.



Medical ultrasound

Ultrasound is commonly used in anaesthetic practice and its principles may betested during the examination.

Ultrasound

Sound waves with a frequency of greater than 20 KHz.

Medical ultrasound usually uses much higher frequency sound waves in the 2.5–15MHz spectrum. Increasing frequency gives rise to greater resolution, however italso reduces the penetrating capacity of the sound wave and so a compromise isoften required.

Piezoelectric effect

The phenomenon by which a mechanical stress may be induced incertain crystalline substances when a potential difference is appliedacross them.orThe phenomenon by which a potential difference may be producedacross certain crystalline substances when they are subject to a mechan-ical stress.

The phenomenon is reversible and so either definition is accurate. The conversionof electrical energy to mechanical energy (vibration) is what allows the ultrasoundprobe to generate the sound wave.

Basic function


The ultrasound probe generates a pulsed sound wave of the required frequencyvia the piezoelectric effect. The sound wave passes through the body to a depthdetermined by its frequency. A proportion of the sound wave is reflected backto the transducer (A, B, C) every time the wave reaches a boundary between twodiffering media. Sound reaching the transducer imparts mechanical energy,which is converted to electrical energy via the piezoelectric effect. The timedelay between the sound wave leaving the transducer and arriving back is usedto calculate the distance it has travelled into the tissue. Themore echo-reflectivethe medium is the higher the energy of the reflected sound wave (A>B>C) andin this way a map can be constructed about the nature of the medium and itsdepth within the tissues for each pulse of ultrasound delivered.

Speed of sound in the body

Assumed to be 1540 m.s−1 at 37 °C.

Spatial resolution

The ability of the ultrasoundmachine to distinguish between two separateobjects. The higher the spatial resolution, the closer the objects may be toeach other while still being identified as separate.

Contrast resolution

The ability of the ultrasoundmachine to distinguish between two separateobjects with similar echo-reflective properties. The higher the contrastresolution, the more similar the objects may be while still being identifiedas separate.



The Doppler effect

The Doppler effect is used in practice to visualize directional blood flow onultrasound, to estimate cardiac output and in some types of flow meter.

Doppler effect

The phenomenon bywhich the frequency of transmitted sound is altered as itis reflected from amoving object. It is represented by the following equation:

V ¼ DF:c2F0:cos�

whereV is velocity of object,ΔF is frequency shift, c is speedof sound in blood,F0 is frequency of emitted sound and θ is the angle between sound and object.

Principle

Sound waves are emitted from the probe (P) at a frequency F0. They are reflected offmoving red blood cells and back towards the probe at a new frequency, FR. The phaseshift can now be determined by FR − F0. The angle of incidence (θ) is shown on thediagram. If ameasurement or estimate of the cross-sectional area of the blood vessel isknown, flow can be derived as area multiplied by velocity (m2.m.s−1 = m3.s−1). This isthe principle behind oesophageal Doppler cardiac output monitoring.

It is also possible to calculate the pressure gradients across heart valves using theDoppler principle to measure the blood velocity and entering the result into theBernoulli equation.

Bernoulli equation

ΔP = 4v2

where ΔP is the pressure gradient and v is the velocity of blood.


Oesophageal doppler

Aswell as cardiac output estimation based on the arterial pressure waveform it is alsopossible to use blood flow as the primary variable. The oesophageal doppler devicehas a graph associated with it that is somewhat different to the usual graphsassociated with cardiac output calculations. The probe is inserted into the oesopha-gus to a point level with the descending thoracic aorta. The patient’s demographicsallow the aortic cross sectional area to be estimated from tables. The trace is derivedfrom the reflection of sound waves back toward the probe and theDoppler effect thatoccurs on reflection of this sound (see ‘The Doppler effect’ above).

The axes are labeled time (x) and velocity (y). The curve extends from thebeginning to the end of systole and the area under the velocity/time profile istherefore stroke distance (velocity x time = distance). This value is multipliedby the estimated cross sectional area of the aorta at this level to give strokevolume (distance x area = volume). Stroke volume (SV) is therefore calculatedon a beat-to-beat basis and can be used as a marker of adequacy of fluidmanagement for patients undergoing goal directed fluid therapy. The othercomponents of the trace, such as peak velocity and mean acceleration, arepresent to add further haemodynamic information but are not critical for theassessment of stroke volume.

FTc

The time during which systolic flow occurs corrected for heart rate. (ms)

The FTc is prolonged with vasodilatation as there is more effective vasculatureinto which blood can flow and it is reduced by vasoconstriction. Hypovolaemia


will reduce the FTc as it causes an effective vasoconstriction of the peripheralvessels.

Peak velocity

The maximum recorded velocity of blood flow during systolic ejection.(cm.s−1)

The peak velocity (PV) is a surrogate for left ventricular contractility and in an agerelated parameter. As well as falling with increasing age it may be significantlyreduced in cases of LV dysfunction.

Oesophageal doppler 91


Cardiac output measurement

The ability to assess a patient’s cardiac output in a dynamic fashion (both over timeand in response to therapeutic interventions) is rapidly becoming a standard ofcare in the operating theatre, as well as for its more established role in intensivecare. It is therefore important to have an understanding of the way in whichdifferent pieces of monitoring equipment function.

The Fick principle

The total uptake or release of a substance by an organ is equal to theproduct of the blood flow to the organ and the arterio-venous concentra-tion difference of the substance.

This observation is used to calculate cardiac output by using a suitable markersubstance, such as oxygen, heat or dye, and the following equation:

V�

O2 ¼ COðCaO2 � C�vO2Þso

CO ¼ V�

O2=ðCaO2 � C�vO2Þ

where V�

O2 is the oxygen uptake, CO is cardiac output, CaO2 is arterial O2

content and C�vO2 is mixed venous O2 content.

Thermodilution and dye dilution

Amarker substance is injected into a central vein. A peripheral arterial line is usedto measure the amount of the substance in the arterial system. A graph ofconcentration versus time is produced and patented algorithms based on theStewart–Hamilton equation (below) are used to calculate the cardiac output.

When dye dilution is used, the graph of concentration versus time may show asecond peak as dye recirculates to the measuring device. This is known as arecirculation hump and does not occur when thermodilution methods are used.

Stewart–Hamilton equation

If the mass of marker is known and its concentration is measured, thevolume into which it was given can be calculated as

V = M/C

If concentration is measured over time, flow can be calculated as


Flow = M/(C .Δt)

where M is mass, V is volume and C is concentration. A special form of theequation used with thermodilution is

Flow ¼ V injðTb � T tÞ:KTbloodðtÞt

where the numerator represents the ‘mass’ of cold and the denominatorrepresents the change in blood temperature over time; K represents com-puter constants.

Dye dilution graphs

Draw a curve starting at the origin that reaches its maximum value at around5 s. The curve then falls to baseline but is interrupted by a recirculation hump ataround 15 s. This is caused by dye passing completely around the vasculatureand back to the sensor a second time.

Cardiac output measurement 93


Demonstrate that the semi-log plot makes the curve more linear during itsrise and fall from baseline. The recirculation hump is still present but isdiscounted by measuring the area under the curve (AUC) enclosed by atangent from the initial down stroke. This is the AUC that is used in thecalculations.

Thermodilution graphs

The actual graph of temperature versus time for the thermodilution method wouldresemble the one below.

Demonstrate that the thermodilution curve has no recirculation hump whencompared with the dye dilution method. Otherwise the line should be drawn ina similar fashion.

For reasons of clarity, the graph is usually presented with temperature decrease onthe y axis so that the deflection becomes positive.



Thermodilution graphs

The semi-log transformation again makes the rise and fall of the graphlinear. Note that this time there is no recirculation hump. As the fall on theinitial plot was exponential, so the curve is transformed to a linear fall byplotting it as a semi-log. The AUC is still used in the calculations of cardiacoutput.

Pulse contour analysis

Pulse contour analysis monitors may be either calibrated or uncalibrated.Calibrated monitors will use one of the techniques above to measure an actualcardiac output once or twice a day according to the manufacturers’ recommenda-tions. In between calibrations, a continuous cardiac output figure is derived bycomparing the area under the arterial pressure waveform during each beat to thearea that was present at the time of calibration. By doing this, changes to the shapeand size of the arterial pressure waveform can be used to estimate the concurrentchanges in cardiac output.

Non-calibrated monitors simply omit the calibration phase and use dem-ographic data about the patient to make some mathematical assumptions.These monitors are less useful as precise cardiac output monitors and moreuseful as trend monitors. They assess the change in the morphology of thearterial trace in response to surgery, pathology, positioning or therapeuticinterventions and help to guide management. Outside the intensive care unitthey are primarily used for the management of goal directed fluid therapyand there are some key terms associated with this. You will see that most ofthem rely on the fact that an increase in intra-thoracic pressure duringpositive pressure ventilation can cause a change in a measured variable ofsome sort.

Cardiac output measurement 95


Pulse pressure variation

The change inmagnitude of the SBP-DBP difference of the arterial pressurewaveformwith concomitant positive pressure ventilation. Used as amarkerof fluid responsiveness. (PPV, %)

The PPV is a validated technique to assess fluid responsiveness. The pre-requisites are that the patient has no dysrhythmias and is anaesthetized,paralyzed and ventilated. The theory is that a patient who is relatively fluiddepleted will show bigger variations in arterial pressure during the ventilatorycycle than one who is euvolaemic. A commonly accepted cut-off for decidingon the requirement for fluid administration is PPV 15%. If it is above this rangethen protocolized fluid boluses should be given until the value returns tonormal.

Plethysmography variabiltiy index

The change in the amplitude of the plethysmograph trace with concom-itant positive pressure ventilation. Used a marker of fluid responsiveness.(PVI, %)

The PVI is a recently applied concept that aims to use the peripheral plethysmo-graph trace in lieu of the more extensively-studied arterial waveform. In otherrespects, the pre-requisites and method of calculation are similar to PPV althougha PVI of 14% is suggested as the marker of likely fluid responsiveness when usingthis device.

Stroke volume

The volume of blood ejected by the heart during systole. (ml)or

SV = CO / HR

where SV is stroke volume, CO is cardiac output and HR is heart rate.



Goal directed fluid therapy

The term goal directed fluid therapy simply implies that fluid is administered inorder to achieve a measurable and repeatable target. The target could be anymeasurable parameter, although using markers such as CVP, urine output orheart rate alone have been shown not to correlate with actual fluid requirements.An overzealous approach to fluid administration leads to increased morbidity inmajor surgery and is to be avoided. A typical algorithm for the administration ofintra-operative fluids may utilize SV as a measurable target.

The target is said to have been reached when fluid administration no longer resultsin an increase in SV, i.e. the SV is maximized. Any further fluid administration atthis stage is thought to be excessive and therefore detrimental.

Stroke volume variation

The difference between the maximum and minimum calculated strokevolume divided by the mean stroke volume over a period of time in aventilated patient. Used as a marker of fluid responsiveness. (SVV, %)

The concept is similar to those already described. Many initial studies cited 5%SVV to reliably predict fluid responsiveness in patients undergoing surgery.


Defibrillators

Defibrillator circuit

You may be asked to draw a defibrillator circuit diagram in the examination inorder to demonstrate the principles of capacitors and inductors.

Charging

When charging the defibrillator, the switch is positioned so that the 5000 V DCcurrent flows only around the upper half of the circuit. It, therefore, causes acharge to build up on the capacitor plates.

Discharging


When discharging, the upper and lower switches are both closed so that thestored charge from the capacitor is now delivered to the patient. The inductoracts to modify the current waveform delivered as described below.

Defibrillator discharge

The inductor is used in a defibrillation circuit to modify the discharge waveform ofthe device so as to prolong the effective delivery of current to the myocardium.

Unmodified waveformC

urre

nt (

I)

Time (ms)

The unmodified curve shows exponential decay of current over time. This is thewaveform that would result if there were no inductors in the circuit.

Modified waveform

Themodified waveform should show that the waveform is prolonged in durationafter passing through the inductor and that it adopts a smoother profile.

Defibrillators 99


Breathing systems

A thorough knowledge of breathing systems is key to the safe delivery of anaes-thesia and it will be examined in this context. There are many ways to classifybreathing systems – open, semi-open, semi-closed, closed – and as long as youhave a routine it will serve you well. TheMapleson classification is still in use and iscovered here.

Mapleson A

The Mapleson A system is efficient during spontaneous ventilation (SV) andinefficient during controlled ventilation (CV). During SV the patient breathesin fresh gas from the inlet and the reservoir bag. During expiration, dead spacegas passes back along the circuit to fill the tubing whilst fresh gas fills thereservoir bag. When the bag is full, the system pressure rises and furtherexhaled air is forced out from the APL valve. During the inspiratory pausefresh gas pushes any residual alveolar gas in the tubing out of the APL valve. Aslong as the FGF is equal to the patient’s alveolar minute volume (0.7 x minutevolume), rebreathing of CO2 will be avoided. During CV, fresh gas is forcedfrom the APL due to high circuit pressure and so the system becomes ineffi-cient. A coaxial or parallel version of this system is called a Lack circuit andmakes scavenging gases more convenient.

Mapleson B


The Mapleson B system is inefficient for both SV and CV. During exhalation amixture of alveolar and fresh gas passes out via the APL valve and duringinspiration a mixture of fresh gas and retained alveolar gas in breathed in.Adequate flushing of alveolar gas within the circuit can only be achieved with aFGF of 2–3 times minute volume.

Mapleson C

A Mapleson C (Water’s) circuit is most commonly found in the recoveryroom. The flow dynamics are similar to a Mapleson B and, as such, it is alsoan inefficient system for both SV and CV. Nevertheless, it is compact andlightweight making it a useful circuit for urgent or emergent situations.

Mapleson D

The Mapleson D system and its coaxial Bain modification are relatively ineffi-cient for both SV and CV. In the case of SV, during exhalation, fresh gas andexhaled gas enter the tubing and as the pressure increases some venting willoccur via the APL valve. On inspiration the patient will receive a mixture of gaswith the amount of fresh gas dependent on the flow rate, duration of thepatients expiratory pause and tidal volume. With longer pauses, more freshgas will be available. At least 2 xminute ventilation FGF is required to minimizeor prevent rebreathing. The picture is similar for CV and the FGF requirementsare the same.

Breathing systems 101


Mapleson E

The Mapleson E system is a modification of the Ayre’s T –piece. It has minimaldead space and very little resistance to breathing and was used primarily forpaediatric anaesthesia until the Mapleson F circuit superseded it.

Mapleson F

The Mapleson F system is a modification of a common T-piece system byJackson and Rees. A double ended bag is attached to the expiratory limb of thecircuit to allow visualization of the respiratory pattern and to enable intermit-tent positive pressure ventilation if required. The system itself has a lowresistance to breathing and, although inefficient, is used commonly in paedi-atric anaesthesia.



Ventilator profiles

The range of ventilator modes used in anaesthetic practice is increasing and anunderstanding of the various functions is therefore important. The underlyingprinciples behind the myriad of ventilator modes are relatively simple but thenomenclature can be confusing.

Ventilators

Ventilators are devices with the ability to move gases into and out of thelungs in order to provide or assist ventilation.

Negative pressure ventilation

A formof ventilation inwhich negative pressure is applied intermittently tothe thorax within a sealed compartment in order to expand the rib cageand cause the in-drawing of air or other gas into the lungs. Now supersededby positive pressure ventilation.

The polio epidemic of the 1940s and 1950s saw a proliferation of so-called ‘ironlungs’ used for ventilating patients with bulbar polio affecting respiration. Thepatient’s body was placed inside the chamber with an airtight seal around the headand neck. Intermittent negative pressure applied to the chamber caused the thoraciccage to expand thereby drawing air into the lungs in a very physiological way.

Positive pressure ventilation

A form of ventilation in which intermittent positive pressure is applied tothe lungs during inhalation and exhalation is allowed to occur passively.

The term positive pressure ventilation reveals little about the way in which anindividual ventilator functions. Unfortunately there are over 40 possible modesof ventilation attracting over 65 names, many of which are manufacturer-specific. Here we consider the function of a ventilator by dividing it into threestages:

Trigger

The event that starts each ventilator breath.

When the patient is making no spontaneous effort, the trigger is usually timewhich, in turn, is dependant on the set respiratory rate.When the patient is making


spontaneous effort the trigger is usually minimum flow or fall in pressure causedby the patient’s effort.

Limit

The factor that controls the inspiratory flow.

The limit is not the factor which brings the inspiratory phase to an end. Ratherit is the mechanism that governs how the breath is delivered to the patient.The breath may be flow-limited (a fixed flow delivered over a set time so thata known tidal volume is delivered) or pressure-limited (a fixed pressure overa fixed time). In flow-limited ventilation the airway pressure will rise towhatever is necessary to deliver the breath risking barotrauma. In pressure-limited ventilation the tidal volume will be governed by lung compliance andmay be inadequate or risk volutrauma in situations where compliance changesrapidly.

Cycling

The factor that governs when the change from inspiratory to expiratoryphase (or to inspiratory pause) occurs.

Common cycling signals are volume, time and flow. Pressure cycling is rarelyused as a primary function although may be used as a secondary cycle factorwhen a high pressure alarm is triggered. In volume-cycled ventilation inspi-ration is arrested when the pre-set volume is attained. If there is an inspir-atory pause expiration will begin after a set time (time-cycled) rather thanimmediately following inspiration so there may be mixed cycling present.In pure time-cycled ventilation the change from inspiration to expirationoccurs after a pre-set time related to the desired respiratory rate. In flow-cycled ventilation, inspiration is arrested once inspiratory flow falls to aminimum level (usually determined by the manufacturer) towards the endof inspiration.

Ventilator waveforms

In addition to an understanding of the terminology of ventilators, common wave-forms may be tested. For clarity, the description of the ventilator traces belowrefers to the limit applied to the ventilated breath, either pressure or flow (volume).These are what are commonly called pressure control (PCV) or volume control(VCV) ventilators. The traces are exaggerated in order to more clearly describe theunderlying principles.



Pressure control ventilation

Pressure waveform. Draw and label the axes as shown. At the beginning ofthe breath there is rapid attainment of the set pressure, which continues untilthe breath has finished. The fall to baseline pressure at the end of the breath israpid. The baseline pressure value is changed by the addition of PEEP asshown. A patient triggered breath should be drawn as a small downwarddeflection (A) due to negative pressure within the system from respiratoryeffort.

Ventilator profiles 105


Volume waveform. Draw and label the axes as shown. Draw a curve abovethe baseline and comment that the baseline volume is equivalent to the FRC.The slope of the curve steepest at the beginning of the breath because thepressure gradient (and therefore flow) is at its highest at this point. As the setpressure is approached, the curve flattens. Some ventilators may use thisdecrease in flow rate to cycle from inspiration to expiration, others may not.During expiration the steepest part of the curve is drawn first as for inspira-tion. The curve flattens as lung volume approaches FRC.

Flow waveform. Draw and label the axes as shown. The period of most rapidflow is immediately upon the initiation of the breath. At the pressuregradient between ventilator and lung reduces from this point onwards, sothe flow velocity reduces towards zero at the end of inhalation. The secondphase of the curve should be drawn with a steep negative deflection indicat-ing that flow has reversed (i.e. exhalation) and a similar pattern with flowvelocity peaking and then reducing towards zero at the end of exhalation. Apatient triggered breath should be drawn as a small upward deflection (A)due to the generation of inspiratory flow within the system.

Volume control ventilation



Pressure waveform. Draw and label the axes as shown. Draw a linearincrease in airway pressure noting that the peak value may be significantlyhigher than that seen in PCV. At the end of inspiration, pressure may dropimmediately (first waveform) if there is no inspiratory pause or may attain apeak followed by a plateau pressure (second waveform) during the inspir-atory pause if one is present. The baseline pressure can be adjusted by theaddition of PEEP as shown. As with PCV a breath may also be triggered bythe patient and you should represent this as a negative deflection prior to theventilated breath as before (A).

Volume waveform. Draw and label the axes as shown. Demonstrate a linearrise in volume as a constant flow is delivered by the ventilator. Duringexpiration the volume falls as a function of passive recoil of the lungs andchest wall. Expiration may follow on from inspiration immediately (firstwaveform) or, if an inspiratory pause is present, there may be a short plateauprior to the volume falling (B).

Flow waveform. Draw and label the axes as shown. Draw a square waveformduring the inspiratory phase to demonstrate a constant flow. During theexpiratory phase the flow is reversed and declines as a smooth curve backtowards the baseline. The patient may trigger a breath and you shoulddemonstrate this by drawing a small positive deflection (C) to represent asmall inspiratory flow. If there is an inspiratory pause then expiration will bedelayed whilst this occurs (D).

Clinical relevance

No particular mode of ventilation is superior to any other but they all have theirplace in certain situations. PCV is thought of as a more physiological way in whichto deliver a breath and protects against barotrauma to a certain degree, as well asbeing able to overcome small circuit leaks if they are present. On the other hand it

Ventilator profiles 107


is likely to be affected by changes in compliance to a much greater extent thanVCV. In theatre, a patient having laparoscopic surgery will need careful manage-ment of their ventilation on PCV as the delivered volume will fall in response to theincreased intra-abdominal pressure (and hence reduced thoracic compliancesecondary to diaphragmatic splinting). Likewise, when the pneumoperitoneumis released, there is a danger of volutrauma as the high pressure that had previouslybeen necessary is now able to deliver pathological volumes to the lungs with all theattendant risks.

VCV enables a reliably constant volume to be delivered and reduces the chanceof under or over ventilation. It can be used where compliance is likely to change inorder to avoid significant changes in the minute volume delivered. However, thevolume delivered is more likely to cause barotrauma if it is inappropriate for thepatient and circuit leaks will be poorly tolerated as part of each breath is lost fromthe circuit yet still counted as being delivered by the ventilator. In the intensive caresetting it may be found that the set volumes are undeliverable in patients withdramatically altered lung compliance and PCV may be the better option.



Pulse oximetry

The equations and definitions associated with the principles behind the pulseoximeter are important to understand. Although simple, youmay see themwrittenin different ways in different texts. The confusion arises because the format of theequations will depend on which variable is being measured. Both laws below dealwith the effect that a substance has on the intensity of the light that passes throughit. If one measures the transmittance (T) of light, the equations are expressed asexponentials because there is an exponential decline in the quantity of lightremaining as it passes through an absorbing substance. If instead we concentrateon the absorbance (A) of light the equations describe a linear relationship as shownbelow. Either way is valid but the second method is far easier to explain in theexamination setting.

Beer’s law

The absorbance (A) of light passing through a medium is proportional tothe concentration (c) of themedium and its molar extinction coefficient (ε).

Draw a line that passes through the origin and which rises steadily as cincreases. The slope of the line is dependent upon the molar extinctioncoefficient (ε), which is a measure of how avidly the medium absorbs light,and by the path length (l). Note that if transmittance (T) is plotted on the yaxis instead of absorbance, the curve should be drawn as an exponentialdecline.

Lambert’s law

The absorbance of light passing through a medium is proportional to thepath length.


The line is identical to that above except that in this instance the slope isdetermined by both ε and the concentration (c) of the medium. Again, iftransmittance (T) is plotted on the y axis instead of absorbance, the curveshould be plotted as an exponential decline.

Both laws are often presented together to give the following equation, known as theBeer–Lambert law, which states that:

A = εlc

whereA is absorbance of light, ε is themolar extinction coefficient, l is pathlength and c is concentration.

In the pulse oximeter, the concentration and molar extinction coefficient areconstant. The only variable becomes the path length, which alters as arterialblood expands the vessels in a pulsatile fashion.

Haemoglobin absorption spectra

The pulse oximeter is a non-invasive device used to monitor the percentagesaturation of haemoglobin (Hb) with oxygen (SpO2). The underlying physicalprinciple that allows this calculation to take place is that infrared light is absorbedto different degrees by the oxy and deoxy forms of Hb.

Two different wavelengths of light, one at 660 nm (red) and one at 940 nm(infrared), are shone intermittently through the finger to a sensor. As the vessels inthe finger expand and contract with the pulse, they alter the amount of light that isabsorbed at each wavelength according to the Beer–Lambert law. The pulsatilevessels, therefore, cause two waveforms to be produced by the sensor.

If there is an excess of deoxy-Hb present, more red than infrared light will beabsorbed and the amplitude of the ‘red’ waveform will be smaller. Conversely, ifthere is an excess of oxy-Hb, the amplitude of the ‘infrared’ waveform will besmaller. It is the ratios of these amplitudes that allows the microprocessor to give



an estimate of the SpO2 by comparing the values with those from tables stored in itsmemory.

In order to calculate the amount of oxy-Hb or deoxy-Hb present from theamount of light absorbance, the absorbance spectra for these compounds must beknown.

Haemoglobin absorption spectra

Oxy-Hb Crosses the y axis near the deoxy-Hb line but falls steeply around600 nm to a trough around 660 nm. It then rises as a smooth curve throughthe isobestic point where it flattens out. This curve must be oxy-Hb as theabsorbance of red light is so low that most of it is able to pass through to theviewer, which is why oxygenated blood appears red.

Deoxy-Hb Starts near the oxy-Hb line and falls as a relatively smooth curvepassing through the isobestic point only. Compared with oxy-Hb, it absorbsa vast amount of red light and so appears ‘blue’ to the observer.

Pulse oximetry 111


Capnography

You will be expected to be familiar with capnography. The points to understandare the shape and meaning of different capnograph traces and the nature of thereaction taking place within the CO2 absorption canister.

Capnometer

The capnometer measures the partial pressure of CO2 in a gas and displaysthe result in numerical form.

Capnograph

A capnographmeasures the partial pressure of CO2 in a gas and displays theresult in graphical form.

A capnometer alone is unhelpful in clinical practice and most modern machinespresent both a graphical and numerical representation of CO2 partial pressure.

Normal capnograph

Assume a respiratory rate of 12 min−1. From zero baseline, the curve initiallyrises slowly owing to the exhalation of dead space gas. Subsequently, it risessteeply during expiration to a normal value and reaches a near horizontalplateau after approximately 3 s. The value just prior to inspiration is the end-tidal CO2 (PETCO2). Inspiration causes a near vertical decline in the curve tobaseline and lasts around 2 s.


Rebreathing

The main difference when comparing rebreathing with the normal trace is thatthe baseline is not zero. Consequently the PETCO2 may rise. If the patient isspontaneously breathing, the respiratory rate may increase as they attempt tocompensate for the higher PETCO2.

Inadequate paralysis

The bulk of the curve appears identical to the normal curve. However, duringthe plateau phase, a large cleft is seen as the patient makes a transient respira-tory effort and draws fresh gas over the sensor.

Capnography 113


Cardiac oscillations

Usually seen when the respiratory rate is slow. The curve starts as normal butthe expiratory pause is prolonged owing to the slow rate. Fresh gas within thecircuit is able to pass over the sensor causing the PCO2 to fall. During this time,the mechanical pulsations induced by the heart force small quantities ofalveolar gas out of the lungs and over the sensor, causing transient spikes.Inspiration in the above example does not occur until point A.

Hyperventilation

In this example, the respiratory rate has increased so that each respiratory cycleonly takes 3 s. As a consequence the PETCO2 has fallen to approx 2.5 kPa.



Malignant hyperpyrexia

Rarely seen. The PETCO2 rises rapidly such that there may be a noticeable increasefrom breath to breath. The excess CO2 is generated from the increased skeletalmuscle activity and metabolic rate, which is a feature of the condition.

Acute loss of cardiac output

The PETCO2 falls rapidly over the course of a few breaths.With hyperventilation,the fall would be slower. Any condition that acutely reduces cardiac output maybe the cause, including cardiac arrest, pulmonary embolism or acute rhythmdisturbances. If the PCO2 falls instantly to zero, then the cause is disconnection,auto-calibration or equipment error.

Breathing system disconnection

Capnography 115


Following a normal trace, there is the absence of any further rise in PCO2. Youshould ensure that your x axis is long enough to demonstrate that this is notsimply a result of a slow respiratory rate.

Obstructive disease

Instead of the normal sharp upstroke, the curve should be drawn slurred. Thisoccurs because lung units tend to empty slowly in obstructive airways disease.In addition, the PETCO2 may be raised as a feature of the underlying disease.

Hypoventilation

The respiratory rate is reduced such that each complete respiratory cycle takeslonger. This is usually a result of a prolonged expiratory phase, so it is theplateau that you should demonstrate to be extended. The PETCO2 will be raisedas a consequence.



Absorption of carbon dioxide

Carbon dioxide is absorbed in most anaesthetic breathing systems by means of acanister that contains a specific absorbingmedium. This is often soda lime but mayalso be baralime in some hospitals.

Soda lime:4% sodium hydroxide NaOH15% bound water H2O81% calcium hydroxide Ca(OH)2Baralime:20% barium hydroxide octahydrate Ba(OH)2.8H2O80% calcium hydroxide Ca(OH)2

Mesh size

The smaller the granules, the larger the surface area for CO2 absorption. However,if the granules are too small then there will be too little space between them and theresistance to gas flow through the canister will be too high. As a compromise, a4/8 mesh describes the situation where each granule should be able to pass througha sieve with four openings per inch but not through one with eight openingsper inch.

Chemical reaction

You may be asked to describe the chemical reaction that occurs when CO2 isabsorbed within the canister. The most commonly cited reaction is that betweensoda lime and CO2. The overall reaction in the presence of water is:

CO2 + Ca(OH)2 → CaCO3 + H2O + Heat

The constituent parts of the overall reaction are:

CO2 + H2O → H2CO3

2NaOH + H2CO3 → Na2CO3 + 2H2O + heat

Na2CO3 + Ca(OH)2 → CaCO3 + 2NaOH + heat

Heat is produced at two stages and water at one. This can be seen and felt in clinicalpractice. Note that NaOH is reformed in the final stage and so acts only as acatalyst for the reaction. The compound that is actually consumed in both bar-alime and soda lime is Ca(OH)2.


Colour indicators

Compound Colour change

Ethyl violet White to purpleClayton yellow Pink to creamTitan yellow Pink to creamMimosa Z Red to whitePhenolphthalein Red to white



Neuromuscular blockade monitoring

This topic tests your knowledge of the physics and physiology behind the use ofneuromuscular blocking drugs (NMBDs). You will benefit from a clear idea in yourmind about what each type of nerve stimulation pattern is attempting to demonstrate.

Single twitch

A single, supra-maximal stimulus is applied prior to neuromuscular block-ade as a control. The diminution in twitch height and disappearance of thetwitch correlates crudely with depth of neuromuscular block.

Supra-maximal stimulus

An electrical stimulus of sufficient current magnitude to depolarize allnerve fibres within a given nerve bundle. Commonly quoted as > 60 mAfor transcutaneous nerve stimulation.

Train of four

Notice that you are being asked to describe the output waveform of the nervestimulator. The axes must, therefore, be time and current as shown. Eachstimulus is a square wave of supra-maximal current delivered for 0.2 ms. Thetrain of four (TOF) is delivered at 2 Hz so there is one stimulus every 500 ms.This means that if the TOF starts at time 0, the complete train takes 1500 ms.

Tetanic stimulus

A supra-maximal stimulus applied as a series of square waves of 0.2 msduration at a frequency of 50 Hz for a duration of 5 s is tetanic stimulation.


Depolarizing block train of four

Notice now that you are being asked to describe the response to a TOFstimulus. The axes are, therefore, changed to show time and percentageresponse as shown. It is important to realize that each twitch is still beingdelivered at the same current even though the response seen may be reduced.Partial depolarizing neuromuscular block causes an equal decrease in thepercentage response to all four stimuli in the TOF. After a period of tetanythat does not cause 100% response, there is no increase in the height ofsubsequent twitches.

Non-depolarizing block train of four

Initial TOF should demonstrate each successive twitch decreasing in ampli-tude: this is fade. The tetanic stimulus should fail to reach 100% response andshould also demonstrate fade. The second TOF should still demonstrate fadebut the twitches as a group should have increased amplitude. This is post-tetanic potentiation.



Train of four ratio

The ratioof theamplitudes of the fourth to thefirst twitches of a TOF stimulusis known as the TOF ratio (TOFR); it is usually given as a percentage T4:T1.

The TOFR is used for assessing suitability for and adequacy of reversal. Threetwitches should be present before a reversal agent is administered and the TOFRafter reversal should be > 90% to ensure adequacy.

Draw four twitches at 0.5 s intervals with each being lesser in amplitude than itspredecessor. In the example, the TOFR is 20% as T4 gives 20% of the responseof T1. Explain that this patient would be suitable for reversal as all four twitchesare present. However, had this trace been elicited after the administration of areversal agent, the pattern would represent an inadequate level of reversal forextubation (TOFR < 90%).

Assessment of receptor site occupancy

Twitches seen Percentage receptor sites blocked

All present <701 twitch lost >702 twitches lost >803 twitches lost >90All lost 95–100

Double-burst stimulation

Two bursts of three stimuli at 50 Hz, each burst being separated by 750 ms.

In double-burst stimulation, the ratio of the second to the first twitch is assessed.There are the same requirements for adequacy of reversal as TOFR (>90%);

Neuromuscular blockade monitoring 121


however, having only two visible twitches makes assessment of the ratio easier forthe observer.

No neuromuscular block

Demonstrate two clusters of three stimuli (duration 0.2 ms, frequency 50 Hz)separated by a 750 ms interval. The heights of both clusters are identical. Ifquestioned, the current should be greater than 60 mA for the same reasons aswhen using the TOF.

Residual neuromuscular block

Demonstrate the two clusters with the same time separation. In the presence ofa neuromuscular blocking agent, the second cluster will have a lesser amplitudethan the first (70% is shown).

Post-tetanic count

A post-tetanic count is used predominantly where neuromuscular blockade is sodeep that there are no visible twitches on TOF. The post-tetanic twitch count can



help to estimate the likely time to recovery of the TOF twitches in these situations.The meaning of the count is drug specific.

Draw a 5 s period of tetany followed by a 3 s pause. Note that the tetanic stimulusfails to reach 100% response as this test is being used in cases of profound musclerelaxation. Next draw single standard twitches at a frequency of 1 Hz: 20 stimuliare given in total. Using atracurium, a single twitch on the TOF should appear inapproximately 4 min if there are four post-tetanic twitches evident.

Phase 1 and phase 2 block

Phase 1 Phase 2

Cause Single dose of depolarizingmuscle relaxant

Repeated doses of depolarizingmuscle relaxant

Nature of block Partial depolarizing Partial non-depolarizingSingle twitch Decreased DecreasedT4:T1 >0.7 <0.71 Hz twitch Sustained FadePost-tetanicpotentiation

No Yes

Effect ofanticholinesterases

Block augmented Block antagonized

Physiology Reduced number of functioningAch receptors due to thepresence of suxamethonium atsome receptor sites.Contraction of fewer musclefibres resulting in reduced butrepeatable twitch strength

Reduced Ach mobilization dueto pre-synaptic blockade.Post-synaptic receptordesensitization. IncreasedNa+-K+ ATPase activityfollowing depolarizationacting to repolarize the post-synaptic membrane

Neuromuscular blockade monitoring 123


Thromboelastography

Thromboelastography (TEG) graphically describes the entire clotting process ofwhole blood. It allows the operator to identify specific factors that may be inhibit-ing the process of adequate clot formation. In the traditional TEG a cup containinga sample of whole blood is placed in the machine and a torsion wire is suspendedwithin the sample. The cup is rotated in a limited arc of 45° every 5 seconds. Asclotting begins, the cup and the wire become linked by the sample and a torsional(twisting) force is therefore applied to the wire. As clotting progresses this forcebecomes greater and this is reflected in an increasing amplitude of the TEG trace.As fibrinolysis begins, the amplitude falls, eventually back to zero. A number of keymeasurements may be taken from the same trace:

Reaction time

The time taken from the start of the test until initial clot formation. (R, s)

The R time may be prolonged by heparinization or factor deficiency.

Kinetics

The time taken to achieve a clot strength of 20mm amplitude. (K, s)

The K time is dependant on the function of fibrinogen and platelets.

Alpha angle

The slope of a line drawn between R+1mm and K reflecting the rate of clotformation. (α, °)

The angle will be reduced by abnormalities of clotting factors, platelets or fibrinogen.

Maximum amplitude

A measure of the strength of the final clot. (MA, mm)

The MA will be affected by platelet number and function and also by defeciency offibrinogen.

30 minute amplitude

The percentage decrease in amplitude taken at 30 minutes post maximumamplitude, a measure of the degree of fibrinolysis. (LY30, %)


Normally the LY30 is below 7.5% but will increase when fibrinolytic activity isincreased.

Diagram

The amplitude of a TEG is measured in mm. A normal trace can be drawn asshown above and encompasses all of the definitions on the preceding page. Youmay be asked how the TEG would change under certain situations. Commonsituations would be anticoagulant use or haemophillia (R and K increased,MAand α reduced), or DIC where the picture is initially reversed with a hyper-coagulable state and fibrinolysis in stage 1 (R and K reduced, MA and αincreased and LY30 increased) and a hypocoagulable state in stage 2 (R and Kincreased, MA and α reduced).

Thromboelastography 125



Section 4Pharmacological principles



Atomic structure

Many of the definitions and diagrams presented here are unlikely to be tested inisolation. However, an understanding of these basic biochemical principles willhelp when considering many of the other subjects that are tested.

Atom

The smallest unit of an element with a nucleus containing protons and(usually) neutrons with surrounding orbiting electrons.

Hydrogen is the exception to this definition as its nucleus contains only a singleproton and no neutrons.

Proton

A stable subatomic positively charged particle found in the nucleus of anatom. The number of protons in the nucleus is the atomic number of theelement.

Electron

A stable subatomic negatively charged particle. Electrons have negligiblemass and are found in shells surrounding the nucleus of the atom.

Each electron shell has a fixed maximum number of electrons that it may contain.The first shell (closest to the nucleus) can contain two, the second shell up to eight,the third shell up to eighteen and so on. Each shell contains one or more sub shellswhich are filled in a specific order. If the outermost shell of electrons contains eightelectrons then it is full and this makes the element particularly stable. Theseelements are known as inert or noble gases. The exception to this rule is heliumatom that has a full outer shell with only two electrons present and is therefore alsoone of the noble gases.

The outermost shell is known as the valence shell and the number of electrons inthis shell determines the reactivity of the atom in terms of the type and number ofbonds it may form (see below).

Isotopes

Atoms of the same element that have different atomic weights, due todifferent numbers of neutrons in the nucleus.


Molecule

The smallest possible part of a substance that can participate in a chemicalreaction. Amolecule of an element may consist of a single atom, whereas amolecule of a compound will contain two or more different atoms. Amolecule is electrically neutral.

Ion

An electrically charged particle formed by the loss or gain of one or moreelectrons from an atom.

This loss or gain of electrons occurs during the formation of bonds (see below) andusually results in a full outer shell of electrons, i.e. the same structure as a noble gas.Metal atoms lose electrons to form positively charged ions called cations and non-metals gain electrons becoming negatively charged ions called anions. To help youremember which way round this is, remember than anANION isANegative ION.Cations are attracted to cathodes and anions to anodes.

130 Section 4 � Pharmacological principles


Oxidation and reduction

Oxidation

A chemical reaction involving loss of electrons froman atom,molecule or ion.orThe combination of a substance with oxygen.

Reduction

A chemical reaction involving gain of electrons.orThe loss of oxygen from a substance.

If you are having trouble remembering which way round this is, then a usefulacronym when considering this definition is OIL RIG. Oxidation Is Loss;Reduction Is Gain.

