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HYPERCAPNIC HYPERVENTILATION SPEEDS
EMERGENCE FROM INHALED
ANESTHESIA
By
Nishant A Gopalakrishnan
A dissertation submitted to the faculty of
The University of Utah in partial fulfillment of the requirements of
Doctor of Philosophy
Department of Bioengineering
The University of Utah
December 2006
Copyright © Nishant A Gopalakrishnan 2006
All Rights Reserved
T H E U N I V E R S I T Y O F U T A H G R A D U A T E S C H O O L
SUPERVISORY COMMITTEE APPROVAL
of a dissertation submitted by
This dissertation has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory. __________________ _________________________________________
Chair: __________________ _________________________________________
__________________ _________________________________________
__________________ _________________________________________
__________________ _________________________________________
T H E U N I V E R S I T Y O F U T A H G R A D U A T E S C H O O L
F I N A L R E A D I N G A P P R O V A L
To the Graduate Council of the University of Utah: I have read the dissertation of in its final form and have found that (1) its format, citations, and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the supervisory committee and is ready for submission to The Graduate School. ________________________ ______________________________________ Date Chair: Supervisory Committee
Approved for the Major Department
_____________________________________
Chair/Dean
Approved for the Graduate Council
_____________________________________ David S. Chapman
Dean of The Graduate School
ABSTRACT
Anesthetic clearance from the lungs and the circle breathing system can be
maximized using hyperventilation and high fresh gas flow. However, the concomitant
clearance of CO2 also lowers arterial partial pressure of CO2 thereby decreasing cerebral
blood flow and hence the clearance of anesthetic from the brain. Emergence time from
inhaled anesthesia can be significantly reduced by maintaining hypercapnia (feedback
controlled infusion of CO2 or rebreathing) during hyperventilation.
We anesthetized seven pigs with 2 MACPIG (minimum alveolar concentration) of
isoflurane and four each with 2 MACPIG of sevoflurane or 1 MACPIG of desflurane. After
two hours of anesthesia, the animals were hyperventilated and the time to movement of
multiple limbs was measured under hypocapnic (EtCO2=22 mmHg) and hypercapnic
(EtCO2=55 mmHg) conditions. Emergence time from isoflurane and sevoflurane
anesthesia was shortened by an average of 65% with rebreathing or with the CO2
controller (p<0.05). The emergence times obtained from rebreathing were not statistically
different from those obtained from precisely tuned feedback controller.
We evaluated the differences in emergence time in fifty two surgical patients
undergoing 1 MAC of isoflurane, sevoflurane or desflurane anesthesia under mild
hypocapnia (EtCO2=29 mmHg) and mild hypercapnia (EtCO2=55 mmHg). The minute
ventilation in half the patients was doubled during emergence and hypercapnia was
maintained by insertion of additional airway dead space to keep the EtCO2 close to 55
v
mmHg during hyperventilation. A charcoal canister adsorbed volatile anesthetic agent
from the rebreathed dead space. Fresh gas flow was raised to 10 L/min during emergence
in all the patients. The time between turning off the vaporizer and the time when the
patients opened their eyes in response to command was faster when hypercapnic
hyperventilation was maintained using the rebreathing adsorber (p<0.05). The time to
tracheal extubation was shortened by 57%.
We used a multi compartmental mathematical model to estimate cerebral
awakening concentration of anesthetic agent (when patients responded to a command to
open eyes) and emergence times from anesthesia. The normalized cerebral awakening
concentration to age adjusted MAC for desflurane, sevoflurane and isoflurane were 0.162
± 0.044, 0.280 ± 0.058 and 0.356 ± 0.105 respectively. The root mean square error of the
performance error (calculated as a percent of the predicted value) was between 10% and
24%. The model estimated that there will be at least a 56% reduction in emergence time
with hypercapnic hyperventilation.
The emergence time after isoflurane, sevoflurane and desflurane anesthesia was
shortened significantly by using hypercapnic hyperventilation. The rebreathing device
described in the study should be considered following a surgical procedure where a high
concentration of the anesthetic agent is maintained right up to the end of the procedure or
when surgery ends abruptly without warning.
TABLE OF CONTENTS
ABSTRACT. . . . . . . . . . . . . . . . . . . . iv LIST OF TABLES . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . ix
ACNOWLEDGEMENTS. . . . . . . . . . . . . . . . xi
1. INTRODUCTION . . . . . . . . . . . . . . . . 1
1.1. Inhaled Anesthetic Agents. . . . . . . . . . . . 1 1.2. Anesthesia Delivery System. . . . . . . . . . . . 2 1.3. MAC and MACawake. . . . . . . . . . . . . . 2 1.4. Pharmacology of Inhaled Anesthetics. . . . . . . . 4 1.5. Recovery from Anesthesia. . . . . . . . . . . 5 1.6. Importance of a Rapid Recovery. . . . . . . . . . . 9 1.7. References. . . . . . . . . . . . . . . . 13
2. ANIMAL STUDIES . . . . . . . . . . . . . . . . 15
2.1. Abstract . . . . . . . . . . . . . . . . 15 2.2. Introduction. . . . . . . . . . . . . . . . 16 2.3. Methods. . . . . . . . . . . . . . . . . 17 2.4. Results. . . . . . . . . . . . . . . . . 27 2.5. Discussion. . . . . . . . . . . . . . . . 38 2.6. Conclusions. . . . . . . . . . . . . . . . 42 2.7. References. . . . . . . . . . . . . . . . 42
3. CLINICAL EVALUATION OF REBREATHING DEVICE . . . . 45
3.1. Abstract . . . . . . . . . . . . . . . . 45 3.2. Introduction. . . . . . . . . . . . . . . . 46 3.3. Methods. . . . . . . . . . . . . . . . . 48 3.4. Results. . . . . . . . . . . . . . . . . 52 3.5. Discussion. . . . . . . . . . . . . . . . 53 3.6. Conclusions. . . . . . . . . . . . . . . . 64 3.7. References. . . . . . . . . . . . . . . . 65
vii
4. MODEL TO PREDICT EMERGENCE FROM INHALED ANESTHESIA . 68
4.1. Abstract . . . . . . . . . . . . . . . . 68 4.2. Introduction. . . . . . . . . . . . . . . . 69 4.3. Methods. . . . . . . . . . . . . . . . . 72 4.4. Results. . . . . . . . . . . . . . . . . 86 4.5. Discussion. . . . . . . . . . . . . . . . 87 4.6. Conclusions. . . . . . . . . . . . . . . . 100 4.7. References. . . . . . . . . . . . . . . . 101
5. SUMMARY AND CONCLUSIONS . . . . . . . . . . . 104
5.1. Project Overview . . . . . . . . . . . . . 104 5.2. Conclusions . . . . . . . . . . . . . . . 108 5.3. Limitations of the Study. . . . . . . . . . . . . 109 5.4. Future Work. . . . . . . . . . . . . . . . 110 5.5. References. . . . . . . . . . . . . . . . 111
APPENDIX: EQUATIONS USED IN THE MATHEMATICAL MODEL. . . 113
LIST OF TABLES
Table Page
1.1. Tissue/blood partition coefficients. . . . . . . . . . . . 6
1.2. Average cost of 1 MAC hour of anesthesia. . . . . . . . . 12
2.1. Average time to spontaneous breathing, EtCO2 during emergence, pre-emergence minute ventilation and emergence minute ventilation. . . 28 3.1. Patient demographics. . . . . . . . . . . . . . . 54
3.2. Duration of surgery and total dose of opioids. . . . . . . . . 55
3.3. EtCO2 at extubation, pre-emergence and emergence BIS and minute ventilation. . . . . . . . . . . . . . . . . . 56
3.4. Time to open eyes, mouth and extubation. . . . . . . . . . 57
4.1. Volume and blood flow for each compartment. . . . . . . . 75
4.2. Partition coefficients used in the model. . . . . . . . . . 76
4.3. Performance measures of the model during each trial. . . . . . . 91
4.4. Estimated emergence times after 0.5, 2 and 8 hours of anesthesia . . . 92
4.5. Estimated total inhaled and exhaled agent after 0.5,2 and 8 hours of anesthesia. . . . . . . . . . . . . . . . . . 93
LIST OF FIGURES
Figure Page
1.1. Circle breathing circuit. . . . . . . . . . . . . . 3
2.1. Block diagram of feedback controller. . . . . . . . . . . 19
2.2. Rebreathing device with rebreathing hose, activated charcoal and one-way valves. . . . . . . . . . . . . . . . . 21 2.3. Simulated EtCO2 for a various rebreathing hose volumes . . . . . 23
2.4. Normalized BIS during emergence from isoflurane and desflurane . . 29
2.5. Average time to movement of multiple limbs after isoflurane, sevoflurane and desflurane anesthesia.. . . . . . . . . . 30 2.6. Average time to normalized BIS to rise to 0.95 after isoflurane, sevoflurane and desflurane anesthesia . . . . . . . . . . 31 2.7. Average time to movement of multiple limbs after 1 MAC of desflurane anesthesia. . . . . . . . . . . . . . . . . . 33
2.8. Typical controller tuning curves for the proportional constant. . . . 34
2.9. Typical controller tuning curves for the integral constant. . . . . . 35
2.10. Response of the controller for a step change in ventilation and set point. . 36
2.11. Inspired agent concentration for the rebreathing device with and without valves. . . . . . . . . . . . . . . . . 37 3.1. Rebreathing device . . . . . . . . . . . . . . . 50
3.2. Normalized BIS during emergence from isoflurane, sevoflurane and desflurane anesthesia. . . . . . . . . . . . . . . 58 3.3. Average time to tracheal extubation after isoflurane, sevoflurane and desflurane anesthesia . . . . . . . . . . . . . 59
x
3.4. Average time to normalized BIS to rise to 0.95 after isoflurane, sevoflurane and desflurane anesthesia. . . . . . . . . . . 60
4.1. Schematic of the compartments in the model. . . . . . . . . 73
4.2. Predicted and measured emergence times from 1 MAC of desflurane . . 88
4.3. Predicted and measured emergence times from 1 MAC of sevoflurane. . 89
4.4. Predicted and measured emergence times from 1 MAC of isoflurane. . 90
4.5. Estimated emergence times from 1 MAC of desflurane for different combinations of EtCO2 and minute ventilation. . . . . . . . 94 4.6. Estimated emergence times from 1 MAC of sevoflurane for different combinations of EtCO2 and minute ventilation. . . . . . . . 95 4.7. Estimated emergence times from 1 MAC of isoflurane for different combinations of EtCO2 and minute ventilation. . . . . . . . 96
ACKNOWLEDGMENTS
First and foremost, I would like to thank Dr Westenskow for his generous support
and for providing me with an opportunity to work with him on this project. I will always
look back on my five years in the Anesthesia Bioengineering Laboratory with great
fondness.