In a chemical reaction oxidation and reduction will be occurring at the sametime and these reactions are thus known as redox reactions. An oxidizing agent is asubstance which oxidizes something else, i.e. it donates its oxygen to anothersubstance. A reducing agent is the opposite: it removes oxygen.


Chemical bonds

A chemical bond is an interaction between two similar or dissimilar atoms ormolecules. Bonds are formed to make the molecule as stable as possible, ideallywith a full complement of electrons in the outer shell.

Interatomic bonds

Bonds between atoms (forming molecules) may be sub-divided into ionic (electro-valent) or covalent bonds.

Ionic or electrovalent bonds

Ionic bonds are formed when electrons are transferred from one atom toanother.

This requires an energy known as ionization energy and results in full outerelectron shells for the atoms which then become electrically charged ions. Theseions are then attracted to each other.

An example of an ionic bond is when a sodium atom, which has one electronin its outer shell, reacts with a chloride atom, which has seven. This results inboth atoms having full outer electron shells. As sodium has lost an electron ithas become a cation (Na+) and chloride has gained an electron to become ananion (Cl−).

Covalent bonds

These are formed when atoms share the electrons in their outer shells to makethem complete.

The number of spaces in the outer shell of an atom determines its combiningpower. For example, oxygen has two spaces and therefore a combining power oftwo. A single bond is formed when one electron is shared; a double bond is whentwo are shared and a triple bond when three are shared.


and

The diagram above shows the covalent bonds in water (H2O) and oxygen (O2)molecules.

In water the two hydrogen atoms each share their single electron with theoxygen molecule forming two single covalent bonds. In the oxygen molecule,two electrons are shared from each atom, forming a double bond.

In some compounds, usually those containing three different elements, there maybe both ionic and covalent bonds. It is important to note that ionic and covalentbonds are two extreme types of bonds. Many bonds are actually intermediate innature, and show features of each type of bond. These may be thought of as polarcovalent bonds. The concept of dipoles discussed below explains this further.

Intermolecular bonds

Intermolecular bonds are weaker than inter-atomic bonds. These interactionsbetween molecules confer some of the properties of the substance such as viscosityand surface tension. The strongest of the intermolecular bonds is the hydrogenbond. Van der Waals forces are, in comparison, much weaker. The concept of thedipole is discussed first, as this helps to explain the formation of hydrogen bonds.

Dipole

A separation of positive and negative charge.

A molecular dipole occurs in a covalently bound molecule formed of dissimilaratoms. When electrons are shared, they are geometrically limited to one part of themolecule (rather than being evenly distributed around the nuclei of the atoms)causing an asymmetrical distribution of charge. This leads to the molecule havingpolar areas with an area of relatively weak positive charge denoted as δ+ and negativecharge as δ−. The direction and strength of the charge separation is known as the

Chemical bonds 133


dipole moment, which is relatively weak compared with the strength of an ionicbond. This is an example of how a covalent bond can have ionic properties.

Hydrogen bond

A strong dipole-dipole attraction.

Relatively strong dipole moments are common in covalently bound moleculescontaining hydrogen and a highly electronegative atom (e.g. oxygen, nitrogen orfluorine). Hydrogen bonds are the name given to intermolecular bonds that occurdue to the attraction between positive and negative dipole moments in differentmolecules. However, they are not exclusive to molecules containing hydrogen, norare they true bonds, and therefore are somewhat of a misnomer. They may alsooccur within large molecules.

The effect of hydrogen bonds is demonstrated by considering the unexpectedlyhigh boiling points of H2O, HF and NH3, compared with what would be expectedbased on their molecular weight alone. They also explain the unusual highsolubility of some covalently bound substances in water.

To demonstrate both dipole moments and hydrogen bonds in water (H2O),draw a series of water molecules as above. As seen in the illustration of covalentbonds in water, the electron cloud around the molecule is distorted with thenegatively charged electrons being pulled towards the oxygen atom. A dipolemoment is therefore present in the molecule with the area around the oxygenatom being relatively negatively charged (δ−) and the areas around the hydro-gen atoms being positively charged (δ+). These areas of positive and negativecharge are attracted to each other and hydrogen bonds (dotted lines) areformed.

Van der Waals forces

Very weak intermolecular forces caused by the fluctuating dipoles thatoccur in non polar molecules due to the motion of electrons in all matter.



Inorganic and organic chemistry

Inorganic compound

Ions and molecules that do not contain carbon.

Inorganic chemistry

The study of the synthesis and behaviour of inorganic ions and molecules.

Carbon dioxide is an important exception to the definition because, although itcontains carbon, it is considered to be an inorganic molecule.

There are many inorganic ions and minerals that are physiologically importantsuch as sodium, potassium, calcium, magnesium, iron, chloride, phosphorus(phosphate), nitrogen (nitrate and ammonium), copper and zinc.

Organic compound

An ion or molecule that contains carbon.

Organic chemistry

The study of the composition, structure, properties and reactions of organiccompounds.

Both organic and inorganic compounds may be named systematically accord-ing to their structure, using sets of rules such as those from the InternationalUnion of Pure and Applied Chemistry (IUPAC). Alternatively they may also beknown by a common, non-systematic name that bears no relation to theirstructure.

Structural formula

A drawing that represents the arrangement of atoms in the molecularstructure of a compound.

Functional group

A molecular module with characteristic properties allowing prediction ofthe chemical and physical properties of a compound.

Classification of organic molecules occurs on the basis of their functional group.Examples include alcohols (C-O-H ), esters (R-COO-R), amides (R-CONH2). A


reference table including many of the common functional groups may be found inthe appendix.

The four main groups of organic compounds are:

CarbohydratesLipidsProteinsNucleic acids.

Carbohydrates

Large organic compounds containing carbon, hydrogen and oxygen in theratio (CH2O)n.

They are classified according to their size into monosaccharides, disaccharides andpolysaccharides.

Lipids

Organic compounds containing carbon, hydrogen and oxygen, that areinsoluble in water but soluble in organic (non polar) solvents.

They include fatty acids, triglycerides, phospholipids and cholesterol.

Proteins

A large organic compound comprising one or more chains of amino acidslinked by peptide bonds.

Unlike carbohydrates and fats, proteins contain nitrogen. Each amino acid has anamine (-NH2) and carboxyl (-COOH) functional group as well as a specific sidechain. Two amino acids joined together is known as a dipeptide, a simple chain is apolypeptide, and proteins are formed from one or more polypeptides chains.Essential amino acids are those that cannot be synthesized by the body and thusmust be consumed. There are four levels of protein structure:

Primary: The unique amino acid orderSecondary: The coiled alpha helix or folded beta pleated sheetTertiary: The 3D polypeptide structureQuaternary: The protein macromolecular structure formed from multiple ter-

tiary subunits

Nucleic acids

Large biologically active molecules consisting of a linear chain of mono-meric nucleotides which encode genetic information.



The two main nucleic acids are de-oxyribonucleic acid (DNA; usually doublestranded) and ribonucleic acid (RNA; usually single stranded).

Nucleotides are formed of:

A purine (adenine or guanine) or pyrimidine (cytosine, thymine or uracil*) baseA pentose sugar: deoxyribose or riboseA phosphate group

*thymine occurs in DNA and uracil in RNAThe sugars and phosphates are joined by phosphodiester links, forming the

‘backbone’ of the molecule.Nucleotides are not just found in nucleic acids, they also form other important

molecules such as adenosine triphosphate (ATP) and nicotinamide adenine dinu-cleotide (NAD).

Inorganic and organic chemistry 137


Isomerism

Isomerism is a subject that can easily become confusing due to the myriad ofdefinitions and nomenclature it involves. Remembering a schematic diagram, suchas the one below, often helps to focus the mind as to where each type of isomer fits.

Isomerism

The phenomenon by whichmolecules with the same atomic formulae havedifferent structural arrangements.

Isomers are important because the three-dimensional structure of a drug maydetermine its effects.

Structural isomerism

Identical chemical formulae but different order of atomic bonds.

Tautomerism

The dynamic interchange between two different forms of a molecularstructure depending on the environmental conditions.

Stereoisomerism

Identical chemical formulae and bond structure but different three-dimensional configuration.

Enantiomers

Compounds that have a single chiral centre and form non-superimposablemirror images of each other.


Diastereoisomers

Compounds containingmore than one chiral centre or which are subject togeometric isomerism and, therefore, havemore than just twomirror imageforms.

Geometric isomerism

Two dissimilar groups attached to two atoms that are in turn linked by adouble bond or ring creates geometric isomerism because of the reducedmobility of the double bond or ring.

Geometric isomerism is sometimes also known as cis-trans isomerism.

Chiral centre

A central atom bound to four dissimilar groups.

Chiral centres encountered in anaesthetics usually have carbon or quaternarynitrogen as the chiral centre. Any compound which contains more than one chiralcentre is termed a diastereoisomer by definition.

Optical isomerism

Differentiation of compounds by their ability to rotate polarized lights indifferent directions.

Dextro- and laevorotatory

Compounds can be labelled according to the direction in which a moleculeof the substance will rotate polarized light. Abbreviated to either d- and l-or + and −.

D- and L-prefixes

The use of D- and L-prefixes is a nomenclature for orientation of atomicstructure of sugar and amino acidmolecules. It is a structural definition andis not related to the optical properties.

Rectus and sinister

Molecules at a chiral centre can be labelled according to the directionin which groups of increasing molecular weight are organized around thecentre: rectus and sinister, abbreviated to R and S, depending on whetherthe direction of increment is clockwise or anti-clockwise, respectively.

Isomerism 139


In the diagram, the chiral centre is shaded and attached to four groups of differentmolecular weights. The smallest group (G1) is then orientated away from theobserver and the remaining groups are assessed. If the groups increase in massin a clockwise direction as in the figure, the compound is labelled R- and vice versa.

Racemic mixture

A mixture of two different enantiomers in equal proportions.

Enantiopure

A preparation with only a single enantiomer present.



Enzyme kinetics

Enzyme

Abiological catalyst that increases the speed of a chemical reactionwithoutbeing consumed in the reaction itself.

The rate of a chemical reaction, therefore, depends on the concentration of thesubstrates and the presence of the catalyzing enzyme.

First-order reaction

A reaction whose rate depends upon the concentration of the reactingcomponents. This is an exponential process.

Zero-order reaction

A reaction whose rate is independent of the concentration of reactingcomponents and is, therefore, constant.

A first-order reaction may become zero order when the enzyme system is saturated.

The Michaelis–Menten equation

Michaelis–Menten equation predicts the rate of a biological reaction accord-ing to the concentration of substrate and the specific enzyme characteristics:

V ¼ Vmax S½ �Km þ S½ �

where V is the velocity of reaction, Vmax is the maximum velocity of reac-tion, Km is the Michaelis constant and [S] is the concentration of substrate.

The value of Km is the substrate concentration at which V = ½ Vmax and is specificto the particular reaction in question. It is the equivalent of the ED50 seen in dose–response curves. This equation has a number of important features.

If [S] is very low, the equation approximates to

V � Vmax S½ �Km

as the + [S] termbecomes negligible. This means thatV is proportional to [S]by a constant of Vmax /Km. In other words the reaction is first order.


If [S] is very high the equation approximates to

V ≈ Vmax

and the reaction becomes zero order, as V is now independent of [S].

Michaelis–Menten graph

The shape of the curve is an inverted rectangular hyperbola approaching Vmax.Ensure you mark Km on the curve at the correct point. The portion of the curvebelow Km on the x axis is where the reaction follows first-order kinetics, asshown by a fairly linear rise in the curve with increasing [S]. The portion of thecurve to the far right is where the reaction will follow zero-order kinetics, asshown by the almost horizontal gradient. The portion in between these twoextremes demonstrates a mixture of properties.

Lineweaver–Burke transformation

Tomake it easier tomeasureKmmathematically a Lineweaver–Burke trans-formation can be performed by taking reciprocals of both sides of theinitial equation.

1V

¼ Km þ S½ �Vmax S½ �

This can be rearranged to give

1V

¼ Km

Vmax S½ � þ1

Vmax



or

1V

¼ Km

Vmax:1S½ �

� �þ 1Vmax

The equation may appear complex but is simply a version of the linearequation

y = (ax) + b

where y is 1/V, a is Km/Vmax, x is 1/[S] and b is 1/Vmax.

Lineweaver–Burke graph

It may help to write the equation down first to remind yourself which functionsgo where. The simple point of this diagram is that it linearizes the Michaelis–Menten graph and so makes calculation of Vmax and Km much easier as theycan be found simply by noting the points where the line crosses the y and x axes,respectively, and then taking the inverse value.

Enzyme kinetics 143


G-proteins and second messengers

G-proteins

Guanine nucleotide-binding proteins are involved in cellular signalling andare part of the GTPase enzyme family. They most commonly consist of α, βand γ polypeptide subunits but also exist as smaller monomers.

G-proteins are important because they are involved in signal transduction cas-cades for many hormones and neurotransmitters and G-protein coupled receptors(GPCRs) are the targets for many drugs used in anaesthesia. GPCRs are found incell membranes and consist of seven trans-membrane domains. You may be askedto draw the G-protein cycle to explain how activation of a GPCR on the cell surfaceleads to intracellular effects.

where GDP is guanosine diphosphate, GTP is guanosine triphosphate and∇ is a ligand

G-proteins are bound to the intracellular surface of GPCRs. When theG-protein is inactive a GDP molecule is bound to the α-subunit, which inturn is bound to the βγ unit (1). Activation of the GPCR by the binding of aligand leads to GDP being displaced by GTP that activates the G-protein (2).The α-GTP subunit (and / or the βγ subunit) then diffuses away from theGPCR to interact with an effector protein (3). The effector protein targetdepends upon the type of G–protein and the subunit. For example Gsα(G stimulatory) activates adenylyl cyclase, Giα (G inhibitory) inhibitsadenylyl cyclase and Gqα activates phospholipase C. Once the interaction


with the effector protein has occurred, the α-subunit of the G-proteinhydrolyzes the GTP to GDP, releasing a phosphate molecule (Pi), afterwhich it is able to bind the βγ subunit (4). The G-protein complex thenbinds to the receptor again, completing the cycle (1).

Second messenger

A molecule that is released intra-cellularly as part of a signal transductioncascade stimulated by activation of a cell surface receptor.

A second messenger may be a specific molecule released as part of a G-proteinmediated cascade (see below) or it may be an intracellular ion whose concentrationhas changed as a result of opening of membrane bound ion channels or releasefrom intracellular stores as with Ca2+. The primary messenger is the ligand thatstimulates the receptor. The G-protein mediated signal transduction cascade maybe thought of in the following steps:

In this flow diagram the receptor will be a G-protein coupled receptor. If the signaltransduction cascade did not involve G proteins, the receptor could be a ligand-gated ion channel and the second messenger would be the ion that flows throughthe channel when it opens, with the G-protein and effector protein steps beingomitted. A summary table of G proteins and second messengers may be found inthe appendix.

G-proteins and second messengers 145


The Meyer–Overton hypothesis

The Meyer–Overton hypothesis is the theory of anaesthetic action whichproposes that the potency of an anaesthetic agent is related to its lipidsolubility.

Potency is described by the minimum alveolar concentration (MAC) of an agentand lipid solubility by the oil:gas solubility coefficient.

Minimum alveolar concentration

The minimum alveolar concentration of an anaesthetic vapour at equili-brium is the concentration required to prevent movement to a standar-dized surgical stimulus in 50% of unpremedicated subjects studied at sealevel (1 atmosphere).

The Meyer–Overton hypothesis proposed that once a sufficient number ofanaesthetic molecules were dissolved in the lipid membranes of cells withinthe central nervous system, anaesthesia would result by a mechanism of mem-brane disruption. While an interesting observation, there are several exceptionsto the rule that make it insufficient to account fully for the mechanism ofanaesthesia.

Meyer–Overton graph of potency versus lipid solubility


After drawing and labelling the axis (note the slightly different scales), drawa straight line with a negative gradient as shown. Make sure you can draw inthe position of the commonly used inhalational agents. Note that the linedoes not pass directly through the points but is a line of best fit, and also thatalthough isoflurane and enflurane have near identical oil:gas partition coef-ficients they have different MAC values and, therefore, this relationship isnot perfect.

The Meyer–Overton hypothesis 147


The concentration and second gas effects

The concentration effect

The phenomenon by which the rise in the alveolar partial pressure ofnitrous oxide is disproportionately rapid when it is administered in highconcentrations.

Nitrous oxide (N2O), although relatively insoluble, is 20 times more soluble in theblood than nitrogen (N2). The outward diffusion of N2O from the alveolus into theblood is therefore much faster than the inward diffusion of N2 from the blood intothe alveolus. Consequently, the alveolus shrinks in volume and the remaining N2Ois concentrated within it. This smaller volume has a secondary effect of increasingalveolar ventilation by drawing more gas into the alveolus from the airways inorder to replenish the reduced volume.

Graphical demonstration

The above concept can be described graphically by considering the fractionalconcentration of an agent in the alveolar gas (FA) as a percentage of its fractionalconcentration in the inhaled gas (FI) over time.

After drawing and labelling the axis draw a series of build-up negative expo-nential curves with different gradients as shown. The order of the curves isaccording to the blood:gas partition coefficients. The more insoluble the agent,the steeper the curve and the faster the rate of onset. The exceptions to this arethe N2O and desflurane curves, which are the opposite way round. This is


because of the concentration effect when N2O is administered at high flows andis the graphical representation of the word ‘disproportionately’ in the defini-tion. You may be asked what would happen as time progressed and you shouldindicate that the lines eventually form a plateau at an FA/FI ratio of 1.0.

The second gas effect

The phenomenon by which the speed of onset of inhalational anaestheticagents is increased when they are administered with N2O as a carrier gas.

This occurs as a result of the concentration effect and so it is always useful todescribe the concentration effect first, even if being questioned directly on thesecond gas effect. If there is another gas present in the alveolus, then it too will beconcentrated by the relatively rapid uptake of N2O into the blood.

The concentration and second gas effects 149


Drug interactions

Summation

The actions of two drugs are additive but each has an independent actionof its own.

Potentiation

The action of one drug is amplified by the addition of another, which hasno independent action of its own.

Synergism

The combined action of two drugs is greater than would be expected froma purely additive effect.

Isobologram

The isobologram shows the amount of drug B that is needed in the face ofincreasing amounts of drug A in order that the end effect remains constant.

A, additive Draw the axes as shown and a linear relationship labelled A. Thisrepresents an additive effect of drug A and drug B such that less of drug B isneeded as the dose of drug A is increased.

B, inhibitory Draw an upwardly convex curve labelled B which begins andterminates at the same points as line A. This represents inhibition becausenow, at any given dose of drug A, more of drug B needs to be given tomaintain a constant effect compared with an additive relationship.

C, synergistic Finally draw a downwardly convex curve labelled C. Thisrepresents synergy in that less of drug B is required at any point comparedwith what would be seen with an additive relationship.


Adverse drug reactions

Although not often tested in depth, a knowledge of the terminology used todescribe adverse drug reactions is useful. True anaphylactic and anaphylactoidreactions clearly require a more detailed knowledge. The official World HealthOrganization (WHO) definition of an adverse drug reaction is lengthy andunlikely to be tested. A more succinct definition is used in relation toanaesthesia.

Adverse drug reaction

The occurrence of any drug effect that is not of therapeutic, diagnostic orprophylactic benefit to the patient.

Types of adverse reactions

The WHO definition encompasses six groups, which need not be memorized butwhich are included for completeness.

Group 1 Dose-related reactionsGroup 2 Non-dose-related reactionsGroup 3 Dose- and time-related reactionsGroup 4 Time-related reactionsGroup 5 Withdrawal reactionsGroup 6 Treatment failure.

The reactions can be more simply defined as one of two types:Type A

� dose dependent� common� extension of known pharmacological effect.

Type B

� dose independent� uncommon� symptoms and signs of drug allergy.

The most important type to the anaesthetist is type B, which encompasses bothanaphylactic and anaphylactoid reactions.


Anaphylactic reaction

A response to a substance to which an individual has been previously sensi-tized via the formation of a specific IgE antibody. It is characterized by therelease of vasoactive substances and the presence of systemic symptoms.

Anaphylactoid reactions

A response to a substance that is not mediated by a specific IgE antibodybut is characterized by the same release of vasoactive substances andpresence of systemic symptoms as an anaphylactic reaction.



Pharmacogenetics

Definition

The variability of a drug’s actions according to the genetic make up of theindividual.

There are two broad areas of pharmacogenetic research:

Identification of new drug targetsSearching for specific genes associated with a particular disease that codefor a protein which can become a drug target.

Identifying genes and their variants that influence the response to a drugThese may be genes coding for drug receptors, drug transporters or cellsignaling pathways that mediate the effects of the drug. Or they may begenes that are involved in drug metabolism and disposition.

An example of a genetic polymorphism that influences an individual’s response toa drug is the Cytochrome P450 CYP2D6 enzyme. This enzyme is responsible forthe metabolism of codeine to morphine but is inactive in about 6% of white people,which leads to a lack of analgesic effect. In other people the gene is amplified, withmultiple copies being present. This results in an individual being an ‘ultra-rapidmetabolizer’ of certain drugs, particularly some antidepressants. Individualsaffected therefore require much larger doses of the drug to have the same clinicaleffect.



Section 5Pharmacodynamics



Drug–receptor interaction

Pharmacodynamics

The pharmacological study of the effects of drugs and the mechanism oftheir action.

Drug actions may be due to the physicochemical properties of the drug (forexample antacids) or via specific structural interactions with receptors. The bio-logical effect of a drug may be due to a change in any one of many different cellularfunctions. Examples include changes in:

Cell membrane permeability, potential or transportContractile or secretory activityProtein synthesis.

Often these processes involve activation or inhibition of chemical cascades andintracellular second messengers. An understanding of the relationship betweenamount (the ‘dose’) of drug at its site of action (remember that the drugs pharma-cokinetic properties determine how it gets there), and the effects it has, boththerapeutic (the ‘response’) and adverse, comprises much of what is covered inthe examinations. As well as the intensity of the response, the duration of action isalso included here, although this will partly be determined by pharmacokinetics.

Drug–receptor interaction

A basic understanding of the interaction between drugs and receptors underliesmuch of what is covered in the examinations.

Ligand

A ligand is a chemical messenger able to bind to a receptor. May beendogenous or exogenous (drugs).

Receptor

A receptor is a component of a cell that interacts selectively with a com-pound to initiate the biochemical change or cascade that produces theeffects of the compound:

D + R ↔ DR

where D is drug, R is receptor and DR is drug–receptor complex.


It is assumed that the magnitude of the response is proportional to the concen-tration of DR (i.e. [DR]).

Types of receptors include ligand gated ion channels (ionotropic receptors),G-protein coupled receptors (metabotropic receptors), tyrosine kinase receptorsand cytoplasmic receptors.

Law of mass action

The rate of a reaction is proportional to the concentration of the reactingcomponents.

D½ � þ R½ �$Kf

Kb

DR½ �

where Kf is the rate of forward reaction and Kb is the rate of backwardreaction.

At equilibrium, the rates of the forward and back reactions will be the same and theequation can be rearranged

Kf[D] [R] = Kb[DR]

The affinity constant

The affinity constant, measured in l/mmol, has the symbol KA where

KA = Kf /Kb

and it reflects the strength of drug–receptor binding

The dissociation constant

The dissociation constant, measured in mmol/l, has the symbol KD where

KD = Kb/Kf

and it reflects the tendency for the drug–receptor complex to split into itscomponent drug and receptor.

Often, KD is described differently given that the law of mass action states that, atequilibrium

Kf[D][R] = Kb[DR]

or

Kb/Kf = [D][R]/[DR]

so

KD ¼ D½ � R½ �DR½ �

158 Section 5 � Pharmacodynamics


If a drug has a high affinity, the DR form will be favoured at equilibrium, hence thevalue of [D][R] will be small and that of [DR] will be high. Therefore, the value ofKD will be small. The opposite is true for a drug with low affinity, where the D andR forms will be favoured at equilibrium.

Another way of looking at KD is to see what occurs when a drug occupies exactly50% of receptors at equilibrium. In this case, the number of free receptors [R] willequal that of occupied receptors [DR] and so cancel each other out of the equationabove, leaving

KD = [D]

In other words

KD is themolar concentration of a drug at which 50%of its receptors areoccupied at equilibrium (mmol.l–1)

Classical receptor theory suggests that the response seen will be proportional to thepercentage of receptors occupied, although this is not always the case.

Drug–receptor interaction 159


Affinity, efficacy and potency

Affinity

A measure of how avidly a drug binds to a receptor.

In the laboratory, affinity can be measured as the concentration of a drug thatoccupies 50% of the available receptors, as suggested by the definition of KD.

The curve should be drawn as a rectangular hyperbola passing through theorigin. KD is shown and in this situation is a marker of affinity (see text). Inpractice, drug potency is of more interest, which encompasses both affinity andintrinsic activity. To compare potencies of drugs, the EC50 and ED50values (seebelow) are used.

Efficacy (intrinsic activity)

A measure of the magnitude of the effect once the drug is bound.

Potency

A measure of the quantity of the drug needed to produce maximal effect.

Potency is compared using themedian effective concentration (EC50) ormedianeffective dose (ED50), the meanings of which are subtly different.


Median effective concentration

The concentration of a drug that induces a specified response exactly halfway between baseline and maximum. (EC50)

This is the measure used in a test where concentration or dose is plotted on the xaxis and the percentage of maximum response is plotted on the y axis. It is alaboratory result of a test performed under a single set of circumstances or on asingle animal model.

Median effective dose

The dose of drug that induces a specified response in 50% of the popula-tion to whom it is administered. (ED50)

This is the measure of potency used when a drug is administered to a population oftest subjects. This time the 50% figure refers to the percentage of the populationresponding rather that a percentage of maximal response in a particular individual.

A drug with a lower EC50 or ED50 will have a higher potency, as it suggests that alower dose of the drug is needed to produce the desired effect. In practice, the termsare used interchangeably and, of the two, the ED50 is the most usual terminology.You are unlikely to get chastised for putting ED50 where the correct term shouldtechnically be EC50.

Dose–response curves

The curve is identical to the first but the axes are labelled differently withpercentage of maximum response on the y axis. This graph will have beenproduced from a functional assay in the laboratory on a single subject and isconcerned with drug potency. Demonstrate that the EC50 is as shown.

Affinity, efficacy and potency 161


Quantal dose–response curves

The curve is again identical in shape but this time a population has been studiedand the frequency of response recorded at various drug doses. It is, therefore,known as a quantal dose–response curve. The marker of potency is now theED50 and the y axis should be correctly labelled as shown. This is the ‘typical’dose–response curve that is tested in the examination.

Log dose–response curve

The curve is sigmoid as the x axis is now logarithmic. Ensure themiddle third ofthe curve is linear and demonstrate the ED50 as shown. Make this yourreference curve for a full agonist and use it to compare with other drugs asdescribed below.

Median lethal dose

The dose of drug that is lethal in 50% of the population to whom it isadministered. (LD50)



Therapeutic index

The therapeutic index of a drug reflects the balance between its usefuleffects and its toxic effects. It is often defined as

LD50/ED50

Both curves are sigmoid as before, The curve on the left represents a normaldosing regimen aiming to achieve the desired effect. Label the ED50 on it asbefore. The curve to the right represents a higher dosing regimen at whichfatalities begin to occur in the test population. The LD50 should be at itsmidpoint. The ED95 is also marked on this graph; this is the point at which95% of the population will have shown the desired response to dosing.However, note that by this stage some fatalities have already started to occurand the curves overlap. You can draw the curves more widely separated if youwish to avoid this but it is useful to demonstrate that a dose that is safe for oneindividual in a population may cause serious side effects to another.

Duration of action

The length of time for which a drug is effective.

There are several factors that influence the duration of action. It is most commonlythought to depend on the plasma half life of the drug, which it does. However it willalso depend on the amount given, the preparation and route of administration, therate of equilibration between the plasma and effect site, the activity of metabolitesas well as the slope of the dose–response curve. Particular patient characteristics,such as the presence of disease, will also play a role.

Affinity, efficacy and potency 163


Agonism and antagonism

Agonist

Adrug that binds to a specific receptor (affinity) and, once bound, is able toproduce a response (intrinsic activity).

Antagonist

A drug that has significant affinity but no intrinsic activity.

Full agonist

A drug that produces a maximal response once bound to the receptor.

Partial agonist

A drug with significant affinity but submaximal intrinsic activity.

Partial agonist curves

Draw a standard log-dose versus response curve as before and label it ‘full agonist’.Next draw a second sigmoid curve that does not rise so far on the y axis. Theinability to reach 100% population response automatically makes this representa-tive of a partial agonist as it lacks efficacy. The next thing to consider is potency.The ED50 is taken as the point that lies half way between baseline and themaximum population response. For a full agonist, this is always half of 100%,but for a partial agonist it is half whatever the maximum is. In this instance, themaximum population response is 50% and so the ED50 is read at 25%. In this plot,both the agonist and partial agonist are equally potent as they share the same ED50.


Partial agonist curve

This graph enables you to demonstrate how the partial agonist curves changewith changes in potency. Curve A is the standard sigmoid agonist curve. CurveB is plotted so that its ED50 is reduced compared with that of A. Drug B is,therefore, more potent than drug A but less efficacious. Curve C demonstratesan ED50 that is higher than that of curve A, and so drug C is less potent thandrug A and less efficacious.

Alternative partial agonist curve

Partial agonists can also behave as antagonists, as demonstrated by this graph.The graph is constructed by starting with a number of different concentrations(A–H) of full agonist to which a partial agonist is successively added. Thecurves are best explained by describing the lines at the two extremes, ‘A’ and‘H’. Lines B–G demonstrate intermediate effects.

Line H This line shows a high baseline full agonist concentration and sobegins with 100%maximal response. As an increasing dose of partial agonistis added, it displaces the full agonist from the receptors until eventually they

Agonism and antagonism 165


are only able to generate the maximal response of the partial agonist (in thiscase 50%). The partial agonist has, therefore, behaved as an antagonist bypreventing the maximal response that would have been seen with a fullagonist alone.

Line A This line shows the opposite effect where there is no initial full agonistpresent and hence no initial response. As more partial agonist is added, theresponse rises to the maximum possible (50%) and so in this instance thepartial agonist has behaved as an agonist by increasing the response seen.

Competitive antagonist

A compound that competes with endogenous agonists for the same bind-ing site; it may be reversible or irreversible.

Non-competitive antagonist

A compound that binds at a different site to the natural receptor andproduces a conformational distortion that prevents receptor activation.

Reversible antagonist

A compound whose inhibitory effects may be overcome by increasing theconcentration of an agonist.

Irreversible antagonist

A compound whose inhibitory effects cannot be overcome by increasingthe concentration of an agonist.

Allosteric modulator

An allosteric modulator binds at a site different from the natural receptorand alters the affinity of the receptor for the ligand, thus increasing ordecreasing the effect of the natural agonist.



Reversible competitive antagonist curves

Draw the standard sigmoid curve and label it as a full agonist. Draw a secondidentical curve displaced to the right. This represents the new [DR] curve for anagonist in the presence of a competitive antagonist. The antagonist has blockedreceptor sites; consequently, more agonist must be added to displace antagonistand achieve the same response. Demonstrate this by marking the ED50 on thegraph and showing that potency of the agonist decreases in the presence of acompetitive antagonist.

Irreversible competitive antagonist curves

The standard curve is displaced to the right initially as some receptor sites areblocked by the antagonist. Given enough agonist, maximum response is stillpossible (line B) at the expense of reduced potency. With higher levels ofantagonist present (line C), the potency and efficacy are both reduced as toomany receptor sites are blocked by the antagonist to enable maximumresponse. With the addition of enough antagonist, no response will be seen.



Non-competitive antagonist curve

Because a non-competitive antagonist alters the shape of the receptor, theagonist cannot bind at all. The usual sigmoid curve is displaced down and tothe right in a similar manner to the graph of agonist versus partial agonistdrawn above. Increasing the dose of agonist does not improve response asreceptor sites are no longer available for binding.

Inverse agonist

A compound that, when bound, produces an effect opposite to the endog-enous agonist.

This plot is more theoretical than most. Draw the y axis so that it enables positiveand ‘negative’ response. The upper curve is a standard sigmoid full agonist curve.The lower curve represents the action of the inverse agonist and should be plottedas an inverted curve. This is different from the curve of a pure antagonist, whichwould simply produce no effect rather than the opposite effect to a full agonist.



Dose ratio

The factor bywhich the agonist concentrationmust be increasedwhen in thepresence of a competitive antagonist to produce an equivalent response:

Dose ratio ¼ Dose of agonist in presence of inhibitorDose of agonist in absence of inhibitor

Affinity of an antagonist for a receptor: pA2

The pA2 is the negative log10 of the concentration of antagonist thatrequires a doubling of the dose of agonist to achieve the same response.

It is a measure of the affinity of the antagonist for the receptor (the equilibriumdissociation constant). It is used to compare the potency of antagonists in a similarmanner to the use of the ED50 to compare the potency of agonists.



Hysteresis

Hysteresis is defined on p. 14 but occurs in pharmacology as well as duringphysical measurement. The phenomenon occurs because the concentration of adrug at the intended site of action (the ‘effector site’ or ‘biophase’) often differsfrom the plasma concentration at any given time. The reasons for this time laginclude the degree of ionization of the drug, its lipid solubility, prevailing concen-tration gradients and many other factors. All these alter the length of time itactually takes a drug to reach its intended site of action.

If a drug was to be administered orally, the following graph may be obtained.

Plasma After drawing and labelling the axes, plot the concentration versustime curve for an orally administered drug. Label this curve ‘plasma’ to showhow the concentration rises and falls with time following an oral dose.

Effector site Now draw a second, similar curve to the right of the first. Thisshows the concentration of the drug at its site of action. The degree ofdisplacement to the right of the first curve is determined by the factorsmentioned above.

Key points When both curves are drawn, mark a fixed concentration pointon the y axis and label it C. Demonstrate that the plasma concentration curvecrosses this value twice, at times t1 and t2. At time t1 the concentration in theplasma is rising and at t2 it is falling. The crucial point now that enables youto define hysteresis is to demonstrate that the effector site concentration isdifferent at these two times depending on whether the plasma concentrationis rising (giving concentration E1) or falling (giving concentration E2).


Tachyphylaxis and tolerance

Tachyphylaxis

A rapid decrease in response to repeated doses of a drug over a short timeperiod.

Tachyphylaxis can occur after a single initial dose or multiple small doses.Increasing the dose administered may restore the response. The effect is usuallydue to a decrease in the stores of the neurotransmitter responsible for producingthe effect of the drug and as such is reversible after a period of withdrawal of thedrug. An example of a drug that commonly exhibits this phenomenon in anaes-thetics is ephedrine.

Tolerance

The phenomenon whereby larger doses of a drug are required over time inorder to produce the same pharmacological effect.

Tolerance usually takes days to weeks to occur and may be reversible following aperiod of withdrawal of the drug. Several possible mechanisms have been proposedwhich relate to how efficiently a receptor is coupled to signal transduction. Theyinclude:

Down-regulation of receptor numbers.

Reduced receptor density, which may be via internalisation of receptors.

Decreased affinity of the receptor for the drug due to a structural change inthe receptor.

Inactivation of the linked signaling protein to the receptor.

These processes may be referred to as receptor desensitization. Tolerance may alsobe pharmacokinetic whereby a decreased amount of the substance reaches itseffector site, for example due to an increase in enzymes that degrade the substance.It may also be psychological as well as physiological. Morphine is an example of adrug that illustrates this effect and tolerance to opioids is a feature of opioiddependance.

Tachyphylaxis may be thought of as a form of acute desensitization, andtolerance chronic desensitization. In both, there is a reduction in the response tothe drug although the mechanisms causing the reduced response are different. Theprinciple of receptor desensitization may be demonstrated graphically as shownbelow.


Draw and label the axes as shown. Draw theoretical time/effect curves thatdecrease in amplitude with every repeated administration of an agonist asshown (A, B and C). The fourth curve (D) demonstrates that a response ofthe same magnitude as the first can be achieved after a period without theagonist (represented above by a break in the x axis). Depending on the timescale chosen, the graph could demonstrate the principles of tachyphylaxis ortolerance but remember that the mechanisms underlying the reduction inresponse are different.



Drug dependance

The WHO definition for a diagnosis of this requires that three or more of thefollowing six characteristics are demonstrated.

A strong desire or sense of compulsion to take the substance.

Difficulties in controlling substance-taking behaviour in terms of its onset,termination, or levels of use.

A physiological withdrawal state when substance use has ceased or havebeen reduced, as evidenced by: the characteristic withdrawal syndrome forthe substance; or use of the same (or closely related) substance with theintention of relieving or avoiding withdrawal symptoms.

Evidence of tolerance, such that increased doses of the psychoactive sub-stance are required in order to achieve effects originally produced by lowerdoses (clear examples of this are found in alcohol and opiate dependentindividuals who may take daily doses sufficient to incapacitate or kill non-tolerant users).

Progressive neglect of alternative pleasures or interests because of psycho-active substance use, increased amount of time necessary to obtain or takethe substance or to recover from its effects.

Persisting with substance use despite clear evidence of overtly harmfulconsequences, such as harm to the liver through excessive drinking, depres-sive mood states consequent to periods of heavy substance use, or drug-related impairment of cognitive functioning; efforts should be made todetermine that the user was actually, or could be expected to be, aware ofthe nature and extent of the harm.

This list is taken from the ICD-10 diagnostic criteria for research.



Section 6Pharmacokinetics



Absorption, distribution and redistribution

Pharmacokinetics

Pharmacokinetics is the study of how the body handles a drug.

It is comprised of several different areas. Firstly there are processes such asabsorption, distribution, metabolism and excretion, which are sometimes referredto as the ADME scheme. Secondly there are various pharmacokinetic measure-ments which are described by equations. This area is called metrics. Thirdly thereis the analysis of measured data from in vivo pharmacokinetic studies. Thisanalysis is done by modelling which may be compartmental, physiological ornon compartmental. This section covers each of these areas in turn.

Absorption

The uptake of substances into or across tissues.

For drug administration it usually refers to uptake into the blood stream via aparticular route of administration such as oral, intramuscular or topical.

Distribution

The reversible transfer of a substance from one location to another withinthe body.

Distribution to a particular tissue will depend upon:

Factors influencing the passage of drug across a membraneMolecular sizeLipid solubilityProtein bindingIonization.Regional blood flow. A substance will initially be distributed to tissues withhigh regional blood flow such as the brain and kidneys.

Vascular permeability.

Distribution may be quantified by assessing the volume of distribution of a drug(see below).

Redistribution

The movement of a substance from an area of high regional blood flow toan area of medium or low regional blood flow.


This phenomenon may determine the duration of action of a drug. For example,thiopentone is rapidly redistributed from its site of action, the highly perfusedbrain, to other tissues, leading to a short duration of action. Factors determiningthe distribution of a substance will also affect its redistribution. For example,highly lipid soluble drugs move rapidly across membranes and so are more rapidlydistributed and redistributed.

178 Section 6 � Pharmacokinetics


First pass metabolismand bioavailability

The degree of metabolic breakdown of an orally administered drug thatoccurs in the intestine or liver before it reaches the systemic circulation.

It is also known as the first pass effect and results in a reduction in the concen-tration of the drug. Drugs which are subject to first pass metabolism includemorphine, buprenorphine, diazepam and midazolam. The process of first passmetabolism can be exploited pharmacologically.