I appreciate the time and guidance provided by the members of my supervisory
committee: Dwayne Westenskow, Joseph Orr, Douglas Christensen, Kenneth Horch and
Derek Sakata. I am also indebted to Robert G. Loeb at the University of Arizona, who
reviewed this dissertation and provided many useful comments.
I would like to thank Dr Sakata for his guidance and assistance with the clinical
studies and Scott Mc James for his assistance with the animal studies. I would also like to
thank Joseph Orr for his able guidance throughout the project.
I am grateful to Anecare Laboratories for their support and interest in this project, to
the Society of Technology in Anesthesia and the Anesthesiology Department at the
University of Utah for the financial support they have provided.
I would like to thank my parents and my wife for the support and encouragement
they have provided over the years.
CHAPTER 1
INTRODUCTION
1.1 Inhaled anesthetic agents
Inhaled anesthetic agents are available as volatile liquids which are vaporized and
mixed with oxygen or air and delivered to the patient’s lungs. The agent is absorbed from
the alveoli into the systemic circulation and is distributed around the body and to the
brain and spinal cord which are the sites of action of the drug. Elimination of agent
occurs mainly through the lungs and a small amount may be eliminated by the kidneys
and liver.
Inhalational anesthetic agents offer the greatest control over the anesthetic state
offering the ability to quickly increase or decrease and monitor anesthetic levels, along
with the advantages of providing anesthesia at a low cost. Inhalational agents by
themselves are able to provide amnesia, muscle relaxation and a limited amount of
analgesia.
The first use of inhalational agents for providing anesthesia dates back to the
1850’s with the administration of nitrous oxide and later with the introduction of diethyl
ether and chloroform. Ether had a slow onset and recovery and also caused a significant
amount of post operative nausea and vomiting. Later non flammable fluorinated
hydrocarbons methoxyflourane, halothane, isoflurane, enflurane, sevoflurane and
2
desflurane were developed. The newer anesthetic agents offered the advantages of less
solubility and resistance to degradation in the body. The volatile agents commonly used
in clinical practice in the United States today include isoflurane, sevoflurane and
desflurane.
1.2 Anesthesia delivery system
The primary method of volatile anesthetic delivery in the United States is the circle
rebreathing system (Figure 1.1). The circle system allows rebreathing of previously
exhaled anesthetic gas, thereby conserving anesthetic vapor as well as retaining heat and
humidity. Soda lime is used to absorb CO2 so that it is not rebreathed by the patient. In
the circle system, fresh gas containing anesthetic vapor flows through the inspiratory
valve and the inspiratory limb to the patient. The expired gas flows through the
endotracheal tube, Y piece, expiratory limb and through the expiratory valve. The gas at
this point either exits the circuit through the pop off valve to the gas scavenging system
or passes through the CO2 absorber. The gas that passes through the absorber mixes with
the fresh gas that flows from the anesthesia machine. During anesthesia maintainenance,
low fresh gas flow (1 to 3 L/min) is used so as to minimize anesthetic loss from the
circuit.
1.3 MAC and MACawake
The alveolar concentration of anesthetic agent is determined by the difference
between the amount of anesthetic introduced into the lungs by minute ventilation and the
amount removed from the lungs by the circulating blood. The minimum alveolar
3
Figure 1.1. Circle breathing circuit
4
concentration (MAC) of anesthetic agent at which 50% of the subjects do not respond to
a surgical incision is used to compare the potency of different anesthetic agents.
When vapor is used as the primary anesthetic, anesthesiologists maintain a
concentration 10 to 30 percent greater than MAC to ensure immobilization of nearly all
patients. MAC decreases with age and the MAC requirements are also reduced by the use
of opioids. MACawake is the average alveolar agent concentration that permits voluntary
response to command. MAC awake for commonly used inhaled agents isoflurane,
sevoflurane and desflurane is approximately one third of the MAC.(1-2)
The alveolar concentration of agent approximates blood concentration, which is
used at a surrogate for cerebral concentration. The cerebral anesthetic concentration is
believed to be a better indicator of the depth of anesthesia, especially during rapid
washout of anesthetic during hyperventilation accompanied by changes in the partial
pressure of CO2.
1.4 Pharmacology of inhalational anesthetics
The rate of uptake, distribution, speed of recovery and relative changes in the
alveolar concentration with changes in minute ventilation are determined by the solubility
of the agent in blood and tissues. A more soluble agent will have a larger inspired to
alveolar concentration difference during induction of anesthesia due to larger amount of
agent being absorbed by the tissues from the blood stream. Relatively insoluble agents
show a more rapid equilibration of alveolar concentration with the inspired concentration
and are less affected by changes in cardiac output and ventilation.
5
The solubility of an anesthetic agent in an equilibrium state is expressed in terms of
a partition coefficient that describes the ratio of the concentration of the agent in the two
phases and hence the affinity of the agent for the two phases. Table 1.1 lists the partition
coefficients for the commonly used inhaled agents.
Amongst the agents, desflurane and sevoflurane have lower blood and tissue
partition coefficients and thus give better control of anesthetic depth during induction of
anesthesia as well as during anesthesia maintenance. Desflurane has a faster recovery
profile when compared to sevoflurane and sevoflurane has a faster recovery profile when
compared to isoflurane.(3-5) With the more soluble anesthetic agents like isoflurane, a
decrease in anesthetic dosage towards the end of the case would be required to achieve
shorter emergence times comparable with the less soluble agents.
1.5 Recovery from anesthesia
The cerebral concentration of anesthetic agent is determined by the concentration
of agent circulating in the arterial blood stream and the amount of cerebral perfusion. The
cerebral blood flow is intrinsically controlled by cerebrovascular resistance and not
affected much by arterial pressure.
For return of consciousness following inhaled anesthesia, the cerebral
concentration of agent must drop below the threshold for emergence. In clinical practice,
this is achieved by turning off the vaporizer and either ventilating the patient with the
same minute ventilation as during anesthesia maintenance or ventilating the patient with a
slightly increased minute ventilation. Fresh gas flow is usually raised to 10 L/min for
rapid removal of agent from the circle system and to prevent re-inhalation of anesthetic
agent. Neuromuscular blockades are reversed before emergence for return of ventilatory
6
Table 1.1
Tissue/Blood partition coefficients(6-7) (Except for Blood/Gas partition coefficients)
Tissue Desflurane Sevoflurane Isoflurane
Blood/gas 0.45 0.65 1.40
Brain 1.22 1.69 1.57
Heart 1.22 1.69 1.57
Liver 1.49 2.00 1.86
Kidney 0.89 1.20 1.00 Muscle 1.73 2.62 2.57 Adipose 29.00 52.00 50.00
Lung 1.30 1.50 1.10 Connective 1.40 1.50 2.00
7
muscle strength.
The alveolar agent concentration during emergence depends on the difference
between the amount of agent delivered to the alveoli by the circulating blood and the
amount of agent removed from the lungs by minute ventilation. The alveolar agent
concentration during the initial stages of washout of anesthetic is mainly from the well
perfused tissues like brain, liver, heart and kidney that receive the largest fraction of the
cardiac output. Subsequently less perfused tissues like muscle and fat also start
contributing a significant fraction of the alveolar concentration. The fraction of anesthetic
cleared from the blood (F) as it passes through the lungs is given by Equation 1.1,
( )
+
=
AVQ
F*1
1*%100λ
(1.1)
where Q is the cardiac output , λ is the blood gas partition coefficient and VA is the
alveolar ventilation.
After a longer duration of anesthesia, more anesthetic will be stored in fat and
tissues and will increase the time to a given decrement in agent concentration. This could
considerably delay emergence for the more soluble agents like isoflurane if the
ventilation is not increased to clear the agent from the blood stream. Increases in cardiac
output during emergence could possibly increase the release of anesthetic stored in
tissues and thereby delay emergence from anesthesia. Thus more ventilation is necessary
to remove a more soluble agent when compared to a less soluble agent.
8
Hyperventilation could be used to accelerate clearance of anesthetic from the lungs.
However, during hyperventilation the rate of CO2 elimination exceeds its rate of
production and as a result, the arterial partial pressure of CO2 (PaCO2) decreases. PaCO2
has to be sufficiently high during emergence to stimulate the ventilatory center to initiate
ventilatory efforts by the patient. PaCO2 also has a significant effect on cerebral blood
flow. A decrease in PaCO2 causes vasoconstriction in cerebral vasculature and decreases
cerebral blood flow. Hypercapnia on the other hand increases cerebral blood flow by 6%
per mmHg increase in PaCO2.(8) Cerebral arterial smooth muscle dilates with a decrease
in the extracellular pH as CO2 is rapidly hydrated to form carbonic acid. The local acidic
environment enhances the vasodilatory effects of adenosine and increases potassium ion
conductance in smooth muscle, resulting in vasodilatation.(9)
PaCO2 during emergence could be increased by hypoventilation. However,
hypoventilation results in a slower clearance of anesthetic from the lungs due to a
decrease in the alveolar-blood anesthetic gradient, thus resulting in a slower emergence.
Clinicians thus have to make a compromise between increasing PaCO2 and hence the
cerebral clearance of anesthetic by hypoventilation and increasing alveolar clearance of
agent by hyperventilation.
Some older anesthesia machines, which are not in current use had a manual valve
to bypass the CO2 absorber and enable rebreathing of CO2 (Ohio 18 Absorber, Ohio
Medical Products, Madison WI) (A100 Absorber, Penlon Limited, Abingdon, UK).(10)
The amount of CO2 rebreathed and the level of hypercapnia was controlled by adjusting
the fresh gas flow to the breathing circuit. The CO2 absorber bypass is of limited utility
because high fresh gas flow is needed to clear exhaled anesthetic from the breathing
9
circuit, which reduces the amount of CO2 rebreathing and limits the rate at which CO2
increases.(11-12) Advocates of low flow anesthesia also used activated charcoal to
rapidly decrease the inspired agent concentration in the circle system without the use of
high fresh gas flows.(13-15) They were able to reduce the inspired agent concentration to
zero within a minute and were able to attain a faster decline in the end tidal isoflurane
concentrations towards MACawake values with the use of activated charcoal. The bypass
option is not available on new anesthesia machines because of the risk of inadvertently
leaving the bypass active at the start of a procedure.(10)
Carbon dioxide could be added to the inspired gas in sufficient concentration so as
to prevent a decrease in PaCO2 during hyperventilation. In the past, many anesthesia
machines were equipped with a tank containing 100% CO2. The flow of CO2 was
adjusted during emergence to maintain normal or slightly elevated PaCO2 during
hyperventilation. In 1989, 60% of the anesthesiologists in the United Kingdom routinely
administered CO2 to their patients.(16) They were however concerned with the risks of
hypoxia and inadvertent hypercapnia and 80% of them thought that limiting the flow of
CO2 to less than 1 L/min would improve safety. The practice is very seldom used in the
United States today because of the risk of inadvertent hypercapnia.(17-18)
1.6 Importance of a rapid recovery
A more rapid recovery and a higher PaCO2 during emergence from anesthesia
might lead to an early return of the patient’s capacity to sustain his own airway, protect
against aspiration and maintain oxygenation. Rapid recovery also promotes return of
normal cardiovascular function.(19) An early recovery might also lead to an early
10
discharge from the post anesthesia care unit if hyperventilation is able to reduce the
residual anesthetic in the body to a level that could allow the return of normal
psychomotor function. A larger amount of agent removed during hyperventilation might
also lead to a lesser amount of agent being left in the body that could undergo
degradation to toxic byproducts.
The ventilatory depressant effects of neuromuscular blocking agents are enhanced
by the presence of inhaled anesthetic agents. A rapid removal of agent from the body
might reduce issues with ventilatory failure due to inadequate reversal of neuromuscular
blocks. Anesthetic concentrations in the 0.1 MAC range instead of decreasing the
perception of pain has a hyperalgesic effect.(20-21) A rapid emergence might lead to a
rapid progression through these low concentrations that are typically encountered during
slow washout of anesthetic and thus possibly decrease post operative pain.
Although greater cost saving could be achieved by improving efficiency in the
operating room rather than minimizing anesthetic cost, anesthetic drugs continue to be a
major part of the pharmacy budget and appropriate use of the agent is recommended to
minimize costs. The cost of inhalation anesthesia is determined by the acquisitions cost of
the agent, amount of vapor produced per ml of anesthetic, fresh gas flow used, equipment
needed for delivering and monitoring the agent, emergence time from anesthesia and post
operative adverse effects (Table 1.2). A rapid emergence from anesthesia might be
possible even with the slower agents which are less expensive using hypercapnic
hyperventilation.
The use of hypercapnia during hyperventilation to speed up emergence from
anesthesia looks promising provided the safety concerns regarding high CO2 could be
11
adequately addressed. This dissertation is organized as follows. Chapter 2 introduces two
methods of raising PaCO2 during hyperventilation. A very simple device using
rebreathing of CO2 and a more complex and accurate device using feedback controlled
infusion of CO2 is described The remainder of Chapter 2 describes the evaluation of the
rebreathing device and the CO2 controller in speeding emergence from isoflurane,
sevoflurane and desflurane anesthesia in 15 pigs. Chapter 3 describes the clinical
evaluation of the rebreathing device in a study involving 52 patients undergoing
anesthesia with 1 MAC of isoflurane, sevoflurane or desflurane. The differences in
emergence times with hypercapnic hyperventilation (EtCO2=55 mmHg).and mild
hypocapnia during hyperventilation (EtCO2=29 mmHg) were compared. Chapter 4
describes a mathematical model of inhaled anesthetic uptake, distribution and elimination
that we modified to simulate working of the rebreathing device as well as changes in
cerebral perfusion with different agents and changes in EtCO2.The data from the clinical
study was used to estimate the cerebral awakening concentration of agent at which the
patients opened their eyes in response to command and estimate the predictive accuracy
of the model using the estimated concentrations. Chapter 4 also describes simulations
which help us better understand the relative contribution of hypercapnia and
hyperventilation in speeding emergence from 1MAC of isoflurane, sevoflurane or
desflurane anesthesia. A summary of the project and concluding remarks are given in
Chapter 5.
12
Table 1.2
Average Cost of agents for 1MAC hour of anesthesia(22)
Anesthetic Cost/ml Average Cost/1 MAC Hour at given FGF Rate
$0.47 at 0.5 L/min
Isoflurane $0.26 $0.94 at 1 L/min $1.88 at 2 L/min $5.39 at 0.5 L/min
Desflurane $0.62 $10.78 at 1 L/min $21.55 at 2 L/min $8.34 at 1 L/min
Sevoflurane $1.27 $16.68 at 2 L/min
$25.02 at 3 L/min
13
1.7 References
1. Katoh T, Suguro Y, Ikeda T et al. Influence of age on awakening concentrations of sevoflurane and isoflurane. Anesth Analg 1993;76:348-52.
2. Chortkoff BS, Eger EI, 2nd, Crankshaw DP et al. Concentrations of desflurane and propofol that suppress response to command in humans. Anesth Analg 1995;81:737-43.
3. Smith I, Ding Y, White PF. Comparison of induction, maintenance, and recovery characteristics of sevoflurane-N2O and propofol-sevoflurane-N2O with propofol-isoflurane-N2O anesthesia. Anesth Analg 1992;74:253-9.
4. Frink EJ, Jr., Malan TP, Atlas M et al. Clinical comparison of sevoflurane and isoflurane in healthy patients. Anesth Analg 1992;74:241-5.
5. Nathanson MH, Fredman B, Smith I, White PF. Sevoflurane versus desflurane for outpatient anesthesia: a comparison of maintenance and recovery profiles. Anesth Analg 1995;81:1186-90.
6. Eger EI, 2nd, Saidman LJ. Illustrations of inhaled anesthetic uptake, including intertissue diffusion to and from fat. Anesth Analg 2005;100:1020-33.
7. Lerou JG, Dirksen R, Beneken Kolmer HH, Booij LH. A system model for closed-circuit inhalation anesthesia. I. Computer study. Anesthesiology 1991;75:345-55.
8. Ito H, Kanno I, Ibaraki M et al. Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography. J Cereb Blood Flow Metab 2003;23:665-70.
9. Brian JE, Jr. Carbon dioxide and the cerebral circulation. Anesthesiology 1998;88:1365-86.
10. Dorsch J, Dorsch, SE. Understanding Anesthesia Eequipment. Second ed. Baltimore, MD: Williams & Wilkins, 1985.
11. Bergman JJ, Eisele JH. The efficiency of partial soda-lime bypass circuits. Anesthesiology 1972;36:94-5.
14
12. Ivanov SD, Nunn JF. Methods of elevation of PCO2 after anaesthesia with passive hyperventilation. Br J Anaesth 1968;40:804.
13. Romano E, Pegoraro M, Vacri A et al. [Charcoal and isoflurane alveolar washout in low-flow circuit]. Minerva Anestesiol 1993;59:223-7.
14. Romano E, Pegoraro M, Vacri A et al. Low-flow anaesthesia systems, charcoal and isoflurane kinetics. Anaesthesia 1992;47:1098-9.
15. Ernst EA. Use of charcoal to rapidly decrease depth of anesthesia while maintaining a closed circuit. Anesthesiology 1982;57:343.