Prodrug

A drug that is converted from an inactive form to an active form by firstpass metabolism.

Codeine is an example of a pro drug and undergoes demethylation to morphine,which is its pharmacologically active component.

Bioavailability

The fraction of drug that reaches the circulation compared with the samedose given intravenously. (%)orThe ratio of the area under the stated concentration–time curve (AUC)divided by the area under the i.v. concentration–time curve. (%)


Intravenous After drawing and labelling the axes, plot an exponential declinecurve to show how concentration changes with time following the intra-venous (i.v.) administration of a drug. Note that the graph assumes a singlecompartment (see below). Although the concentration at time zero is notpossible to measure, it is still conventional to plot the curve crossing they axis. If you are asked how to calculate this initial concentration, it requiresyou to perform a semi-log transformation on the curve and to extrapolate theresultant straight line back to the y axis.

Oral Draw a second curve that shows the concentration of the same drugchanging with time following its oral administration. The second curve doesnot have to be contained entirely within the i.v. curve although this is oftenthe case in practice.

Extraction ratio

Fraction of total drug removed from the blood by an organ in each passthrough that organ.



Volume of distribution

Volume of distribution

The theoretical volume into which a drug distributes following its admin-istration. (ml)

VD ¼ DoseC0

whereVD is the volume of distribution and C0 is the concentration at time 0.

It is not possible to measure C0 since mixing is not instantaneous; therefore, asemi-logarithmic plot is drawn and extrapolated back to the y axis in order tocalculate this concentration.

After drawing and labelling the axes as shown, plot a straight line (solid) thatdoes not cross the y axis. This will be the curve which is found in the real worldsituation. To calculate C0 the line must be extrapolated back (dotted) to they axis and the concentration (ln C0) read at that point. Taking the antilog of thisvalue will give C0. The slope of the graph is k and the half life can therefore alsobe calculated.

Using a simple one-compartment model, the loading dose and the infusion raterequired to maintain a constant plasma concentration can be calculated as follows.

LD = VD.C


where LD is the loading dose and C is the required plasma concentration.and

Rinf = C.Cl

where Rinf is the infusion rate required and Cl is the clearance.



Clearance

Clearance

The volume of plasma fromwhich a drug is removed per unit time (ml.min−1).

It is important to remember that clearance refers to the amount of plasma concernedas opposed to the amount of a drug. Try to remember the units of ml.min−1, which, inturn, should help you to remember the definition:

Cl ¼ DoseAUC

where AUC is the area under concentration–time curveor

Cl = Q.ER

where Q is the flow rate and ER is the extraction ratio.or

Cl = VD . K

where VD is the volume of distribution and K is the rate constant ofelimination

Clearance gives a value for the amount of plasma cleared of a drug. The mecha-nism of this clearance can involve elimination, excretion or both.

Elimination

Removal of drug from the plasma. This may be via distribution, metabolismor excretion.

Relim = Concentration × Clearance

or

Relim = VD × K

Relim is the rate of elimination and K is the rate constant of elimination.

First-order elimination

A situation where the rate of drug elimination at any time depends uponthe concentration of the drug present at that time.


This is an exponential process and a constant proportion of drug is eliminated in agiven time.

Zero-order elimination

A situation where the rate of drug elimination is independent of theconcentration of drug and is, therefore, constant.

This time a constant amount of drug is eliminated in a given time rather than aconstant proportion. First-order elimination may become zero order when theelimination system (often a metabolic pathway) is saturated.

Excretion

The removal of drug from the body.



Time constant and half life

Time constant

The time taken for the plasma concentration of a drug to fall to 1/e of itsformer value. (τ)orThe time that would be taken for the initial concentration to fall to zerowere the initial rate of decline to continue.or

τ ¼ 1K

or

τ ¼ VD

Cl

where K is the rate constant of elimination of the reaction and Cl is theclearance.

As the value of K rises so the time τ falls. The symbol e has a numerical value of2.718 and so 1/e is 0.368. The time constant is also covered in section 1.

Half life

The time taken for the plasma concentration of a drug to fall by half. (t1/2)or, for a zero order reaction

t1=2 ¼ C0

2K

where t1/2 is half life, C0 is the concentration at time zero and K is the rateconstant of elimination for the reaction

Zero order reactions are fairly uncommon in pharmacological and physiologicalterms and so the more appropriate equation for first order reactions is as shown.

t1=2 ¼ lnð2ÞK

so

t1=2 ¼ 0:693K

but as τ is the reciprocal of K


t1/2 = 0.693τ

or

t1=2 ¼ 0:693VD

Cl

The value of t1/2 is always shorter than that of τ as the reaction is only 50%complete after 1 half life compared to 63% complete after one time constant.The half life is also covered in section 1.



Non-compartmental modelling

Pharmacokinetic models are mathematical models that are used to interpretpharmacokinetic data from experiments and may also be used to predict theplasma concentration of a drug at a given time. There are several different typesof modelling which vary in the complexity of the mathematics involved:

Non-compartmental modelling.Compartmental modelling which is subdivided into catenary andmamillary.

Physiological modelling.

These are discussed in turn below.

Non-compartmental modelling

This is the simplest form of pharmacokinetic modelling and it does not make anyassumptions about the number of compartments to which a drug distributes.Instead it uses information from a concentration vs. time curve to estimatepharmacokinetic variables such as bioavailability, volume of distribution andclearance. It uses the trapezoidal rule (see integration definition in Section 1) tocalculate the area under the curve (AUC) that provides an estimate of the exposureto a drug.

However, there are some limitations to non-compartmental analysis:

It requires a drug to follow linear kinetics.It cannot be used to make predictions about the concentration of a drug atany given time, which is possible with more complex types of modelling.


Compartmental modelling

The concept of compartmental modelling allows predictions of drug behaviour tobe made from mathematical models of the body that are more accurate than theassumption of the body being a simple container.

Compartment

One or more components of a mathematical model that aim to replicatethe drug-handling characteristics of a proportion of the body.

Models may contain any number of compartments but single-compartment modelsare generally inaccurate for studying pharmacokinetics. A three-compartment modelallows fairly accurate modelling with only limited complexity.

Catenary

A form of multicompartmental modelling in which all compartments arelinked in a linear chain with each compartment connecting only to its imme-diate neighbour.

Mamillary

A formofmulticompartmentalmodelling inwhich there is a central compart-ment to which a stated number of peripheral compartments are connected.

Mamillary models are the most commonly used and are described below.

One-compartment model

The terminology for the so-called ‘central’ compartment is C1. There are variousrate constants that should be included in the diagram: K01 is the rate constant for adrug moving from the outside of the body (compartment 0) to the centralcompartment (compartment 1); K10 is the rate constant of elimination from C1

to C0. Single-compartment models do not occur physiologically.


Two-compartment model

A second (peripheral) compartment can now be added, which may mathemati-cally represent the less vascular tissues of the body. All the rate constants thatwere in the previousmodel still apply but in addition youmust indicate that thereare additional constants relating to this new compartment. The terminology isthe same; K12 represents drug distribution from C1 to C2 and K21 represents drugredistribution back intoC1. Demonstrate in your diagram that elimination occursonly from C1 no matter how many other compartments are present.

A semi-log plot of drug concentration versus time will no longer be linear as the drughas two possible paths to move along, each with their own associated rate constants.

To show the concentration time curve for two compartments, first draw andlabel the axes as on p. 106. Instead of being linear, a bi-exponential curve shouldbe drawn. Phase 1 equates to distribution of drug from C1 toC2 whereas phase 2represents drug elimination from C1. A tangent (b) to phase 2 intercepts the yaxis at B. Subtracting line b from the initial curve gives line a, which interceptsthe y axis at A and is a tangent to phase 1. The values of A and B sum to give C0.Because the scale is logarithmic on the y axis, B is small in comparison with Aand, therefore, C0 and A are close.

Compartmental modelling 189


Formula for two-compartment model

Ct = A.e−αt + B.e−βt

where Ct is the concentration at time t, A is the y intercept of line a, α is theslope of line a, B is the y intercept of line b and β is the slope of line b.

The value of Ct can, therefore, be found simply by adding the values of exponentialdeclines a and b at any given time. The terms α and β are the rate constants forthese processes.

Three-compartment model

A third compartment can now be added that mathematically represents theleast vascular tissues of the body. All the rate constants that were in theprevious model still apply but in addition you must indicate that there areadditional constants relating to this new compartment. The terminology isthe same. Demonstrate in your diagram that elimination occurs only fromC1 no matter how many other compartments are present. Most anaestheticdrugs are accurately modelled in this way. Remember that the compart-ments are not representing precise physiological regions of the body. Insteadthey are designed to model areas of the body that share similar properties interms of rates of equilibration with the central compartment. Your diagramshould show, however, that one of the peripheral compartments modelsslowly equilibrating tissues while the other models tissues that are equili-brating more rapidly.



Concentration versus time

Draw and label the axes as before. This time draw a tri-exponential decline. Drawa tangent to phase 3 (line b) as before giving a y intercept at B. Next drawa tangent to phase 2 (line c) that would occur if line b were subtractedfrom the original tri-exponential decline. Show that this line intercepts the yaxis at C. Finally draw a tangent to phase 1 (line a), which would occur iflines b and c were subtracted from the original tri-exponential decline. Showthat this intercepts the y axis at A. As before, A + B + C should equal C0. Line arepresents distribution to rapidly equilibrating tissues and line c representsdistribution to slowly equilibrating tissues. Line b always represents eliminationfrom the body.

Formula for three-compartment model

Ct = A.e−αt + B.e−βt + C.e−γt

where C is the y intercept of line c and γ is the slope of line c.

The equation is compiled in the same way as that for a two-compartment model:B.e−βt continues to represent the terminal elimination phase and the term C.e−γt isadded to represent slowly equilibrating compartments.

Three-compartment models show how drug first enters a central (first) com-partment, is then distributed rapidly to a second and slowly to a third whilst beingeliminated only from the first. Distribution to, and redistribution from, theperipheral compartments occurs continuously according to prevailing concentra-tion gradients. These peripheral compartments may act as reservoirs keeping thecentral compartment full even as elimination is occurring from it. The ratio of the

Compartmental modelling 191


rate constants to and from the central compartment will, therefore, affect thelength of time taken to eliminate a drug fully.

Therefore it can be seen that prediction of the concentration of a drug at a giventime using a three compartmental model requires the combination of data frommultiple exponential curves. To create this form of pharmacokinetic modellingtherefore requires specialist computer software.



Physiological modelling

This type of modelling uses realistic physiological parameters to construct themodel. These include organ blood flow, the volume of different tissues and thetissue:blood partition coefficient. This is also known as physiologically basedpharmacokinetic (PBPK) modelling and is the most complex type of modelling.

In physiological models the compartments are defined according to differentorgans or tissues. More complex models will have many different compartments,whereas simpler versions will group organs or tissues with similar perfusion ratesand lipid contents together. Equations are written to describe the rate of transferinto and out of each compartment, with each compartment having a differentequation.

The rate of distribution of drug to a tissue may either be limited by the perfusionof the tissue (for example for small lipophilic drugs which rapidly cross mem-branes) or the permeability of the tissue membrane to the drug.

Although this type of modelling is potentially the most accurate as it moreclosely represents what happens in the body, in reality it has some significantlimitations. Often much of the data used is actually based on extrapolation fromanimal models because human data would require intensive tissue sampling and isnot practical.

The diagram below is an example of a simple structure for a PBPK model for aninhalational anaesthetic agent.


Context-sensitive half time

The use of compartmental models leads onto the subject of context-sensitive halftime (CSHT).

Context-sensitive half time

The time taken for the plasma concentrationof a drug to fall byhalf after thecessation of an infusion designed tomaintain a steady plasma concentration(time).

Although there is not a recognized definition for the term ‘context’, it is used toidentify the fact that the half time will usually alter in the setting of varyingdurations of drug infusion.

Draw and label the axes as shown. In terms of accuracy, it is often easiest todraw in the curves from the drugs with the shortest CSHT first before plottingthe others.

Remifentanil This is the exceptional drug in anaesthetic practice in that it iscontext insensitive. Draw a straight line starting from the origin and becom-ing near horizontal after the CSHT reaches 5min. This demonstrates that thehalf time is not dependent on the length of infusion as clearance by plasmaesterases is so rapid.

Propofol Starting at the origin, draw a smooth curve rising steadily towardsa CSHT of around 40 min after 8 h of infusion. Propofol is not contextinsensitive as its CSHT continues to rise; however it remains short even afterprolonged infusions.

Alfentanil The curve rises from the origin until reaching a CSHT of 50 minat around 2 h of infusion. Thereafter the curve becomes horizontal. This


demonstrates that alfentanil is also context insensitive for infusion durationsof 2 h or longer.

Thiopental The curve begins at the origin but rises more steeply than theothers so that the CSHT is 50 min after only 30 min infusion duration. Thecurve should be drawn like a slightly slurred build-up exponential reaching aCSHT of 150 min after 8 h of infusion. As the CSHT continues to rise,thiopental does not become context insensitive

Fentanyl The most complex curve begins at the origin and is sigmoid inshape. It should cross the alfentanil line at 2 h duration and rise to a CSHT of250 min after 6 h of infusion. Again, as the CSHT continues to rise, fentanyldoes not become context insensitive.

It is important to realize that the CSHT does not predict the time to patientawakening but simply the time until the plasma concentration of a drug has fallenby half. The patient may need the plasma concentration to fall by 75% in order toawaken, and the time taken for this or any other percentage fall to occur is knownas a decrement time.

Decrement time

The time taken for the plasma concentration of a drug to fall to thespecified percentage of its former value after the cessation of an infusiondesigned to maintain a steady plasma concentration (time).

The CSHT is, therefore, a form of decrement time when the ‘specified percentage’is 50%. When using propofol infusions, the decrement time is commonly quotedas the time taken to reach a plasma level of 1.2 μg.ml−1, as this is the level at whichwake up is thought likely to occur in the absence of any other sedative agents.

Context-sensitive half time 195


Target controlled infusions

Target controlled infusion

An infusion controlled by a microprocessor-driven pump that alters theinfusion rate to maintain a user defined target plasma concentration.

The target controlled infusion (TCI) microprocessor is programmed with phar-macokinetic models for different drugs. These are generally three compartmentmodels based on pharmacokinetic studies in volunteers and they are adjustedaccording to patient variables such as age, weight and height. When first intro-duced, the user selected a plasma concentration (Cp) to target. However, now it ismore common to target an effect site concentration (Ce). The effect site is anadditional compartment that has been introduced more recently to reflect thehysteresis between plasma concentration and the clinical effect observed.

Infusion rates are calculated as an initial bolus to fill the central compartmentto the concentration targeted (B), followed by a continuous infusion at a rateequal to the elimination rate from the plasma (E) plus the redistribution rate tothe peripheral compartments (also know as the transfer rate, T). This BETregimen was first proposed in 1968 although TCI pumps were not introduceduntil 1997.

Common models in clinical practice are the modified Marsh model andSchnider models for propofol and the Minto model for remifentanil.

keo

The first order rate constant that describes the rate of equilibrationbetween the plasma and the effect site (e).

keo depends upon the pharmacological characteristics of the drug as well aspatient factors affecting drug delivery. You will notice that this terminology isnot consistent with that of the three compartment model and, to be completelyaccurate, it should be used to describe the removal of the drug directly from theeffect site, out of the body. However, the effect site is considered to havenegligible volume and so separate constants for movement in and out of thecompartment are felt to be unnecessary. Therefore it can be considered to be theproportional change in concentration gradient between the plasma and effectsite per unit time.

A small (slow) keo value leads to a larger initial dose being given to provide agreater concentration gradient and a more rapid achievement of the effect-siteconcentration programmed.


Effect-site targeting

This describes the process by which a user programs an effect-site concentration asa target. The microprocessor calculates the initial bolus dose required to achievethis concentration as quickly as possible. This calculation is based on allowing theplasma concentration to rise to an optimum level above the effect site concen-tration (to provide a concentration gradient between the plasma and effect-site)whilst also preventing an overshoot of the effect-site concentration. After admin-istration of the bolus dose the infusion pauses to allow the plasma concentration tofall to that of the effect-site. A more rapid estimation for speed of removal of drugfrom the plasma will lead to a larger initial dose being administered.

Plasma-site targeting

This is when the user programs a plasma concentration for the microprocessor totarget. This will lead to a smaller initial dose being administered. This mode israrely used.

You may be asked to explain how a TCI pump operates and this is best donewith the aid of a graph. To demonstrate understanding, give a clinical situation ofinduction of anaesthesia, followed by an increase in Ce followed by a decrease. Theexample below is consistent with the modified Marsh model for propofol.

Infusion rate (solid line). Draw and label some appropriate axes. Once started,the machine delivers an initial dose at a fast infusion rate (1200 ml.h−1) toachieve the targeted effect site concentration (3.0 μg.ml−1 in this example).The infusion then pauses to allow the plasma concentration to fall to that ofthe effect site, which occurs by elimination and redistribution of the initialbolus. The infusion then re-starts at a much lower rate to maintain theprogrammed concentration. This maintenance rate will depend upon the

Target controlled infusions 197


ongoing redistribution and clearance rates. Increasing the target concentra-tion to 6.0 μg.ml−1 leads to a repeat of this process, with a further rapid bolusbeing administered before a pause in infusion rate and a re-commencementat a higher maintenance rate. Decreasing the target concentration back to3.0 μg.ml−1 at 10 minutes leads to a pause in the infusion to allow the plasmaconcentration to fall. This time when the infusion restarts a small bolus isgiven to bring Cp back up to the same concentration as Ce, before theinfusion restarts at a lower rate.

Ce (dashed line). Draw a curve exponentially increasing to a concentration of3.0 μg.ml−1 after which it plateaus as the infusion maintains a constantconcentration. When the user increases the target concentration, a similarshaped curve should be drawn, with this time the plateau being 6.0 μg.ml−1.When the target concentration decreases an exponential decreasing curveshould be drawn back to 3.0 μg.ml−1, where the curve plateaus again.

Cp (dotted line). During the initial bolus the Cp increases above that of theCe. The magnitude of the overshoot will depend on the keo and thus differsaccording to the pharmacokinetic model (see above). The peak concen-tration will be just after the infusion terminates and then the Cp will fallto that of the Ce targeted. A similar pattern occurs when the second bolusis given. When the target is decreased again the Cp falls more rapidly thanthe Ce, which reflects the hysteresis between the two. The short bolus asthe infusion recommences rapidly increases the Cp to match that of theeffect site.

Important points to know about the models when using them clinically:

The plasma and effect site concentrations are calculated not measured (ascompared with end tidal agent monitoring).

The target concentration must be adjusted for the individual patients andclinical circumstances and used in conjunction with clinical observation.

The cardiovascular effects of the drug will depend upon the maximumplasma concentration achieved and so in frail, elderly patients a largeovershoot in the plasma concentration when a bolus is given can lead tosignificant haemodynamic compromise.

In morbidly obese patients with a BMI > 42, with increasing body weightthe calculation of LBM used in the Schnider model paradoxically decreases.This decrease leads to a higher estimated clearance and thus a larger initialbolus dose and higher infusion rate will be administered. The manufac-turers of TCI systems thus prevent programming of their pumps withweight and height combinations giving a BMI outside this range.



Note that V1 is fixed in the Schnider model, whereas it is weight adjusted inthe modified Marsh model. When using plasma site targeting in theSchnider model then the bolus dose, which is directly proportional to V1,is not adjusted for weight. With effect site targeting this is not the case asthe overshoot accounts for age, weight and height. Thus, in most circum-stances, the Schnider model should be used in effect site mode only.

Target controlled infusions 199



Section 7Respiratory physiology



Lung volumes

Most lung volumes can be measured with a spirometer except total lung capacity(TLC), functional residual capacity (FRC) and residual volume (RV). The FRC canbe measured by helium dilution or body plethysmography.

Tidal volume

The volume of gas which is inhaled or exhaled during the course of anormal resting breath. (TV or VT, ml)

Residual volume

The volume of gas that remains in the lungs after a maximal forced expira-tion. (RV, ml)

Inspiratory reserve volume

The volume of gas that can be further inhaled after the end of a normaltidal inhalation. (IRV, ml)

Expiratory reserve volume

The volume of gas that can be further exhaled after the end of a normaltidal exhalation. (ERV, ml)

Capacity

The sum of one of more lung volumes.

Vital capacity

The volume of gas inhaled when a maximal expiration is followed imme-diately by a maximal inspiration. The sum of the ERV, IRV and TV. (VC, ml)

Functional residual capacity

The volume of gas that remains in the lungs after a normal tidal expiration.It is the sum of the ERV and the RV. (FRC, ml)

You may be asked for the definitions above, and to explain them clearly it is oftenuseful to refer to a diagram. You will be expected to be familiar with a diagram ofnormal respiratory volumes against time, and to be able to explain its maincomponents.


Lung volumes

As the FRC is around 3000 ml, the TV should be drawn as an undulating linewith its baseline at 3000 ml rising to 3500 ml on inspiration. Consider, and beprepared to explain, how the curve would shift in pathological situations. Forexample, in asthmatics the FRC may increase while the IRV decreases as aconsequence of gas trapping.

Closing volume

The volume of gas over and above residual volume that remains in thelungs when the small airways begin to close. (ml)

Closing capacity

The lung capacity at which the small airways begin to close. It is a combi-nation of residual volume and closing volume. (ml)

Closing volume is calculated by measuring the nitrogen concentration in expiredgas after a single breath of 100% oxygen. The nitrogen wash-out test is the samemethod used to measure anatomical dead space. Closing capacity is then found byadding this value to the value for residual volume that has been calculated by thehelium dilution method. Closing capacity increases with age and reaches thestanding FRC at 70 years and the supine FRC at 40 years.

204 Section 7 � Respiratory physiology


Spirometry

Simple spirometry using a Vitalograph or similar produces a well-defined curvethat can aid in the interpretation of various lung diseases.

Normal spirometry

Draw and label the axes as shown. Next draw a horizontal line at the level of theforced vital capacity (FVC; 4500 ml) to act as a target point for where the curvemust end. Normal physiology allows for 75% of the FVC to be forcibly expired in1 s (FEV1). The normal FEV1 should, therefore, be 3375 ml. Mark this volume ata time of 1 s. Construct the curve by drawing a smooth arc passing through theFEV1 point and coming into alignment with the FVC line at the other end.

Obstructive pattern


On the same axes, draw a horizontal line at a lower FVC to act as a target endpoint. Obstructive airway diseases limit the volume of gas that can be forciblyexpired in 1 s and, therefore, the FEV1/FVC ratio will be lower. In the graphabove, the ratio is 33% giving a FEV1 of 1000 ml for a FVC of 3000 ml.Construct the curve in the same way as before.

Restrictive pattern

On the same axes, draw a horizontal line at a lower FVC than normal to act as atarget end point. Restrictive lung disease curtails the FVC but generally doesnot affect early expiration. For this reason, the FEV1/FVC ratio is normal orhigh. In the graph above, the ratio is 85%, giving a FEV1 of 3000ml for a FVC of3500 ml. Construct the curve in the same way as before.



Flow–volume loops

You should be able to draw the following loops as examples of various respiratorysystem pathologies.

Normal loop

Draw and label the axes as shown; the x axis need not display numerical valuesbut a note should be made of the TLC and RV. Note that the highest volume(TLC) is on the left of the x axis. The units on the y axis are litres per second asopposed to litres per minute. Positive deflection occurs during expiration andnegative deflection during inspiration. The patient takes a VC breath beforestarting the test with a forced expiration. The loop is drawn in a clockwisedirection starting from TLC. The normal loop (A) rises rapidly to a flow rate of8–10 l.s−1 at the start of forced expiration. The flow rate then decreases steadilyas expiration continues in a left to right direction so that a relatively straightcurve is produced with a slight concavity at its centre. An important point todemonstrate is the phenomenon of dynamic compression of the airways. Thecurve traced by the normal loop represents the maximum possible flow rate ateach lung volume. Even if patients ‘holds back’ their maximal effort by expiringslowly at first (B), they will be unable to cross this maximal flow line. This isbecause the airways are compressed by a rise in intrathoracic pressure, thuslimiting flow. Themore effort that is put into expiration, themore these airwaysare compressed and so total flow remains the same. The inspiratory limb has amuch squarer shape to it and a maximum flow of 4–6 l.s−1 is usually achieved.Inspiration occurs from RV to TLC in a right to left direction as shown.


Obstructive disease

Obstructive disease reduces peak expiratory flow rate (PEFR) and increases RVvia gas trapping. The TLC may also be higher although this is difficult todemonstrate without values on the x axis. The important point to demonstrateis reduced flow rates during all of expiration, with increased concavity of theexpiratory limb owing to airway obstruction. The inspiratory limb is lessaffected and can be drawn as for the normal curve but with slightly lowerflow rates.

Restrictive disease

In contrast to obstructive disease, restrictive disease markedly reduces TLCwhile preserving RV. The PEFR is generally reduced. Demonstrate these pointsby drawing a curve that is similar in shape to the normal curve but in which theflow rates are reduced. In addition, the left-hand side of the curve is shifted tothe right, demonstrating a fall in TLC.



Variable intrathoracic obstruction

An intrathoracic obstruction is more likely to allow gas flow during inspirationas the negative intrathoracic pressure generated helps to pull the airways open.As such, the inspiratory limb of the curve may be near normal. In contrast, thepositive pressure generated during forced expiration serves only to exacerbatethe obstruction, and as such the expiratory limb appears similar to that seen inobstructive disease. Both TLC and RV are generally unaffected.

Variable extrathoracic obstruction

An extrathoracic obstruction is more likely to allow gas flow during expiration asthe positive pressure generated during this phase acts to force the airway open. Assuch, the expiratory limb may be near normal. In contrast, the negative pressuregenerated in the airway during inspiration serves to collapse the airway furtherand the inspiratory limb will show markedly reduced flow rates at all volumeswhile retaining its square shape. Both TLC and RV are generally unaffected.

Flow–volume loops 209


Fixed large airway obstruction

This curve is seen where a large airway has a fixed orifice through which gas isable to flow, such as may be seen in patients with tracheal stenosis. The peakinspiratory and expiratory flow rates are, therefore, dependent on the diameterof the orifice rather than effort. The curves should be drawn almost sym-metrical as above, with both limbs demonstrating markedly reduced flow.The TLC and RV are generally unaffected.



The alveolar gas equation

The alveolar gas equation is used to estimate the PAO2 of a ‘perfect’ alveolus withvarying fractions of inspired oxygen and it states that

PAO2 = [FIO2 × (PATM − PH2O)] − (PACO2 /R)

where PAO2 is the alveolarO2 partial pressure, PACO2 is the alveolar CO2 partialpressure, PATM is the atmospheric pressure, F IO2 is the fraction of inspiredoxygen, PH2O is the standard vapour pressure (SVP) of water at 37 °C and R isthe respiratory quotient.

Note that the SVP of water in the airways is subtracted from the atmosphericpressure before multiplying by the F IO2. This is because the fractional concen-tration of O2 only applies to the portion of inhaled mixture that is dry gas.

The PACO2 is assumed to be in equilibriumwith arterial CO2 tension (PaCO2) andthis number will either be given or will be assumed to be within the normal range.

The value of R varies according to which energy substrates make up thepredominant part of the diet. With a normal diet, it is assumed to have a valueof 0.8; pure carbohydrate metabolism gives a value of 1.0.

Therefore, under normal conditions:

PAO2 ¼ ½0:21� ð101:3� 6:3Þ� � ð5:3=0:8Þ¼ ð0:21� 95Þ � 6:6¼ 19:95� 6:6¼ 13:35 kpa

Note that there is no difference between the ideal alveolar value and the normalarterial PaO2 of 13.3 kPa. In practice a difference of up to 2 kPa is allowable owingto ventilation–perfusion ðV� =Q� Þ mismatch and shunt.


The shunt equation

The purpose of the shunt equation is to give a ratio of shunt blood flow to totalblood flow. The normal ratio is 0.3. Under abnormal conditions, the ratio will tendto increase and so markedly reduce the PaO2.

Shunt

Those areas of the lung that are perfused but not ventilated:

Q�

S

Q�

T¼ ðCc0o2 � Cao2Þ

ðCc0o2 � C�vo2Þ

where Q�

T is total blood flow, Q�

S is shunted blood flow, Cc′O2 is end-capillary blood content, C�vo2 is shunt blood O2 content and CaO2 is arterialblood O2 content.

Principle of the shunt equation

Start with the theoretical lungs shown above and remember that blood entering thesystemic circulation has a component that is shunted past the pulmonary circu-lation Q

�

S

� �and another component that passes through it Q

�

T � Q�

S� �

.

Now consider the blood flow generated in a single beat. The O2 delivered in thisvolume of blood is equal to Q

�

T:Cao2� �

. This must be made up of shunted bloodQ

�

S:C�vo2� �

and capillary blood ½Q�

T � Q�

S�:Cc0o2� �

.

Q�

T:Cao2 ¼ Q�

S:C�vo2

� �þ ½ðQ�

T �Q�

SÞ:Cc0o2�


Derivation

Q�

T:Cao2 ¼ ðQ�

S:C�vo2Þ þ ½ðQ�

T �Q�

SÞ:Cc0o2�Rearrange the brackets to give

Q�

T:Cao2 ¼ ðQ�

S:C�vo2Þ þ ðQ�

T:Cc0o2Þ � ðQ�

S:Cc0o2Þ

Q�

S needs to be moved to the left, aiming for Q�

S=Q�

T in the final equation.

ðQ�

T:Cao2Þ þ ðQ�

S:Cc0o2Þ ¼ ðQ�


T:Cc0o2Þthen

ðQ�

S:Cc0o2Þ ¼ ðQ�



T:Cao2Þthen

ðQ�

S:Cc0o2Þ � ðQ�

S:C�vo2Þ ¼ ðQ�


T:Cao2Þ

Then simplify the brackets

Q�

SðCc0o2 � C�vo2Þ ¼ Q�

TðCc0o2 � Cao2Þ

To get Q�

S=Q�

T on the left, both sides must be divided by Q�

T. At the sametime, the term Cc0o2 � Cvo2ð Þ can be moved from left to right by alsodividing both sides by Cc0o2 � Cvo2ð Þ.

Q�

S

Q�

T¼ Cc0o2 � Cao2ð Þ

Cc0o2 � C�vo2ð Þ

The O2 content of the mixed venous (shunt) and arterial blood can be calculatedfrom the relevant samples by using the equations below, which are explained laterin the section.

Cvo2 ¼ 1:34½Hb�Satsð Þ þ 0:0225:Pvo2ð Þor

Cao2 ¼ 1:34½Hb�Satsð Þ þ 0:0225:Pao2ð Þ

The value for Cc0o2 cannot be calculated in this way very easily as a sample istechnically difficult to take without a catheter in the pulmonary vein. It is, there-fore, assumed to be in equilibrium with the PAO2, which, in turn, is given by thealveolar gas equation.

The shunt equation 213


Pulmonary vascular resistance

Pulmonary vascular resistance (PVR) is given by:

PVR¼ MPAP� LAPð ÞCO

� 80

where MPAP is mean pulmonary artery pressure, LAP is left atrial pressureand CO is cardiac output.

The units for PVR are dyne.s−1 .cm−5 and 80 is used as a conversion factor toaccount for the different units used within the equation

Factors affecting PVR

Increased by Decreased by

Increased PaCO2 Decreased PaCO2Decreased pH Increased pHDecreased PaO2 Increased PaO2Adrenaline (epinephrine) IsoprenalineNoradrenaline (norepinephrine) AcetylcholineThromboxane A2 Prostacyclin (prostaglandin I2)Angiotensin II Nitric oxide (NO)Serotonin (5-hydroxytryptamine) Increased peak airway pressureHistamine Increased pulmonary venous pressureHigh or low lung volume Volatile anaesthetic agents

Lung volume versus PVR graph


The point to demonstrate is that resistance is lowest around the FRC. The curverises at low lung volumes as there is direct compression of the vessels. At highlung volumes, the vessels are overstretched, which alters the flow dynamics andincreases resistance further. The curve will be moved up or down by those otherfactors (above) which increase or decrease PVR.

Pulmonary vascular resistance 215


Distribution of pulmonary blood flow

The distribution of blood flow to the upright lung varies and this has beendescribed in terms of zones, often referred to as West’s zones. Although originallydescribed in terms of three zones, a fourth zone is sometimes added to representthe effect of low lung volumes.

Draw a schematic diagram of a lung and divide into three zones. Draw circles torepresent alveoli in each zone and tubes to represent their accompanyingcapillaries. Draw and label the axes of the graph next to it as these describe inmore detail how blood flow varies throughout the lung. The standard nomen-clature Pa, PA and Pv is used to describe the alveolar, arterial and venouspressures respectively.

Zone 1 PA>Pa>Pv (Collapse) In this model there is no blood flow in zone 1as alveolar pressure is higher than arterial pressure. Indicate this by the bloodvessels being squashed flat in the alveolus. This zone does not exist in thenormal lung but may occur during positive pressure ventilation. It equates toalveolar dead space.

Zone 2 Pa>PA>Pv (Waterfall) Blood flow increases down zone 2 and youshould demonstrate this by drawing the diagonal line in zone 2 of the graph.In this zone, blood flow is determined by the difference between arterial andalveolar pressure (rather than between arterial and venous) and as both ofthese are cyclic, it will be intermittent. In the alveolus demonstrate thatalveolar pressure is greater than venous pressure by compression of thevenous end of the capillary.

Zone 3 Pa>Pv>PA (Distension) As both arterial and venous pressures aregreater than alveolar pressure, blood flow will be constant in this zone andthis is shown by the open blood vessel in the alveolus. Most of the normal


healthy lung comprises of this zone. On the graph, demonstrate that bloodflow also increases down the lung within this zone, by drawing a diagonalline but not that there is less difference between the upper and lower areas ofthe lung in this zone.

Zone 4 This is a region of reduced blood flow that occurs at low lung volumesand is due to increased resistance in extra alveolar vessels (demonstrated onthe lung volume versus peripheral vascular resistance graph).

Distribution of pulmonary blood flow 217


Ventilation/perfusion mismatch

The V�

=Q�

term describes the imbalance between ventilation ðV� Þ and perfusion ðQ� Þin different areas of the lung. Given that alveolar ventilation is 4.5 l.min−1 andpulmonary arterial blood flow is 5.0 l.min−1, the overall V

�

=Q�

ratio is 0.9. Bothventilation and perfusion increase from top to bottom of the lung, but perfusion bymuch more than ventilation.

Ventilation/perfusion graph

The graph can be drawn with either one or two y axes. The example above hastwo, flow and V

�

=Q�

ratio, and gives a slightly more complete picture. The x axisshould be arranged from the bottom to the top regions of lung in a left to rightdirection as shown. Both ventilation and perfusion decrease linearly frombottom to top. Perfusion starts at a higher flow but decreases more rapidlythan ventilation so that the lines cross approximately one third of the way downthe lung. At this point the V

�

=Q�

ratio must be equal to 1. Using this point and amaximumV

�

=Q�

ratio of around 3, draw a smooth curve passing through both ofthese as it rises from left to right. The graph demonstrates that higher lungregions tend towards being ventilated but not perfused (dead space,V

�

=Q� � 1� �

and lower regions tend towards being perfused but not ventilated(shunt, V

�

=Q� � 0

� �.


Dead space

Dead space is an important concept in anaesthesia. As dead space increases, asmaller proportion of the inhaled gas mixture takes part in gas exchange.

Dead space

The volume of the airways in which no gas exchange occurs. It can be eitheranatomical or alveolar (ml).

Anatomical dead space

The volume of the conducting airways that does not contain any respira-tory epithelium. This stretches from the nasal cavity to the generation 16terminal bronchioles. (ml)

The anatomical dead space can be measured by Fowler’s method. In adults it isapproximately 2 ml.kg−1.

Alveolar dead space

The volume of those alveoli that are ventilated but not perfused, and socannot take part in gas exchange (ml).

Physiological dead space

The sum of the anatomical and alveolar dead space (ml).

The physiological dead space can be calculated using the Bohr equation.


Fowler’s method

Fowler’s method principle

The patient takes a single vital capacity breath of O2 and exhales through a N2

analyser. Dead space gas, which is pure O2, passes the analyser first, followed by amixture of dead space and alveolar gas.When pure alveolar gas passes the analyser,a plateau is reached. At closing capacity, small airways begin to close, leading topreferential exhalation from the larger-diameter upper airways. These airwayscontain more N2 as they are less well ventilated, so the initial concentration ofN2 within them was not diluted with O2 during the O2 breath.

Fowler’s method graph

Phase 1 Pure dead space gas so no value on the y axis.Phase 2 Amixture of dead space gas and alveolar gas. The curve rises steeply to aplateau. Demonstrate a vertical line that intercepts this curve such that area Aequals area B. The anatomical dead space is taken as the volume expired at thispoint.

Phase 3 Plateau as alveolar gas with a steady N2 content is exhaled. Note thecurve is not completely horizontal during this stage.

Phase 4 Draw a final upstroke. This occurs at the closing volume. Note thatthe volume on the x axis at this point is not the value for the closing volumeitself but rather the volume exhaled so far in the test. The closing volumerepresents the volume remaining within the lung at this point.


The Bohr equation

The purpose of the Bohr equation is to give a ratio of physiological dead spacevolume to tidal volume. Dead space volume is normally around 30% of tidalvolume and so the normal ratio is quoted as 0.3. Under abnormal conditions,the ratio will tend to increase and so make ventilation inefficient.

The equation is:

VD/VT = (PaCO2 − PECO2)/PaCO2

where VD is the physiological dead space volume, VT is the tidal volume,and PECO2 is the partial pressure of CO2 in expired air.

Principle of the Bohr equation

Start with the theoretical lungs shown in the figure and remember that eachVT hasa component that is dead space (VD) and a remainder that must take part in gasexchange at the alveolus (VT − VD). This is the alveolar volume.

The fractional CO2 concentrations are FI for inhaled, FE for exhaled and FA foralveolar CO2.

Now consider a single tidal exhalation. The CO2 in this breath is equal to FE. VT.This must be made up of alveolar gas (FA [VT − VD]) and dead space gas (FI.VD).

Derivation

FE.VT = (FI.VD) + (FA[VT − VD])

But FI = 0 so the term (F I.VD) can be ignored

FE.VT = FA /(VT − VD)

Rearrange the brackets to give

FE.VT = (FA.VT) − (FA.VD)


The term VD needs to be moved to the left, aiming for VD/VT in the finalequation. Start by adding (FA.VD) to both sides and subtracting (FE.VT) fromboth sides to give

(FE.VT) + (FA.VD) = FA.VT

or

FA.VD = (FA.VT) − (FE.VT)

Then simplify the brackets

FA.VD = VT(FA − FE)

To getVD/VT on the left, both sidesmust be divided byVT. At the same time,the term FA can bemoved from left to right by also dividing both sides by FA

VD/VT = (FA − FE)/FA

Since the concentration of a gas is proportional to its partial pressure(Dalton’s law) FA and FE can be substituted for some more familiar units

FA = PACO2

FE = PECO2

Giving the Bohr equation as

VD/VT = (PACO2 − PECO2)/PACO2

As arterial CO2 tension is practically identical to alveolar CO2 partial pressure, itcan be used as a surrogate measurement. This is desirable as measuring arterialCO2 tension involves only a simple blood gas analysis. The term PACO2, therefore,becomes PaCO2 and so the equation is often written as

VD/VT = (PaCO2 − PECO2)/PaCO2

Some forms of the equation have the modifier +[R] added to the end as acorrection for high inspired CO2.



Oxygen delivery and transport

Oxygen cascade

Oxygen flux is a term used to describe delivery of O2 to the tissues. An under-standing of how the PO2 changes according to the location in the body is, therefore,useful when considering how the mitochondrial O2 supply is achieved. It can berepresented by the O2 cascade.

Stage Process Notes and equations

Air − PO2 = FIO2. PATMTrachea Humidification PO2 = FIO2 (PATM − PH2O)Alveolus Ventilation PAO2 = [FIO2 (PATM − PH2O) − (PACO2/R)Capillary Diffusion Diffusion barrier negligible for O2

Artery Shunt, V�

=Q�

mismatch A−a gradient usually < 2 kPaMitochondria − Low PO2 of around 1.5 kPa is usualVeins − Normal Pvo2 ¼ 6:3 kpa


The Pasteur point

The Pasteur point is the oxygen concentration below which oxidativephosphorylation cannot occur in the mitochondria. It is considered to bearound 1 mmHg (0.13 kPa).

The delivery of any substance to an organ can be calculated if the concentration ofthe substance and the flow rate are measured.

DO2 = CO.CaO2.10

where DO2 is delivery of O2, CO is cardiac output and CaO2 is arterial O2

content.

The multiplier 10 is used because CaO2 is measured in ml.dl−1 whereas CO ismeasured in l.min−1. Normal DO2 is around 1000 ml.min−1 or 500 ml.min−1.m−2.The O2 content of the blood is calculated using a specific equation that dependsmainly on haemoglobin concentration, [Hb] and saturation (Sats).

CaO2 = (1.34[Hb]Sats) + (0.0225.PaO2)

if PaO2 is measured in kilopascalsor

CaO2 = 1.34[Hb]Sats) + (0.003.PaO2)

if PaO2 is measured in millimetres of mercury.

The number 1.34 is known as Hüffner’s constant. It describes the volume of O2 (ml)that can combine with each 1 g Hb. In vitro, its value is 1.39 but this becomes 1.34in vivo because abnormal forms of Hb such as carboxyhaemoglobin and methae-moglobin are less able to carry O2.

Supply and demand



This curve demonstrates the relationship between oxygen delivery (DO2) andoxygen consumption ðV�

O2Þ. The latter is normally around 250–500 ml.min−1

at rest and you should demonstrate that it is not affected until delivery falls tobelow the same value. Label the inflexion point on the graph as ‘critical DO2’.Until this point, a fall inDO2 leads to no change in VO2 because of an increase inthe oxygen extraction ratio but when this mechanism has been maximized, VO2

begins to fall. Below critical DO2, consumption is termed supply dependent.Above critical DO2 it is termed supply independent.

Critical DO2

The degree of oxygen delivery below which supply is inadequate to meetoxygen demand.

The exact degree of Do2 that fulfills this definition is not fixed but is dependant onmany other patient factors although it has been variously defined as lying in theregion between 4–8 ml.kg−1.min−1.

Oxygen extraction ratio

The fraction of delivered oxygen that is taken up by the tissues.

O2ER = VO2 / DO2

The normalO2ER is 0.2 to 0.3, indicating that only 20–30% of the delivered oxygenis utilized. This spare capacity enables the body to cope with a fall in oxygendelivery without initially compromising aerobic respiration. The O2ER variesbetween organs with the heart being particularly sensitive to ischaemia becauseof an O2ER of 0.6.

Oxygen delivery and transport 225


Classification of hypoxia

Definition

The condition in which there is an insufficient supply of oxygen to thetissues to maintain normal cellular function. It may be generalized orregional.

Classification

Hypoxia is not caused by a single factor. Broadly speaking there are four groups ofcausation which can be classified as shown here.

Hypoxaemic hypoxia

Insufficient tissue oxygenation arising from an abnormal reduction in thepartial pressure of oxygen in arterial blood.

The definition above demonstrates the important difference between the termshypoxia and hypoxaemia. Although the terms are often used interchangeably inday-to-day practice, this is not strictly correct as it is quite possible to be hypoxicyet not hypoxaemic. Causes may include all types of diffusion defect or VQmismatch as well as hypoventilation, breathing hypoxic mixtures and others.

Anaemic hypoxia

Insufficient tissue oxygenation arising from a failure of the oxygen carryingcapacity of blood in the face of a normal partial pressure of oxygen.

Although severe chronic anaemia may cause this condition, perhaps a morecommon event is carbon monoxide poisoning as the formation of carboxyhaemo-globin in preference to oxyhaemoglobin reduces the effective oxygen carryingcapacity.

Ischaemic hypoxia

Insufficient tissue oxygenation arising from a failure of perfusion.

This is classically the form of hypoxia that is seen in septic shock as the micro-circulation to tissues and organs fails progressively.


Histotoxic hypoxia

Insufficient tissue oxygenation in the face of normal oxygen delivery due tothe failure of oxidative phosphorylation.

The process can be thought of as an inability of the tissues to utilize the oxygen thatis being supplied. The archetypal agent is cyanide, which achieves its effect byuncoupling oxidative phosphorylation as per the definition.

Classification of hypoxia 227


The oxyhaemoglobin dissociation curve

The oxyhaemoglobin (oxy-Hb) dissociation curve is core knowledge for theexamination and in clinical practice. You will be expected to have a very clearunderstanding and to be able to construct a very precise graph.

P50

The partial pressure of O2 in the blood at which haemoglobin is 50%saturated. (kPa)

The oxyhaemoglobin dissociation curve

Draw and label the axes as shown; O2 content can also be used on the y axis with arange of 0−21 ml.100 ml−1. Your graph should accurately demonstrate three keypoints. The arterial point is plotted at 100% saturation and 13.3 kPa. The venouspoint is plotted at 75% saturation and 5.3 kPa. The P50 is plotted at 50%saturation (definition) and 3.5 kPa. Only when these three point are plottedshould you draw in a smooth sigmoid curve that passes through all three. Thecurve is sigmoid because of the cooperative binding exhibited by Hb. In thedeoxygenated state (deoxy-Hb), the Hb molecule is described as ‘tense’ and it isdifficult for the first molecule of O2 to bind. As O2 binds to Hb the moleculerelaxes (a conformational change occurs) and it become progressively easier forfurther molecules to bind. If asked to compare your curve with that of a differentO2 carrier such as myoglobin, draw a hyperbolic curve to the left of the originalline. Myoglobin can only carry one O2 molecule and so the curve does not have asigmoid shape.


Factors affecting the curve

It is the change in position of the P50 that determines whether the curve has shiftedto the left or to the right. You will be expected to be familiar with a number offactors that alter the position of the P50.

Change in position of the P50

Left shift (increased affinity for O2) Right shift (decreased affinity for O2)

Decreased PaCO2 Increased PaCO2Alkalosis AcidosisDecreased temperature Increased temperatureDecreased DPG Increased DPGFetal haemoglobin PregnancyCarbon monoxide Altitudea

Methaemoglobin Haemoglobin S

DPG, 2,3-diphosphoglycerate.aHigh altitude can also cause a left shift of the P50 where PaO2 is critically low.

The effect of pH on the affinity of Hb for O2 is described as the Bohr effect.

The Bohr effect

The situation whereby the affinity of haemoglobin for oxygen is reducedby a reduction in pH and increased by an increase in pH.

A decrease in pH results in a rightward shift of the curve and decreases the affinityof Hb for O2. This tends to occur peripherally and allows the offloading of O2 to thetissues. Conversely, in the lungs, the pH rises as CO2 is offloaded and, therefore, O2

affinity is increased to encourage uptake.

The oxyhaemoglobin dissociation curve 229


Carriage of carbon dioxide

Carbon dioxide is 20 times more soluble in blood than O2 and is carried in threedifferent forms.

Arterial(%) Venous(%)

Dissolved 5 10Bicarbonate 90 60Carbamino compounds 5 30

The following reaction occurs in erythrocytes in the tissues and explains how CO2

is carried as HCO3�

CO2 þ H2O $ H2CO3 $ Hþ þ HCO3�

The reverse reaction occurs in the pulmonary capillaries.

The Haldane effect

The phenomenon by which deoxygenated haemoglobin is able to carrymore CO2 than oxygenated haemoglobin.

This occurs because deoxy-Hb forms carbamino-complexes with CO2 more read-ily than oxy-Hb. Secondly, deoxy-Hb is a better buffer of H+ than oxy-Hb and thisincreases the amount of HCO3

� formed. Once formed, HCO3� diffuses out of the

erythrocyte. To maintain electrical neutrality Cl− moves in. This is known as theCl− shift or the Hamburger effect.

The Hamburger effect (chloride shift)

The transport of chloride ions into the cell as a result of outwards diffusionof bicarbonate in order to maintain electrical neutrality.


Dissociation of carbon dioxide versus oxygen

Carbon dioxide dissociation curves

Dissolved The curve passes though the origin, rising as a shallow straight lineas PaCO2 rises.

Oxygenated The curve does not extend below 2 kPa as this lies outside thephysiological range. It rises steeply at first before levelling off at approxi-mately 60 ml.100 ml−1.

Deoxygenated It is important to plot this line. At any PaCO2, the CO2 contentwill be higher than that of oxy-Hb. This is a graphical representation of theHaldane effect. As a result, the curve is plotted slightly above that of oxy-Hb.Be sure to point this relationship out to the examiner.

Other The amount of CO2 lying between the dissolved line and the upperlines is that carried as HCO3

�. The graph also demonstrates, therefore, for agiven PaCO2, that a greater amount is carried as HCO3

� in venous blood (areabetween deoxygenated and dissolved) than in arterial blood (area betweenoxygenated and dissolved).

.

Carriage of carbon dioxide 231


Work of breathing

Work of breathing

In normal circumstances, the work done on expiration utilizes energy stored withinthe elastic tissues on inspiration. Expiration is, therefore, said to be passive unless theenergy required to overcome airway resistance exceeds that which is stored.

Work of breathing graph

The purpose of the graph is to demonstrate the effect of airway and tissueresistance on the pressure–volume relationship within the chest.

Draw and label the axes as shown. Remember the curve should only start to risefrom −0.5 kPa on the x axis as the intrapleural pressure within the lung remainsnegative at tidal volumes. If there were no resistance to breathing, each tidalbreath would increase its volume along the theoretical line AC and back againon expiration along the line CA.

Inspiration The line ABC is the physiological line traced on inspiration. Thearea ACDA represents work to overcome elastic tissues resistance. The extraarea enclosed by ABCA represents the work done in overcoming viscousresistance and friction on inspiration. If this resistance increases, the curvebows to the right as shown.

Expiration The line CB′A is the physiological line traced on expiration. Thearea enclosed by CB′AC is the work done on expiration against airway resist-ance. As this area is enclosed within the area ACDA, the energy required can besupplied from the stored energy in the elastic tissues. If this resistance increases,the curve bows to the left, as shown. The difference in area between ACB′A andACDA represents the energy lost as heat.


Control and effects of ventilation

You may be asked to draw the curves related to the control of ventilation or to theresponse of PACO2/PAO2 to changes in ventilation. It is important to be very clearabout what question is being asked. The axes can be labelled in very similar waysbut the curves are very different. There is no harm in asking for clarification in aviva setting before embarking on a description that may not be what the examineris asking for.

Control of ventilation

Minute ventilation versus alveolar oxygen partial pressure

At PACO2 of 5 kPa The line should demonstrate that, under normal conditions,the minute volume (MV) remains relatively constant around 6 l.min−1 untilthe PAO2 falls below 8 kPa. Show that the rise inMV following this is extremelysteep. This illustrates the hypoxic drive, which is so often talked about in thesetting of COPD.

At PACO2 of 10 kPa This line is plotted above and to the right of the first anddemonstrates the effect of a coexisting hypercarbia on hypoxic ventilatorydrive.


Minute ventilation versus alveolar carbon dioxide partial pressure

Normal Draw and label the axes as shown. Plot a normal PACO2 (5 kPa) at anormal MV (6 l.min−1). If the PACO2 is doubled, the MV increases four-foldin a linear fashion. Therefore, join the two points with a straight line. Above10−11 kPa, the line should fall away, representing depression of respirationwith very high PACO2. At the lower end of the line, the curve also flattens outand does not reach zero on either axis.

Raised threshold Plot a second parallel curve to the right of the first. Thisrepresents the resetting of the respiratory centre such that a higher PACO2 isrequired at any stage in order to achieve the same MV. This is seen withopiates.

Reduced sensitivity Plot a third curve with a shallower gradient. This rep-resents decreased sensitivity such that a greater increment in PACO2 isrequired in order to achieve the same increment in MV. Also seen withopiates.

The following graphs deal with the effect that changes in ventilation have on thePACO2 or PAO2, respectively. Make sure that you are clear about the differencesbetween these graphs and the ones shown above.



Alveolar carbon dioxide partial pressure versus minute ventilation

Draw and label the axes as shown. This graph demonstrates the effect thatventilation has on PACO2 rather than the control of ventilatory drive by CO2

itself. As MV doubles, so the PACO2 halves. The curve is, therefore, a rectangularhyperbola. Begin by plotting a normal PACO2 (5 kPa) at a normal MV (6 l.min−1).Draw one or two more points at which MV has doubled (or quadrupled) andPACO2 has halved (or quartered). Finish by drawing a smooth curve through allthe points you have drawn.

Alveolar oxygen partial pressure versus minute ventilation

Draw and label the axes as shown. This graph demonstrates the effect ofventilation on PAO2. Start by marking a point at a normal MV of 6 l.min−1

and a normal PAO2 of 13.3 kPa. Draw a hyperbolic curve passing through thispoint just before flattening out. It should not pass through the origin as this isunphysiological. The curve illustrates how large increases in MV have littleeffect on PAO2. The only reliable way to increase the PAO2 is to increase the FIO2,which is demonstrated by drawing additional parallel curves as shown.

Control and effects of ventilation 235


Compliance and resistance

Compliance

The volume change per unit change in pressure. (ml.cmH2O−1 or l.kPa−1)

Lung compliance

When adding compliances, it is their reciprocals that are added (as with capaci-tance) so that:

1/CTOTAL = (1/CCH E S T ) + (1/CLUNG)

where CCHEST is chest compliance (1.5−2.0 l.kPa−1 or 150−200 ml.cmH2O−1),

CLUNG is lung compliance (1.5−2 l.kPa−1 or 150−200 ml.cmH2O−1) and CTOTAL is

total compliance (7.5−10.0 l.kPa−1 or 75−100 ml.cmH2O−1).

Static compliance

The compliance of the lung measured when all gas flow has ceased.(ml.cmH2O

−1 or l.kPa−1)

Dynamic compliance

The compliance of the lungmeasured during the respiratory cyclewhen gasflow is still ongoing. (ml.cmH2O

−1 or l.kPa−1)

Static compliance is usually higher than dynamic compliance because there is timefor volume and pressure equilibration between the lungs and the measuringsystem. The measured volume tends to increase and the measured pressuretends to decrease, both of which act to increase compliance. Compliance is oftenplotted on a pressure–volume graph where it will be represented by the gradient ofthe line at any given point.

Resistance

Thepressure changeper unit change inflow. (cmH2O.l−1.sec−1 or kPa.l−1.sec−1)

Lung resistance

When adding resistances, they are added as normal integers (as with electricalresistance)

Total resistance = Chest wall resistance + lung resistance


Time constant of a lung unit

The product of compliance and resistance, and a measure of how quickly alung unit will fill or empty.Time constant (τ, sec) = Compliance (l.cmH2O

−1) x Resistance (cmH2O.l−1.sec−1)orThe time taken for the lung unit to inflate 63% of its volume. (See timeconstant definition – Section 1)

You will see that the units of compliance and resistance cancel each other out,except for seconds. A lung unit with a long time constant will have either a highcompliance or resistance and will fill and empty slowly. Conversely, a unit with ashort time constant will have a low resistance or compliance and will empty or fillrelatively quickly. For a given pressure this results in units with long time constantshaving larger volumes and short time constants having smaller volumes. In realitythe lung comprises of units with many different time constants, which results in avariety of filling and emptying velocities and volumes. The impact of disease on thetime constant of lung units is important to consider. For example the decreasedcompliance in ARDS results in a short time constant, whereas the increasedresistance in asthma leads to a longer time constant.

Whole lung pressure–volume loop

This graph can be used to explain a number of different aspects of compliance.The axes as shown are for spontaneous ventilation as the pressure is negative.The curve for compliance during mechanical ventilation looks the same but thex axis should be labelled with positive pressures. The largest curve should bedrawn first to represent a vital capacity breath.

Inspiration The inspiratory line is sigmoid and, therefore, initially flat asnegative pressure is needed before a volume change will take place. The mid

Compliance and resistance 237


segment is steepest around FRC and the end segment is again flat as the lungsare maximally distended and so poorly compliant in the face of furtherpressure change.

Expiration The expiratory limb is a smooth curve. At high lung volumes, thecompliance is again low and the curve flat. The steep part of the curve isaround FRC as pressure returns to baseline.

Tidal breath To demonstrate the compliance of the lung during tidal ven-tilation, draw the dotted curve. This curve is similar in shape to the first butthe volume change is smaller. It should start from, and end at, the FRC bydefinition.

Regional differences You can also demonstrate that alveoli at the top of thelung lie towards the top of the compliance curve, as shown by line A. Theyare already distended by traction on the lung from below and so are lesscompliant for a given pressure change than those lower down. Alveoli at thebottom of the lung lie towards the bottom of the curve, as shown by lineB. For a given pressure change they are able to distend more and so theircompliance is greater. With mechanical ventilation, both points move downthe curve, resulting in the upper alveoli becoming more compliant.



Section 8Cardiovascular physiology



Einthoven’s triangle and axis

Willem Einthoven was a Dutch doctor who invented the first ECG. Current ECGterminology still reflects his work. Einthoven’s triangle is an imaginary trianglemade up of three vectors which we call leads I, II and III on a modern ECG.

Einthoven’s triangle

If electrodes are attached to the right arm (RA), left arm (LA), and left leg (LL) thenthey create three virtual leads that can measure potential difference across themyocardium.

The cross in the middle of the triangle represents the axis of vectors arising fromdifferent electrical views of the myocardium. The nomenclature is in degrees asshown with the normal axis lying between 0 and 90°.


Einthoven’s law

I – II + III = 0

On any ECG the total voltage from each lead I, II and III will sum to zero whencombined in this way. The total voltage is the sum of any negative QRS voltagedeflection from the isoelectric line and any positive deflection. So if a waveform hasa Q deflection of −0.2 mV from the isoelectric line and an R deflection of +1.0 mVthen the total voltage is read is +0.8 mV.

If the total voltage of lead II is −1.0 mV then lead III must be:

(+0.8) – (−1.0) + III = 0

III = 0 – (+0.8) + (−1.0)

III = +0.2 mV

Axis

The normal ECG axis is 0 to 90° on the above diagram. This is because the vectorsare weighted towards potential difference arising from the muscular left ventricle.

Axis determination

Lead I and aVF may be used to quickly determine the axis.

Lead I points left to tight across the myocardium. If it shows mainly positivedeflection on the ECG the axis will lie on the positive (right) side of the circle. LeadaVF points top to bottom across the myocardium in a direction perpendicular tolead I. If it shows mainly positive deflection on the ECG the axis will lie on thepositive (bottom) side of the circle. The axis, by default, must lie somewhere in thedarker shaded (normal) quadrant to satisfy both these conditions.

242 Section 8 � Cardiovascular physiology


Axis Lead I Lead aVF Other

Normal axis Positive PositiveLeft axis deviation Positive Negative Check lead II

Positive – Normal axisNegative – LAD

Right axis deviation Negative PositiveIntermediate axis Negative Negative

Einthoven’s triangle and axis 243


Cardiac action potentials

General definitions relating to action potentials are given in Section 9. This sectiondeals specifically with action potentials within the cardiac pacemaker cells andconducting system.

Pacemaker action potential

Phase 0 Spontaneous ‘baseline drift’ results in the threshold potential beingachieved at – 40 mV. Slow L-type Ca2+ channels are responsible for furtherdepolarization so you should ensure that you demonstrate a relativelyslurred upstroke owing to slow Ca2+ influx.

Phase 3 Repolarization occurs as Ca2+ channels close and K+ channels open.Efflux of K+ from within the cell repolarizes the cell fairly rapidly comparedwith Ca2+-dependent depolarization.

Phase 4 Hyperpolarization occurs before K+ efflux has completely stoppedand is followed by a gradual drift towards threshold (pacemaker) potential.This is reflects a Na+ leak, T-type Ca2+ channels and a Na+/Ca2+ pump,which all encourage cations to enter the cell. The slope of your line duringphase 4 is altered by sympathetic (increased gradient) and parasympathetic(decreased gradient) nervous system activity.


Cardiac conduction system action potential

Phase 0 Rapid depolarization occurs after threshold potential is reachedowing to fast Na+ influx. The gradient of this line should be almost verticalas shown.

Phase 1 Repolarization begins to occur as Na+ channels close and K+ chan-nels open. Phase 1 is short in duration and does not cause repolarizationbelow 0 mV.

Phase 2 A plateau occurs owing to the opening of L-type Ca2+ channels,which offset the action of K+ channels and maintain depolarization. Duringthis phase, no further depolarization is possible. This is an important point todemonstrate and explains why tetany is not possible in cardiac muscle. Thistime period is the absolute refractory period (ARP). The plateau should notbe drawn completely horizontal as repolarization is slowed by Ca2+ channelsbut not halted altogether.

Phase 3 The L-type Ca2+ channels close and K+ efflux now causes repolari-zation as seen before. The relative refractory period (RRP) occurs duringphases 3 and 4.

Phase 4 The Na+/K+ pump restores the ionic gradients by pumping 3 Na+ outof the cell in exchange for 2 K+. The overall effect is, therefore, the slow loss ofpositive ionic charge from within the cell.

Cardiac action potentials 245


The cardiac cycle

The key point of the cardiac cycle diagram is to be able to use it to explain the flowof blood through the left side of the heart and into the aorta. An appreciation of thetiming of the various components is, therefore, essential if you are to draw anaccurate diagram with which you hope to explain the principle.

Cardiac cycle diagram

Timing reference curves

Electrocardiography It may be easiest to begin with an ECG trace. Make surethat the trace is drawn widely enough so that all the other curves can beplotted without appearing too cramped. The ECG need only be a stylizedrepresentation but is key in pinning down the timing of all the other curves.

Heart sounds Sound S1 occurs at the beginning of systole as the mitral andtricuspid valves close; S2 occurs at the beginning of diastole as the aortic andpulmonary valves close. These points should be in line with the beginning ofelectrical depolarization (QRS) and the end of repolarization (T), respec-tively, on the ECG trace. The duration of S1 matches the duration ofisovolumic contraction (IVC) and that of S2 matches that of isovolumicrelaxation (IVR). Mark the vertical lines on the plot to demonstrate this fact.


Pressure curves

Central venous pressure (CVP) The usual CVP trace should be drawn on ata pressure of 5–10 mmHg. The ‘c’ wave occurs during IVC owing to bulgingof the closed tricuspid as the ventricle begins to contract. The ‘y’ descentoccurs immediately following IVR as the tricuspid valve opens and allowsfree flow of blood into the near empty ventricle.

Left Ventricle (LV) A simple inverted ‘U’ curve is drawn that has its baselinebetween 0 and 5 mmHg and its peak at 120 mmHg. During diastole, itspressure must be less than that of the CVP to enable forward flow. It onlyincreases above CVP during systole. The curve between points A and Bdemonstrates why the initial contraction is isovolumic. The LV pressure isgreater than CVP so the mitral valve must be closed, but it is less than aorticpressure so the aortic valve must also be closed. The same is true of the curvebetween points C and D with regards to IVR.

Aorta A familiar arterial pressure trace. Its systolic component follows theLV trace between points B and C at a slightly lower pressure to enableforward flow. During IVR, closure of the aortic valve and bulging of thesinus of Valsalva produce the dicrotic notch, after which the pressure falls toits diastolic value.

The cardiac cycle 247


Important timing points

A Start of IVC. Electrical depolarization causes contraction and the LVpressure rises above CVP. Mitral valve closes (S1).

B End of IVC. The LV pressure rises above aortic pressure. Aortic valveopens and blood flows into the circulation.

C Start of IVR. The LV pressure falls below aortic pressure and the aorticvalve closes (S2).

D End of IVR. The LV pressure falls below CVP and the mitral valve opens.Ventricular filling.

The cardiac cycle diagram is sometimes plotted with the addition of a curve toshow ventricular volume throughout the cycle. Although it is a simple curve, it canreveal a lot of information.

Left ventricular volume curve

This trace shows the volume of the left ventricle throughout the cycle. Theimportant point is the atrial kick seen at point a. Loss of this kick in atrialfibrillation and other conditions can adversely affect cardiac function throughimpaired LV filling. The maximal volume occurs at the end of diastolic fillingand is labelled the left ventricular end-diastolic volume (LVEDV). In the sameway, the minimum volume is the left ventricular end-systolic volume (LVESV).The difference between these two values must, therefore, be the stroke volume(SV), which is usually 70 ml as demonstrated above. The ejection fraction (EF)is the SV as a percentage of the LVEDV and is around 60% in the diagramabove.



Electrocardiographic changes

Underlying pathophysiological processes may present themselves as a change inthe pattern of the ECG trace. An understanding of what these changes mayrepresent will be valuable both for the examination and for your professionalpractice.

Hypokalaemia

The ECG changes seen with progressive hypokalaemia include increasedamplitude and width of the P wave (A), prolongation of the PR interval (B),ST segment depression with associated flattening or inversion of the T wave (C)and prominent U waves (D). Changes are usually only seen with markedhypokalaemia below 2.7 mmol.l−1. Further reduction in serum potassiumconcentration lead to arrhythmias including ventricular tachycardia andTorsades de Pointes which can be fatal.

Hyperkalaemia


Many of the changes of hyperkalaemia are the inverse of those seen withhypokalaemia. The P wave broadens, reduces in amplitude and may disappear(A), the PR interval is prolonged (B), the QRS complex broadens and maybecome bizarre in its morphology (C) and the T waves become tall and tented(D). The T wave changes are the most sensitive to hyperkalaemia and tend tooccur first at a serum potassium concentration of over 5.5 mmol.l−1. Otherchanges develop as the severity of the hyperkalaemia worsens with the pre-terminal finding of a ‘sine wave’ ECG leading to death from asytole, ventricularfibrillation or PEA.

Hypocalcaemia / Long QT syndrome

The corrected QT interval (QTc) is taken as the time between the beginning ofthe QRS complex and the end of the T wave, it is less than 440 ms in men and460 ms in women. Severe hypocalcaemia (less than 1.9 mmol.l−1) may cause aprolongation of the QTc (A) as may some medications. A QTc greater than500 ms is associated with an increased risk of Torsades de Pointes arrhythmia.

Torsades de Pointes

Torsades de Pointes is a relatively rare subgroup of the polymorphic ventriculartachycardias (VT) that occurs only in the context of pre-existing QTc prolon-gation. Polymorphic VT simply denotes that there are multiple foci of electricalactivity within the ventricle that result in QRS complexes of varying amplitudeand axis. Torsades de Pointes has a characteristic morphology which isdescribed as ‘twisting’ around the isoelectric line. Diagnosis allows specifictreatment (magnesium or overdrive pacing) to be instigated prior to degener-ation into ventricular fibrillation.



Digoxin effect

Digoxin effect is seen at therapeutic levels and is a separate phenomenon to theECG findings of digoxin toxicity. The effect of digoxin is to cause down-slopingST segment depression (A) with flattened or inverted T waves (B) and thedevelopment of U waves (C) that together give the characteristic ‘reverse tick’sign. It is the shortening of both atrial and ventricular refractory periods thatleads to the repolarization abnormalities that underlie these changes. In digoxintoxicity there is a combination of increased automaticity due to increasedintracellular Ca2+ and a profound AV conduction block. These typically leadto an underlying atrial tachyarrhythmia such as atrial fibrillation with a slowventricular response.

Hypothermia

Hypothermia is defined as a core body temperature of less than 35°C. The ECGfeatures tend to become more marked with increasing severity of hypothermia.Initially, shivering artefact and bradycardia are common findings. With afurther reduction in core temperature prolongation of the PR (A), QRS (B)and QT (D) intervals may be seen along with the development of arrhythmiasor Osborn waves (also called J waves). Osborn waves are a positive deflectionoccurring at the J point (C) with an amplitude proportional to the severity ofthe hypothermia. At very low temperatures (below 30°C) theymay be of greateramplitude than the QRS complex.

Electrocardiographic changes 251


1st degree heart block

First degree heart block is present when the PR interval measures greater than200 ms (A). When marked block is present the P wave (B) can be ‘lost’ withinthe preceding T wave.

2nd degree heart block, Mobitz I (Wenckebach Phenomenon)

In this form of second degree heart block there is a progressive prolongation ofthe PR interval (A-C) until conduction fails and a QRS complex is missed (D).The rhythm is usually benign and requires no treatment.

2nd degree heart block, Mobitz II

In this form of heart block there is a fixed conduction abnormality withoutprogressive prolongation of the PR interval so that only a certain ratio of Pwaves lead to conduction. This ratio may be variable or fixed. In the illustrationabove there is a fixed 3:1 ratio with three P waves (P1-P3) for each QRScomplex conducted (Q1). Unlike Mobitz I second degree heart block, Mobitz



II block has a much stronger association with haemodynamic instability,bradycardia or progression to complete heart block and pacemaker insertionis mandated.

Complete heart block

In this type of block, none of the atrial impulses are conducted to the ventricleand cardiac output is maintained only by ventricular escape beats or junctionalrhythm. Although both regular, the P waves (arrows) and QRS complexes areindependent of each other and there is a high risk of ventricular standstill andsudden cardiac death. Patients require temporary followed by permanentpacing.

Electrocardiographic changes 253


Pressure and flow calculations

Mean arterial pressure

MAP ¼ SBPþ ð2DBPÞ3

or

MAP = DBP + (PP/3)

MAP is mean arterial pressure, SBP is systolic blood pressure, DBP is diastolicblood pressure and PP is pulse pressure.

Draw and label the axes as shown. Draw a sensible looking arterial waveformbetween values of 120 and 80 mmHg. The numerical MAP given by the aboveequations is 93 mmHg, so mark your MAP line somewhere around this value.The point of the graph is to demonstrate that the MAP is the line which makesarea A equal to area B

Coronary perfusion pressure

Themaximum pressure of the blood perfusing the coronary arteries (mmHg).orThe pressure difference between the aortic diastolic pressure and theLVEDP (mmHg).So

CPP = ADP − LVEDP

CPP is coronary perfusion pressure and ADP is aortic diastolic pressure.


Coronary blood flow

Coronary blood flow reflects the balance between pressure and resistance

CBF ¼ CPPCVR

CBF is coronary blood flow, CPP is coronary perfusion pressure and CVR iscoronary vascular resistance.

Coronary perfusion pressure is measured during diastole as the pressure gradientbetween ADP and LVEDP is greatest during this time. This means that CBF is alsogreatest during diastole, especially in those vessels supplying the high-pressure leftventricle. The trace below represents the flow within such vessels.

Draw and label two sets of axes so that you can show waveforms for both aorticpressure and coronary blood flow. Start bymarking on the zones for systole anddiastole as shown. Remember from the cardiac cycle that systole actually beginswith isovolumic contraction of the ventricle. Mark this line on both graphs.Next plot an aortic pressure waveform remembering that the pressure does notrise during IVC as the aortic valve is closed at this point. A dicrotic notchoccurs at the start of diastole and the cycle repeats. The CBF is approximately100 ml.min−1.100 g−1 at the end of diastole but rapidly falls to zero during IVCowing to direct compression of the coronary vessels and a huge rise in intra-ventricular pressure. During systole, CBF rises above its previous level as theaortic pressure is higher and the ventricular wall tension is slightly reduced.The shape of your curve at this point should roughly follow that of the aorticpressure waveform during systole. The key point to demonstrate is that it is notuntil diastole occurs that perfusion rises substantially. During diastole,

Pressure and flow calculations 255


ventricular wall tension is low and so the coronaries are not directly com-pressed. In addition, intraventricular pressure is low and aortic pressure is highin the early stages and so the perfusion pressure is maximized. As the rightventricle (RV) is a low-pressure/tension ventricle compared with the left, CBFcontinues throughout systole and diastole without falling to zero. Right CBFranges between 5 and 15 ml. min−1. 100 g−1. The general shape of the trace isotherwise similar to that of the left.



Central venous pressure

The central venous pressure is the hydrostatic pressure generated by theblood in the great veins. It can be used as a surrogate of right atrial pressure(mmHg).

The CVP waveform should be very familiar to you. You will be expected to be ableto draw and label the trace below and discuss how the waveform may change withdifferent pathologies.

Central venous pressure waveform

The a wave This is caused by atrial contraction and is, therefore, seen beforethe carotid pulsation. It is absent in atrial fibrillation and abnormally large ifthe atrium is hypertrophied, for example with tricuspid stenosis. ‘Cannon’waves caused by atrial contraction against a closed tricuspid valve would alsooccur at this point. If such waves are regular they reflect a nodal rhythm, andif irregular they are caused by complete heart block.

The c wave This results from the bulging of the tricuspid valve into the rightatrium during ventricular contraction.

The v wave This results from atrial filling against a closed tricuspid valve.Giant v waves are caused by tricuspid incompetence and these mask the ‘x’descent.

The x descent The fall at x is caused by downward movement of the heartduring ventricular systole and relaxation of the atrium.

The y descent The fall at y is caused by passive ventricular filling afteropening of the tricuspid valve.


Pulmonary capillary wedge pressure

The pulmonary capillary wedge pressure (PCWP), also known as the pulmonaryartery occlusion pressure (PAOP), is an indirect estimate of left atrial pressure. Acatheter passes through the right side of the heart into the pulmonary vessels andmeasures changing pressures. After the catheter has been inserted, a balloon at itstip is inflated, which helps it to float through the heart chambers. It is possible tomeasure all the right heart pressures and the PCWP. The PCWP should ideally bemeasured with the catheter tip in west zone 3 of the lung. This is where thepulmonary artery pressure is greater than both the alveolar pressure and pulmo-nary venous pressure, ensuring a continuous column of blood to the left atriumthroughout the respiratory cycle. The PCWPmay be used as a surrogate of the leftatrial pressure and, therefore, LVEDP. However, pathological conditions mayeasily upset this relationship.

Pulmonary capillary wedge pressure waveform

Chamber

Right atrium (RA) The pressure waveform is identical to the CVP. Thenormal pressure is 0–5 mmHg.

Right ventricle (RV) The RV pressure waveform should oscillate between0–5 mmHg and 20–25 mmHg.

Pulmonary artery (PA) As the catheter moves into the PA, the diastolicpressure will increase owing to the presence of the pulmonary valve. Normal


PA systolic pressure is the same as the RV systolic pressure but the diastolicpressure rises to 10–15 mmHg.

PCWP This must be lower than the PA diastolic pressure to ensure forwardflow. It is drawn as an undulating waveform similar to the CVP trace. Thenormal value is 6–12 mmHg. The values vary with the respiratory cycle andare read at the end of expiration. In spontaneously ventilating patients, thiswill be the highest reading and in mechanically ventilated patients, it will bethe lowest. The PCWP is found at an insertion length of around 45 cm.

Pulmonary capillary wedge pressure 259


The Frank–Starling relationship

Before considering the relationship itself, it may be useful to recap on a few of thesalient definitions.

Cardiac output

CO = SV × HR

where CO is cardiac output, SV is stroke volume and HR is heart rate.

Stroke volume

Thevolumeofbloodejected fromthe left ventriclewithevery contraction (ml).

Stroke volume is itself dependent on the prevailing preload, afterload andcontractility.

Preload

The initial length of the cardiac muscle fibre before contraction begins.

This can be equated to the end-diastolic volume and is described by the Frank–Starling mechanism. Clinically it is equated to the CVP when studying the RV orthe PCWP when studying the LV.

Afterload

The tension which needs to be generated in cardiac muscle fibres beforeshortening will occur.

Although not truly analogous, afterload is often clinically equated to the systemicvascular resistance (SVR).

Contractility

The intrinsic ability of cardiac musclefibres to doworkwith a given preloadand afterload.

Preload and afterload are extrinsic factors that influence contractility whereasintrinsic factors include autonomic nervous system activity and catecholamineeffects.


Frank–Starling law

The strength of cardiac contraction is dependent upon the initial fibrelength.

Normal The LVEDP may be used as a measure of preload or ‘initial fibrelength’. Cardiac output increases as LVEDP increases until a maximum isreached. This is because there is an optimal degree of overlap of the musclefilaments and increasing the fibre length increases the effective overlap and,therefore, contraction.

Inotropy Draw this curve above and to the left of the ‘normal’ curve. Thispositioning demonstrates that, for any given LVEDP, the resultant cardiacoutput is greater.

Failure Draw this curve below and to the right of the ‘normal’ curve.Highlight the fall in cardiac output at high LVEDP by drawing a curve thatfalls back towards baseline at these values. This occurs when cardiac musclefibres are overstretched. The curve demonstrates that, at any given LVEDP,the cardiac output is less and the maximum cardiac output is reduced, andthat the cardiac output can be adversely affected by rises in LVEDP whichwould be beneficial in the normal heart.Changes in inotropy will move the curve up or down as described above.Changes in volume status will move the status of an individual heart alongthe curve it is on.

The Frank–Starling relationship 261


Venous return and capillary dynamics

Venous return

Venous return will depend on pressure relations:

VR ¼ MSFP� RAPð ÞRven

� 80

where VR is venous return, MSFP is mean systemic filling pressure, RAP isright atrial pressure and Rven is venous resistance.

The MSFP is the weighted average of the pressures in all parts of the systemiccirculation.

Draw and label the axes as shown. Venous return depends on a pressuregradient being in place along the vessel. Consider the situation where thepressure in the RA is was equal to the MSFP. No pressure gradient exists andso no flow will occur. Venous return must, therefore, be zero. This wouldnormally occur at a RAP of approximately 7 mmHg. As RAP falls, flowincreases, so draw your middle (normal) line back towards the y axis in a linearfashion. At approximately −4 mmHg, the extrathoracic veins tend to collapseand so a plateau of venous return is reached, which you should demonstrate.Lowering the resistance in the venous system increases the venous return and,therefore, the cardiac output. This can be shown by drawing a line with asteeper gradient. The opposite is also true and can similarly be demonstrated onthe graph. Changes in MSFP will shift the intercept of the line with the x axis.


Changes to the venous return curve

The slope and the intercept of the VR curve on the x axis can be altered asdescribed above. Although it is unlikely that your questioning will proceed thisfar, it may be useful to have an example of how this may be relevant clinically.

Increased filling

Construct a normal VR curve as before. Superimpose a cardiac function curve(similar to the Starling curve) so that the lines intercept at a cardiac output of5 l.min−1 and a RAP of 0 mmHg. This is the normal intercept and gives theinput pressure (RAP) and output flow (CO) for a normal ventricle. If MSFP isnow increased by filling, the VR curve moves to the right so that RAP = MSFPat 10 mmHg. The intercept on the cardiac function curve has now changed.The values are unimportant but you should demonstrate that the CO and RAPhave both increased for this ventricle by virtue of filling.