16. Razis PA. Carbon dioxide--a survey of its use in anaesthesia in the UK. Anaesthesia 1989;44:348-51.
17. Shipton EA, Roelofse JA, van der Merwe CA. Accidental severe hypercapnia during anaesthesia. Case reports and a review of some physiological effects. S Afr Med J 1983;64:755-6.
18. Prys-Roberts C, Smith WD, Nunn JF. Accidental severe hypercapnia during anaesthesia. A case report and review of some physiological effects. Br J Anaesth 1967;39:257-67.
19. Widmark C, Olaison J, Reftel B et al. Spectral analysis of heart rate variability during desflurane and isoflurane anaesthesia in patients undergoing arthroscopy. Acta Anaesthesiol Scand 1998;42:204-10.
20. Sonner J, Li J, Eger EI, 2nd. Desflurane and nitrous oxide, but not nonimmobilizers, affect nociceptive responses. Anesth Analg 1998;86:629-34.
21. Zhang Y, Eger EI, 2nd, Dutton RC, Sonner JM. Inhaled anesthetics have hyperalgesic effects at 0.1 minimum alveolar anesthetic concentration. Anesth Analg 2000;91:462-6.
22. Sakai EM, Connolly LA, Klauck JA. Inhalation anesthesiology and volatile liquid anesthetics: focus on isoflurane, desflurane, and sevoflurane. Pharmacotherapy 2005;25:1773-88.
CHAPTER 2
ANIMAL STUDIES
2.1 Abstract
Anesthetic clearance from the lungs and the circle breathing system can be
maximized by using hyperventilation and high fresh gas flows. However, the concomitant
clearance of CO2 also lowers PaCO2 thereby decreasing cerebral blood flow and hence the
clearance of anesthetic from the brain. This study shows that in addition to hyperventilation,
hypercapnia (CO2 infusion or rebreathing) is a significant factor in decreasing emergence
time from inhaled anesthesia.
We anesthetized 7 pigs with 2 MACPIG of isoflurane (3.1%) and 4 each with 2
MACPIG of sevoflurane (3.94%) or 1 MACPIG of desflurane (10.0%). After two hours of
anesthesia, the animals were hyperventilated and the time to movement of multiple limbs was
measured under hypocapnia (EtCO2=22 mmHg) and hypercapnia (EtCO2=55 mmHg). The
time between turning off the vaporizer and to movement of multiple limbs was faster with
hypercapnia during hyperventilation. Emergence time from isoflurane and sevoflurane
anesthesia was shortened by an average of 65% with rebreathing or with feedback controlled
infusion of CO2 (p<0.05).
Hypercapnia in conjunction with hyperventilation may be used clinically to decrease
emergence time from inhaled anesthesia. This time savings could potentially reduce drug and
16
personnel costs. Anesthesiologists will also feel less pressure to titrate anesthetic towards the
end of the case to shorten emergence time, possibly decreasing the incidence of intra
operative awareness. In addition, higher PaCO2 during emergence may enhance respiratory
drive and airway protection following extubation.
2.2 Introduction
Rapid removal of anesthetic during emergence allows for a rapid egress from stage II
of anesthesia. In addition, a rapid return of consciousness is desirable to allow patients to
quickly leave the operating suite, thereby reducing personnel costs.(1) Rapid removal of
anesthetic is also desirable in clinical procedures that require the patient to be awakened
during the surgery.(2)
Recovery time after inhaled anesthesia depends on alveolar ventilation, solubility of
the agent in blood and tissues and anesthesia duration.(3-4) However, when hyperventilation
is used during emergence to quickly lower the alveolar and arterial concentration of the
agent, the rate of CO2 removal from the lungs exceeds its rate of production and hypocapnia
ensues. Hypocapnia decreases cerebral blood flow, which decreases the rate of clearance of
anesthetic from the brain. Veseley et al maintained normocapnia during hyperventilation and
showed the role of increased minute ventilation in decreasing emergence time.(5) We
maintained hypercapnia during hyperventilation to show the role of increased cerebral blood
flow in decreasing emergence time.
Normocapnia or hypercapnia can be maintained during hyperventilation by
introducing CO2 into the inspired gas mixture. A survey of anesthesiologists in the United
Kingdom in 1989 showed that 60% of them infused CO2 during emergence. They were
17
however concerned with the risks of hypoxia and inadvertent hypercapnia and 80% of them
thought that limiting the flow of CO2 to less than 1 L/min would improve safety.(6-8)
Perhaps a safer approach would be to add dead space to the breathing circuit to induce
hypercapnia.(9) Rebreathing of CO2 recovers the CO2 that would otherwise be eliminated
during hyperventilation.
Our study measures the decrease in emergence time in pigs after isoflurane,
sevoflurane or desflurane anesthesia when hypercapnia was maintained during
hyperventilation using rebreathing of CO2 or feedback controlled infusion of CO2.
2.3 Methods
We tested two methods of raising PaCO2 during hyperventilation. EtCO2 can be more
accurately maintained during hyperventilation using feedback controlled infusion of CO2.
However, a relatively simple and inexpensive method is to use rebreathing of CO2. The
feedback controller introduced CO2 into the breathing circuit at the optimum rate and
provided an ideal control condition against which to compare rebreathing.
2.3.1 Feedback controller
Figure 2.1 shows the block diagram of the feedback controller we implemented and
tuned to actively induce and maintain hypercapnia during hyperventilation. The controller
consists of a CO2SMO Plus monitor (Respironics Inc, USA) to measure EtCO2, inspired tidal
volumes and respiratory rate. The computer ran a proportional-integral (PI) control algorithm
which compared the measured EtCO2 from the previous breath to the desired target EtCO2
18
and determined the amount of CO2 to be added to the inspired gas in the subsequent breath.
The PI controller used the equation
( ) ( ) ( ) ( )[ ] ( )[ ]tEtCOSetCOTKtEtCOtEtCOKtCOtCO ip 2222 11 −+−−−−= (2.1)
where ( )tCO and ( )1−tCO are the controller outputs for the current and previous breath,
( )tEtCO2 and ( )12 −tEtCO are the end tidal CO2 for the current and previous breath, 2SetCO
is the target end tidal CO2, pK and iK are the proportional and integral constants and T is
the sampling period.
A timer circuit was used to regulate the amount of CO2 added to the inspired gas
depending on the value sent to it by the PI controller. The inlet pressure to the valve was
maintained at 20 psi. The integral and proportional constants were tuned as functions of
minute volume and respiratory rate using a mechanical test lung (TTL Test Lung, Michigan
Instruments, MI, USA) connected to an anesthesia ventilator (Modulus CD, Ohmeda,
Madison, WI). CO2 was introduced into the mechanical test lung at constant flow rate using a
mass flow controller to simulate metabolic CO2 production. The constants were functions of
respiratory rate and tidal volume so that the controller would have the same response time
irrespective of the patient’s minute ventilation. The controller was tuned to produce a stable
response and achieve its target level within 30 seconds. CO2 was introduced into the inspired
gas mixture during the start of inspiration to prevent artifacts in the capnogram that would
have been seen if the patient should exhale spontaneously during the inspiratory period.
When exhalation occurred during inspiration the CO2 waveform was segmented into six
sections to calculate EtCO2 accurately. The section with the minimum standard deviation of
19
Figure 2.1. Block diagram of feedback controller.
Patient
CO2SMO
(Novametrix Medical Systems Inc)
Computer
(Proportional Integral Controller)
Valve
Timer Circuit
CO2 tank
20
CO2 after the dead-space gas had been exhaled was used to calculate EtCO2.
2.3.2 Rebreathing device
We used the device shown in Figure 2.2 to passively increase PaCO2 during
hyperventilation. The device consists of a rebreathing hose, a canister filled with anesthetic
adsorbent and two valves to maintain unidirectional flow of gas through the adsorbent. The
rebreathing hose is a 22mm ID corrugated breathing hose having 150 ml of dead space when
collapsed and 665 ml when fully extended. The canister 7.5 cm diameter and 0.95 cm thick
holds 18 gm of medical grade activated charcoal to adsorb anesthetic agent from the inspired
gas as it is rebreathed.
2.3.2.1 Volume of rebreathing hose
The volume of rebreathing hose should be sufficient to raise the PaCO2 of a patient to
55mmHg during emergence. We estimated the volume of rebreathing that would be required
using a mathematical simulation implemented in Matlab. Rebreathing of CO2 was simulated
for a 70 kg and a 140 kg patient. A constant metabolic CO2 production based on body weight
was assumed. The model also assumed that 85% of the volume of CO2 left in the rebreathing
hose from the previous breath is inhaled in the subsequent breath. The change in CO2 in the
body is given by the difference between the total CO2 increase in the body (due to metabolic
CO2 production and inspiration of CO2 from the hose) and the amount excreted by the lungs.
The resting ventilation was set to maintain an EtCO2 of 33 mmHg was 5.04 L/min at a
respiratory rate of 8 breaths/min for the 70 kg patient and 10 L/min at 8 breaths/min for the
140 kg patient. The simulated patients were hyperventilated by doubling the minute
21
Figure 2.2. Rebreathing device with rebreathing hose, activated charcoal and one-way valves.