Altered venous resistance

Venous return and capillary dynamics 263


Construct your normal curves as before. This time the patient’s systemic resist-ance has been lowered by a factor such as anaemia (reduced viscosity) or drugadministration (vessel dilatation). Assuming that the MSFP remains the same,which may require fluid administration to counteract vessel dilatation, the COand RAP for this ventricle will increase. Demonstrate that changes in resistancealter the slope of your line rather than the ‘pivot point’ on the x axis.

Capillary dynamics

As well as his experiments on the heart, Starling proposed a physiological explan-ation for fluid movement across the capillaries. It depends on the understanding offour key terms.

Capillary hydrostatic pressure

The pressure exerted on the capillary by a column of whole blood within it(Pc; mmHg).

Interstitial hydrostatic pressure

The pressure exerted on the capillary by the fluid which surrounds it in theinterstitial space (Pi; mmHg).

Capillary oncotic pressure

The pressure that would be required to prevent the movement of wateracross a semipermeable membrane owing to the osmotic effect of largeplasma proteins. (πc; mmHg).

Interstitial osmotic pressure

The pressure that would be required to prevent the movement of wateracross a semipermeable membrane owing to the osmotic effect of inter-stitial fluid particles (πi; mmHg).

Fluid movement

The ratios of these four pressures alter at different areas of the capillary network sothat net fluid movement into or out of the capillary can also change as shown below.

Net filtration pressure = Outward pressures − Inward pressures

= K[(Pc + πi) − (Pi + πc)]

whereK is the capillaryfiltration coefficient and reflects capillarypermeability.



Arteriolar end of capillary

Centre region of capillary

Venular end of capillary

The precise numbers you choose to use are not as important as the concept that,under normal circumstances, the net filtration and absorptive pressures are thesame. Anything which alters these component pressures such as venous conges-tion (Pc increased) or dehydration loss (πc increased) will, in turn, shift the balancetowards filtration or absorption, respectively. You should have some examplesready to discuss.

Venous return and capillary dynamics 265


The above information may also be demonstrated on a graph, which can help toexplain how changes in vascular tone can alter the amount of fluid filtered orreabsorbed.

Draw and label the axes and mark a horizontal line at a pressure of 23 mmHg torepresent the constant πc. Next draw a line sloping downwards from left to rightfrom 35 mmHg to 15 mmHg to represent the falling capillary hydrostaticpressure (Pc). Area A represents the fluid filtered out of the capillary on thearteriolar side and area B represents that which is reabsorbed on the venousside. Normally these two areas are equal and there is no net loss or gain of fluid.

Arrow a This represents a fall in πc; area A, therefore, becomes much largerthan area B, indicating overall net filtration of fluid out of the vasculature.This may be caused by hypoalbuminaemia and give rise to oedema.

Arrow b This represents an increased Pc. If only the arteriolar pressure rises,the gradient of the line will increase, whereas if the venous pressure rises intandem the line will undergo a parallel shift. The net result is again filtration.This occurs clinically in vasodilatation. The opposite scenario is seen inshock, where the arterial pressure at the capillaries drops. This results innet reabsorption of fluid into the capillaries and is one of the compensatorymechanisms to blood loss.

Other features An increase in venous pressure owing to venous congestionwill increase venous hydrostatic pressure. If the pressure on the arterial sideof the capillaries is unchanged, this moves the venous end of the hydrostaticpressure line upwards and the gradient of the line decreases. This increasesarea A and decreases area B, again leading to net filtration.



Ventricular pressure–volume relationship

Graphs of ventricular (systolic) pressure versus volume are very useful tools and canbe used to demonstrate a number of principles related to cardiovascular physiology.

End-systolic pressure–volume relationship

The line plotted on a pressure–volume graph that describes the relationshipbetweenfilling status and systolic pressure for an individual ventricle (ESPVR).

End-diastolic pressure–volume relationship

The line plotted on a pressure–volume graph that describes the relationshipbetweenfilling statusanddiastolic pressure for an individual ventricle (EDPVR).

A–F This straight line represents the ESPVR. If a ventricle is taken and filledto volume ‘a’, it will generate pressure ‘A’ at the end of systole. When filled tovolume ‘b’ it will generate pressure ‘B’ and so on. Each ventricle will have acurve specific to its overall function but a standard example is shown below.Changes in contractility can alter the gradient of the line.

a–f This curve represents the EDPVR. When the ventricle is filled to volume‘a’ it will, by definition, have an end-diastolic pressure ‘a’. When filled tovolume ‘b’ it will have a pressure ‘b’ and so on. The line offers someinformation about diastolic function and is altered by changes in compli-ance, distensibility and relaxation of the ventricle.


Pressure–volume relationship

After drawing and labelling the axes as shown, plot sample ESPVR and EDPVRcurves (dotted). It is easiest to draw the curve in an anti-clockwise directionstarting from a point on the EDPVR that represents the EDV. A normal valuefor EDV may be 120 ml. The initial upstroke is vertical as this is a period ofisovolumic contraction during early systole. The aortic valve opens (AVO) whenventricular pressure exceeds aortic diastolic pressure (80 mmHg). Ejection thenoccurs and the ventricular blood volume decreases as the pressure continues to risetowards systolic (120mmHg) before tailing off. The curve should cross the ESPVRline at a point after peak systolic pressure has been attained. The volume ejectedduring this period of systole is the SV and is usually in the region of 70 ml. Duringearly diastole, there is an initial period of isovolumic relaxation, which is demon-strated as another vertical line. When the ventricular pressure falls below the atrialpressure, the mitral valve opens (MVO) and blood flows into the ventricle soexpanding its volume prior to the next contraction. The area contained within thisloop represents the external work of the ventricle (work = pressure × volume).

Ejection fraction

The percentage of ventricular volume that is ejected from the ventricleduring systolic contraction: (%)

EF ¼ EDV� ESVEDV

� 100

where EF is ejection fraction, EDV is end-diastolic volume, ESV is end-systolic volume and (EDV – ESV) is stroke volume.



Increased preload

Although an isolated increase in preload is unlikely to occur physiologically, it isuseful to have an idea of how such a situation would affect your curve.

Based on the previous diagram, a pure increase in preload will move the EDVpoint to the right by virtue of increased filling during diastole. This will widen theloop and thus increase the stroke work. As a consequence, the SV is alsoincreased. Note that the end systolic pressure (ESP) and the ESV remainunchanged in the diagram above. Under physiological conditions these wouldboth increase, with the effect of moving the whole curve up and to the right.

Increased afterload

Again, increased afterload is non-physiological but it helps with understandingduring discussion of the topic.

Ventricular pressure–volume relationship 269


A pure increase in afterload will move the ESPVR line and thus the ESVpoint to the right by virtue of reduced emptying during systole. Emptying iscurtailed because the ventricle is now ejecting against an increased resist-ance. As such, the ejection phase does not begin until a higher pressure isreached (here about 100 mmHg) within the ventricle. The effect is to create atall, narrow loop with a consequent reduction in SV and similar or slightlyreduced stroke work.

Altered contractility

A pure increase in contractility shifts the ESPVR line up and to the left. TheEDV is unaltered but the ESV is reduced and, therefore, the EF increases. Theloop is wider and so the SV and work are both increased. A reduction incontractility has the opposite effect.



The failing ventricle

Diastolic function depends upon the compliance, distensibility and relaxation ofthe ventricle. All three aspects combine to alter the curve.

Draw and label the axes as shown. Note that the x axis should now containhigher values for volume as this plot will represent a distended failing ventricle.Plot a sample ESPVR and EDPVR as shown. Start by marking on the EDV ata higher volume than previously. Demonstrate that this point lies on theup-sloping segment of the EDPVR, causing a higher diastolic pressure thanin the normal ventricle. Show that the curve is slurred during ventricularcontraction rather than vertical, which suggests that there may be valvularincompetence. The peak pressure attainable by a failing ventricle may be loweras shown. The ESV should also be high, as ejection is compromised and theventricle distended throughout its cycle. The EF is, therefore, reduced (30% inthe above example) as is the stroke work.

Ventricular pressure–volume relationship 271


Systemic and pulmonary vascular resistance

Systemic vascular resistance

The resistance to flow in the systemic circulation against which the leftventricle must contract (dyne.s.cm−5)

Dyne

The force that will give a mass of 1 g an acceleration of 1 cm.s−2

The dyne is, therefore, numerically 1/100 000 of a newton and represents a tiny force.

Equation

Systemic bloodpressure is a functionof vascular resistance and cardiac output:

SBP = CO × SVR

where SBP is systemic blood pressure, CO is cardiac output and SVR issystemic vascular resistance.

This relationship equates to the well-known relationship of Ohm’s law:

V = IR

where SBP is equivalent to V (voltage), CO to I (current) and SVR to R(resistance).

To find resistance the equation must be rearranged as R = V/I or

SVR ¼ ðMAP� CVPÞCO

� 80

whereMAP is mean arterial pressure, CVP is central venous pressure and 80is a conversion factor. This can also be expressed as

SVR ¼ ðMAP� RAPÞCO

� 80

where RAP is right atrial pressure.

A conversion factor of 80 is used to convert from the base units in the equation(mmHg and l.min−1) to the commonly used units of the result (dyne.s.cm−5. It is thepressure difference between input (CVP or RAP) and output (MAP) that is used inthese equations rather than simply SBP. The SVR is usually 1000–1500 dyne.s.cm−5.


Pulmonary vascular resistance

The resistance toflow in the pulmonary vasculature against which the rightventricle must contract (dyne.s.cm−5):

PVR ¼ ðMPAP� LAPÞCO

� 80

where PVR is pulmonary vascular resistance, MPAP is mean pulmonaryartery pressure and LAP is left atrial pressure.

The relationship for pulmonary vascular resistance is very non-linear owing to theeffect of recruitment and distension of vessels in the pulmonary vascular bed inresponse to increased pulmonary blood flow. The PVR is usually around 10 timeslower than the systemic vascular resistance, at 50–150 dyne.s.cm−5.

Systemic and pulmonary vascular resistance 273


The Valsalva manoeuvre

The patient is asked to forcibly exhale against a closed glottis for a period of 10 s.Blood pressure and heart rate are measured. Four phases occur during themanoeuvre. Phase 1 begins at the onset and is of short duration. Phase 2 continuesuntil the end of the manoeuvre. Phase 3 begins as soon as the manoeuvre hasfinished and is of short duration. Phase 4 continues until restoration of normalparameters.

Draw and label all three axes. The uppermost trace shows the sustained rise inintrathoracic pressure during the 10 s of the manoeuvre. Mark the four phaseson as vertical lines covering all three plot areas, so that your diagram can bedrawn accurately.

Curves Draw normal heart rate and BP lines on the remaining two axes. Notethat the BP line is thick so as to represent SBP at its upper border and DBP atits lower border.

Phase 1 During phase 1, the increased thoracoabdominal pressure transi-ently increases venous return, thereby raising BP and reflexly loweringheart rate.

Phase 2 During phase 2, the sustained rise in intrathoracic pressure reducesvenous return VR and so BP falls until a compensatory tachycardia restores it.


Phase 3 The release of pressure in phase 3 creates a large empty venousreservoir, causing BP to fall. Show that the heart rate remains elevated.

Phase 4 The last phase shows how the raised heart rate then initially leads to araised BP as venous return is restored. This is followed by a reflex brady-cardia before both parameters eventually return to normal.

Uses

The Valsalva manoeuvre can be used to assess autonomic function or to terminatea supraventricular tachycardia.

Abnormal responses

Autonomic neuropathy/quadriplegia

There is an excessive drop in BP during phase 2 with no associated overshoot inphase 4. There is no bradycardia in phase 4. The response is thought to be causedby a diminished baroreceptor reflex and so the normal compensatory changes inheart rate do not occur.

Congestive cardiac failure

There is a square wave response that is characterized by a rise in BP during phase 2.This may be because the raised venous pressure seen with this condition enablesvenous return to be maintained during this phase. As with autonomic neuropathy,there is no BP overshoot in phase 4 and little change in heart rate.

The Valsalva manoeuvre 275


Control of heart rate

The resting heart rate of 60–80 bpm results from dominant vagal tone. Theintrinsic rate generated by the sinoatrial (SA) node is 110 bpm. Control of heartrate is, therefore, through the balance of parasympathetic and sympathetic activityvia the vagus and cardioaccelerator (T1–T5) fibres, respectively.

Parasympathetic control

The pathway of parasympathetic control is shown below and acts via both the SAnode and the atrioventricular (AV) node.


Sympathetic control

Sympathetic control is shown below.

Paediatric considerations

In neonates and children the sympathetic system is relatively underdevelopedwhile the parasympathetic supply is relatively well formed. Despite a high restingheart rate in this population, many insults may, therefore, result in profoundbradycardia. The most serious of these insults is hypoxia.

Post-transplant considerations

Following a heart transplant, both sympathetic and parasympathetic innervation islost. The resting heart rate is usually higher owing to the loss of parasympathetictone. Importantly, indirect acting sympathomimetic agents will have no effect. Forexample, ephedrine will be less effective as only its direct actions will alter heartrate. Atropine and glycopyrrolate will be ineffective and neostigmine may slow theheart rate and should be used with caution. Direct acting agents such as adrenaline(epinephrine) and isoprenaline will work and can be used with caution.

Control of heart rate 277


Materno-fetal and neonatal circulations

The examination will require an understanding of the physiological differencesbetween the fetal and adult circulations. The anatomy is quite complicated but itcan be simplified with a schematic diagram. The easiest way to explain the conceptis to describe the passage of a red blood cell through the circulation from theplacenta to the fetus and back.

Fetal circulation

Saturations at various points are shown in hexagonal boxes. Deoxygenatedblood arrives at the placenta via the umbilical arteries (UA), is oxygenated andreturned to the fetus in the umbilical vein (UV). Around 60% blood flowbypasses the liver via the ductus venosus (DV) before streaming with venousblood from the body in the IVC and returning to the LA – via the foramen ovale(FO) – and RA. A tissue flap at the junction of the IVC and RA called theeustachian valve preferentially diverts the more highly oxygenated blood acrossthe FO to the LA. Relatively well-oxygenated blood travels from left heart tohead and neck via the ascending aorta. 90% of blood leaving the right heartpasses directly to the descending aorta via the ductus arteriosus (DA), only 10%enters the lungs due to the high pulmonary vascular resistance (PVR) of thefetus. The aorta supplies blood to the body and venous return to the placentafor oxygenation.


Neonatal circulation

At birth the cessation of placental flow following clamping of the cord isaccompanied by a rapid and dramatic reduction in PVR as breathing com-mences. This reduction in PVR and PA pressure allows more blood to flowthrough the lungs thus increasing the volume of blood (and therefore pressure)in the LA above that of the RA. These changes result in functional closure of theFO so that right heart outflow now passes through the lungs and left heart as inthe adult circulation. The pressure in the aorta increases as the umbilical vesselsare clamped resulting in an increased SVR and reverse flow reverse flow fromthe high pressure aorta to the, now low pressure, pulmonary artery via thepatent ductus arteriosus (PDA).

Adult circulation

By way of contrast, the adult circulation is characterized by the flow of blood inseries through right heart, pulmonary vasculature and left heart. The DV andDA become anatomically closed 2–3 weeks after birth, although functionalclosure happens within hours.

Materno-fetal and neonatal circulations 279


Shock

Definition

A pathophysiological condition in which there is insufficient perfusion tosustain normal function of the vital organs.

Shock can be further classified into five subgroups depending on the causativeinsult. It is important to have a clear understanding of both the cause and treat-ment of each of these types.

Hypovolaemic shock

A state of shock caused by a loss of circulating volume and a subsequentreduction in cardiac preload and cardiac output.

Cardiogenic shock

A state of shock caused bymyocardial dysfunction and a subsequent reduc-tion in systolic function and cardiac output.(Myocardial infarction, valve lesion)

Obstructive shock

A state of shock caused by physical obstruction to filling of the heart with asubsequent reduction in cardiac preload and cardiac output.(Tamponade, pulmonary embolus)

Distributive shock

A state of shock caused by a significant reduction in systemic vascularresistance such that organ perfusion cannot be maintained despite a risein cardiac output.(Septic shock, neurogenic shock)

Cytotoxic shock

A state of shock caused by the uncoupling of tissue oxygen delivery andmitochondrial oxygen uptake.(CO poisoning, CN- poisoning)

The precise treatment of shock will depend upon the cause but all are aimed atimproving oxygen delivery to the tissues and vital organs.


Section 9Renal physiology



Acid–base balance

When considering the topic of acid base balance, there are several key terms withwhich you should be familiar.

Acid

A proton donor. The strength of the acid relates it tendency to donate itsproton: a strong acid dissociates more readily.

Base

A proton acceptor.

Thus acid-base reactions involve the transfer of protons from an acid to a base.

pH

The negative logarithm to the base 10 of the H+ concentration.

Normal hydrogen ion concentration [H+] in the blood is 40 nmol.l−1, giving a pHof 7.4. As pH is a logarithmic function, there must be a 10-fold change in [H+] foreach unit change in pH.

Draw and label the axes as shown. At a pH of 6, 7 and 8, [H+] is 1000, 100 and10 nmol.l−1, respectively. Plot these three points on the graph and join themwith a smooth line to show the exponential relationship between the twovariables.


pKa

The negative logarithm of the dissociation constant.orThe pHatwhich 50%of the drugmolecules are ionized and 50%un-ionized.

The pKa depends upon the molecular structure of the drug and is not related towhether the drug is an acid or a base.

284 Section 9 � Renal physiology


Buffers and the anion gap

Buffer

A substance (or mixture of substances) that minimizes the change in pHthat would otherwise occur when a stronger acid or base is added.

Physiological buffers are often a solution of a weak acid and its conjugate base.They work because the amount of weak acid and base are much greater than theamounts of acid (H+) or base (OH−) added. Examples include the carbonic acid–bicarbonate buffer system (discussed below) and phosphate. Note that the car-bonic acid–bicarbonate system is particularly effective because it is an open systemat both ends, with the body also controlling the amount of carbon dioxide present.Other important buffers include haemoglobin for carbon dioxide (see Haldaneeffect) and plasma proteins.

Isohydric principle

All buffering systems in the body are in equilibrium with each other at asingle point in time. Addition of acid or base will result in changes to all thebuffer systems present as they all contribute to maintenance of acid-basebalance.

Therefore, assessment of any one of these systems provides a reflection of theoverall acid base status. The system conventionally used to assess acid base status isthe carbonic acid–bicarbonate buffer system.

Henderson–Hasselbach equation

The Henderson–Hasselbach equation allows the ratio of ionized:unionized com-pound to be found if the pH and pKa are known. Consider carbonic acid (H2CO3)bicarbonate (HCO3

−) buffer system

CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3−

Note that, by convention, the dissociation constant is labelled Ka (‘a’ for acid) asopposed to KD, which is a more generic term. Although confusing, you should beaware that a difference in terminology exists.


The dissociation constant is given as

Ka ¼ Hþ� HCO�

3

� H2CO3½ �

Taking logarithms gives

log Ka ¼ log Hþ� þ logHCO�

3

� H2CO3½ �

Subtract log [H+] from both sides in order to move it to the left

log Ka � log Hþ� ¼ logHCO�

3

� H2CO3½ �

Next do the same with log Ka in order to move it to the right

–log Hþ� ¼ �logKa þ logHCO�

3

� H2CO3½ �

which can be written as

pH ¼ pKa þ logHCO�

3

� H2CO3½ �

As H2CO3 is not routinely assayed, CO2 may be used in its place. The blood [CO2]is related to the PaCO2 by a factor of 0.23 mmol.l−1.kPa−1 or 0.03 mmol.l−1.mmHg−1. The generic form of the equation states that, for an acid

pH ¼ pKa þ logionized form½ �

un� ionized form½ �

and for a base

pH ¼ pKa þ logun� ionized form½ �

ionized form½ �

The Davenport diagram

The Davenport diagram shows the relationships between pH, PCO2 and HCO3−. It

can be used to explain the compensatory mechanisms that occur in acid–basebalance. At first glance it appears complicated because of the number of lines but ifit is drawn methodically it becomes easier to understand.



After drawing and labelling the axes, draw in the two sets of lines. Thesolid lines are lines of equal PaCO2 and the dashed lines are the bufferlines. Normal plasma is represented by point A so make sure this pointis accurately plotted. The shaded area represents the normal pH andpoints C and E should also lie in this area. The line BAD is the normalbuffer line.

ABC Line AB represents a respiratory acidosis as the PaCO2 has risen from 5.3 to8 kPa. Compensation is shown by line BC, which demonstrates retention ofHCO3

−. The rise in HCO3− from 28 to 38 mmol.l−1 (y axis) returns the pH to

the normal range.AFE Line AF represents a metabolic acidosis as the HCO3

− has fallen.Compensation occurs by hyperventilation and the PaCO2 falls as shown byline FE.

ADE Line AD represents a respiratory alkalosis with the PaCO2 falling to the2.6 kPa line. Compensation is via loss of HCO3

− to normalize pH, as shownby line DE.

AGC Line AG represents a metabolic alkalosis with a rise in HCO3− to

35 mmol.l−1. Compensation occurs by hypoventilation along line GC.

The anion gap

The difference between the serum cation and anion concentrations. It is anartificial, calculated measure that only accounts for the cations and anionspresent in the highest concentrations in the serum.

Buffers and the anion gap 287


Anion gap = ([Na+] + [K+]) – ([Cl−] + [HCO3−])

In daily practice the [K+] is often omitted. A normal anion gap is 10–15 mmol.l−1

due to the presence of unmeasured cations in the serum. The anion gap is used tohelp determine of the cause of a metabolic acidosis and may be divided into‘normal’ or ‘high’.



Glomerular filtration rate andtubulo–glomerular feedback

The balance of filtration at the glomerulus and reabsorption and secretion in thetubules allows the kidneys to maintain homeostasis of extracellular fluid, nutrientsand acid–base balance and to excrete drugs and metabolic waste products.

Glomerular filtration rate

The glomerular filtration rate (GFR) measures the rate at which blood isfiltered by the kidneys.

GFR = Kf (PG − PB − πG)

where Kf is glomerular ultrafiltration coefficient, PG is glomerular hydro-static pressure, PB is Bowman’s capsule hydrostatic pressure and πG is glo-merular oncotic pressure.or

GFR = Clearance

Clearance

The volumeofplasma that is clearedof the substanceper unit time (ml.min−1).

Cx ¼ UxVPx

where C is clearance, U is urinary concentration, V is urine flow and P isplasma concentration.

Clearance is measuredmost accurately using inulin, which is freely filtered and notsecreted, reabsorbed, metabolized or stored, but creatinine is a more practicalsurrogate.

Renal blood flow

Renal blood flow (RBF) is a function of renal plasma flow and the density ofred blood cells.

RBF = RPF/(1 − Haematocrit)

Where RPF is renal plasma flow.


The RPF can be calculated using the same formula as the clearance formula butusing a substance that is entirely excreted; p-aminohippuric acid is usually used.

RBF ¼ RPPRVR

where RPP is renal perfusion pressure and RVR is renal vascular resistance.

This last equation follows the general rule of V = I/R.

Tubulo–glomerular feedback

The process whereby the renal tubules regulate their own blood flow andtherefore the glomerular filtration rate.

The macula densa (a collection of epithelial cells) sits at the junction where thethick ascending limb of the loop of Henle and first part of the distal convolutedtubule meet the angle between the afferent and efferent arterioles. These cells usethe concentration of sodium chloride in the tubular fluid as an indicator of theGFR with a higher concentration indicating a higher GFR. When high levels aredetected, mediators (including adenosine) are released, which cause constrictionof the afferent arteriole and dilatation of the efferent arteriole thus reducing RBFand GFR. The converse is also true. This feedback mechanism occurs withinminutes, therefore maintaining a constant flow in the distal tubule.



Autoregulation and renal vascularresistance

Autoregulation of blood flow

Draw and label the axes as shown. Your line should pass through the origin andrise as a straight line until it approaches 125 ml.min−1. The flattening of thecurve at this point demonstrates the beginning of the autoregulatory range. Youshould show that this range lies between a MAP of 80 and 180 mmHg. At MAPvalues over 180 mmHg, your curve should again rise in proportion to the BP.Note that the line will eventually flatten out if systolic BP rises further, as amaximum GFR will be reached.

Renal vascular resistance

The balance of vascular tone between the afferent and efferent arterioles determinesthe GFR; therefore, changes in tone can increase or decrease GFR accordingly.

Afferent arteriole Efferent arteriole Result

Dilatation Constriction Increased GFRProstaglandins Angiotensin IIKinins Sympathetic stimulationDopamine Atrial natriuretic peptideAtrial natriuretic peptideNitric oxide


Afferent arteriole Efferent arteriole Result

Constriction Dilatation Reduced GFRAngiotensin II Angiotensin II blockadeSympathetic stimulation ProstaglandinsEndothelinAdenosineVasopressinProstaglandin blockade



The loop of Henle

The function of the loop of Henle is to enable production of a concentratedurine. It does this by generating a hypertonic interstitium, which provides agradient for water reabsorption from the collecting duct. This, in turn,occurs under the control of antidiuretic hormone (ADH). There are severalimportant requirements without which this mechanism would not work.These include the differential permeabilities of the two limbs to water andsolutes and the presence of a blood supply that does not dissipate theconcentration gradients produced. This is a simplified description to conveythe principles.

Start by drawing a schematic diagram of the tubule as shown above. Use thenumerical values to explain what is happening to urine osmolarity in eachregion.

Descending limb Fluid entering is isotonic. Water moves out down a con-centration gradient into the interstitium, concentrating the urine within thetubules. Thin ascending limb Fluid entering is hypertonic. The limb isimpermeable to water but ion transport does occur, which causes the urineosmolarity to fall.

Thick ascending limb This limb is also impermeable to water. It contains ionpumps to pump electrolytes actively into the interstitium. The main pump is


the Na+/2Cl−/K+ co-transporter. Fluid leaving this limb is, therefore, hypo-tonic and passes into the distal convoluted tubule.

Collecting duct The duct has selective permeability to water, which is con-trolled by ADH. In the presence of ADH, water moves into the interstitiumdown the concentration gradient generated by the loop of Henle.



Glucose handling

Filtered After drawing and labelling the axes, draw a line passing throughorigin, rising at an angle of approximately 45°. This demonstrates that theamount of glucose filtered by the kidney is directly proportional to theplasma glucose concentration.

Reabsorbed This line also passes through the origin. It matches the ‘filtered’line until 11 mmol.l−1 and then starts to flatten out as it approaches maximaltubular reabsorption (TMAX). Demonstrate that this value is 300 mg.min−1

on the y axis.Excreted Glucose can only appear in the urine when the two lines drawn so

far begin to separate so that less is reabsorbed than is filtered. This happens at11 mmol.l−1 plasma glucose concentration. The line then rises parallel to the‘filtered’ line as plasma glucose continues to rise.


Sodium handling

Sodium concentration graph

PCT is proximal convoluted tubule, DL is descending limb of the loop of Henle,Thin AL is thin ascending limb of the loop of Henle, Thick AL is thick ascendinglimb of the loop of Henle, DCT is distal convoluted tubule and CD is collectingduct. (This figure is reproduced with permission from Fundamental Principles andPractice of Anaesthesia, P. Hutton, G. Cooper, F. James and J. Butterworth.Martin-Dunitz 2002 pp. 487, illustration no. 25.16.)

The graph shows how the concentration of Na+ in the filtrate changes as itpasses along the tubule. An important point to demonstrate is how much of aneffect ADH has on the final urinary [Na+]. Draw and label the axes as shown.The initial concentration should be just below 200 mmol.l−1 The loop of Henleis the site of the countercurrent exchange mechanism so should result in ahighly concentrated filtrate at its tip, 500–600 mol.l−1 is usual. By the end of thethick ascending limb, you should demonstrate that the urine is now hypotonicwith a low [Na+] of approximately 100 mmol.l−1. The presence of maximalADHwill act on the distal convoluted tubule and collecting duct to retain waterand deliver a highly concentrated urine with a high [Na+] of approximately600 mmol.l−1. Conversely, show that in the absence of ADH the urinary [Na+]may be as low as 80–100 mmol.l−1.


Potassium handling

Potassium concentration graph

PCT is proximal convoluted tubule, DL is descending limb of the loop of Henle,Thin AL is thin ascending limb of the loop of Henle, Thick AL is thick ascendinglimb of the loop of Henle, DCT is distal convoluted tubule and CD is collectingduct. (Reproduced with permission from Fundamental Principles and Practice ofAnaesthesia, P. Hutton, G. Cooper, F. James and J. Butterworth. Martin-Dunitz2002 pp. 488, illustration no. 25.17.)

The graph shows how the filtrate [K+] changes as it passes along the tubule.Draw and label the axes as shown. The curve is easier to remember as it staysessentially horizontal at a concentration of approximately 5–10 mmol.l−1 untilthe distal convoluted tubule. Potassium is secreted here along electro-chemicalgradients, which makes it unusual. You should demonstrate that at low urinaryflow rates, tubular [K+] is higher at approximately 100 mmol.l−1 and so less K+

is excreted as the concentration gradient is reduced. Conversely, at higherurinary flow rates (as are seen with diuretic usage) the [K+] may only be70 mmol.l−1 and so secretion is enhanced. In this way, K+ loss from the bodymay actually be greater when the [K+] of the urine is lower, as total loss equalsurine flow multiplied by concentration.



Section 10Neurophysiology



Action potentials

Resting membrane potential

The potential difference present across the cell membrane when no stim-ulation is occurring (mV).

The potential depends upon the concentration of charged ions present,the relative membrane permeability to those ions and the presence ofany ionic pumps that maintain a concentration gradient. The resting mem-brane potential is − 60 to − 90 mV, with the cells being negatively chargedinside.

Action potential

The spontaneous depolarization of an excitable cell in response to astimulus.

Gibbs–Donnan effect

The differential separation of charged ions across a semipermeablemembrane.

The movement of solute across a semipermeable membrane depends upon thechemical concentration gradient and the electrical gradient. Movement occursdown the concentration gradient until a significant opposing electrical potentialhas developed. This prevents further movement of ions and the Gibbs–Donnanequilibrium is reached. This is electrochemical equilibrium and the potentialdifference across the cell is the equilibrium potential. It can be calculated usingthe Nernst equation.

The Nernst equation

E ¼ RTzF

� ln Co½ �C i½ �

where E is the equilibrium potential, R is the universal gas constant, T isabsolute temperature, z is valency and F is Faraday’s constant.


The values for Cl−, Na+ and K+ are − 70, + 60 and − 90 mV, respectively. Note thatthe equation only gives an equilibrium for individual ions. If more than one ion isinvolved in the formation of a membrane potential, a different equation must beused, as shown below.

Goldman constant field equation

E ¼ RTF

� lnNaþ�

O:PNaþ þ Kþ� O:PKþ þ Cl�½ �O:PCl�

� �Naþ�

i:PNaþ þ Kþ� i:PKþ þ Cl�½ �i:PCl�

� �where E is membrane potential, R is the universal gas constant, T is absolutetemperature, F is Faraday’s constant, [X]o is the concentration of given ionoutside the cell, [X]i is the concentration of given ion inside cell and PX is thepermeability of given ion.

Action potentials

You will be expected to have an understanding of action potentials in nerves,cardiac pacemaker cells and cardiac conduction pathways.

Absolute refractory period

The period of time following the initiation of an action potential when nostimulus will elicit a further response (ms).

It usually lasts until repolarization is one third complete and corresponds to theincreased Na+ conductance that occurs during this time.

Relative refractory period

The period of time following the initiation of an action potential when alarger than normal stimulus may result in a response (ms).

This is the time from the absolute refractory period until the cell’s membranepotential is less than the threshold potential. It corresponds to the period ofincreased K+ conductance.

Threshold potential

The membrane potential that must be achieved for an action potential tobe propagated (mV).

302 Section 10 � Neurophysiology


Nerve action potential

Draw and label the axes as shown.

Phase 1 The curve should cross the y axis at approximately – 70 mV andshould be shown to rapidly rise towards the threshold potential of – 55 mV.

Phase 2 This portion of the curve demonstrates the rapid rise in membranepotential to a peak of + 30mV as voltage-gated Na+ channels allow rapid Na+

entry into the cell.Phase 3 This phase shows rapid repolarization as Na+ channels close and K+

channels open, allowing K+ efflux. The slope of the downward curve isalmost as steep as that seen in phase 2.

Phase 4 Show that the membrane potential ‘overshoots’ in a process knownas hyperpolarization as the Na+/K+ pump lags behind in restoring thenormal ion balance.

Cardiac action potential

For cardiac action potentials and pacemaker potentials see Section 8.

Types of neurone

You may be asked about different types of nerve fibre and their function. The tableis complicated but remember that the largest fibres conduct at the fastest speeds. Ifyou can remember some of the approximate values given below it will help topolish your answer.

Action potentials 303


Fibre type Function Diameter (µm) Conduction (m.s −1)

Aα Proprioception, motor 10–20 100Aβ Touch, pressure 5–10 50Aγ Muscle spindle motor 2–5 25Aδ Pain, temperature, touch 2–5 25B (autonomic) Preganglionic 3 10C Pain, temperature 1 1C (sympathetic) Postganglionic 1 1

Velocity calculations

For myelinated nerves

V ∝ d

whereV is the velocity of transmission andd is the diameter of the neurone.

For unmyelinated nerves

V ∝ √d

Neurotransmitter

A chemical synthesized by a neuron which is released when the neuron isstimulated, transmitting a signal across a synapse to a target cell.



Muscle structure and function

Neuromuscular junction

You may be questioned on the structure and function of the neuromuscularjunction and could be expected to illustrate your answer with a diagram. A well-drawn diagram will make your answer clearer.

The diagram shows the synaptic cleft, which is found at the junction of thenerve terminal and the muscle membrane.

Vesicle You should demonstrate that there are two stores of acetylcholine(ACh), one deep in the nerve terminal and one clustered beneath the surfaceopposite the ACh receptors in the so-called ‘active zones’. The deep storesserve as a reserve of ACh while those in the active zones are required forimmediate release of ACh into the synaptic cleft.

ACh receptor These are located on the peaks of the junctional folds of themuscle membrane as shown. They are also found presynaptically on thenerve terminal, where, once activated, they promote migration of AChvesicles from deep to superficial stores.

Acetylcholinesterase (AChE) This enzyme is found in the troughs of thejunctional folds of the muscle membrane and is responsible for metabolizingACh within the synaptic cleft.

Sarcomere

The contractile unit of the myocyte.


You may be asked to draw a diagram of the sarcomere. It is made up of actin andmyosin filaments, as shown below. The thick myosin filaments contain many cross-bridges, which, when activated, bind to the thin actin filaments. Tropomyosinmolecules (containing troponin) run alongside the actin filaments and play animportant role in excitation–contraction coupling.

The diagram should be drawn carefully so that the actin and myosin filamentsare shown to overlap while ensuring that enough space is left between them toidentify the various lines and bands.

Z line The junction between neighbouring actin filaments that forms theborder between sarcomeres. It has a Z-shaped appearance on the diagram.

M line The ‘middle’ zone of the sarcomere, formed from the junction betweenneighbouring myosin filaments. There are no cross-bridges in this region.

A band This band spans the length of the myosin filament although it isconfusingly given the letter A.

I band This band represents the portion of actin filaments that are notoverlapped by myosin. It comes ‘in between’ the Z line and the A band.

Hband This band represents the portion of the myosin filaments that are notoverlapped by actin.

Excitation–contraction coupling

The series of physiological events that link the depolarization of themusclemembrane to contraction of the muscle fibre.

This is a complicated chain of events that can easily cause confusion in theexamination setting. The list below gives a summary of the salient points.

1. The action potential is conducted into muscle fibre by T-tubules.2. Depolarization of the T-tubules results in calcium release from the sarcoplas-

mic reticulum.



3. Calcium-induced Ca2+ release increases the amount of intracellular Ca2+ bypositive feedback.

4. Calcium binds to troponin C on tropomyosin, causing a conformationalchange that exposes myosin-binding sites on actin.

5. Myosin heads energized at the end of the previous cycle, can now bind to actin.6. Binding of myosin to actin triggers pivoting of the myosin head and short-

ening of the sarcomere. This is the powerstroke.7. High concentrations of Ca2+ now cause Ca2+ channel closure.8. Calcium is pumped back into the sarcoplasmic reticulum. This requires

adenosine triphosphate (ATP).9. ATP binds to the myosin cross-bridges, leading to release of the bond between

actin and myosin.10. The ATP is hydrolysed, energizing the myosin ready for the next contraction.11. The muscle relaxes.12. The decreased [Ca2+] causes tropomyosin to resume its previous configura-

tion, blocking the myosin-binding site.

Muscle structure and function 307


Muscle reflexes

There is only one monosynaptic reflex known to exist in humans – the stretchreflex. For this reason, it is commonly examined and an overview of its compo-nents and their functions is given below.

The stretch reflex

A monosynaptic reflex responsible for the control of posture.

Stretching of the muscle is sensed in the muscle spindle and leads to firing inmuscle spindle afferent. These nerves travel via the dorsal root and synapse inthe anterior horn of the spinal cord directly with the motor neurone to thatmuscle. They stimulate firing of the motor neurones, which causes contractionof the muscle that has just been stretched. The muscle spindle afferent alsosynapses with inhibitory interneurons, which inhibit the antagonistic muscles.This is called reciprocal innervation.

Muscle spindles

Stretch transducers encapsulated in the muscle fibre responsible for main-tenance of a constant muscle length despite changes in the load.

Muscle spindles are composed of nuclear bag (dynamic) and chain (static) fibresknown as intrafusal fibres and these are innervated by γ motor neurones.Extrafusal fibres make up the muscle bulk and are innervated by α motor neuro-nes. Stimulation of the muscle spindle leads to increased skeletal muscle con-traction, which opposes the initial stretch and maintains the length of the fibre.This feedback loop oscillates at 10 Hz, which is the frequency of a physiologicaltremor.


In the same way that muscle spindles are responsible for the maintenance ofmuscle length, Golgi tendon organs are responsible for maintenance of muscletension.

Golgi tendon organs

These are found in muscle tendons and monitor the tension in the muscle.Their function is to limit the tension that is generated in the muscle.

Tension is the force that is being opposed by the muscle and is a different conceptto stretch. The reflex can be summarised as below.

Golgi tendon organs are in series with the muscle fibres. They are stimulated byan increase in tension in the muscle, which may be passive owing to musclestretch or active owing to muscle contraction. Stimulation results in increasedfiring in afferent nerve fibres, which causes inhibition of the muscle in question,increasing muscle stretch and, therefore, regulating muscle tension. The antag-onistic muscle is simultaneously stimulated to contract.

All these muscle reflexes are under the control of descending motor pathways andare integrated in the spinal cord.

Muscle reflexes 309


The Monro–Kelly doctrine

The skull is a rigid container of constant volume. TheMonro–Kelly doctrinestates that any increase in the volume of one of its contents must becompensated for by a reduction in volume of another if a rise in intracranialpressure (ICP) is to be avoided.

This volume of the skull comprises three compartments:

� brain (85%)� cerebrospinal fluid (CSF) (10%)� blood (5%).

Compensation for a raised ICP normally occurs in three stages. Initially there is areduction in venous blood volume followed by a reduction in CSF volume andfinally arterial blood volume.