22
ventilation. We expect the emergence times with the device to be less than 10 minutes and
hence the EtCO2 ten minutes since start of hyperventilation was recorded for different
rebreathing hose volumes. Figure 2.3 shows the EtCO2 ten minutes since the start of
hyperventilation for varying rebreathing hose volumes. From the simulations it appears that a
rebreathing hoses volume greater than 0.5 L would be required for a typical 70 kg patient.
2.3.2.2 Amount of activated charcoal
The amount of activated charcoal in the rebreathing device should be sufficient to
adsorb anesthetic agent exhaled by the patient during emergence so that none is re-inhaled by
the patient. Desflurane requires a larger volume % of agent for a MAC of anesthesia when
compared to sevoflurane or isoflurane due to its lower potency. For estimating the amount of
activated charcoal required, we implemented a model of inhaled anesthetic uptake,
distribution and elimination described by Lerou, et al.(10) We simulated anesthesia
maintainenance at 1 MAC of desflurane (6.44 % for humans) for a 140 kg, 1.83 m adult male
for 8 hours of anesthesia. During anesthesia maintainenance, the minute volume was set to 10
L/min to maintain an EtCO2 of 33 mmHg. Emergence times for desflurane after 8 hours of
anesthesia are expected to be much less than 15 min with hypercapnic hyperventilation. We
simulated emergence from anesthesia by setting the vaporizer to zero and doubling the
minute ventilation. We recorded the total amount of agent exhaled by the subject during the
15 min period.
The total amount of agent exhaled by the subject was estimated to be 1064 standard
cubic centimeter (scc). Assuming an 85% rebreathing efficiency, the total amount of
desflurane to be adsorbed would be 904 scc. The equilibrium capacity of activated charcoal
23
20
25
30
35
40
45
50
55
60
65
0 0.2 0.4 0.6 0.8 1 1.2Rebreathing hose volume (L)
EtC
O2
(mm
Hg)
70 Kg 140 kg
Figure 2.3. EtCO2 10 min since start of hyperventilation for a simulated 70 kg and 140 kg patient for with varying of rebreathing hose volumes.
24
for desflurane at 24°C is approximately 75 scc/g. Thus 12 g of charcoal would be adequate to
adsorb all the agent expired by the patient so that none of it is reinhaled. It is safer to use
charcoal in excess of 12 gm as a safety measure.
We tested the adsorption efficiency of the device for agent isoflurane with a canister
7.5 cm diameter and 0.95 cm thick holding 18 gm of activated charcoal. The device was
connected between an anesthesia ventilator (NarkoMed 2B, North American Drager, Telford,
PA) and a mechanical test lung (TTL, Michigan Instruments Inc, Grand Rapids, MI). The
minute ventilation as set to 10L/min and the vaporizer was set to give an inspired agent
concentration of 2%. The concentration of agent that flows into the device and the
concentration of agent that exits the device were recorded using two anesthetic gas analyzers
(CapnoMAC Ultima, Datex-Ohmeda, Helsinki, Finland).The adsorption efficiency was
calculated as the ratio of the difference between the input and exit agent concentration to the
input agent concentration through the device.
The device showed an adsorption efficiency of 80% until 1200 ml of isoflurane had
been adsorbed. We believe that the adsorption performance of the device with 18gm of
activated charcoal would be adequate for the worst possible scenario that might be
encountered in clinical practice.
2.3.3 Study protocol
After Institutional Animal Care and Use Committee approval we studied 15 pigs of
either sex weighing 34 to 44 kg. We induced anesthesia with telazol (tiletamine
hydrochloride, zolazepam hydrochloride) (10mg/kg). The animal’s trachea was intubated
without the use of muscle relaxants. Anesthesia was maintained in 7 pigs with 2 MACPIG of
25
isoflurane (3.1%). In 4 pigs anesthesia was maintained with 2 MACPIG of sevoflurane
(3.94%) and another 4 were anesthetized with 1 MACPIG of desflurane (10.0%). The volatile
anesthetic agent concentration was monitored continuously using an anesthetic gas analyzer
(CapnoMAC Ultima, Datex-Ohmeda, Helsinki, Finland). We placed ECG leads, pulse
oximetry probe, invasive blood pressure sensor with arterial line, rectal temperature probe
and BIS electrodes to monitor vital signs. Sedation level was monitored using Bispectral
Index (BIS, Aspect Medical Systems, Nutton, Massachusetts). The mean arterial blood
pressure was maintained above 50 mmHg by titrating the infusion of Lactated Ringers
solution. The respiratory rate was set at 10 breaths/min. The tidal volume was adjusted to
maintain EtCO2 at 33 mmHg with a circle absorber rebreathing circuit (Modulus CD,
Ohmeda, Madison, WI). Anesthesia was maintained for 2 hours for each animal
studied.EtCO2, inspired and expired agent concentrations and BIS were recorded
electronically using a personal computer running custom software written in Borland C++
Builder (Inprise Corporation, USA).
Emergence time was measured after 2 hours of anesthesia. Emergence began when
the vaporizer was turned off. The fresh gas flow was raised to 10 L/min and the respiratory
rate was set to 20 breaths per minute, resulting in an approximate doubling of minute
ventilation during emergence. Once awake, each animal was reanesthetized with the
anesthetic agent by turning on the vaporizer. Each animal was emerged from anesthesia three
times under the following conditions.
• EtCO2 increased slowly from 33 to 55 mmHg by CO2 rebreathing.
• EtCO2 increased rapidly from 33 to 55 mmHg by the CO2 controller.
26
• EtCO2 falls to hypocapnic level (~22mmHg) during hyperventilation without
adding CO2.
In additions to the three emergence conditions listed above the animal was also
emerged from desflurane anesthesia at an EtCO2=30 mmHg by maintaining the same
ventilation settings as during anesthesia maintenance and turning up the fresh gas flow
during emergence.
We recorded the time between when the vaporizer was turned off until the return of
spontaneous breathing and movement of two or more limbs. Spontaneous breathing during
mechanical ventilation was ascertained by movement of the chest wall and out of sync
spontaneous breaths observed in the capnogram. Once the movement of multiple limbs
occurred, the animals were reanesthetized with anesthetic vapor by turning on the vaporizer
and increasing fresh gas flow to 10 L/min. Once the BIS, blood pressure, and heart rate
returned to the values recorded prior to turning off the vaporizer, anesthesia was maintained
for an additional 30 min before the next emergence occurred. To minimize the possibility of
a prior emergence influencing our results, the order of emergence was randomly selected.
The BIS data recorded electronically for each emergence was normalized using the
following equation:
( )( )BIScepreEmergenBISimum
BISemergencepreBISBISNormalized
−−−
=max
(2.2)
where pre-emergence BIS is the average BIS two minutes prior to turning off the vaporizer
and maximum BIS is the maximum BIS value observed during emergence and subsequent
27
induction. The time for the normalized BIS to reach 0.95 from the time the vaporizer was
turned off was calculated for each emergence.
2.3.4 Statistical analysis
Analysis was performed using SigmaStat version 2.03 (SPSS Inc).The effect of the
anesthetic agent and method of emergence on the time to movement of multiple limbs, time
to spontaneous breathing and time for the normalized BIS to rise to 0.95 were compared
using 2 way repeated measures ANOVA. Post hoc Bonferroni tests were performed when the
interaction effects were found to be significant.
2.4 Results
Table 2.1 lists the time from when the vaporizer was turned off to the return of
spontaneous breathing. Figure 2.4 shows the normalized BIS during emergence from agent’s
isoflurane and sevoflurane. Figures 2.5 and 2.6 shows the average time to movement of
multiple limbs and the average time for the normalized BIS to rise to 0.95, respectively.
The time to movement of multiple limbs, time to spontaneous breathing and time to
normalized BIS to rise to 0.95 were significantly shorter when hypercapnia was maintained
during emergence from isoflurane and sevoflurane (p<0.05). Emergence times were not
statistically different when rebreathing was used from those obtained when the CO2
controller was used.
Normalization of BIS values assumes that the pre-emergence BIS and maximum BIS
are similar for each emergence within each animal. The maximum standard deviation of pre-
emergence BIS (within each animal) in the animals receiving isoflurane, sevoflurane and
28
Table 2.1
Average time to spontaneous breathing (mean ± SD), average EtCO2 at time of movement of multiple limbs, average minute ventilation during anesthesia maintenance as recorded immediately before turning off the vaporizer(maintenance) and average minute ventilation at the time of movement of multiple limbs(emergence) (mean ± SD).
Isoflurane (n=7)
Sevoflurane (n=4)
Desflurane (n=4)
Hypocapnia 19.1 ± 3.7 18.4 ± 6.1 6.9 ± 4.8
Rebreathing device 3.8 ± 1.0 3.4 ± 0.9 3.1 ± 1.9
Time to spontaneous breathing (min) CO2
controller 4.2 ± 1.1 3.9 ± 0.7 2.4 ± 0.5
Hypocapnia 22.1 ± 1.0 23.3 ± 1.3 21.0 ± 2.9
Rebreathing device 54.7 ± 1.6 57.8 ± 2.1 51.3 ± 4.2
EtCO2 at emergence (mmHg)
CO2 controller 54.7 ± 0.8 55.3 ± 1.0 55.5 ± 1.3
Hypocapnia 6.1 ± 0.7 5.9 ± 0.8 *
Rebreathing device 6.1 ± 0.8 5.9 ± 0.7 *
Minute ventilation during maintenance (L/min) CO2
controller 5.6 ± 1.7 5.5 ± 1.0 5.8 ± 0.6
Hypocapnia 12.5 ± 1.5 12.4 ± 1.7 *
Rebreathing device 12.6 ± 1.2 12.1 ± 1.3 *
Minute ventilation during emergence (L/min)
CO2 controller 12.2 ± 1.1 12.2 ± 1.9 11.8 ± 1.2
* Minute ventilations were not logged.