Intracranial volume–pressure relationship

Draw and label the axes as shown. Note that the x axis is usually drawn withoutany numerical markers. Normal intracranial volume is assumed to be at the leftside of the curve and should be in keeping with an ICP of 5–10 mmHg. Draw acurve similar in shape to a positive tear-away exponential. Demonstrate onyour curve that compensation for a rise in the volume of one intracranialcomponent maintains the ICP < 20 mmHg. However, when these limitedcompensatory mechanisms are exhausted, ICP rises rapidly, causing focalischaemia (ICP 20–45 mmHg) followed by global ischaemia (ICP > 45mmHg).

Brain compliance

Compliance is defined as the change in volume for a given change in pressure (seeSection 7). Strictly speaking, where ICP is concerned it is the change in volume thatproduces a change in pressure. If you consider the intracranial volume–pressure


relationship curve, initially small increases in volume have little or no associatedincrease in pressure and thus the brain may be thought of as being compliant.However, as volume increases, small further increases in volume lead to largechanges in pressure and thus brain compliance is reduced. This term is thereforeused to indicate the degree of compensatory reserve before a catastrophic rise inICP occurs.

Intracranial pressure (ICP) waveform

The ICP wave is a modified arterial pressure wave that is transmitted from thelarge cerebral blood vessels throughout the CSF. It is usually measured via anexternal ventricular drain (EVD) placed in the anterior horn of the lateral ven-tricle, or via a subarachnoid bolt for a variety of indications, for example aftersevere traumatic brain injury. The waveform has three components:

� A pulse wave (see diagram below)� A respiratory component, whereby the baseline of the waveform varies with therespiratory cycle

� Slow waves, which are changes in the baseline of the waveform.

Draw and label the axes. Each waveform should have the same duration as anarterial trace, but will lag slightly behind it. You may wish to mark on the upperlimit of normal value for ICP (dotted line). The normal ICP trace consists ofthree peaks or waves of decreasing amplitude.

P1 – Percussive This wave is a result of the transmitted arterial pressurewave.

P2 –Tidal This wave reflects brain compliance and is thought to occur due tothe arterial waveform reflecting off the brain parenchyma. It is usually 80% ofthe amplitude of P1 but its amplitude varies inversely with brain compliance.

The Monro–Kelly doctrine 311


P2 ends with the dicrotic notch, which coincides with closure of the aorticvalve.

P3 – Dicrotic This wave is related to venous pressure and thus its amplitudewill increase as CVP rises.In the non-compliant brain the amplitude of P2 increases to be greater thanP1, with the whole waveform becoming more rounded. The baseline of thewave will also increase as ICP rises.

Changes to baseline of the ICP trace

Slow (Lundberg) waves. These are changes in the baseline of the ICP trace,and are usually indicative of pathology.

A waves Also known as plateau waves, they are characterized by a steep risein the baseline to >50mmHg for 2–20 minutes followed by an abrupt fall tothe previous or lower baseline. They indicate a significant reduction inintracranial compliance and as such are always pathological.

Bwaves Sharply peaked rhythmic oscillations at a frequency of 0.5 to 2 wavesper minute, where ICP rises by 20–30mmHg and then falls to baseline. Theyare associated with an unstable ICP and are possibly the result of cerebralvasospasm.

C waves These oscillations occur at a frequency of 4–8 waves per minute andpeak at 20mmHg. They are thought to be related to changes in systemicvasomotor tone. Although they may be suggestive of raised ICP, they mayalso be a normal finding.

Despite these descriptions of abnormalities in the ICP waveform, ICP monitoringis most commonly used to measure the mean ICP value and to use this to calculateCPP so that it may be optimized.

There has been some work done on defining an index of compensatory reserveknown as the RAP which is the Relationship between the Amplitude of the ICPwaveform and themean ICP (over 1–3minutes). Other brain compliancemonitorsare also in development.



Cerebral blood flow

Cerebral blood flow (CBF)

The amount of blood flow to the brain in a given time. The normal value is50ml.100g−1.min−1.

There are many factors that affect CBF and for some of these the relationship iswell described graphically. The factors can be related to the Hagen Poiseuilleequation for laminar flow described in Section 2. For example, the pressuregradient (ΔP) is the cerebral perfusion pressure (defined below), and the radiusof the blood vessels will be determined by the degree of vasoconstriction ordilatation.

Cerebral perfusion pressure

The pressure gradient driving cerebral blood flow.

CPP = MAP − (ICP + CVP)

where CPP is cerebral perfusion pressure and CVP is central venouspressure.

Often, CVP is left out of this equation as it is normally negligible. In order tomaintain cerebral perfusion when ICP is raised, the MAP must also be elevated.

CPP may also be defined as follows:

CPP = CBF x CVR

Where CVR is cerebral vascular resistance. This is analogous to Ohm’s law.

Autoregulation

The ability of an organ to regulate its blood flow despite changes in itsperfusion pressure.


Autoregulation of cerebral blood flow

Draw and label the axes as shown. Mark the two key points on the x axis(50 and 150mmHg). Between these points, mark a horizontal line at a y value of50 ml.100g−1. min−1. Label this segment the ‘autoregulatory range’. Above thisrange, cerebral blood flow (CBF) will increase as mean arterial pressure (MAP)increases. There will, however, be a maximum flow at some MAP where nofurther increase is possible. Below 50mmHg, CBF falls withMAP; however, theline does not pass through the origin as neither MAP nor flow can be zero inlive patients. Demonstrate the response to chronic hypertension by drawing anidentical curve displaced to the right to show how the autoregulatory range‘resets’ itself under these conditions.

Effects of PaCO2 on cerebral blood flow



Draw and label the axes.

Normal Mark a point at the intersection of a normal Paco2 and cerebralblood flow as shown. As CBF will approximately double with a doubling ofthe Paco2 extend a line from this point up to a Paco2 of around 10 kPa. At theextremes of Paco2 there arise minimum and maximum flows that depend onmaximal and minimal vasodilatation, respectively. The line should, there-fore, become horizontal as shown at these extremes.

Chronic hypercapnoea The curve is identical but shifted to the right of thenormal curve as buffering acts to reset the autoregulatory range.

Effects of Pao2 on cerebral blood flow

Draw and label the axes. Plot a point at a normal Pao2 and CBF as shown.Draw a horizontal line extending to the right of this point. This demonstratesthat for values > 8 kPa on the x axis, CBF remains constant. Below this point,hypoxia causes cerebral vasodilatation and CBF rises rapidly. At flow rates>100 ml.100g−1.min−1, maximal blood flow will be attained and the curve willtail off. Remember that the vasodilatory effect of hypoxia will override any otherreflexes to ensure maximal oxygenation of the brain tissue.

Cerebral blood flow 315


Flow-metabolism coupling

Cerebral metabolic rate of oxygen utilization (CMRO2)

The rate of oxygen consumption by the brain formetabolism. Normal value3.3 ml.100g−1.min−1

Cerebral metabolic rate can also be determined by looking at the rate of glucoseutilization.

Flow-metabolism coupling

The phenomenonwhereby the perfusion to an area of the brain is matchedto the metabolic rate of that area. This may occur locally or globally.

The following graph demonstrates this principle.

Draw and label the axes as above. Mark on the graph the normal values for CBFand CMRO2, 50ml.100g−1min−1 and 3.3ml.100g−1min−1 respectively. Cerebralischaemia and cell death results at a CBF of less than 18–20 ml.100g−1min−1

and thus the line is not continued below this level.


Effect of temperature on cerebral metabolic rate

Draw and label the axes. Note that temperature decreases along the x axis andthe y axis is labelled as a percentage change in temperature from baseline. Therelationship between cerebral metabolic rate and temperature is linear but witha change in gradient of the line at about 27°C. Cerebral metabolic rate falls 7%for every 1°C fall in temperature, so it will be 30% of baseline at 27°. It has alsobeen shown to be about 10% of baseline at 17°C. Using these points, constructthe graph as shown.

The effect of anaesthetic agents on cerebral blood flowand metabolism

Anaesthetic agents have differing effects on CBF and CMR. These can be explainedwith the help of the diagram below.

Flow-metabolism coupling 317


Draw and label the axes as above. As the graph demonstrates the principle ofhow anaesthetic agents affect the coupling between CMRO2 and CBF, it issufficient to simply label the axes as increasing or decreasing values a ratherthan exact numbers. The dashed line represents coupling between CMRO2 andCBF so draw this first. Having done this, mark on the graph where the variousanaesthetic agents lie.

Inhalational anaesthetic agents All these except sevoflurane cause dosedependent vasodilatation which results in an increase in CBF. They alsodecrease CMRO2, uncoupling the flow-metabolism relationship. When con-centrations of 1.5 MAC are reached then cerebral autoregulation is abol-ished. Sevoflurane has minimal vasodilatory effect until a concentration of1.5 MAC is reached. Therefore its position will depend on the concentrationadministered and at concentrations >1.5 MAC it will move directly upwards.Nitrous oxide causes cerebral vasodilatation and thus an increase in CBF andalso increases CMR.

Intravenous agents The intravenous anaesthetic agents, with the exceptionof ketamine, decrease both CMRO2 and CBF and maintain the couplingbetween the two. Ketamine is unusual in that it increases both, but increasesCBF more. Hence it is often avoided in patients whose ICP is known to be ormay be increased.

Opioids Opioids have little effect on cerebral blood flow or metabolismdirectly. However, it is important to remember than they may have indirecteffects due to respiratory depression induced hypercapnia.

Remember that as well as direct vasoactive effects on the cerebral circulation,anaesthetic agents will also influence CBF according to their effect on MAP andthus CPP.



Formation and circulationof cerebrospinal fluid

Formation of cerebrospinal fluid

The choroid plexus in the ventricles of the brain produce CSF at a constant rate of500 ml.day−1 or 0.35 ml.min−1. The total volume of CSF is around 150 ml in theaverage adult. The rate of reabsorption of CSF is proportional to its outflow pressure.

Circulation of cerebrospinal fluid

An understanding of this well-documented circulatory route for CSF will beexpected in the examinations.


Pain

Pain is an unpleasant sensory and/or emotional experience associated withactual or potential tissue damage.

Nociception

The sensation of the noxious stimulus occurring within the brain.

Nociceptive pain

Pain occurring due to stimulation of peripheral sensory nerve fibres thatrespond to potentially harmful stimuli (nociceptors).

Nociceptors may respond to a single harmful stimulus such as a mechanical,chemical or thermal stimulus, or they may respond to a combination of these(polymodal nociceptors). Nociceptive pain may be classified into somatic andvisceral according to the location of the nociceptors. Alternatively it may beclassified according to the cause of the pain, for example, inflammatory orischaemic pain.

Somatic pain

Relatively well localized pain due to activation of peripheral nociceptors.

Somatic pain may be divided into deep or superficial according to the location ofthe structures affected. For example, pain from a broken bone is deep somatic pain,whereas a burn would cause superficial somatic pain.

Visceral pain

Diffuse pain that may be difficult to localize or referred to a superficialstructure which is usually distant to the source of the pain.

Chronic pain

Pain that persists after removal of the stimulus and beyond the normalrecovery period.

Some believe that pain should be present for at least three months in order to be‘chronic’ although most examiners should accept the definition above.


Neuropathic pain

Pain that occurs due to a primary lesion or dysfunction in the nervous systemitself.

The following may be features of neuropathic pain:

Allodynia

A painful response to a normally painless stimulus.

Hyperalgesia

An exaggerated response to a normally painful stimulus.

Primary hyperalgesia occurs within the zone of injury and is caused by changes atthe injury site itself. Secondary hyperalgesia occurs around the zone of injury andresults from neuroplasticity and remodelling.

Hyperpathia

Pain in response to a stimulus despite sensory impairment.

Phantom pain

A type of neuropathic pain that is felt in part of the bodywhich is no longerpresent or from which the brain no longer receives signals.

Plasticity

The ability of the nervous system to adapt or change according to itsenvironment.

The gate control theory of pain

Melzack and Wall theorized that the transmission of a peripheral painful stimulusto the CNS occurs via a gate at spinal cord level. This gate comprises an inhibitoryinterneurone in the substantia gelatinosa that may be either stimulated orinhibited by different afferent inputs. A simple line diagram can be useful whenexplaining the mechanism to avoid confusion.

Pain 321


Neuronal connections

The Aβ fibres are examples of afferents that stimulate inhibitory interneurones(in the substantia gelatinosa (SG)) and, therefore, prevent nociceptive trans-mission to the CNS. The C fibres are examples of afferents that inhibit inhib-itory interneurones and, therefore, enhance nociceptive transmission. Notethat both types of fibre stimulate the second-order neurone (2°) directly butit is the interneurone that modifies the transmission.

Pain pathway

The diagram below shows the pathway of pain transmission from the peripheralnerves to the cerebral cortex. There are three levels of neuronal involvement andthe signals may be modulated at two points during their course to the cerebralcortex. Descending inhibitory pathways arise in the midbrain and pass to thedorsal horn as shown. Multiple different neurotransmitters are involved in thepathway and include gamma-aminobutyric acid (GABA), N-methyl-D-aspartate(NMDA), noradrenaline and opioids.



Section 11Applied sciences



The stress response

Following surgical insult or other trauma there are a complex series of reactionsthat occur in a predictable manner and which have been grouped together intowhat we know as the stress response.

Stress response

The name given to a group of neuro-endocrine andmetabolic changes thatoccur in response to injury or trauma.

The overall effect of these changes is to increase catabolism therefore mobilizingsubstrates to provide energy and to maintain fluid volume via salt and waterretention. In evolutionary terms the stress response was probably a protectiveone, increasing the chances of survival following injury. In current practice theresponse is now felt to be detrimental to recovery and efforts have been made toobtund it where possible.


Pituitary Adrenal Pancreatic Others

Increased secretionGrowth hormone (GH) Catecholamines Glucagon ReninAdrenocorticotrophic hormone

(ACTH)Cortisol

β-Endorphin AldosteroneProlactinAnti diuretic hormone (posterior

pituitary) (ADH)Unchanged secretionThyroid stimulating hormone

(TSH)Luteinizing hormone (LH)Follicle stimulating hormone (FSH)Decreased secretion

Insulin TestosteroneOestrogenTri-iodothyronine (T3)

Overall effects

CarbohydrateHyperglycaemiaIncreased glucose production and reduced utilizationImpaired wound healing and increased infection rates with a blood glucose over

12 mmol.l−1

ProteinInhibition of protein anabolismEnhanced protein catabolism if the response is severe500g per day of lean body mass may be lost from skeletal muscle

LipidsIncreased lipolysisTriglycerides broken down to free fatty acids (FFAs)Ketone body production

Salt and waterRetention of water and salt via ADH

Clinical effects of anaesthesia

Opioids are known to suppress both hypothalamic and pituitary hormone secre-tion although the doses required to fully achieve this (around 50 mcg.kg−1) are

326 Section 11 � Applied sciences


sufficiently large as to be undesirable in everyday practice. Lower doses will have aproportionally lower suppressant effect. Etomidate suppresses corticosteroid pro-duction via its reversible inhibition of 11-β-hydroxylase. An induction dose of0.3 mg.kg−1.min−1 will block the production of aldosterone and cortisol for up to8 h. Clonidine acts centrally to decrease the sympatho-adrenal response to surgery.Although there is no evidence to suggest that regional anaesthesia leads to betteroutcomes, changes in glucose, ACTH, cortisol, GH and adrenaline are allobtunded by regional anaesthesia. Of note however is that cytokine activityseems to remain largely unchanged. Nutrition, minimally invasive surgical tech-nique and maintenance of normothermia all offer some benefit in reducing theseverity of the stress response and should be considered.

The stress response 327


Cardiopulmonary exercise testing

Cardiopulmonary exercise testing (CPET) is a dynamic integrated test of respiratory,cardiac and circulatory function. Its use in anaesthetics is primarily to objectify theassessment of functional capacity in patients about to undergo major surgery. Incontrast to static tests such as echocardiography or pulmonary function tests, CPETallows for an assessment of how the heart, lungs and circulation work together andattempts to mimic the stress that the patient will be put under during the peri-operative phase. The test is usually performed by exercising a patient on a static cyclevia the application of a steadily increasing resistance.

Physiological data are plotted on a standard 9 panel plot and the interpretationof a test relies, in part, on a recognition of certain patterns. Some of the valuesquoted in the literature may be familiar.

Anaerobic threshold

The oxygen uptake occurring at the point when the oxygen requirementsof exercising muscle exceeds supply and energy provision begins to be metby anaerobic metabolic pathways. (AT, ml.kg−1.min−1)

The available evidence seems to suggest that an AT of less than 11 ml.kg−1.min−1

places patients in a high risk category (>18%) for cardiovascular side effectsfollowing major general surgery.

Identifying the AT

The AT is determined graphically by looking at a number of parameters:

V-slope method


Individual VCO2 points are plotted against the corresponding VO2 measurementtaken at that time. There is an inflection point in the graphwhere the production ofCO2 relative to oxygen uptake suddenly increases due to increased CO2 productionfrom anaerobicmetabolism. The inflexion point is theAT and theVO2 at that pointis indexed to body weight to give the AT in the usual units of ml.kg−1.min−1. In theabove example the AT would be around 18 ml.kg−1.min−1 for a 70 kg adult.

VO2 and VCO2 against work rate

Both parameters are plotted against work rate (or occasionally time) to give curvessimilar to those shown. Initially the VCO2 is less than theVO2 at any given point butat the AT the gradient of the VCO2 curve increases as more CO2 is generated by theonset of anaerobic metabolism via lactate. The point just before the curves cross istaken as the AT as this is where the gradient can be shown to have increased suchthat the curves are coming closer together. The work rate at the AT can be read offthe data log to find the corresponding VO2 at that stage.

VE against work rate

Cardiopulmonary exercise testing 329


Ventilation is plotted against work rate (or occasionally time) to give a similarcurve to the V-slope graph. Ventilation rises in a near linear fashion withincreasing work at the early stages of exercise but then increases rapidly atthe AT due to the extra requirement for the respiratory system to clear the CO2

load generated by anaerobic metabolism via lactate. The work rate at the ATcan be read off the data log to find the corresponding VO2 at that stage.

VO2Max

The maximum recorded oxygen uptake during incremental exercise.(ml.min−1, ml.min−1.m−2 or ml.kg−1.min−1)

Technically the VO2Max is only seen if there is a plateau in the oxygen uptake atpeak exercise indicating that the maximum physiological oxygen uptake capacityhas been reached. If no plateau is seen then one can only assume that the value isthe peak obtained during that particular test – on another occasion a higher valuemay be possible – and so it is better termed VO2Peak. The available evidencesuggests that a VO2Max of less than 800 ml.min−1.m−2 is associated with increasedcardiovascular risk (>44%) following oesophagogastric surgery and less than 10ml.kg−1.min−1 is usually prohibitive for lung resection surgery.

Evidence

The evidence base for the use of CPET in predicting outcomes is still in its infancy,although increasing rapidly. There is good evidence for use as a diagnostic tool forcryptogenic dyspnoea, pulmonary hypertension (primary and secondary), inter-stitial lung disease and mitochondrial or neuromuscular disease. It is also used forprognostication and monitoring of heart failure patients and those with knownrespiratory pathology as well as for the monitoring of improvement followingexercise prescription. The predictive value for post surgical complications is lessconvincing, although many agree that it offers objectivity and can help withchoosing the appropriate high care area to use in the post operative phase.



Pregnancy

There are many anatomical and physiological changes that occur in normalpregnancy to support the growth, development and delivery of the fetus.

Timing

The first trimester is the period of most physiological change and is also when thefetus is most at risk from potential teratogens. These early changes are stimulatedby increased production of progesterone and oestrogen by the placenta. From midpregnancy onwards the mechanical effects of an enlarged uterus also have phys-iological consequences. Most of the physiological changes are reversed and returnto pre-pregnancy levels relatively soon after delivery.

Implications of pregnancy by system

Broadly speaking, the changes seen in pregnancy can be divided into those that aidoxygen delivery and support the increase in uterine blood flow, those that protectagainst blood loss at delivery, and those that occur as a consequence of theenlarging uterus.

Cardiovascular

Draw and label the axes as indicated. You may wish to subdivide the graph areainto trimesters (shaded areas).

Cardiac output (50% increase) The majority of the increase in cardiac out-put occurs in the first trimester, with an increase of about 30% by 12 weeks. Itpeaks by 28 weeks at 50%, after which it plateaus. Construct the lineaccordingly. In labour, cardiac output may rise by an additional 45% and


post delivery the auto-transfusion of blood that occurs with uterine contrac-tion may cause a further increase. Therefore, women with pre-existingcardiac disease are likely to decompensate relatively early in the pregnancy,in labour or post delivery. (Note that some studies have shown a decrease incardiac output in the third trimester but it is thought that this did notaccount for aortocaval compression.)

Stroke volume (35% increase) The majority of the early increase in cardiacoutput is due to an increase in stroke volume, so draw this line with a steeperincline in the first trimester and then a gentler slope up to 35% at 28 weeks,when it plateaus.

Heart rate (25% increase) This can be thought of as the opposite to thestroke volume increase: a gentle upslope initially and then a steeper rise inthe second trimester, which accounts for the later increase in cardiac output.

Other changes

Decreased SVRReduced systolic (10%) and diastolic (20%) blood pressureUpward/leftward displacement of the heartECG changes include LAD, ST depression, T wave flatteningRisk of aorto-caval compression when supine

Haematology

Physiological anaemia of pregnancy.

Draw and label the axes, noting that the y axis extends to -10%.

RBC volume (20% increase) This does not start to increase until after10 weeks gestation. In fact, it drops in early pregnancy and is back at thepre-pregnancy level at the end of the first trimester, after which it increases



steadily to term. With iron supplementation, this increase in RBC volume isgreater.

Plasma volume (45% increase) This increases from about 6 weeks in preg-nancy and is about 15% above pre-pregnancy values at the end of the firsttrimester. It continues to rise to a peak of a 45% increase at about 32 weeksand then it plateaus.

The discrepancy between the increases in RBC volume and plasmavolume explain the physiological anaemia of pregnancy. The maximal differ-ence between the 2 lines should be between 30–32 weeks to reflect when theanaemia is at its most pronounced.

Other haematological changes

Increased white cell countIncrease in fibrinogen and all clotting factors except XI and XIIIPossible decreased platelet count despite increased production, due to increasedactivity and consumption

Normal laboratory tests of coagulationReduced fibrinolysis

Respiratory

The changes in the lung volumes can be shown using the diagram below.

Draw and label the axes as above. You may wish to indicate that cranialdisplacement of the diaphragm occurs when you draw the x axis. Then drawa spirometry trace as described in Section 7. The reduction in functionalresidual capacity (FRC) of 20% results in a decrease in both the residual volume(RV) and expiratory reserve volume (ERV). This will cause more rapid desatu-ration as pre-oxygenation will be less effective (as well as oxygen consumption

Pregnancy 333


being increased). Tidal volume (TV) is increased by 35% and thus the inspir-atory reserve volume (IRV) and vital capacity (VC) are unchanged. Total lungcapacity (TLC) is slightly reduced.

The ventilatory changes in pregnancy may also be explained using a diagram.

Draw and label the axes and divide the graph into trimesters.

Respiratory rate The increase of 15% in respiratory rate occurs in the firsttrimester and is stimulated by progesterone mediated CO2 hypersenstivity.Thereafter the respiratory rate plateaus.

Tidal volume Tidal volume increases rapidly in the first trimester and thensteadily to term, when it has increased by 35%.

Ventilation The increase in respiratory rate and tidal volume lead to an increaseinminute ventilation. However, as dead space is unchanged, alveolar ventilationis increased proportionallymore, hence the divergence of theminute ventilation(max 50% increase) and alveolar ventilation (max 70% increase) lines.

Other respiratory changes

Reduced chest wall complianceReduced PACO2 (4.3kPa) causing a mild respiratory alkalosis (pH 7.44)Increased 2, 3 DPG (shifts the P50 from 3.5 kPa to 4 kPa)Airway mucosal oedemaIncreased breast size may impede intubation

Renal and Acid-Base

Increased renal plasma flow and GFR (50%)Increased clearance of urea and creatinine result in lower plasma levels



Mild glycosuria and proteinuria may be seen in normal pregnancyReduced plasma osmolalityIncreased bicarbonate excretion counteracts the respiratory alkalosis

Endocrine and Metabolic

Increase in size of pituitary glandIncrease in thyroid binding globulin, thyroxine and triiodothyronine but freethyroxine index unchanged

Increased insulin production, but this is outweighed by increased insulin resist-ance. (Insulin does not cross the placenta)

Maternal hyperglycaemia will lead to increased fetal insulin production andpotential neonatal hypoglycaemia

Increased oxygen consumption and carbon dioxide production (by 60% atterm)

Gastrointestinal and Hepatic

Cephalad displacement of stomach and intestineIncreased intra-gastric pressure and reduced lower oesophageal sphincter tonelead to increased likelihood of reflux

Delayed gastric emptying in labourMildly elevated GGT, ALT, AST, LDH may occur in normal pregnancyElevated ALP (x3) due to placental productionGallstones more commonReduced protein synthesis (25%)

Neurological

Reduced volume of the epidural space due to epidural vein engorgementIncreased sensitivity to opioids and sedatives

Pharmacokinetics

Increased volume of distribution results in a prolonged elimination half life formany drugs

Reduced plasma cholinesterase levels

Pharmacodynamics

Reduction in MACAltered response to other drugs. (For example, the dose of thiopentone requiredin early pregnancy has been shown to be reduced)

Pregnancy 335


Placenta

Uterine perfusion increases to 10% of cardiac output with uterine blood flow(UBF) increasing from 50 ml.min−1 to 700ml.min−1

Uterine blood flow: UBF � ðUAP� UVPÞUVR

Where UAP is uterine artery pressure, UVP is uterine venous pressure and UVR isuterine vascular resistance

A reduction in maternal blood pressure (reducing UAP) or an increase in UVPor UVR will lead to a reduction in UBF, which is not auto-regulated, unlike bloodflow to other organs

Drug transfer across the placenta occurs by diffusion, obeying Fick’s law ofdiffusion (see Section 2). The principles of drug transfer across a lipid membranealso apply (see Distribution in Section 6)



Paediatrics

The legal definition of a child is up to the age of 16 years. This period may besubdivided as follows:

Neonate: Up to the age of 28 days (or 44 weeks post conception)Infant: 28 days to 1 yearChild: 1–12 yearsAdolescent: 13–16 years

Implications of paediatrics by system

The most pronounced physiological differences between children and adults areobviously seen in neonates. In adults, physiological systems are designed tomaintain homeostasis. In children they have the added task of facilitating growth.The rate of growth declines as the child ages and the differences between childrenand adults reduce. Most of the differences listed below are therefore features ofneonates.

Respiratory system

Relatively large head and tongue and short neckPreferential nasal breathingAnterior larynx with long epiglottisAirway narrowest at cricoidFewer alveoli at birth (10% adult)Primarily diaphragmatic ventilation due to horizontal ribs and increased chestwall compliance

Reduced FRC, with closing volume > FRC until 6–8 yearsMinute ventilation rate dependent (increased dead space ventilation withincreasing respiratory rates)

Reduced respiratory reserveWork of breathing = 15% oxygen consumptionApnoeas common in premature babies

Cardiovascular system

Functional transition from fetal to adult circulation occurs at birth (see Section 8)Cardiac output rate dependent (less compliant ventricle)Dominant vagal tone


Fluids / Renal

Body fluid composition changes

Draw and label the axes. To make the graph simpler to construct and todemonstrate the principles clearly, the x axis consists of four discrete timepoints.

TBW A preterm neonate has 80–90% of their body weight as water (thevalue rises with increasing prematurity). At term TBW is 70% and by about1 year has fallen to the adult value of 60% (females a have slightly lowervalue of 55%). It continues to fall during adulthood and is 50% in theelderly.

ECF and ICF An extremely preterm infant will have up to 60% of bodyweight as ECF. On the graph make sure the sum of the ECF and ICF valuesequal the TBW. So if a preterm infant has 80% TBW, 55% is ECF and 25%ICF. At birth the values for ECF and ICF are 40% and 35% respectively. Asthe ECF volume contracts over the first year of life the values change to 20%and 40% respectively. Draw the lines for ECF and ICF to demonstrate thesevalues.

Fluid deficit (ml) = % dehydration x weight (kg) x 10(The % dehydration is determined by temperature of the extremities on clinical

examination)High renal vascular resistance causes reduced RBF and GFRImmature tubular function until eight months of age

Haematology

HbF: 80% at birth; 5% at three months (HbF P50 = 3.6 kPa)Increased Hb concentration at birth, falling to minimum at three monthsVitamin K dependent clotting factors deficient at birth



Metabolic (including thermoregulation)

Metabolic rate double adult valuesProne to hypoglycaemiaProne to heat loss as large surface area: weight ratio and immature thermoregulation

Hepatic

Decreased function of liver enzymes

Neurology

Incomplete myelinationSpinal cord finishes lower (L3 at birth)

Pharmacokinetics and pharmacodynamics

Increased volume of distribution and decreased protein binding may necessitatedose alteration

More rapid uptake and distribution lead to faster onset of actionImmature liver and kidney function may lead to prolonged duration of actionMinimum alveolar concentration decreases with increasing age (except forneonates)

Increased sensitivity to centrally acting drugs as blood brain barrier immature

Paediatric physiology calculations

Variable Calculation

Oxygen consumption 7 mls.kg−1.min−1

Tidal volume 7 mls.kg−1.min−1

Cardiac output 300–400 mls.kg−1.min−1 (birth)200 mls.kg−1.min−1 (infants)100 mls.kg−1.min−1 (adolescents)

Stroke volume 1 ml.kg−1

Mean systolic blood pressure 80 + (2 x age (years)) (over 1 year)Blood volume 90 ml.kg−1 (neonate)

85 ml.kg−1 (infant)80 ml.kg−1 (child)

Maintenance fluid requirements < 10kgs = 100ml/kg/24h or 4ml/kg/h +10-20kgs = 50ml/kg/24h or 2ml/kg/h +> 20kgs = 20ml/kg/24h or 1ml/kg/h

Urine output 1–2 ml.kg−1.h−1

Paediatrics 339


Ageing

The process of growing old, characterized by the gradual impairment ofthe structure and functional reserve of tissues and organs.

The ageing process is progressive, cumulative, deleterious, inevitable and univer-sally affects the whole population. Note that disease may also be defined asimpairment of structure and function, so some age-related changes may indeedbe manifest as disease.

Older people

People aged 65 years or more. (WHO definition)

As life expectancy is increasing, the proportion of the population defined as elderlyis growing. It is important to understand the physiological changes that occur andlearn how these changes impact on anaesthetic techniques.

Timing

The physiological changes that occur as we age usually begin in the fourth decadeand are progressive. Some of themmay be avoided or delayed by adopting a fit andhealthy lifestyle. Morbidity and mortality associated with surgery and anaesthesiaincrease with advancing age, with a steep increase over the age of 75.

Implications of ageing by system

The changes listed below are changes that occur with normal ageing. As well asthese changes, the incidence of disease increases with advancing age althoughsymptoms may not be as clearly defined. Also, the presence of the residual effectsof previous disease may also result in impairment to physiology.

The overriding key point to remember is that themargins of safety are smaller inthe elderly patient as the ability of the body to cope with physiological stress isreduced.


Reduced maximal heart ratePredisposition to atrial fibrillation due to loss of atrial pacemaker cellsReduced cardiac output due to loss of active myocardial fibresReduced compliance of both arterial and venous systems


Decreased baroreceptor sensitivityDecreased responsiveness of myocardium to catecholamines despite increasedcatecholamine levels

Respiratory system

Increased compliance (emphysema-like) due to loss of elastic recoilIncreased residual volume and reduced vital capacityIncreased closing capacity (see graph below) leading to increased ventilationperfusion mismatching

Weakened muscles of respirationImpaired reflexes and airway reactivity

The effects of age on closing capacity and the relationship with FRC are welldemonstrated graphically

Draw and label the axes as above. The normal upright FRC (dashed line) isapproximately 3000ml, so draw this horizontal line accordingly. FRC isreduced by up to 30% (0.5–1.0L) in the supine position so draw this line next(dotted line). Closing capacity (the sum of closing volume and residual volume)increases with age and reaches the supine FRC at about 44 years and the uprightFRC at 66 years. Therefore draw a third up-sloping straight line to representclosing capacity that crosses the FRC lines at these points. Highlight that thismeans that by 70 years the closing capacity is well above the supine FRC andthus encroaches on tidal ventilation. The result of this is that a larger propor-tion of the lung is atalectatic, ventilation perfusion mismatch increases and thealveolar-arterial oxygen gradient widens. Note that the (lack of) effect of age onFRC seems to be contentious. Most physiology texts quote that there is noincrease in FRC with age, however some state that it does increase. Theimportant point is to consider the relationship between FRC and closingcapacity and there is no doubt that closing capacity increases to above theFRC in the elderly.

Ageing 341


Gastrointestinal / Hepatic

Poor dentitionDecreased peristalsisReduced liver size and blood flow leads to delayed clearance of drugsReduced synthesis of albumin and other proteins

Renal

Decreased GFR in proportion to decrease in cardiac outputReduced ability to regulate salt and water balance due to loss of cortical glomeruliReduced skeletal muscle leads to less creatinine to excrete and can mask renal

dysfunction

Endocrine

Glucose intolerance due to a reduction in the sensitivity of β cells to glucose andthus reduced insulin secretion

Decreased growth hormone, cortisol and aldosterone secretionReduced levels of androgens

Neurological

Loss of nerve fibres, both centrally and peripherallyReduced CBF and CMRO2 proportionally to reduced neural densityDepletion of neurotransmitters (reduced synthesis and increased destruction)Reduced conduction velocities due to loss of myelinMuscle atrophy due to denervationLoss of response to autonomic organs despite increased catecholamine levelsPre-disposition to post operative cognitive impairment (POCD)

Pharmacokinetics

Increased duration of action of many drugs due to prolonged elimination half life.This is caused by an increased volume of distribution and prolonged organ basedelimination. For example intravenous induction agents, benzodiazepines andopioids

Pharmacodynamics

Reduced dose requirement of intravenous induction agents due to a decreasedplasma volume and reduced protein binding

Slower onset of action of intravenously administered drugs due to prolongedarm-brain circulation time



Reduced MAC value for inhalational anaesthetic agents. For example sevoflur-ane has a MAC of 1.8 for a 40 year old and 1.4 for an 80 year old and the MAC ofisoflurane is reduced from 1.17 (40 year old) to 0.91 (80 year old).

Miscellaneous

Reduced lean body massLoss of collagen from connective tissuePredisposed to pressure soresArthritis and osteoporosis common

Ageing 343


Obesity

Definition

An individual with a body mass index greater than 30 kg.m−2.

Body mass index

Body mass index (BMI) is used frequently to identify the category of obesity. It iscertainly not an infallible measure but easy to calculate and understood bypatients.

BMI = Body mass / Height2

= kg / m2

NICE classification

Definitions of obesity vary around the world but the NICE classification sharessome similarities with most other grading scales.

Overweight = BMI > 25 kg.m−2

Obese class 1 = BMI > 30 kg.m−2



Implications of obesity by system


Moderate to severe hypertension commonAtherosclerosis and ischaemic heart diseaseRight or left heart failureDifficult IV access and non-invasive BP monitoring

Respiratory system

Reduced mouth and neck mobilityNeck fat pad and difficult airway riskHigh intra-gastric pressure and reflux riskReduced chest wall complianceIncreased V/Q mismatchDecreased FRC (see below)


Obstructive sleep apnoea and obesity hypoventilation syndromeReliance on hypoxic drive – Pickwickian syndrome

The FRC is reduced in obesity as a consequence of the reduction in expiratoryreserve volume. During normal tidal ventilation there is no small airwayclosure but with increasing obesity (A) such closure can occur at rest. Theresulting wheeze may be mistaken for COPD or similar. With worseningobesity or with the induction of anaesthesia the FRC is reduced even more(B) and all tidal ventilation occurs at volumes less than the closing volume.Ramping the patient head up prior to anaesthesia reduces the reduction in FRCand should always be considered.

Metabolic system

DiabetesPoor nutritional statusHypercholesterolaemiaDeranged liver function

Pharmacokinetics

The greater size of the lipid compartment and relative reduction of the watercompartment may alter the volume of distribution of many drugs. Drugs alsoundergo altered binding and clearance. Drug dosing is usually undertaken by usingthe ideal body weight (IBW) or the lean body weight (LBW) as below.

IBW

IBW (Male) = Height (cm) – 100IBW (Female) = Height (cm) – 105

Obesity 345


LBW

Calculations inaccurate in obesity. Society for Obesity and BariatricAnaesthesia (SOBA) recommend using:Estimated LBW (Male): 90kgEstimated LBW (Female): 70kg

Important exceptions where a total body weight (TBW) dose is appropriate are forsuxamethonium (maximum 200mg) and neostigmine (maximum 5mg). Extremecaution should always be taken with the prescription of long acting opiates.

Miscellaneous

Increased risk of wound infectionLong predicted operative timeRegional anaesthesia technically difficultHigher risk of thromboembolic complications


C:/ITOOLS/WMS/CUP-NEW/4469668/WORKINGFOLDER/CRSS/9781107615885C12.3D 347 [347–376] 28.10.2013 12:07PM

Section 12Statistical principles



Types of data

Population

The entire number of individuals of which the sample aims to berepresentative.

Sample

A group taken from the wider population. A sample aims to be represen-tative of the population from which it is taken.

As samples are smaller, they are easier to collect and to analyse statistically.However, as they do not contain all of the values in the population, they canmisrepresent it. Statistical analysis is often used to decide whether samples of datacome from the same or from different populations. Populations are described byparameters and samples by statistics.

Categorical (qualitative) data

Nominal

Data that have no numerically significant order, such as blood groups.

Ordinal

Data that have an implicit order of magnitude, such as ASA score.

Numerical (quantitative) data

Discrete

Data that have finite values, such as number of children.

Continuous

Data that can take any numerical value including fractional values.Examples include weight or height.

Ratio

Any data series that has zero as its baseline value, for example bloodpressure or the Kelvin temperature scale.


Interval

Any data series that includes zero as a point on a larger scale, for examplethe centigrade temperature scale.

There is a hierarchy of usefulness of data, according to how well it can bestatistically manipulated. The accepted order is continuous data > ordinaldata > nominal data.

350 Section 12 � Statistical principles


Indices of central tendency and variability

Describing data

Once data have been collected, the values will be distributed around a central pointor points. Various terms are used to describe both the measure of central tendencyand the spread of data points around it.

Measures of central tendency

Mean

The average value: the sum of the data values divided by the number ofdata points. Denoted by the symbol x when describing a sample mean andμ when describing a population mean.

Themean is always used when describing the normal distribution and, therefore, itis the most important measure with regards to the examination.

Median

The middle value of a data series, having 50% of the data points above itand 50% below.

If there are an even number of data points, the median value is assumed to be theaverage of the middle two values.

Mode

The most frequently occurring value in a set of data points.

The data can be plotted on a graph to demonstrate the distribution of the values.The individual values are plotted on the x axis with the frequency with which theyoccur on the y axis.

Measures of spread

Variance

A measure of the spread of data around a central point. Described by thefollowing equation.