29
Figure 2.4. Normalized BIS during emergence from 2 MACPIG of isoflurane and sevoflurane anesthesia for the 3 emergence scenarios.
30
0.0
5.0
10.0
15.0
20.0
25.0
Hypocapnia Rebreathing Device CO2 Controller
Tim
e to
mov
emen
t of m
ultip
le li
mbs
(min
±SD
)
DESISO SEVO DES SEVO SEVO DESISO ISO
Figure 2.5. Average time from turning off the vaporizer to time to movement of multiple limbs after 2 MACPIG of isoflurane, 2 MACPIG of sevoflurane and 1 MACPIG of desflurane anesthesia (mean + SD).
31
0
5
10
15
20
25
Hypocapnia Rebreathing Device CO2 Controller
Tim
e to
Nor
mal
ized
BIS
to r
ise
t o0.
95 (m
in±S
D)
ISO ISO ISOSEVO SEVO SEVODES DES DES
Figure 2.6. Average time from turning off the vaporizer to time to normalized BIS to rise to 0.95 during emergence after 2 MACPIG of isoflurane, 2 MACPIG of sevoflurane and 1 MACPIG of desflurane anesthesia (mean + SD).
32
desflurane anesthesia were 4.7, 5.6 and 5.0 respectively. The maximum standard deviation of
the peak BIS value (within each animal) during emergence from isoflurane, sevoflurane and
desflurane anesthesia was 3.4, 4.2 and 2.3, respectively.
With desflurane, the results were not statistically significant. The time to movement
of multiple limbs was shortest when hypercapnia in conjunction with hyperventilation was
used during emergence. Maintaining normocapnic CO2 by keeping the same minute
ventilation as during maintenance gave a lower emergence time when compared to
hypercapnic hyperventilation (Figure 2.7).
Figures 2.8 and 2.9 show the proportional and integral constants used in the controller
for various respiratory rates and minute ventilations. After isoflurane anesthesia, the
feedback controller increased the EtCO2 from 33 mmHg to a target of 55 mmHg in 30.68 ± 6
seconds (95% of target value) (Figure 2.10). In steady state, the average EtCO2 was 55.06 ±
0.63 mmHg.
Figure 2.11 shows the performance of the rebreathing adsorber device with regard to
adsorption of anesthetic with and without the valves for a pig emerging from 2 MAC of
sevoflurane anesthesia. Without the valves, the inspired agent showed an increase to 0.15%
and the device started functioning like an anesthetic conserving device providing a fixed
inspired agent concentration. With the added valves, the performance of the device was
significantly improved and the inspired agent concentrations remained below 0.02% during
the emergence.
33
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Hypocapnia (21 mmHg) Normocapnia (31 mmHg)* Hypercapnia (55 mmHg)
Tim
e to
mov
emen
t of m
ultip
le li
mbs
(min
±SD
Figure 2.7. Average time from turning off the vaporizer to time to movement of multiple limbs during emergence from 1 MACPIG of desflurane. * Maintainenance ventilation was used during emergence.
34
0
500
1000
1500
2000
2500
0 2 4 6 8 10 12 14 16 18Minute Ventilation (L/min)
Prop
ortio
nal c
onst
ant (
Kp)
10 16 18 26 34 38
Figure 2.8. Typical controller tuning curves for the proportional constant (Kp) for different respiratory rates.
35
0
1000
2000
3000
4000
5000
0 2 4 6 8 10 12 14 16 18
Minute Ventilation (L/min)
Inte
gral
con
stan
t (K
i)
10 16 18 26 34 38
Figure 2.9. Typical controller tuning curves for the integral constant (Ki) for different respiratory rates.
36
Figure 2.10. Response of the controller for a step change in the CO2 controller’s set point and a doubling of minute ventilation in 7 pigs.
37
Figure 2.11. Inspired agent concentrations for a single pig during emergence from 2 MACPIG of sevoflurane for the rebreathing device with and without one-way valves.
38
2.5 Discussion
The time to emergence from isoflurane and sevoflurane anesthesia was 66 ± 6%
faster when hypercapnia was induced by partial CO2 rebreathing and 63 ± 4% faster when
induced by feedback control of the inspired CO2. If similar results are obtained in patients,
anesthesiologists might be inclined to use the simpler rebreathing device. Use of the device
might reduce drug costs by allowing the use of more soluble, less expensive agents. Higher
PaCO2 during emergence may help to enhance respiratory drive following extubation. The
possibility of intra-operative awareness towards the end of the case could be decreased since
anesthetic agent would not have to be titrated to achieve the desired emergence time.
Increasing ventilation in combination with artificially maintained normal to high
EtCO2 shortens emergence time from volatile anesthetics. Veseley, et al. compared
emergence times from isoflurane-nitrous oxide anesthesia with and without hyperventilation
when EtCO2 was kept at 46.8 mmHg.(5) Their study found a 70% decrease in emergence
time (8.5 min) between the experimental and control groups with minute ventilations of 17
L/min and 5.9 L/min respectively. Veseley’s study clearly shows the importance of
hyperventilation in decreasing emergence time. Hyperventilation with even larger minute
volume could shorten emergence time further but might also cause barotrauma, decrease
stroke volume in critically ill patients and induce release of mediators like cytokines into the
circulation.(11-13)
Our results show that hypercapnia is a significant factor in reducing emergence time
during hyperventilation. After two hours of isoflurane or sevoflurane anesthesia, the time to
movement of multiple limbs decreased by 64% when hypercapnia was maintained during
hyperventilation. Hypercapnia increases cerebral blood flow by 6.0 ± 2.6% per mmHg
39
increase in PaCO2 and thus accelerates the rate of clearance of anesthetic from the brain.(14)
Increasing PaCO2 during emergence might have shortened emergence by mechanisms other
than increasing anesthetic clearance, such as increasing sympathetic response and increased
respiratory response of the animal attempting to breathe against mechanical ventilation.(15-
16)
Hypercapnia reduced the standard deviation between emergence times by 72%
(rebreathing device). By increasing the rate of fall in cerebral agent concentration,
hypercapnia shortened the transition from asleep to awake state and thus makes emergence
time more predictable. Predictability of emergence time is important when anticipating and
planning for the end of a clinical procedure.
After a study in 1923 found that hypercapnia and hyperventilation shortened
emergence time from 74 to 15 min after ether anesthesia, Ohio Medical Inc and Dräger both
manufactured anesthesia machines that were equipped with a tank of CO2 that was used to
maintain hypercapnia during hyperventilation.(17) However, CO2 is rarely used today due to
the inherent risks of hypercapnia.(6-7) An alternative technique would be to use computer
based feedback to control the end tidal CO2 by infusion of CO2 where a computer could
monitor the process for safety.
Emergence times are similar for rebreathing and for an optimally tuned controller.
Therefore partial CO2 rebreathing with careful monitoring is potentially the simpler and safer
technique to produce hypercapnia during hyperventilation because it avoids the safety issues
associated with a tank of 100% CO2. Clinicians may well be inclined to use the rebreathing
device rather than the controller because of its low cost. The volume of the
expandable/compressible rebreathing tube can be adjusted to achieve the optimum dead
40
space to tidal volume ratio. Although we do not yet have enough experience to identify the
optimum ratio, a one-to-one ratio appears to provide enough non-rebreathing to rapidly
washout nitrous oxide as well as adequate uptake of fresh oxygen. The corrugated tube used
in the rebreathing tube promotes enough mixing of the fresh gas and the rebreathed gas to
provide fresh oxygen uptake and N2O washout when the tidal volume is equal to the dead
space volume. Our recommendation is to always use tidal volumes somewhat in excess of the
dead space volume.
An anesthetic adsorbent is needed to remove anesthetic agent from the rebreathed
gas. With rebreathing, adsorption efficiency of activated charcoal is nearly 100% for all
volatile anesthetic agents. Advocates of closed circuit anesthesia techniques were the first to
use charcoal in their closed circle absorber breathing circuits to rapidly lower the inspired
agent concentration during emergence.(18-19) The efficiency of charcoal decreases due to
adsorption of water vapor by the charcoal granules with subsequent reduction in the surface
area (Figure 2.11).(20) We placed one way valves in the device to ensure that moist gas
exhaled by the patient bypasses the activated charcoal while inspired gas flows through the
activated charcoal.
Besides speeding emergence, mild hypercapnia has the following potential benefits. It
may provide better tissue oxygenation, attenuate lung injury, promote an early return of
spontaneous respiration and improve post surgery cognition.(21-24) It should be noted that
EtCO2 is routinely elevated to 65 mmHg without adverse effects in the sedated patients in the
ICU and in patients undergoing laparoscopic procedures with CO2 insufflation. Hypercapnia
is clearly contraindicated in patients at risk from increased intracranial pressure or pulmonary
hypertension.(25)
41
We were surprised to find that during hypercapnia, pigs that received isoflurane
emerged faster than pigs that received sevoflurane (Figure 2.5). Sevoflurane has a lower
blood/gas partition coefficient and a faster recovery profile.(26) However, sevoflurane
produces a lower change in cerebrovascular resistance with changes PaCO2 when compared
to isoflurane.(27) Thus hypercapnia during hyperventilation could have caused a larger
percent increase in cerebral blood flow with isoflurane leading to a faster emergence. The
observed differences could also be due to inter-animal variability which becomes more
significant with a small sample size as in our study.