Var ¼P

x � xð Þ2n� 1


Standard deviation

A measure of the spread of data around a central point. Described by thefollowing equation (σ for population, SD for sample):

SD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

X � X� �2n� 1

s

Begin by finding the mean value X� �

of the distribution and then subtracteach data point from it to find the difference between the values

X � X

Square the results to ensure that all values are positive numbers:

X � X� �2

Sum the results:PX � X� �2

Next divide the result by the number of observations (minus 1 for statisticalreasons) to give the mean spread or variance

PX � X� �2n� 1

The units for variance are, therefore, squared, which can cause difficulties. If theobservations are measuring time for instance, the variance may be given in secondssquared (s2), which is meaningless. The square root of the variance is, therefore,used to return to the original units. This is the SD.

SD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

X � X� �2n� 1

s

The spread of data is often described by quoting the percentage of the sample orpopulation that will fall within a certain range. For the normal distribution, 1SDeither side of the mean will contain 68% of all data points, 1.96SD 95%, 2SD 95.7%and 3SD 99.7%.



Standard error of the mean

The standard deviation of a group of sample means taken from the samepopulation (SEM):

SEM ¼ � = √ n� 1ð Þ

where σ is the SD of the population and n is the number in the samples.

In practice, the population SD is unlikely to be known and so the sample SD is usedinstead, giving

SEM ¼ SD = √ n� 1ð Þ

In the same way as the SD is used as a measure of spread around a mean, the SEMis used as a measure of the spread of a group of sample means around the truepopulation mean. It is used to predict how closely the sample mean reflects thepopulation mean.

As the sample size increases, SEM becomes smaller. For this reason, the SEM issometimes quoted in study results rather than the SD in order to make the datalook better.

Degrees of freedom

Statistics frequently involve calculations of the mean of a sample. In order tobe able to calculate a mean, there must be at least two values present. For thisreason, when describing sample size, the term n − 1 is often used instead ofthe actual number. One of the sample points must be present in order thateach of the other points can be used in the mean calculation. In other words,the size of the freely chosen sample must always be one less than are actuallypresent.

For large sample sizes, the correction factor makes no difference to the calcu-lation, but for small sample sizes it can be quite important. It is, therefore, bestalways to describe the sample size in this way.

Confidence intervals

The range of values that will contain the true population mean with astated percentage confidence. Used in parametric tests.

A 95% confidence interval is ±1.96SD and is the most frequently quoted. There is a95% certainty that this range of values around the mean will contain the popula-tion mean.

Indices of central tendency and variability 353


Quartile

Any one of the three values that divide a given range of data into fourequal parts.

In order to tear a piece of paper into four equally wide strips, three tears must bemade. One to tear the original paper in half and the other two to tear those halvesin half again. A quartile is the mathematical equivalent of this to a range of ordereddata. You should realize that the middle quartile (Q2) is, in effect, the median forthe range. Similarly, the first quartile (Q1) is effectively the median of the lower halfof the dataset and the third quartile (Q3) the median of the upper half. In the sameway as for the median calculation, a quartile should be represented as the mean oftwo data points if it lies between them.

Interquartile range

The range of values that lie between the first and third quartiles and,therefore, represent 50% of the data points. Used in non-parametric tests.

Calculating quartiles and using the interquartile range is useful in order to negatethe effect of extreme values in a dataset, which tend to create a less stable statistic.



Types of distribution

The normal distribution

A bell-shaped distribution in which the mean, median and mode all havethe same value, with defined SD distribution as above.

The curve is symmetrical around the mean, which is numerically identical tothe median and mode. The SD should be indicated; 1SD lies approximately onethird of the way between x and the end of the curve.

Positively skewed distribution

The curve is asymmetrical with a longer tail stretching off towards the morepositive values. The mean, median and mode are now separated so that x isnearest the tail of the curve; the mode is at the peak frequency and the median isin between the two. This type of distribution can sometimes be made normal bylogarithmic transformation of the data.


Negatively skewed distribution

The curve is asymmetrical with a longer tail stretching off towards the morenegative values. The mean, median and mode are now separated in the otherdirection, with x remaining closest to the tail. This type of distribution cansometimes be made normal by performing a power transformation (squaringor cubing the data).

Bimodal distribution

The curve need not be symmetrical nor have two modes of exactly the sameheight but the above curve demonstrates the principle well. The low pointbetween the modes is known as the antimode. This curve could represent theheights of the population, with one mode for men and one for women.



Methods of data analysis

When performing a study, the first step is to pose a question. The question isformulated as a hypothesis that must be proved or disproved. This question isknown as the null hypothesis.

The null hypothesis

The hypothesis states that there is no difference between the samplegroups; that is, they both are from the same population. (H0)

The study then examines whether this is true. The amount of data needed to provea difference between the samples depends on the size of the difference that is to bedetected. Enough data must be collected to minimize the risk of a false-positive orfalse-negative result. This is determined by a power calculation.

Power

The ability of a statistical test to reveal a difference of a certain magni-tude (%):

1 − β

where β is the β error (type II error).

Acceptable power is 80–90%, which equates to a β value of 10–20%. In effect, thismeans a 10–20% chance of a false-negative result.

The p value

The likelihood of the observed value being a result of chance alone.

Conventionally a p (probability) value of < 0.05 is taken to mean statisticalsignificance. This means that if p = 0.05 then the observed difference couldoccur by chance on 1 in 20 (5%) of occasions. In effect, this means a 5% chanceof a false-positive result.

Number needed to treat

The number of patients that have to be treated to prevent one outcomeevent occurring.


Absolute risk reduction

The numerical difference between the risk of an occurrence in the controland treatment groups.

Incidence in treatment groupð Þ � Incidence in control groupð Þ

Relative risk reduction

The ratio of the absolute risk reduction to the control group incidence (%):

Absolute risk reductionð ÞControl incidenceð Þ

Relative risk

The ratio of the risk of an occurrence in the treatment group to that in thecontrol group:

Incidence in treatment groupð ÞIncidence in control groupð Þ

If the control incidence is low, this can lead to an overestimation of the treatmenteffect.

Odds ratio

Ratio of the odds of outcome in the treatment group to the odds of out-come in the control group.

Unpaired test

Different patients are studied in each of the intervention groups.

Paired test

The same patient is studied for each intervention, thereby acting as theirown control. Matched patients can also be used.

Student’s t-test

A parametric test for comparison of sample means where

t ¼ Difference between sample meansEstimated SE of the difference



Once a value for t is obtained, it is read from a table to see if it represents astatistically significant difference at the level of probability required, for examplep < 0.05.

One-tailed test

A statistical test in which the values that will allow rejection of the nullhypothesis are located only at one end of the distribution curve.

For example, if a study were to investigate the potential of a new antihypertensivedrug, a one-tailed test may be used to look for a decrease but not an increase in BP.

Two-tailed test

A statistical test in which the values that will allow rejection of the nullhypothesis are located at either end of the distribution curve.

A study investigating the effect of a drug on serumNa+ levels could use a two-tailedtest to identify both an increase and a decrease. In general, unless you are sure thata variable can only move in one direction, it is wise to use a two-tailed test.

Chi-square (χ2) test

Compares the frequency of observed results against the frequency thatwould be expected if there were no difference between the groups.

�2 ¼ P O� Eð Þ2E

where χ2 is the chi-square statistic, E is the number of expected occurrencesand O is the number of observed occurrences.

It is best demonstrated by constructing a simple 3 × 3 table. You may be providedwith a pre-printed table in the examination but be prepared to draw your own.

Methods of data analysis 359


The numbers in the unshaded portion of the table give you the observedfrequency. The expected percentage of smokers if there were no difference betweenthe sexes would be 100/180 (55.6%) smokers and 80/180 (44.4%) non-smokers ineach group. To find the actual frequency in each group, this percentage is multi-plied by the respective row total.

E ¼ Column totalGrand total

� Row total

The table now has an expected frequency in parentheses in each cell along withthe observed frequency. The calculation (O − E)2/E is performed for each cell andthe results summed to give the χ2 statistic.

Degrees of freedom for χ2

Degrees of freedom for a table are calculated in a similar way to those fordistributions.

DF ¼ No: of rows� 1ð Þ � No: of columns � 1ð Þ

Therefore for a 2 × 2 table

DF ¼ 2� 1ð Þ � 2� 1ð ÞDF ¼ 1� 1DF ¼ 1

When the χ2 statistic has been calculated, it is cross-referenced to a table of valuestogether with various degrees of freedom. The table will enable the statistician tosee if the groups are statistically different or not.

Fisher’s exact test

This is a variation of the χ2 test that is used when the value for E in any cell is 5or less.



Correlation

A representation of the degree of association between two variables.

Importantly, this does not identify a cause and effect relationship but simply anassociation.

Correlation coefficient

A numerical description of how closely the points adhere to the best fitstraight line on a correlation plot (r).

The value of r lies between ±1. A value of +1 indicates a perfect positive correlationand a value of −1 a perfect negative correlation. A value of 0 indicates that there isno correlation between the two variables.

Regression coefficient

A numerical description of the gradient of the line of best fit using linearregression analysis (b).

The regression coefficient allows prediction of one value from another. However, itis only useful when the intercept on the y axis is also known, thereby describing therelationship by fixing the position of the line as for the equation y = bx + a.

Positive correlation

Draw and label the axes. The x axis is traditionally where the independentvariable is plotted. Draw a line of best fit surrounded by data points. As the lineof best fit has a positive slope, both b and r will be positive. However, r will notbe +1 as the data points do not lie exactly on the line. In this case r isapproximately + 0.8.



Negative correlation

This plot is drawn in exactly the same way but now with a negative slope to theline of best fit. Both b and r will now be negative but, again, r will not be −1 asthe data points do not lie exactly on the line. In this case r is approximately −0.8.

Exact negative correlation

This plot is drawn in the same way as the negative plot but now the line of bestfit becomes a line of exact fit. Both b and r will now be negative and r will be −1as the data points lie exactly on the line.



No correlation

Draw and label the axes as before but note that on this plot there is nomeaningful line of best fit as the data points are truly random. It is not possibleto give a value for b as a line of best fit cannot be generated but the value of r is 0.

Bland–Altman plot

The Bland–Altman plot is superior to regression/correlation analysis when used tocompare two methods of measurement. It is the method of choice when compar-ing one method to an agreed gold standard.

The true value being measured by the two methods is assumed to be the averageof their readings. This is then plotted against the difference between the tworeadings at that point. The level of agreement or disagreement at every value is,therefore, obtained and a mean and SD can be calculated.

Bias

The extent to which one method varies with respect to another when thetwo methods are compared.

The mean difference between methods should ideally be zero. However, if it is feltthat the clinical difference between the methods is not significant, then the meandifference can simply be added to or subtracted from the results of one method inorder to bring them into line with the gold standard. The amount by which themean differs from zero is called the bias.



No agreement

Draw and label the axes as shown. Widely scattered data points as shownsuggest no firm comparison between methods x and y. Demonstrate that ±2SD(95% CI) is wide and the distribution of the points appears arbitrary. Bias canbe demonstrated by showing amean point that does not lie at zero on the y axis.

Good agreement

On the same axes draw a tightly packed group of data points centred around amean difference of zero. The ±2SD should show a narrow range. This plotdemonstrates good agreement between the methods used.

Interpretation

The test does not indicate which method is superior, only the level of agreementbetween them. It is entirely possible that a method which shows no agreement with



a current standard is, in fact, superior to it, although other tests would have to beused to determine its suitability.

Reference table of statistical tests

Two groups More than two groups

Type of data Unpaired Paired Unpaired Paired

ParametricContinuous Student’s

unpairedt-test

Student’spaired t-test

ANOVA PairedANOVA

Non-parametricNominal χ2 with Yates’

correctionMcNemar’s test χ2 –

Ordinal or numerical Mann–WhitneyU test

Wilcoxonsigned ranktest

Kruskal–Wallis Friedman



Error and outcome prediction

In medicine, we often try to predict an outcome based on the result of a test. Thereare various terms used to describe how useful a test is, which may be best under-stood by reference to a table such as the one below.

Type I error

The occurrence of a positive test resultwhen the actual value is negative. (%)

This type of error equates to box B and is variously described as a type I error, afalse-positive error or the α error. A type I error in a study result would lead to theincorrect rejection of the null hypothesis.

Type II error

The occurrence of a negative test resultwhen the actual value is positive. (%)

This type of error equates to box C and is variously described as a type II error, afalse-negative error or the β error. A type II error in a study result would lead to theincorrect acceptance of the null hypothesis.

Sensitivity

The ability of a test to correctly identify a positive outcome where oneexists. (%)

The number correctly identified as positiveTotal number that are actually positive

or, in the Figure:

A= A þ Cð Þ


Specificity

The ability of a test to correctly identify a negative outcome where oneexists. (%)

The number correctly identified as negativeTotal number that are actually negative

or

D= B þ Dð Þ

Positive predictive value

The certainty with which a positive test result correctly predicts a positivevalue. (%)

The number correctly identified as positiveTotal number with positive outcome

or

A= A þ Bð Þ

Negative predictive value

The certainty with which a negative test result correctly predicts a negativevalue. (%)

The number correctly identified as negativeTotal number with negative outcome

or

D= C þ Dð Þ

The following graph helps to explain the principles of outcome prediction dis-cussed above.

Error and outcome prediction 367


Draw and label the axes as shown. The bell shaped curve with the solid linerepresents a population that does not have a condition; the curve with thedotted line represents those with a condition. Assume there is a test that is ableto differentiate between the two. The test is considered negative if the result isbelow a set level (dashed line), and positive if above the set level. However, asthe populations overlap the test cannot perfectly distinguish between the twopopulations. There will be a group of people with the condition who have anegative test result, the false negative group (C) as well as a group of people whodo not have the condition who have a positive test result, the false positives (B).Moving the cut off value of the test will determine the size of each of thesegroups. As mentioned previously, the sensitivity of the test is the ability of thetest to identify the true positives (A) and the specificity is the ability of the test toidentify true negatives (D).



Receiver operating characteristic curve

A graphical representation of the ability of a test, or scoring system, topredict an outcome.

Draw and label the axes as shown. Receiver operating characteristic (ROC)curves show the accuracy of a binary test. The x axis shows the false positive rate(1-specificity) and it is plotted against the true positive rate (sensitivity) on they-axis for a series of results obtained as the discrimination threshold for the testis progressively altered. The area under the curve (AUC) is then calculated,which is a measure of the accuracy of the test. A perfect test will have an AUC of1 (or 100%) and a useless test (dotted line) 0.5 (50%). Different tests can beplotted on the same graph to enable comparisons. The curve can then be usedto select the best cut-off to use clinically: the uppermost left point being the bestbalance between sensitivity and specificity. In the graph above it can be seenthat test A is a more useful test than test B. Examples of tests could beMallampati class 1–4 at predicting difficult intubation or APACHE scorepredicting intensive care mortality.


Clinical trials

Phases of clinical trials

Clinical trials will be preceded by in-vitro and animal studies before progressingthrough the stages shown in the table.

Phase Description Numbers

1 Healthy volunteers: pharmacokinetic and pharmacodynamiceffects

20–50

2 More pharmacokinetic and dynamic information: different drugdoses and frequencies

50–300

3 Randomized controlled trials: comparison with current treatments;assessment of frequent side effects

250–1000 +

PRODUCT LICENCE4 Post-marketing surveillance: rare side effects 2000–10 000 +

Trial design flow sheet

The design of a clinical trial is of paramount importance. Mistakes in trial designare very difficult to rectify, whereas flaws in the analysis of data may be correctedmore easily.


Outcome

The clinical endpoint that is being studied.

The primary outcome is the most important and will be used in the powercalculations. Secondary outcomes are additional endpoints that are investigated.

Power calculation

A calculation performed to determine the sample size needed for thestudy.

The sample size depends upon the type I and type II errors, the magnitude of thedifference that needs to be detected (also known as the effect size: the smaller theeffect size the larger the sample needed) and the variability of the data. The powercalculation performed depends on the design of the study and the type of datacollected.

Randomization

The process of assigning patients to a particular group in a deliberately haphazardmanner that simulates chance. It is important in clinical trials to prevent selectionor allocation bias and also allows blinding to occur. The first stage is generation of arandom sequence, analogous to coin tossing. The second stage is allocationconcealment.

Allocation concealment

The procedure of concealing the randomization process so that the partic-ipants and investigators do not know what the upcoming assignments are.

Allocation concealment prevents investigators from interfering with the random-ization process.

Blinding

The process of concealing from the person the intervention they are receiv-ing, or in the case of the investigator, the intervention that the person theyare studying has received.

Blinding is important to minimize bias.

Bias

A systematic error that results in an incorrect or imprecise result or conclusion.

Clinical trials 371


There are many different types of bias. For example, selection bias, performancebias, and reporting bias, which are all reduced by proper randomization andblinding. Publication bias is another type of bias whereby studies with positiveresults are more likely to be published than those with negative results.

Data collection

The method by which information is gathered.

Data collection may be done in the following ways:

1. A survey. If the survey includes the whole population, it is called acensus; otherwise it is a sample survey. If the survey respondents arerandomly chosen from the population then the results will be able to begeneralized to the population as a whole.

2. An observational study. Observational studies are used to investigatecausal relationships. However, the observer cannot control the study toensure that the groups observed are both randomly selected and ran-domly assigned to an intervention. This means that it is difficult toaccurately generalize results to the whole population and it is notpossible to prove a causal relationship this way. Observational studiesare often performed when it is not possible, ethically or practically, toperform an experiment. Examples of observational studies are cohortand case-control studies.a. Cohort study. In a cohort study a group of individuals are studied over

a period of time to investigate if particular risk factors are associatedwith outcomes. They usually involve large groups of individuals andtake a relatively long period as they need to be followed longenough for an outcome to occur. This makes them comparativelylabour and resource intensive.

b. Case-control study. This is an observational study in which, as thename suggests, a group of individuals with a condition (‘cases’) arecompared with a similar group without the condition (‘controls’) tolook for possible pre-disposing factors. They are usually shorter andinvolve smaller groups than cohort studies.

3. An experiment. Experiments are also used to investigate causal relation-ships, but are controlled by the researcher. This means that samplingcan be randomized, which if done appropriately, means that the resultscan be generalized to the relevant population. In an experiment theresearcher determines the intervention (the independent variable) andmeasures the response to it: the dependent variable. Groups receiving anintervention are compared with control groups who do not receive anintervention, the two groups being as closely matched as possible in allother ways. In this way it is possible to determine a causal relationship.



Statistical significance

A result that is unlikely to be due to chance.

As mentioned above, a p value of <0.05 is conventionally taken to be statisticallysignificant, meaning that there is a less than 1 in 20 probability of the result beingdue to chance. Remember that statistical significance cannot be directly related tothe magnitude of any difference between groups.

Clinical significance

Whether or not a result is important when applied to clinical practice.

Clinical significance is different to statistical significance, although they are related.An observed difference that is not statistically significant is more likely to be due tochance, and therefore is less likely to be clinically important. Clinical significancedepends on the magnitude of the difference between groups (which may or maynot be statistically significant) and whether the results given by a study are ofrelevance and importance to an individual’s practice. Assessment of the numberneeded to treat may help to determine this. Remember that it is also possible for anegative result (no difference between groups studied) to be clinically important.Assessment of the design of the study is crucial to determining clinical significanceas flaws in the study may mean that the results cannot reliably be generalizedoutside the study population.

Clinical trials 373


Evidence-based medicine

The use of current best evidence, clinical expertise and patient values tomake decisions about the care of individual patients.

Levels of evidence

In this era of evidence-based medicine, there needs to be a method of categorizingthe available evidence to indicate how useful it is. The following system is the oneused by the UK National Institute for Health and Clinical Excellence (NICE).Other organizations that produce guidelines may use slightly different systems butthe hierarchy of usefulness remains the same. The levels of evidence are based onstudy design, with some systems, such as this one, subdividing the grades furtherdepending on the methodological quality of individual studies.

Level Evidence description

1a Systematic review or meta-analysis of one or more randomized controlled trials(RCT)

1b At least one RCT2a At least one well-designed, controlled, non-randomized study2b At least one well-designed quasi-experimental study; for example a cohort study3 Well-designed non-experimental descriptive studies; for example comparative,

correlation or case–control studies, or case series4 Expert opinion

Grade of recommendations

Similarly, the strength of any recommendation made on the basis of the evidencecan be categorized. This is an example from NICE.

Grade Recommendation description

A Based directly on level 1 evidenceB Based directly on level 2 evidence or extrapolated from level 1 evidenceC Based directly on level 3 evidence or extrapolated from level 1 or level 2 evidenceD Based directly on level 4 evidence or extrapolated from level 1, level 2 or level 3

evidenceGPP Good practice point based on the view of the Guideline Development Group


An alternative is to think in terms of ‘do it’ or ‘don’t do it’, based on conclusionsdrawn from high-quality evidence or ‘probably do it’ or ‘probably don’t do it’ basedon moderate quality evidence. Low-quality evidence leads to uncertainly andinability to make a recommendation.

Meta-analysis

A statistical technique that combines the results of several independentstudies that address a similar research hypothesis.

Meta-analysis aims to increase the statistical power of the available evidence bycombining the results of smaller trials together using specific statistical methods.The validity of the meta-analysis will depend on the quality of the evidence onwhich it is based and how homogeneous or comparable the samples are.Combining very heterogeneous study populations can lead to bias.

Forest plot

A graphical representation of the results of a meta-analysis.

Begin by drawing and labelling the axes as shown. Draw a vertical line from 1on the x axis. This is the line of no effect. The results of the individual trials areshown as boxes with the size of the box relating to the size of the trial and itsposition relating to the result of the trial. The lines are usually the 95%confidence intervals. The combined result is shown at the bottom of all thetrials as a diamond, the size of which represents the combined numbers from allthe trials. The result can be considered statistically significant if the confidenceintervals of the combined result do not cross the line of no effect.

Evidence-based medicine 375


Kaplan Meier curves

A graphical representation of the probability of survival against time for acensored population or populations.

Draw and label the axes as shown. Percent survival (y-axis) is plotted againsttime (x-axis) with the vertical stepwise changes in the probability of survivalcorresponding to times at which data was censored. It enables several differentgroups to be compared, and the effect of different interventions on survival tobe graphically represented. In the graph above it can be seen that population Ahas a greater survival than population B over the five year period, althoughinitially the survival for both is very similar.

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Appendix

Intravenous induction agents

Thiopental Methohexital Propofol Ketamine Etomidate

Chemical composition Thiobarbiturate Oxybarbiturate 2,6 Diisopropylphenol Phenylcyclidinederivative

Imidazole ester

Dose (mg.kg−1) 3−7 1−1.5 1−2 1−2 i.v., 5−10 i.m. 0.3pKa 7.6 7.9 11.0 7.5 4.0pH in solution 10.5 11 6−8.5 3.5−5.5 8.1Volume of distribution (l.kg−1) 2.5 2.0 4.0 3.0 3.0Protein binding (%) 80 60 98 25 75Racemic ✓ ✓ x ✓ ✓

Action ↑ duration of GABAA

opening, leading to ↑ Cl−

current

Stimulates GABA;inhibits NMDA

Inhibits NMDA andopioid μ receptors(stimulates κ and δ)

Stimulates GABA

Metabolism Oxidation GlucuronidationHydroxylation

N-DemethylationHydroxylation

Plasma andhepaticesterases

Metabolites Active Minimal activity Inactive Active InactiveClearance (ml.kg−1.min−1) 3.5 11 30–60 17 10–20Elimination rate (telim) (h) 6−15 3−5 5−12 2 1−4Hypersensitivity Anaphylaxis 1:20 000 More common than

thiopental but lesssevere

Rashes in 15% Rare

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Intravenous induction agents: physiological effects

Thiopental Methohexital Propofol Ketamine Etomidate

Blood pressure ↓ ↓ ↓↓ ↑ ↔

Cardiac output ↓ ↓ ↓↓ ↑ ↔

Heart rate ↑ ↑ ↓→ ↑ ↔

Systemic vascular resistance ↕ ↕ ↓↓ ↔ ↔

Respiratory rate ↓ ↓ ↓ ↑ ↓

Intracranial pressure ↓ ↓ ↓ ↑ ↔

Intraocular pressure ↓ ↓ ↓ ↑ ↔

Pain on injection No Yes Yes No YesNausea/vomiting No No No Yes YesMiscellaneous Intra-arterial injection

→ crystallization↓ Fit threshold ? Toxic in children

(metabolic acidosisand bradycardia)

↑ Salivation;‘dissociativeanaesthesia’

Adrenal suppression

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Inhalational anaesthetic agents

Halothane Isoflurane Enflurane Sevoflurane DesfluraneNitrousOxide Xenon

Molecular weight 197 184.5 184.5 200.1 168 44 131Boiling Point (°C) 50.2 48.5 56.5 58.5 23.5 −88 −108SVP at 20 °C (kPa) 32.3 33.2 23.3 22.7 89.2 5200 N/ABlood:Gas 2.4 1.4 1.8 0.7 0.45 0.47 0.14Oil:Gas 224 98 98 80 29 1.4 1.9MAC 0.75 1.17 1.68 1.8–2.2 6.6 105 71Odour Non irritant Irritant Non irritant Non irritant Pungent Odourless Odourless% metabolized 20 0.2 2 3.5 0.02 0.01 NilMetabolites Trifluoroacetic

acid, Cl−, Br−Trifluoroacetic

acid, F−,Inorganic andorganic fluorides

Inorganic and organic fluoridesCompounds A–E

Trifluoroaceticacid

Nitrogen Nil

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Inhalational agents: physiological effects

Halothane Isoflurane Enflurane Sevoflurane Desflurane Nitrous oxide

Contractility ↓↓↓ ↓ ↓↓ ↓ ↔ ↓

Heart rate ↓↓ ↑↑ ↑ ↔ ↑ (↑↑ > 1.5 MAC) ↔

Systemic vascular resistance ↓ ↓↓ ↓ ↓ ↓↓

Blood pressure ↓↓ ↓↓ ↓↓ ↓ ↓↓ −Sensitivity tocatecholamines

↑↑↑ − ↑ − −

Respiratory rate ↑ ↑↑ ↑↑ ↑↑ ↑↑ ↑

Tidal volume ↓ ↓↓ ↓↓↓ ↓ ↓↓ ↓

PaCO2 ↔ ↑↑ ↑↑↑ ↑ ↑↑ ↔

Bronchodilatation Yes Yes Yes Irritant –

Cerebral blood flow ↑↑↑ ↑ (Yes MAC > 1) ↑ Preservesautoregulation

↑ ↑

Cerebral metabolic rate ofO2 consumption

↓ ↓ ↓ ↓ ↓ ↑

Electroencephalography Burst suppression Burst suppression Epileptiformactivity

Burstsuppression

Burst suppression

Uterus Some relaxation Some relaxation Some relaxation Some relaxation Some relaxationMuscle relaxation Some Significant Significant Significant SignificantAnalgesia Some Some Some Some SomeMiscellaneous Hepatotoxicity; stored in

0.01% thymol; lightsensitive

Coronary steal?;maintains renalblood flow

Hepatotoxic; avoidin renalimpairment

Renal toxicity Oxidizes cobaltion in vitaminB12

MAC, minimum alveolar concentration.

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Opioidsa

Morphine Diamorphine Codeine Pethidine Fentanyl Alfentanil Remifentanil

Chemicalcomposition

Diacetylmorphine Methylmorphine ←---------------------------------------- Synthetic phenylpiperidines ----------------------------------------→

pKa 8.0 7.6 8.2 8.7 8.4 6.5 7.1Relative lipidsolubility

1 250 30 600 90 20

Relative potency 1 2 0.1 0.1 100 10–20 100Protein binding (%) 35 40 7 60 83 90 70Volume ofdistribution (l.kg−1)

3.5 5 5.4 4.0 4.0 0.6 0.3

Oralbioavailability (%)

25–30 Low 50 (20–80) 50 33 N/A N/A

Metabolism Glucuronidation;N-demethylation

Ester hydrolysisto morphine

Glucuronidation;demethylation(CYP2D6)

Ester hydrolysis;N-demethylation

N-Dealkylation,thenhydroxylation

N-Demethylation Plasma andtissueesterases

Clearance(ml.kg−1.min−1)

16 3.1 23 12 13 6 40

Elimination rate(min)

170 5 (t1/2) 170 210 190 100 10

aOpioids are bases.

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Local anaestheticsa

Esters (-COO-) Amides (-NHCO-)

Procaine Amethocaine Lidocaine Prilocaine Bupivicaine Ropivicaine Mepivicaine

Relative potencyb 1 8 2 2 8 8 2Onsetc Slow Slow Fast Fast Medium Medium SlowDurationd Short Long Medium Medium Long Long MediumMaximum dose(mg.kg−1)

12 1.5 3 6 2 3.5 5

Toxic plasma level(mg.ml−1)

>5 >5 >1.5 >4 >5

pKa 8.9 8.5 7.9 7.7 8.1 8.1 7.6Protein bound (%) 6 75 70 55 95 94 77Relative lipid solubility 1 200 150 50 1000 300 50Volume of distribution (l) 92 191 73 59Metabolism By esterases to

para-aminobenzoic acid(allergenic)

←---------------------------------------------------------- By hepatic amidases ----------------------------------------------------------→

Clearance (l.min−1) 1 2.4 .6 0.82Elimination rate (min) 100 100 160 120 115

a Local anaesthetics are weak bases. They have hydrophilic plus hydrophobic components linked by an ester or amide group (hence classification). Localanaesthetics can act as vasodilators; prilocaine > lignocaine > bupivicaine > ropivicaine.bPotency is related to lipid solubility.c Speed of onset is related to pKa.dDuration of action is related to protein binding.

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Non-depolarizing muscle relaxants

Aminosteroids Benzylisoquinoliniums

Vecuronium Rocuronium Pancuronium Atracurium Cis-atracurium Mivacurium Gallamine Tubocurare

Structure Monoquaternary Monoquaternary Bisquaternary 10 stereoisomers 3 stereoisomers MonoquaternaryDose (mg.kg−1) 0.1 0.6 (0.9 RSI) 0.1 0.5 0.2 0.2 2.0 0.5Onset Medium Rapid Medium Medium Medium Medium Rapid SlowDuration Medium Medium Long Medium Medium Short Medium LongCardiovasculareffects

↓ HR − ↑ HR − − − ↑ HR ↓ BP

Histaminerelease

− − − Mild Rare Mild Rare Common

Protein bound(%)

10 10 20–60 15 15 10 10 30–50

Volume ofdistribution(l.kg−1)

0.2 0.2 0.3 0.15 0.15 0.2–0.3 0.2 0.3

Metabolism(%)

20a < 5a 30a 90b 95 90c 0 0

Elimination inbile (%)

70 60 20 0 0 0 0 30

Elimination inurine (%)

30 40 80 10 5 5 100 70

Renal failure ←------------------------------- Prolonged action-------------------------------→ – – – ←--------Prolonged action--------→

HR, heart rate; BP, blood pressure.aBy deacetylation.bBy Hoffman degradation and ester hydrolysis.cBy plasma cholinesterases.

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Intravenous fluids: crystalloids

Na+

(mmol.l−1)K+

(mmol.l−1)Ca2+

(mmol.l−1)Cl−

(mmol.l−1)HCO3

−

(mmol.l−1)Osm(mmol.l−1) pH

Glucose(g.1−1)

0.9% Saline 154 0 0 154 0 300 5 05% Dextrose 0 0 0 0 0 280 4 5010% Dextrose 0 0 0 0 0 560 4 1004% Dextrose, 0.18%saline

31 0 0 31 0 255 4.5 40

Hartmann’s solution 131 5 2 111 29 278 6 08.4% NaHCO3 1000 0 0 0 1000 2000 8 0

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Intravenous fluids: colloids

Composition Mw

(kDa)Na+

(mmol.l−1)K+

(mmol.l−1)Ca2+

(mmol.l−1)Mg2+

(mmol.l−1)Cl−

(mmol.l−1)Osm(mmol.l−1)

pH

Gelofusine Succinylated gelatin 30−35 154 0.4 0.4 0.4 125 279 7.4Volplex Succinylated gelatin 30−35 154 0 0 0 125 284 7.4Isoplex Succinylated gelatin 30−35 145 4 0 0.9 105 284 7.4*Haemaccel Polygelines 30−35 145 5.1 6.25 0 145 301 7.3Hydroxyethyl starch(HES)

Esterified amylopectin 450 154 0 0 0 154

Volulyte HES 130/0.4 (a tetrastarch) 130 137 4 0 1.5 110 286 5.7–6.5*Dextran 70 Polysaccharides in 5%

dextrose70 0 0 0 0 0 287 3.5–7

HES 4.5% Fractionation of plasma 69 100−160 <2 0 0 100−160 270−300 6.4−7.4HES 20% 69 50−120 <10 0 0 <40 135−138 6.4−7.4

Mw, relative molecular mass.* Isoplex also contains lactate 25 mmol.l−1; Volulyte also contains acetate 34 mmol.l−1.

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Vaughan–Williams classification of antiarrhythmic drugs

Class ActionEffect on cardiacconduction Examples

I Sodium channelblockade

Ia Prolongs refractory period Quinidine, procainamide,disopyramide

Ib Shortens refractory period Lidocaine, mexilitine,phenytoin

Ic None Flecainide, propafenoneII Beta blockade Slows atrioventricular

conductionPropranolol, atenolol, esmolol

III Potassium channelblockade

Slows atrioventricularconduction

Amiodarone, sotolol

IV Calcium channelblockade

Prolongs refractory period Verapamil, diltiazem

Gases: physical properties

Gas Mw (kDa) BP (°C) CT (°C) CP (bar) η ρ

Nitrogen 28 −196 −147 34 17.6 1.165Oxygen 32 −182 −118 50 20.4 1.331Carbon dioxide 44 −78.5 31 74 14.7 1.831Air 29 −195 −149 38 18.2 1.196Nitrous oxide 44 −88 36.5 72 14.6 1.83Helium 4 −269 −268 2.3 19.6 0.166

Mw, relative molecular mass; BP, boiling point; CT, critical temperature; CP, criticalpressure; η, viscosity; ρ, density.

386 Appendix


Body fluid composition

Componenta Plasma Interstitial Intracellular

Percentage total body waterb 5 15 40Na+ (mmol.l−1) 145 140 10K+ (mmol.l−1) 4 5 155Ca2+ (mmol.l−1) 3 2 <1Mg2+ (mmol.l−1) 1 2 40Cl− (mmol.l−1) 110 112 3HCO3

− (mmol.l−1) 26 28 7Othersc (mmol.l−1) 7 9 150Proteins (mmol.l−1) 10 − 45

aThe numbers will vary depending on the source but the cations (positively charged ions)should always equal the anions (negatively charged ions).bWater is 60% of total body weight in an adult male.c Include sulphates, phosphates and inorganic acids.

Daily nutritional requirements for a 70 kg male

Requirement per kg body weight

EnergyCalories (kcal) 30−40Food components(g)Glucose 3−4Fat 1Protein 1Nitrogen 0.2Fluid (ml) 30−40Electrolytes (mmol)Sodium 1−2Potassium 1Calcium 18Magnesium 12Chloride 1Phosphate 18

Appendix 387


Urinary electrolytes in renal failure: this table is always difficult to recall but try toremember that in intrinsic renal failure the kidney is unable to concentrate urineeffectively and so a poor quality, dilute urine is produced

Pre-renal Renal

Urine (mmol.l−1)Osmolarity >450 (concentrated) <350 (dilute, poor quality)Sodium <15 (Na+ retention) >40 (Na+ loss)Urea >250 (excreting lots) <160 (not excreting much)Urine: plasma concentrationsa

Osmolarity >2 (urine more concentrated) <1.5 (urine less concentrated)Creatinine >40 <40Urea >8 <3

a If the ratio is high, it means that there is relatively more of the substance in the urine.

Types of muscle fibre

FibreSlow oxidative(type I)

Fast oxidative(type IIa)

Fast glycolytic(type IIb)

Diameter Small Intermediate LargeConduction velocity Slow Fast FastTwitch Long Short ShortColour Red Red WhiteMyoglobin +++ +++ +Source of ATP Oxidative

phosphorylationOxidativephosphorylation

Glycolysis

Glycogen and glycolyticenzymes

+ ++ +++

Fatiguability + ++ +++

388 Appendix

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Cardiac pacemakersThe accepted nomenclature for any pacemaker is defined by the NAPSE/BPEG* code that consists of five letters, each one relating to aseparate function:I: Relates to the chamber(s) being pacedII: Relates to the chamber(s) being sensedIII: Describes the mode of responseIV: Relates to programmable functionsV: Relates to anti-tachycardia functions

IChamber(s) paced

IIChamber(s) sensed

IIIMode of response

IVProgrammable functions

VAnti-tachycardia functions

V(Ventricle)

V(Ventricle)

T(Triggered)

R(Rate modulated)

O(None)

A(Atrium)

A(Atrium)

I(Inhibited)

C(Communicating)

P(Paced)

D(Atrium & ventricle)

D(Atrium & ventricle)

D(Triggered & inhibited)

M(Multi-programmable)

S(Shocks)

O(None)

O(None)

O(None)

P(Simple programmable)

D(Paces & shocks)

O(None)

As an example, a pacemaker labelled DDDRwill pace and sense both chambers (atrium and ventricle), will be either triggered or inhibited by the presenceof electrical activity in the myocardium depending on the timing of such activity and that is able to modulate (alter) the rate according to need.*NAPSE: North American Society of Pacing and Electrophysiology – BPEG: British Pacing and Electrophysiology Group

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Symbols of basic electrical components

Battery Resistor Inductor Fuse Type BType BDefibrillator safe

AC power source Variable resistor Capacitor On/Off Type BF Type BF Defibrillator safe

Switch Transformer Earth Class II equipment Type CF Type CF Defibrillator safe

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Antimicrobial classification

Cell wall synthesis inhibition Protein synthesis inhibition Nucleic acid synthesis inhibitionCell membranefunction inhibition

Uncertainmechanism

Work by inhibiting formation ofcomponents essential forbuilding the cell wall resultingin cell lysis and death

β-Lactams*:Penicillin, cephalosporin,carbapenem, monobactam

Glycopeptides*:Vancomycin, teicoplaninPolypeptides*:Bacotrecin*Cycloserine*

Work by inhibiting thetranscription of RNA into afunctional protein chain

Aminoglycosides*:Streptomycin, gentamicin,tobramycin, netilmicin,amikacin, spectinomycin,neomycin

Tetracyclines:Tetracycline, doxycycline,LinezolidChloramphenicolLincosamides:Clindamycin, lincomycinMacrolides:Erythromycin, azithromycin,clarithromycin, spiramycin

StreptograminsFusidic acid

Fewer in this category as all cellscontain nucleic acid and it isdifficult to target bacteriaspecifically

Folic acid synthesis inhibitorsSulphonamides, trimethoprim*RNA polymerase inhibition*:Rufampicin, rifabutinDNA structural disruption*:MetronidazoleTopo-isomerase targeting*:Norfloxacin, ciprofloxacin

Tend to be highly toxic as theydisrupt the function of humanand pathogenic cells alike

Colistin*Amphotericin B*Nystatin*

Isoniazid*Ethambutol

*Bacteriocidal

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Blood Flow and Oxygen Consumption

Resting blood flowMaximum blood flowml.100g.min−1

% Cardiac outputat rest

Resting oxygenconsumption mls.min−1Organ ml.min−1 ml.100g.min−1

Brain 750 50White matter = 20Grey matter = 70

150 15 50

Heart (Coronary) 250 80 400 5 30Kidneys 1100 400

Cortex = 500Outer medulla = 100Inner medulla = 20

450 22 15

Skeletal muscle 1000 1–4 50–100 20 60Splanchnic 1250

350 hepatic artery900 mesenteric portal

50 3–4 l.min−1

(NB different units)25 55

Skin 400 10 200 8 5Other 250 5 35Total 5000 100 250

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The Autonomic Nervous System

System Sympathetic effect Receptor Parasympathetic effect Receptor

Neurotransmitter Pre-ganglionic synapses = Acetylcholine Nicotinic Acetylcholine (ACh) MuscarinicPost-ganglionic synapses = Norepinephrine* Adrenoceptors

Central nervoussystem

Pupil dilatationCiliary muscle relaxation Aqueous humour production

α1β2

Pupillary constrictionCiliary muscle constriction Emesis

M3

Cardiovascular Vasoconstriction α1 Negative chronotropy; Negative inotropy M2Presynaptic inhibition of norepinephrine release(negative feedback)

Mixed effects on smooth muscle (↑BP then↓BP)

α2

Positive chronotropy; Positive inotropy β1 Vasodilatation M3Vasodilatation β2

Respiratory Bronchodilatation β2 Bronchoconstriction M3Salivary gland Viscous (protein rich) secretion β1, β2 Increased secretion M3, M1

Watery secretion α1Gastrointestinal Relaxation of GIT α2, β2 Increased peristalsis and tone M3

Contraction of GIT sphincters α1 Relaxation of sphincters except loweroesophageal

M3

Increased secretion of glands (exceptpancreas)

M1

Hepatic/ Metabolic Glycogenolysis & gluconeogenesis α1, β2 Constriction of biliary tract M3Stimulation of lipolysis β1, β3Inhibition of lipolysis α2

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The Autonomic Nervous System (cont.)