This study has several limitations. The observer that measured the time when the
animal moved multiple limbs and time to return of spontaneous breathing was not blinded to
the presence or absence of the rebreathing device or the feedback controller. However, BIS
data is not subject to observer bias and the BIS monitor gave differences in emergence time
similar to those observed by the investigators. The difference in time taken for the
normalized BIS to rise to 0.95 was statistically significant for isoflurane and sevoflurane and
followed a trend similar to that of the time to movement of multiple limbs (Figures 2.5, 2.6).
Because the study found large time differences in emergence time with and without the
devices and since statistically significant differences were observed in the BIS rise times, we
believe CO2 makes a difference in emergence time.
Anesthesia was maintained at 2 MAC for only 30 min in between the first and second
emergence and the second and third emergence, which could have affected emergence time.
Emergence from anesthesia is dependent on the duration of anesthesia and tissue depots of
anesthetic agent. These stores may not be equal at the end of each 30 minutes period. The
order of emergence for each animal was randomized to minimize the effects of a prior
42
emergence and longer anesthesia duration. But our sample size may have been too small to
avoid cross over effects.
2.6 Conclusions
Hypercapnia in conjunction with hyperventilation was found to decrease emergence
time from inhaled anesthetic agents. Both rebreathing and CO2 infusion shortened emergence
time following volatile anesthesia. The rebreathing device described in this study provides a
simple means of enabling hypercapnic hyperventilation in a clinical setting. Further studies
are required to determine the optimal level of hypercapnia and hyperventilation for the most
rapid and safest emergence.
2.7 References
1. Eger EI, White PF, Bogetz MS. Clinical and economic factors important to anaesthetic choice for day-case surgery. Pharmacoeconomics 2000;17:245-62.
2. Grottke O, Dietrich PJ, Wiegels S, Wappler F. Intraoperative wake-up test and postoperative emergence in patients undergoing spinal surgery: a comparison of intravenous and inhaled anesthetic techniques using short-acting anesthetics. Anesth Analg 2004;99:1521-7; table of contents.
3. Eger EI 2nd L. Anaesthetic solubility in blood and tissues: values and signficance. Br J Anaesth 1964;36:140-4.
4. Wiesner G, Wild K, Merz M, Hobbhahn J. [Rates of awakening, circulatory parameters and side-effects with sevoflurane and enflurane. An open, randomized, comparative phase III study]. Anasthesiol Intensivmed Notfallmed Schmerzther 1995;30:290-6.
5. Vesely A, Fisher JA, Sasano N et al. Isocapnic hyperpnoea accelerates recovery from isoflurane anaesthesia. Br J Anaesth 2003;91:787-92.
43
6. Shipton EA, Roelofse JA, van der Merwe CA. Accidental severe hypercapnia during anaesthesia. Case reports and a review of some physiological effects. S Afr Med J 1983;64:755-6.
7. Prys-Roberts C, Smith WD, Nunn JF. Accidental severe hypercapnia during anaesthesia. A case report and review of some physiological effects. Br J Anaesth 1967;39:257-67.
8. Razis PA. Carbon dioxide--a survey of its use in anaesthesia in the UK. Anaesthesia 1989;44:348-51.
9. Haryadi DG, Orr JA, Kuck K et al. Partial CO2 rebreathing indirect Fick technique for non-invasive measurement of cardiac output. J Clin Monit Comput 2000;16:361-74.
10. Lerou JG, Dirksen R, Beneken Kolmer HH, Booij LH. A system model for closed-circuit inhalation anesthesia. I. Computer study. Anesthesiology 1991;75:345-55.
11. von Bethmann AN, Brasch F, Nusing R et al. Hyperventilation induces release of cytokines from perfused mouse lung. Am J Respir Crit Care Med 1998;157:263-72.
12. Dreyfuss D, Basset G, Soler P, Saumon G. Intermittent positive-pressure hyperventilation with high inflation pressures produces pulmonary microvascular injury in rats. Am Rev Respir Dis 1985;132:880-4.
13. Donn SM, Sinha SK. Can mechanical ventilation strategies reduce chronic lung disease? Semin Neonatol 2003;8:441-8.
14. Ito H, Kanno I, Ibaraki M et al. Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography. J Cereb Blood Flow Metab 2003;23:665-70.
15. Shoemaker JK, Vovk A, Cunningham DA. Peripheral chemoreceptor contributions to sympathetic and cardiovascular responses during hypercapnia. Can J Physiol Pharmacol 2002;80:1136-44.
16. Matalon S, Nesarajah MS, Krasney JA, Farhi LE. Effects of acute hypercapnia on the central and peripheral circulation of conscious sheep. J Appl Physiol 1983;54:803-8.
44
17. JC W. Deetherization by means of carbon dioxide inhalations. Arch Surg 1923;7:347–70.
18. Ernst EA. Use of charcoal to rapidly decrease depth of anesthesia while maintaining a closed circuit. Anesthesiology 1982;57:343.
19. Romano E, Auci A. [Adsorption of volatile anesthetics on activated charcoal. Efficiency of an experimental filter during low-flow circuit ventilation]. Minerva Anestesiol 1995;61:437-40.
20. Maggs FA, Smith ME. Adsorption of anaesthetic vapours on charcoal beds. Anaesthesia 1976;31:30-40.
21. Akca O, Liem E, Suleman MI et al. Effect of intra-operative end-tidal carbon dioxide partial pressure on tissue oxygenation. Anaesthesia 2003;58:536-42.
22. Laffey JG, Honan D, Hopkins N et al. Hypercapnic acidosis attenuates endotoxin-induced acute lung injury. Am J Respir Crit Care Med 2004;169:46-56.
23. Nattie E. CO2, brainstem chemoreceptors and breathing. Prog Neurobiol 1999;59:299-331.
24. Hovorka J. Carbon dioxide homeostasis and recovery after general anaesthesia. Acta Anaesthesiol Scand 1982;26:498-504.
25. van Hulst RA, Hasan D, Lachmann B. Intracranial pressure, brain PCO2, PO2, and pH during hypo- and hyperventilation at constant mean airway pressure in pigs. Intensive Care Med 2002;28:68-73.
26. Cantillo J, Goldberg ME, Larijani GE, Vekeman D. Recovery parameters after sevoflurane and isoflurane anesthesia. Pharmacotherapy 1997;17:779-82.
27. Nishiyama T, Matsukawa T, Yokoyama T, Hanaoka K. Cerebrovascular carbon dioxide reactivity during general anesthesia: a comparison between sevoflurane and isoflurane. Anesth Analg 1999;89:1437-41.
CHAPTER 3
CLINICAL EVALUATION OF REBREATHING DEVICE
3.1 Abstract
To shorten emergence time after a procedure using volatile anesthesia, 78% (Survey of
120 anesthesiologists at ASA 2005 meeting) of anesthesiologists use hyperventilation to
rapidly clear the agent from the lungs. Hyperventilation has not been more widely adapted
into clinical practice because it also lowers PaCO2, which decreases cerebral blood flow and
depresses respiratory drive. Adding dead space to the patient’s airway may be a simple and
safe method of maintaining a normal or slightly elevated PaCO2 during hyperventilation.
We evaluated the differences in emergence time in 52 surgical patients undergoing 1
MAC of isoflurane, sevoflurane or desflurane anesthesia under mild hypocapnia (EtCO2=29
mmHg) and mild hypercapnia (EtCO2=55 mmHg). The minute ventilation in half the patients
was doubled during emergence and hypercapnia was maintained by insertion of additional
airway dead space to keep the EtCO2 close to 55 mmHg during hyperventilation. A charcoal
canister adsorbed the volatile anesthetic agent from the dead space. Fresh gas flows were
raised to 10 L/min during emergence in all the patients.
The time between turning off the vaporizer and the time when the patients opened their
eyes and mouth in response to command, the time to tracheal extubation and the time for
normalized BIS to rise to 0.95 were faster when hypercapnic hyperventilation was
46
maintained using the rebreathing adsorber (p< 0.05). The time to tracheal extubation was
shortened by an average of 57%.
The emergence time after isoflurane, sevoflurane or desflurane anesthesia can be
shortened significantly by using hyperventilation to rapidly remove the agent from the lungs
and CO2 rebreathing to induce hypercapnia during hyperventilation. When it is important to
provide a rapid emergence, the device should be considered, especially following surgical
procedures where a high concentration of the volatile anesthetic was maintained right up to
the end of the procedure or where surgery ends abruptly without warning.