System Sympathetic effect Receptor Parasympathetic effect Receptor

Urinary Contraction of detrusor (minor effect compared with β3effect)

α1 Micturition (detrusor contraction &sphincter relaxation)

M3

Urinary retention (detrusor relaxation and sphinctercontraction)

β2, β2

Uterine (pregnant) Uterine contraction α1Uterine relaxation β2

Other Platelet aggregation α2Piloerection α1Renin release from JGA β1, β2Thermogenesis β3

*Exceptions are post-ganglionic sweat glands (ACh via muscarinic receptors) and chromaffin cells of the adrenal medulla (directly release norepinephrineand epinephrine into the blood).β1 receptors are found in the cerebral cortex, β2 receptors are found in the cerebellum and all types of muscarinic receptors are found in the centralnervous system.

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Drugs acting in the Autonomic Nervous System

Drugs acting in the Sympathetic nervous system

Norepinephrine (Nor), Epinephrine (Epi) and Isoprenaline (Iso) all act at all adrenoceptors, but with differing potency. The order of potency is indicatednext to the receptor sub type.

Drugs acting at α- adrenoceptors

Non – specific α α1 Nor>Epi>Iso α2 Epi>Nor>Iso

+ − + − + −PhenylephrineEphedrine

PhentolamineLabetolol

MethoxamineMetaraminol

PrazosinPhenoxybenzamine* DoxazosinAlfuzosin

ClonidineDexmedetomidine

YohimbineTrazodone

Drugs acting at β – adrenoceptors

Non – specific βIso>Epi>Nor

β1 β2

+ − + − + −Ephedrine Propranolol Timolol Dobutamine Atenolol

MetoprololBisoprololEsmolol

SalbutamolRitodrineTerbutaline

Butoxamine

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Drugs acting in the Autonomic Nervous System (cont.)

Drugs acting in the Parasympathetic nervous system

+ −AnticholinesterasesEdrophoniumNeostigminePyridostigminePhysostigmineOrganophosphorus compunds

AntimuscarinicsAtropineHyoscineGlycopyrollateTropicamide

* non selective but increased affinity for α1

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Inotropes and Vasopressors

Drug Receptor Direct CVS effects Metabolism Half life

HRContr-actility SVR MVO2

Dobutamine β1 (α + β2) ↑ ↑ ↓ ↑ COMT 2–3 minutesDopamine D1 + D2 (low dose) ↑ ↑ ↓/↑ ↑ MAO 2 minutes

β (5–10 mcg.kg.min−1) Effects are dose dependent COMTα (>15 mcg.kg.min−1) At low doses also ↑RBF

Dopexamine D1, D2, β2 ↑ ↑ ↓ −/↑ Methylation, sulphate conjugation 5–10 minutes(elimination)

Inhibits uptake 1 Also ↑ renal and splanchnicblood flow

Enoximone Inhibits Type IIIphosphodiesterase

− ↑ ↓ ↑ Hepatic 6 hours (elimination)

Also ↑ myocardial DO2

Ephedrine α + β directly and indirectly ↑ ↑ ↑ ↑ Oxidation, demethylation, hydroxylation,conjugation

(resistant to MAO / COMT)

4–6 hours (elimination)

Epinephrine α + β ↑ ↑ ↓/↑ ↑ MAO (uptake 1)COMT (uptake 2)

2 minutes

Isoprenaline β ↑ ↑ ↓ ↑ COMT (Liver)Resistant to MAO

1–7 minutes

Levosimendan Calcium sensistiser − ↑ ↓ ↓ Hepatic 1 hourMetaraminol α1 direct + indirect − − ↑ Hepatic

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Inotropes and Vasopressors (cont.)

Drug Receptor Direct CVS effects Metabolism Half life

Methoxamine α1 − − ↑

Milrinone Inhibits Type III − ↑ ↓ ↑ Hepatic (glucuronidation) 1–2.5 hours(elimination)

phosphodiesterase Also ↑ myocardial DO2

Norepinephrine α, (β) (↑) (↑) ↑ ↑ MAO (uptake 1) COMT (uptake 2) 2 minutesPhenylephrine α1 − − ↑ MAO 2–3 hours (elimination)Vasopressin V1 − − ↑ Hepatic and renal 10–35 minutes

(elimination)

MVO2 = myocardial oxygen consumption; RBF = renal blood flow; D = dopamine receptor; MAO = monoamine oxidase; COMT = catechol-O-methyltransferase; V = vasopressin receptorUptake 1 = active uptake back into nerve terminal for recycling or metabolism by MAO; Uptake 2 = diffusion away from nerve

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Functional groups in organic chemistryHydrocarbon: A compound containing carbon and hydrogen.Saturated: consisting of carbon atoms bound by single bonds.Unsaturated: consisting of carbon atoms bound by double or triple bonds.Aliphatic: consisting of a hydrocarbon chain, branched chain or non aromatic ring.Aromatic: consisting of a conjugated (alternating single and double carbon bonds) ring structure (for example benzene).

Some examples of common functional groups. (R refers to a carbon based group.)

GroupStructure /Example Description / Notes Group Structure Description / Notes

Alkane Saturated hydrocarbon chain. The name dependson the length of chain

Methane = CH4

Ethane = C2H6 (shown)Propane = C3H8

Amide Present in amide local anaesthetics

Alkyl An alkane groupMethyl = CH3 (shown)Ethyl = C2H5

Propyl = C3H7

Amine Primary

Secondary

Tertiary is:

A quaternary nitrogen (NOT an amine) is anitrogen atom with 4 bonds and a permanentpositive charge

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Functional groups in organic chemistry (cont.)

GroupStructure /Example Description / Notes Group Structure Description / Notes

Alkene Unsaturated (double bond) hydrocarbon chainEthene (C2H4)

Carbamyl Present in some anticholinesterases such asneostigmine

Alkyne Unsaturated (triple bond) hydrocarbon chainEthyne = C2H2 (shown)

Carboxyl If R = H, the molecule is formic acid.If R = CH3, the molecule is acetic acid

Acetyl If R = H, the molecule is acetic acid.If R = choline, the molecule is acetylcholine

Catechol Also known as 1,2-hydroxybenzene

Alcohol Alkane with hydroxyl substitution. Ether Important in the structure of volatile anaestheticagents

Aldehyde A carbon with a double bond to oxygen and asingle bond to hydrogen. Also known as aformyl group

Ester Present in ester local anaesthetics

Benzyl An unsaturated (double bond) 6 carbon ringstructure. For e.g benzene, drawn in 2 differentways

Ketone A carbonyl (C=O) group bound to two alkylgroups

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Target controlled infusion models

Model Fixed values Weight adjusted Age adjusted keo

Modified Marsh All rate constants Compartment volumes (V1, V2, V3)Clearance (k10)

0.26

Schnider V1, V3, k13, k31 Clearance (k10) – weight, height (highervalues increase clearance) and leanbody mass (LBM) (higher valuesdecrease clearance)

V2, k12, k21 (decreases as age increases) 0.456

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Index

A band, sarcomere 306absolute humidity 43absolute refractory period 302absolute risk reduction 358absorption 177

CO2 117–118acceleration, SI units 24accuracy 19

precision and 20–21acetylcholine (ACh) receptor 305acetylcholinesterase (AChE) 305acid 283acid–base balance 283–286

anion gap 287buffers 285Davenport diagram 286Henderson–Hasselbach equation 285pregnancy effects 334–335

actin 305action potentials 301–304

absolute refractory period 302Gibbs–Donnan effect 301Goldman constant field equation 302Nernst equation 301nerve 303relative refractory period 302resting membrane potential 301threshold potential 302velocity calculations 304see also cardiac action potentials

adenosine triphosphate, muscle contraction306–307

ADH see antidiuretic hormoneadverse drug reactions 151–152

anaphylactic reactions 152anaphylactoid reactions 152types of 151

affinity 160antagonist affinity for a receptor (pA2)

169affinity constant (KA) 158afterload 260

increased 269

ageing 340–343implications of by system 340–342

cardiovascular 340endocrine 342gastrointestinal/hepatic 342neurological 342renal 342respiratory 341

pharmacodynamic effects 342pharmacokinetic effects 342timing 340

agonists 164full 164inverse 168partial 164, 165

alfentanil 381context-sensitive half time 194

allodynia 321allosteric modulator 166alternating current (AC), resistance 59alveolar dead space 219alveolar gas equation 211amethocaine 382amino acids 136ampere 23anaemic hypoxia 226anaerobic threshold 328identification of 328–330

V-slope method 328VE against work rate 329VO2 and VCO2 against work rate329

anaesthetic agentsclinical effects 326effect on cerebral blood flow and metabolism

317–318inhalational 318, 379

Meyer–Overton hypothesis 146minimum alveolar concentration 146physiological effects 380second gas effect 149

intravenous 318, 377physiological effects 378


local 382see also specific agents

anaphylactic reactions 152anaphylactoid reactions 152anatomical dead space 219anion gap 287antagonists 164

affinity for a receptor (pA2) 169competitive 166, 167irreversible 166, 167non-competitive 166, 168reversible 166, 167

antiarrhythmic drugs 386antidiuretic hormone (ADH) 293antimicrobials, classification 391aorta, pressure curve 247area, SI units 24arterial pressure, mean 254asymptote 8atom 129atomic structure 129–130atracurium 383autonomic nervous system 393

drugs acting in 13:21autonomic neuropathy, Valsalva manoeuvre

response 275autoregulation 313

cerebral blood flow 314renal blood flow 291

Avogadro’s hypothesis 34

baralime, CO2 absorption 117base 283Beer’s law 109Beer–Lambert law 109Bernoulli equation 89Bernoulli principle 38bias 363

clinical trials 371bicarbonate buffer 285bimodal distribution 356bioavailability 179Bland–Altman plot 363blinding, clinical trials 371blood:gas solubility coefficient 53blood flow 392

cerebral 313, 392coronary 255, 392FTc 90

peak velocity (PV) 91pulmonary 216–217renal 289, 392uterine 336see also Doppler effect

body fluid composition 387body mass index (BMI) 344Bohr effect, oxyhaemoglobin dissociation curve

229Bohr equation 220

derivation 221principle 221

Boyle’s law 34brain

blood flow 313, 392compliance 310

breathing, work of 232graph 232see also ventilation control

breathing systems 100–102Mapleson A 100Mapleson B 100Mapleson C 101Mapleson D 101Mapleson E 102Mapleson F 102

buffers 285Bunsen solubility coefficient 53bupivacaine 382

calibration 19candela 23capacitance 60

SI units 24capacitors 60–62

AC circuits 61, 62high frequency 62low frequency 61

DC circuit 61definition 60principles of 60

capacity, lung 203closing capacity 204

capillary dynamics 264–266fluid movement 264–266

capillary hydrostatic pressure 264capillary oncotic pressure 264capnography 112–116

acute loss of cardiac output 115

Index 403


capnography (cont.)breathing system disconnection 115capnograph 112capnometer 112cardiac oscillations 114hyperventilation 114hypoventilation 116inadequate paralysis 113malignant hyperpyrexia 115normal findings 112obstructive disease 116rebreathing 113

carbohydrates 136stress response effects 326

carbon dioxide 386absorption 117–118

baralime 117chemical reaction 117colour indicators 118mesh size 117soda lime 118

carriage 230–231dissociation curves 231Haldane effect 230Hamburger effect 230

physical properties 386see also respiratory physiology

carbonic acid–bicarbonate buffer system 285cardiac action potentials 244, 303

pacemaker 244cardiac conduction system 245cardiac cycle 246–248

diagram 246left ventricular volume curve 248pressure curves 247

aorta 247central venous pressure (CVP) 247left ventricle 247

timing points 248timing reference curves 246

cardiac oscillations, capnography 114cardiac output 260

acute loss of, capnography 115measurement 92–96

dye dilution 92Fick principle 92graphs 93, 94–95pulse contour analysis 95thermodilution 92

paediatric 339plethysmography variability index 96pregnancy effects 331pulse pressure variation 96stroke volume 96

variation 97, 98–99cardiogenic shock 280cardiopulmonary exercise testing 328–329anaerobic threshold 328

identification of 328–330evidence for 330VO2Max 330

cardiovascular physiologyadult circulation 279ageing effects 340capillary dynamics 264–266cardiac cycle 246–248central venous pressure (CVP) 257ECG changes 249–253fetal circulation 278Frank–Starling relationship 260–261heart rate control 276–277neonatal circulation 279obesity effects 344paediatrics 337pregnancy effects 331–332pressure–flow calculations 254–256

coronary blood flow 255coronary perfusion pressure 254mean arterial pressure 254

pulmonary capillary wedge pressure 258shock 280systemic vascular resistance 272

pulmonary vascular resistance 214–215, 273venous return 262–264ventricular pressure–volume relationship

267–271failing ventricle 271

case-control studies 372categorical (qualitative) data 349catenary modelling 188CBF see cerebral blood flowcelsius 40census 372central venous pressure (CVP) 257pressure curve 247waveform 257

cerebral blood flow 313, 392anaesthetic agent effects 317–318

404 Index


autoregulation 314flow-metabolism coupling 316–316PaCO2 effects 314PaO2 effects 315

cerebral metabolic rateanaesthetic agent effects 317–318of oxygen utilisation (CMROO2) 316temperature effect 317

cerebral perfusion pressure 313cerebrospinal fluid (CSF) 319

circulation 319formation 319

Charles’ law 34chemical bonds 132–134

interatomic bonds 132covalent bonds 132ionic bonds 132

intermolecular bonds 133dipole 133hydrogen bond 134Van der Waals forces 134

chi-square test 359degrees of freedom 360

children see paediatricschiral centre 139chloride shift 230chronic pain 320circulation

adult 279cerebrospinal fluid 319fetal 278neonatal 279see also cardiovascular physiology

cis-atracurium 383cleaning 70

methods 71clearance 183, 289

see also pharmacokineticsclinical trials 370–373

allocation concealment 371bias 371blinding 371clinical significance 373data collection 372case-control studies 372cohort studies 372experimental studies 372observational studies 372surveys 372

design flow sheet 370outcome 371phases 370power calculation 371randomisation 371statistical significance 373

coagulation, surgical diathermy 85Coanda effect 39codeine 381cohort studies 372colligative properties 55

Raoult’s law 55colloids 385compartment models 188–192

catenary 188concentration versus time 191mamillary 188one-compartment 188three-compartment 190formula 191

two-compartment 189formula 190

competitive antagonists 166compliance 236

brain 310lung 236dynamic 236static 236whole lung pressure–volume loop 237

concentration, SI units 24concentration effect 148

graphs 148conductive heat loss 50confidence intervals 353congestive cardiac failure, Valsalva manoeuvre

response 275conservation of energy 38context-sensitive half time 194–195continuous data 349contractility 260

altered 270convective heat loss 50coronary blood flow 255, 392coronary perfusion pressure 254correlation 361

exact negative 362negative 362no correlation 363positive 361

Index 405


correlation coefficient 361coulomb 24covalent bonds 132critical damping 69critical pressure 49critical temperature 49crystalloids 384CSF see cerebrospinal fluidcurrent

density 24SI units 23, 24

cutting, surgical diathermy 84CVP see central venous pressurecytochrome P450 CYP2D6 enzyme 153cytotoxic shock 280

D-isomerism 139daily nutritional requirements 387damping 66, 67

coefficient 67critical 69optimal 69over-damping 68under-damping 68zero damping 67

data analysis see statisticsDavenport diagram, acid–base balance 286dead space 219

alveolar 219anatomical 219physiological 219

decontamination 70decrement time 195defibrillators 97, 98–99

charging 98circuit 98discharging 98

degrees of freedom 353chi-square test 360

deoxy-haemoglobin absorption spectra 111desflurane 379

concentration effect graph 148physiological effects 380

dew point 43dextrorotatory compounds 139diamorphine 381diastereoisomers 139differentiation 17–18diffusion, Fick’s law 53

digoxin, ECG effects 251dipole 133direct current, resistance 59discrete data 349disinfection 70methods 71

dissociation constant (KD) 158dissociation curvesCO2 231oxyhaemoglobin 228–229

distance, SI units 23distribution, pharmacokinetics 177distributive shock 280Doppler effect 89Bernoulli equation 89oesophageal doppler 90–91principle 89

dose ratio 169dose–response curves 161drift 19, 21drug dependence 173drug interactions 150–150isobologram 150

drug target identification 153drug tolerance 171drug–receptor interactions 157–159see also pharmacodynamics

dynamic compliance 236dyne 272

ECG see electrocardiographyefficacy 160Einthoven’s law 242Einthoven’s triangle 241ejection fraction 268electrical charge, SI units 24electrical components, symbols of 390electrical resistance see resistance, electricalelectrocardiography (ECG) 246axis 242

determination 242changes 249–253

1st degree heart block 2522nd degree heart block (Mobitz I) 2522nd degree heart block (Mobitz II) 252complete heart block 253digoxin effect 251hyperkalaemia 249hypocalcaemia/long QT syndrome 250

406 Index


hypokalaemia 249hypothermia 251Torsades de Pointes 250

Einthoven’s law 242Einthoven’s triangle 241

electromotive force (EMF) 63electron 129elimination 183enantiomers 138enantiopure preparation 140end-diastolic pressure–volume relationship 267end-systolic pressure–volume relationship 267energy 32

conservation of 38requirements 387SI units 24

enflurane 379physiological effects 380

enzyme kinetics 141–143first-order reaction 141Lineweaver–Burke transformation 142Michaelis–Menton equation 141zero-order reaction 141

enzymes 141see also enzyme kinetics

error 366–367type I 366type II 366

etomidate 377physiological effects 378

Euler’s number 9evaporative heat loss 50evidence-based medicine 374–375

grades of recommendations 374levels of evidence 374meta-analysis 375Forest plot 375

excretion 184experimental studies 372expiratory reserve volume 203exponential relationships 9–15

basic negative exponential 10basic positive exponential 10clinical tear away positive exponential 11Euler’s number 9half life 12, 185physiological build-up negative exponential 11physiological negative exponential 11rate constant 13

time constant 12, 185transformation to a straight line graph 14

extraction ratio 180oxygen 225

failing ventricle 271farad 24, 60fentanyl 381

context-sensitive half time 195fetal circulation 278fibre-optics 79Fick’s law 53first pass metabolism 179first-order elimination 183first-order reaction 141Fisher’s exact test 360flow

Bernoulli principle 38laminar 36turbulent 37Venturi effect 38see also blood flow

flow–volume loops 207–210normal 207obstructive disease 208fixed large airway obstruction 210variable extrathoracic obstruction 209variable intrathoracic obstruction 209

restrictive disease 208force 31

SI units 24Forest plot 375Fowler’s method 219, 220–220

graph 220Frank–Starling relationship 260–261frequency

natural 66SI units 24surgical diathermy 84

full agonists 164functional groups 13:23functional residual capacity, lung 203fusion, specific latent heat of 46

G-proteins 144gallamine 383gas laws 34–35

see also specific lawsgases 386

Index 407


gate control theory of pain 321gauss 75Gay–Lussac’s law 34geometric isomerism 139Gibbs–Donnan effect 301glomerular filtration rate 289, 291

tubulo-glomerular feedback 290glucose handling, renal 295goal directed fluid therapy 97Goldman constant field equation 302Golgi tendon organs 309Graham’s law 53

H band, sarcomere 306haematology

paediatrics 338pregnancy effects 332–333

haemoglobin absorption spectra 110Hagen–Poiseuille equation 36Haldane effect 230half life 12, 185halothane 379

physiological effects 380Hamburger effect 230heart block, ECG changes

1st degree block 2522nd degree block (Mobitz I) 2522nd degree block (Mobitz II) 252complete block 253

heart ratepregnancy effects 332regulation 276–277

paediatric considerations 277parasympathetic control 276post-transplant considerations 277sympathetic control 277

heart sounds 246heat 40–42

definition 40heat capacity 46heat loss 50–52

conduction 50convection 50during surgery 51evaporation 50radiation 50respiration 50

helium, physical properties 386Henderson–Hasselback equation 285

henry, definition 63Henry’s law 53hertz 24histotoxic hypoxia 227Hüffner constant, oxygen delivery 224humidity 43–45absolute 43clinical relevance 44–45

efficiency of inhaled gas humidifiers 45dew point 43graph 43hygrometer 43hygroscopic material 43relative 43

hydrocarbons 13:23hydrogen bond 134hygrometer 43hygroscopic material 43hyperalgesia 321hyperbolic relationships 8hyperkalaemia, ECG changes 249hyperpathia 321hyperventilation 114hypocalcaemia, ECG changes 250hypokalaemia, ECG changes 249hypothermia, ECG changes 251hypoventilation 116hypovolaemic shock 280hypoxia 226–227anaemic 226histotoxic 227hypoxaemic 226ischaemic 226

hysteresis 19, 22, 170

I band, sarcomere 306impedance 59inductance 63inductors 63–64definition 63graphs 64principles of 63

inhalational anaesthetic agents 318, 379physiological effects 380see also specific anaesthetics

inorganic chemistry 135inorganic compounds 135inotropes 13:22inspiratory reserve volume 203

408 Index


integration 16–17interquartile range 354interstitial fluid composition 387interstitial hydrostatic pressure 264interstitial osmotic pressure 264interval 350intracellular fluid composition 387intracranial pressure (ICP)

changes to baseline of the ICP trace 312intracranial volume relationship 310waveform 311see also cerebral blood flow; cerebral perfusion

pressureintravenous fluids 384

colloids 385crystalloids 384

intravenous induction agents 318, 377physiological effects 378

inverse agonists 168ion 130, 131ionic bonds 132ischaemic 226isobologram 150isoflurane 379

physiological effects 380isohydric principle 285isomerism 138–140

chiral centre 139dextrorotatory 139diastereoisomers 139enantiomers 138enantiopure preparation 140geometric 139laevorotatory 139optical 139racemic mixture 140rectus 139sinister 139stereoisomerism 138structural 138tautomerism 138

isotherms 48–49nitrous oxide 48

isotopes 129

joule 24, 32

Kaplan Meier curves 376kelvin 23, 40

ketamine 377physiological effects 378

kilogram 23

L-isomerism 139laevorotatory compounds 139Lambert’s law 109laminar flow 36

Hagen–Poiseulle equation 36LaPlace’s law

sphere 57tube 58

laser 81–83coherent 82collimated 82definition 81monochromatic 81principle 81

latent heat 46–47heat capacity 46specific heat capacity 46specific latent heat of fusion 46specific latent heat of vaporization 46water heating curve 47

law of mass action 158LD50 (median lethal dose) 162lidocaine 382ligand 157linear relationships 7Lineweaver–Burke graph 143Lineweaver–Burke transformation

142lipids 136

stress response effects 326local anaesthetics 382logarithms 9

rules 9long QT syndrome, ECG changes 250loop of Henle 293luminous intensity, SI units 23lung

capacity 203closing capacity 204

compliance 236, 237flow–volume loops 207–210normal 207obstructive disease 208, 209, 210restrictive disease 208

resistance 236

Index 409


luminous intensity, SI units (cont.)volumes 203–204

closing volume 204expiratory reserve volume 203functional residual capacity 203inspiratory reserve volume 203pulmonary vascular resistance relationship214

residual volume 203tidal volume 203vital capacity 203

whole lung pressure–volume loop 237see also respiratory physiology

M line, sarcomere 306MAC (minimum alveolar concentration) 146magnetic resonance imaging 75–78

basic principles 75, 76precession 77

malignant hyperpyrexia 115mamillary modelling 188Mapleson breathing systems see breathing

systemsmass, SI units 23mathematical relationships 7–8

asymptote 8hyperbolic relationships 8linear relationships 7parabolic relationships 8see also exponential relationships

mean 351mean arterial pressure 254measurements 19–22

accuracy 19, 20–21drift 19, 21hysteresis 19, 22non-linearity 19, 22precision 19, 20–21

mechanics 31–33median 351median effective concentration (EC50) 161median effective dose (ED50) 161median lethal dose (LD50) 162medical ultrasound 87–88

basic function 87contrast resolution 88spatial resolution 88

membrane potential 301see also action potentials

mepivacaine 382meta-analysis 375Forest plot 375

methohexital 377physiological effects 378

metre 23Meyer–Overton hypothesis 146graph 146

Michaelis–Menten equation 141Michaelis–Menten graph 142minimum alveolar concentration (MAC) 146minute ventilationalveolar carbon dioxide partial pressure

relationships 234, 235alveolar oxygen partial pressure relations 233,

235mivacurium 383Mobitz I type heart block 252Mobitz II type heart block 252mode 351mole 23molecule 130Monro–Kelly doctrine see neurophysiologymorphine 381muscle fibres 388muscle physiology 305–307excitation–contraction coupling 306–307neuromuscular junction 305sarcomere 305see also muscle fibres

muscle reflexes 308–309Golgi tendon organs 309muscle spindles 308stretch reflex 308

muscle relaxants 383muscle spindles 308myelinated nerves, action potential velocity 304myosin 305

natural frequency 66negative predictive value 367negative pressure ventilation 103negatively skewed distribution 356neonatal circulation 279Nernst equation 301neuromuscular blockade monitoring 119–123double-burst stimulation 121no neuromuscular block 122phase 1 and phase 2 block 123

410 Index


post-tetanic count 122receptor site occupancy assessment 121residual neuromuscular block 122single twitch 119supra-maximal stimulus 119tetanic stimulus 119train of four (TOF) 119depolarising block 120non-depolarising block 120ratio (TOFR) 121

neuromuscular junction 305neuropathic pain 321neurophysiology

action potentials 301–304Monro–Kelly doctrine 310–312brain compliance 310changes to baseline of the ICP trace 312intracranial pressure waveform 311intracranial volume–pressure relationship

310neurone types 303see also cerebral blood flow; pain

neurotransmitter 304newton 24, 31nitrogen, physical properties 386nitrous oxide 379

concentration effect 148isotherms 48physical properties 386physiological effects 380

nociception 320nociceptive pain 320nominal data 349non-compartmental modelling 187non-linearity 19, 22non-SI units 26

conversion factors 26normal distribution 355nucleic acids 136nucleotides 136null hypothesis 357number needed to treat 357numerical (quantitative) data 349nutritional requirements 387

obesity 344–346implications of by system 344–345cardiovascular 344metabolic 345

respiratory 344NICE classification 344pharmacokinetic effects 345

observational studies 372obstructive disease

capnography 116flow–volume loop 208fixed large airway obstruction 210variable extrathoracic obstruction 209variable intrathoracic obstruction 209

peak expiratory flow rate (PEFR) 208shock 280spirometry 205

odds ratio 358oesophageal doppler 90–91ohm 24Ohm’s law 59oil:gas solubility coefficient 53older people 340

see also ageingone-tailed test 359opioids 318, 326, 381optical isomerism 139optimal damping 69ordinal data 349organic chemistry 135

carbohydrates 136functional group 135lipids 136nucleic acids 136proteins 136structural formula 135

organic compounds 135osmolality 55osmolarity 55osmole 55osmometer 56osmosis 55–56

graph 56osmotic pressure 55Ostwald solubility coefficient 54outcome prediction 367–368

negative predictive value 367positive predictive value 367

over-damping 68oxidation 130, 131oxygen

consumption 392delivery 223–225

Index 411


oxidation (cont.)critical 225oxygen cascade 223oxygen extraction ratio 225oxyhaemoglobin dissociation curve 228–229Pasteur point 224supply and demand 224

physical properties 386oxyhaemoglobin

absorption spectra 111dissociation curve 228–229

affecting factors 229Bohr effect 229P50 228, 229

p value 357P50 228

changes in position 229pA2 169pacemakers 389

action potentials 244paediatrics 337–339

heart rate regulation 277implications by system 337–339

cardiovascular 337metabolic 339renal 338respiratory 337

pharmacodynamics 339pharmacokinetics 339physiological calculations 339

pain 320–322chronic 320gate control theory 321neuronal connections 322neuropathic 321nociceptive 320pathway 322phantom 321somatic 320visceral 320

paired test 358pancuronium 383parabolic relationships 8partial agonists 164, 165pascal 24, 32Pasteur point 224peak expiratory flow rate (PEFR), obstructive

disease 208

Peltier effect 56perfect gases 34pethidine 381pH 283phantom pain 321pharmacodynamics 157affinity 160affinity constant (KA) 158ageing effects 342dissociation constant (KD) 158dose ratio 169dose–response curves 161

logarithmic 162quantal 162

drug–receptor interactions 157–159law of mass action 158

duration of action 163efficacy 160hysteresis 170median effective concentration (EC50) 161median effective dose (ED50) 161median lethal dose (LD50) 162paediatrics 339potency 160pregnancy effects 335tachyphylaxis 171therapeutic index 163tolerance 171see also agonists; antagonists

pharmacogenetics 153pharmacokinetics 177absorption 177ageing effects 342bioavailability 179clearance 183compartmental modelling 188–192context-sensitive half time 194–195decrement time 195distribution 177elimination 183

first-order 183zero-order 184

excretion 184extraction ratio 180non-compartmental modelling 187obesity effects 345paediatrics 339physiological modelling 193pregnancy effects 335

412 Index


redistribution 177volume of distribution 181

physiological modelling 193piezoelectric effect 87pKa 284placenta 278, 336plasma

composition 387volume, pregnancy effects 333

plethysmography variability index 96population 349positive predictive value 367positive pressure ventilation 103positively skewed distribution 355potassium handling, renal 297potency 160potential difference, SI units 24potentiation, drug actions 150power 33

SI units 24statistical 357

power calculation, clinical trials 371precession 77precision 19

accuracy and 20–21pregnancy 331

implications of by system 331cardiovascular 331–332endocrine and metabolic 335gastrointestinal and hepatic 335haematology 332–333neurological 335renal and acid-base 334–335respiratory 333–334

pharmacodynamic effects 335pharmacokinetic effects 335placenta 336timing 331

preload 260increased 269

pressure 32critical 49SI units 24

pressure control ventilation 105prilocaine 382procaine 382prodrug 179propofol 377

context specific half time 194

physiological effects 378proteins 136

stress response effects 326proton 129pulmonary blood flow distribution 216–217pulmonary capillary wedge pressure (PCWP) 258

waveform 258pulmonary vascular resistance 214–215, 273

factors affecting 214lung volume relationship 214

pulse contour analysis 95pulse oximetry 109–111

Beer’s law 109haemoglobin absorption spectra 110deoxyhaemoglobin 111oxyhaemoglobin 111

Lambert’s law 109

quadriplegia, Valsalva manoeuvre response 275quantal dose–response curves 162quartile 354

racemic mixture 140radiant heat loss 50randomisation, clinical trials 371Raoult’s law 55rate constant 13ratio 349reactance 59rebreathing, capnography 113receiver operating characteristic curve (ROC) 369receptor 157rectus configuration 139red blood cell (RBC) volume, pregnancy effects

332redistribution 177reduction 131refraction 79regression coefficient 361relative humidity 43relative refractory period (RRP) 302relative risk 358remifentanil 381

context specific half time 194renal blood flow 289, 392renal failure, urinary electrolytes 388renal physiology

acid–base balance 283–286ageing effects 342

Index 413


renal failure, urinary electrolytes (cont.)clearance 289glomerular filtration rate 289, 291

tubulo-glomerular feedback 290glucose handling 295haematology 338loop of Henle 293paediatrics 338potassium handling 297pregnancy effects 334–335renal blood flow 289

autoregulation 291renal vascular resistance 291sodium handling 296

residual volume, lung 203resistance (electrical) 59

alternating current 59definition 59direct current 59impedance 59reactance 59SI units 24temperature measurement 41

resistance (respiratory) 236lung resistance 236

resonance 66definition 66natural frequency 66

respiratory physiologyageing effects 341alveolar gas equation 211Bohr equation 221–222carbon dioxide carriage 230–231

dissociation curves 231Haldane effect 230Hamburger effect 230

compliance 236, 237dead space 219

alveolar 219anatomical 219physiological 219

heat loss 50hypoxia 226–227obesity effects 344oxygen delivery 223–225

oxyhaemoglobin dissociation curve 228–229paediatrics 337pregnancy effects 333–334pulmonary blood flow distribution 216–217

pulmonary vascular resistance 214–215, 273resistance 236shunt equation 212–213time constant of a lung unit 237ventilation control 233–235ventilation/perfusion mismatch 218work of breathing 232see also lung; spirometry

resting membrane potential 301restrictive diseaseflow–volume loop 208spirometry 205–206

Reynold’s number 37rocuronium 383ropivacaine 382

sample 349sarcomere 305second 23second gas effect 149second messengers 145Seebeck effect 42sensitivity 366sevoflurane 379physiological effects 380

shock 280cardiogenic 280cytotoxic 280definition 280distributive 280hypovolaemic 280obstructive 280

shunt 212shunt equation 212–213derivation 213principle 212

SI units 23–25base units 23derived 24

with special symbols 24prefixes 24see also specific units

signal to noise ratio 27sinister configuration 139soda lime, CO2 absorption 117sodium handling, renal 296solubility 53–54blood:gas solubility coefficient 53Bunsen solubility coefficient 53

414 Index


Graham’s law 53Henry’s law 53oil:gas solubility coefficient 53Ostwald solubility coefficient 54

somatic pain 320specific heat capacity 46specific latent heat of fusion 46specific latent heat of vaporization 46specificity 367speed

of sound, in the body 88SI units 24

spirometry 205–206normal findings 205obstructive pattern 205restrictive pattern 206

standard deviation 352standard error of the mean 353static compliance 236statistics

categorical (qualitative) data 349nominal 349ordinal 349

central tendency measures 351mean 351median 351mode 351

data analysis methods 357–365absolute risk reduction 358bias 363Bland–Altman plot 363chi-square test 359correlation 361, 362correlation coefficient 361Fisher’s exact test 360good agreement 364interpretation 364no agreement 364null hypothesis 357number needed to treat 357odds ratio 358one-tailed test 359p value 357paired test 358power 357regression coefficient 361relative risk 358statistical tests 365Student’s t-test 358

two-tailed test 359unpaired test 358see also specific tests

data types 349–350distribution types 355–356bimodal distribution 356negatively skewed distribution 356normal distribution 355positively skewed distribution 355

error 366–367sensitivity 366specificity 367type I 366type II errors 366

Kaplan Meier curves 376numerical (quantitative) data 349continuous 349discrete 349interval 350ratio 349

outcome prediction 367–368negative predictive value 367positive predictive value 367

population 349receiver operating characteristic curve (ROC) 369sample 349spread, measures of 351–354confidence intervals 353degrees of freedom 353interquartile range 354quartile 354standard deviation 352standard error of the mean 353variance 351

stereoisomerism 138sterilization 70

methods 71Stewart–Hamilton equation 92stress response 325–327

anaesthesia effects 326effects of 326

stretch reflex 308stroke volume 96, 260

variation 97, 98–99structural isomerism 138Student’s t-test 358summation, drug actions 150surface tension 57–58

diagram 57

Index 415


surface tension (cont.)LaPlace’s law 57, 58

surgical diathermy 84–86blended 86coagulation 85cutting 84frequency 84

survey 372synergisms, drug actions 150systemic vascular resistance 272

tachyphylaxis 171target controlled infusion (TCI) 196–199

effect-site targeting 197keo 196models 401plasma-site targeting 197

tautomerism 138temperature 40

critical 49resistance wire measure 41Seebeck effect 42SI units 23thermistor 41thermocouple 42triple point 40see also heat

tesla 75therapeutic index 163thermistor 41thermocouple 42thermodilution 92

graphs 94–95thiopental 377

context-sensitive half time 195physiological effects 378

threshold potential 302thromboelastography (TEG) 124–125

30 minute amplitude 124alpha angle 124diagram 125kinetics 124maximum amplitude 124reaction time 124

tidal volume 203time constant 12, 185

of a lung unit 237transformation to a straight line graph 14

time, SI units 23

timing points, cardiac cycle 248tolerance 171Torsades de Pointes, ECG changes 250total internal reflection 79train of four (TOF) 119depolarising block 120non-depolarising block 120ratio (TOFR) 121

triple point 40tropomyosin 305tubocurare 383tubulo-glomerular feedback 290turbulent flow 37Reynold’s number 37

two-compartment models 189two-tailed test 359type I error 366type II error 366

ultrasound 87under-damping 68universal gas equation 35unmyelinated nerves, action potential velocity

304unpaired test 358urinary electrolytes, renal failure 388uterine blood flow 336

Valsalva manoeuvre 274–275abnormal responses 275applications 275

Van der Waals forces 134vaporization, specific latent heat of 46variance 351vascular resistancepulmonary 214–215, 273renal 291systemic 272

vasopressors 13:22Vaughan–Williams classification, antiarrhythmic

drugs 386vecuronium 383velocitySI units 24Venturi effect 38

venous return 262–264altered venous resistance 263changes 263increased filling 263

416 Index


ventilation control 233–235minute ventilation versus alveolar PaCO2

234, 235minute ventilation versus alveolar PaO2

233, 235ventilation/perfusion mismatch 218

graph 218ventilator profiles 103–108

clinical relevance 107negative pressure ventilation 103positive pressure ventilation 103waveforms 104pressure control ventilation 105volume control ventilation 106

ventilators 103cycling 104limit 104trigger 103see also ventilator profiles

ventriclefailing 271left ventricular pressure curve 247left ventricular volume curve 248

ventricular pressure–volume relationship267–271

altered contractility 270ejection fraction 268end-diastolic 267end-systolic 267

increased afterload 269increased preload 269

Venturi effect 38vesicle, neuromuscular junction 305visceral pain 320vital capacity, lung 203volt 24volume control ventilation 106volume of distribution 181volume, SI units 24

water heating curve 47watt 24, 33wave number 24weber 75weight 31Wenckebach phenomenon 252Wheatstone bridge 65

equation 65work 32

SI units 24

xenon 379

Z line, sarcomere 306zero damping 67zero-order elimination 184zero-order reaction 141zeroing 19

Index 417


Documents

Physics, Pharmacology and Physiology for Anaesthetists: Key Concepts for the FRCA