3.2 Introduction In a recent survey we found that it is common practice at the end of an anesthesia case
to increase fresh gas flow to rapidly remove anesthetic agent from the breathing circuit. 78%
of the anesthesiologists surveyed also used hyperventilation for rapid removal of agent from
the lungs (Survey of 120 anesthesiologists at ASA 2005 meeting). Hyperventilation has not
been universally adapted into clinical practice because it lowers PaCO2, decreases cerebral
blood flow, depresses respiratory drive and may actually slow emergence.(1)
To prevent a fall in PaCO2 during hyperventilation, some anesthesia machines were
equipped with a tank containing 100% CO2. During hyperventilation, the flow of CO2 was
adjusted to maintain normal or slightly elevated PaCO2. In 1989, 60% of the anesthetists in
the United Kingdom routinely administered CO2 to their patients.(2) Today, the practice is
seldom used in the United States because of the risk of inadvertent hypercapnia.(3)
Sasano, et al. used a tank containing 6% CO2 in oxygen as a safer alternative to the use
of 100% CO2.(4) When their device was used in dogs after isoflurane-nitrous oxide
anesthesia, the time to extubation decreased from 17.5 to 6.6 min. The same group used a
47
more complex apparatus that delivered a blend of 6% CO2 and 96% oxygen and were able to
reduce time to emergence after isoflurane anesthesia from 12.1 to 3.6 min.(5).
In the past, some anesthesia machines had a manual valve to bypass the CO2 absorber
(Ohio 18 Absorber, Ohio Medical Products, Madison WI) (A100 Absorber, Penlon Limited,
Abingdon, UK).(6) The amount of CO2 rebreathed and the level of hypercapnia were
controlled by adjusting the fresh gas flow to the breathing circuit.(7-9) The bypass option is
not available on new anesthesia machines because of the risk of inadvertently leaving the
bypass active at the start of a procedure.(6) The CO2 absorber bypass is of limited utility
because high fresh gas flow is needed to clear exhaled anesthetic from the breathing circuit,
which reduces the amount of CO2 rebreathing and limits the rate at which CO2 increases.(7-8)
Adding dead space to the patient’s airway may be a simpler and safer method of
increasing PaCO2 during hyperventilation. A charcoal adsorber in series with the dead space
could be used to remove rebreathed anesthetic vapor. Added dead space is routinely used for
the noninvasive measurement of cardiac output (NICO, Respironics Inc, Murrysville, PA)
and to stimulate respiratory drive.(10) We tested our device in animals and found a 60%
reduction in emergence time after two hours of isoflurane anesthesia when hypercapnia was
maintained during hyperventilation.(11) The current patient study compares the emergence
times following isoflurane, sevoflurane, and desflurane anesthesia when hypercapnia is
maintained during hyperventilation using the rebreathing adsorber and at mild hypocapnia
during mild hyperventilation.
48
3.3 Methods
3.3.1 Rebreathing device
Figure 3.1 shows our device that enables hypercapnic hyperventilation. The device
adds deadspace to the patient’s airway as the patient breathes through a 22 mm ID corrugated
collapsible breathing hose having 150 ml of dead space when collapsed and 665 ml when
fully extended. The device includes 18 gm of medical grade activated charcoal in a 0.95 cm
thick canister that is 7.5 cm in diameter. The charcoal adsorbs the volatile anesthetic agent
from the deadspace by trapping it in micropores located on the surface of the charcoal
granules. The charcoal granules are retained in a polycarbonate filter housing between layers
of filter cloth.
3.3.2 Study protocol
After IRB approval, we obtained written and informed consent from 52 ASA Class I or
II patients scheduled to receive elective surgery. Table 3.1 shows patient demographics,
duration of surgery and total dose of opioids administered. A coin was tossed at the
beginning of the study and subsequently after every 6 patients had been studied to decide if
the patient would receive the device or not. The subsequent 5 patients that qualified for the
study were alternately assigned to one of the two groups (with and without the device). The
patients that received the device were emerged at hypercapnic EtCO2 during hyperventilation
while the patients that did not receive the device were emerged at mildly hypocapnic EtCO2
during mild hyperventilation.
49
The 20 patients that received isoflurane underwent anterior cruciate ligament repair
surgery. Each patient was premedicated with 1-2 mg of midazolam and was given a femoral
nerve block before surgery. The patients were induced with 150 mcg of remifentanil, 2.0
mg/kg of propofol, and 1.0 mg/kg of succinylcholine. Anesthesia was maintained with 1.2%
isoflurane (1 MAC) for the duration of the procedure. Nitrous oxide was not used for
maintaining anesthesia. A continuous infusion of remifentanil was titrated to meet the
patient’s needs beyond 1 MAC of the inhaled agent. Infusion of remifentanil was stopped at
least 10 min before the vaporizer was turned off at the end of the case.
The 32 patients that received sevoflurane and desflurane underwent general anesthesia
lasting longer than one hour. Each patient was premedicated with 1-2 mg of midazolam.
Anesthesia was maintained with either 2% sevoflurane (1 MAC) or 6% desflurane (1 MAC)
for the duration of the procedure. Up until one hour before the end of the case, the clinicians
gave what they considered to be therapeutic amounts of opioids to meet the patient’s needs
beyond 1 MAC of inhaled agent. During the hour before the end of the case, opioids were
limited to remifentanil. The remifentanil infusion was discontinued 10 min before the
vaporizer was turned off.
For all patients, we set the respiratory rate at 8 breaths/minute and adjusted the tidal
volume to keep the endtidal CO2 concentration at 33 mmHg (Narkomed II, North American
Drager, Telford, PA). A gas analyzer (Datex AS/3, Datex-Ohmeda, Helsinki, Finland)
measured the inspired agent and end tidal CO2 and anesthetic agent concentrations
continuously. Sedation level during emergence as well as during anesthesia maintenance was
monitored using Bispectral Index (BIS, Aspect Medical Systems, Nutton, Massachusetts).
50
Figure 3.1. Rebreathing device with rebreathing hose, activated charcoal and one-way valves.
51
The anesthesiologist was blinded to the BIS during anesthesia maintenance as well as during
emergence. We kept the expired concentration at 1 MAC until the end of the case, without
decreasing the concentration in anticipation of the case ending.
When the surgeon applied the first adhesive wound closure strip, we turned off the
vaporizer and increased the fresh gas flow to 10 L/min. In the patients where the device was
used, we inserted the device in the airway with the rebreathing hose fully extended to 665 ml.
We increased the respiratory rate to 16 breaths/minute and increased the tidal volume as
needed to double the minute ventilation. We adjusted the length of the rebreathing hose to
prevent the end tidal CO2 concentration from rising higher than 55 mmHg. In the patients
where the device was not used, we left the tidal volume unchanged. Extubation occurred
following the patients ability to open eyes and mouth on command.
We recorded the time from when the vaporizer was turned off until the patients
opened their eyes in response to command, until the patients opened their mouths in response
to command, until the normalized BIS rose to 0.95 and until extubation.
The BIS data was normalized using the equation
( )
( )BIScepreEmergenBISimumBISemergencepreBISBISNormalized
−−−
=max
(3.1)
where pre-emergence BIS is the average of all BIS recording over the two minutes prior to
turning off the vaporizer and maximum BIS is the highest BIS number recorded after the
vaporizer was turned off.
52
3.3.3 Statistical analysis
Analysis was performed using SigmaStat version 2.03 (SPSS Inc). The effect of the
anesthetic agent used and method of emergence on time to eye opening, time to extubation
and time for normalized BIS to rise to 0.95 were compared using a 2 way ANOVA. Post hoc
Bonferroni tests were performed when interaction effects were found to be significant.
3.4 Results
The two groups studied with and without the device were comparable with respect to
the duration of anesthesia, body mass index (BMI) and the total dose of opioids administered
(Table 3.1 and 3.2). The average pre emergence BIS and the maximum BIS observed during
emergence were comparable in the two groups tested (Table 3.3). Hypercapnic
hyperventilation was tolerated in patients without coughing or gagging.
The time to open eyes, time to open mouth and time to tracheal extubation was faster
when hypercapnic hyperventilation was maintained using the rebreathing adsorber device
(Table 3.4). The time to tracheal extubation was 10.5, 6.5 and 5.6 min sooner with agents
isoflurane, sevoflurane and desflurane when the device was used. All differences were
statistically significant (p< 0.05).
The normalized BIS recorded after the vaporizer was turned off for the agent’s
isoflurane, sevoflurane and desflurane are shown in Figure 3.2. Figure 3.3 shows the average
time to extubation and Figure 3.4 shows the average time for normalized BIS to rise to 0.95
with and without the device. The time for normalized BIS to rise to 0.95 was 8.83, 6.08 and
3.79 min sooner for agents isoflurane, sevoflurane and desflurane respectively when the
53
rebreathing device was used to maintain hypercapnia during hyperventilation. All differences
were statistically significant (p<0.05).
When the charcoal absorber was used, the inspired agent concentration dropped below
0.1 vol% following the first breath and remained below 0.1 vol% until tracheal extubation.
3.5 Discussion
We tested a device that used partial CO2 rebreathing and hyperventilation to shorten
emergence time from a volatile anesthetic. The time to tracheal extubation was shortened by
an average of 57% when the minute ventilation was doubled and airway deadspace was
added to keep the end tidal CO2 near 52 mmHg. When it is important to provide a rapid
emergence for patient assessment or for rapid patient turnover, the device should be
considered, especially following surgical procedures where it is important to maintain a high
concentration of the volatile anesthetic right up to the end of the procedure (i.e. to reduce the
risk of patient movement, intraoperative awareness, or muscle rigidity). The device might
prove useful should a surgery end abruptly without warning.
The device maintains hypercapnia during hyperventilation. Both factors are important
in reducing time to emergence.(12) Vesely, et al. kept all study patients hypercapnic (endtidal
CO2 at 47 mmHg) and measured emergence times when half his study patients were
hyperventilated and half were not.(5) They found that the time to extubation was 3.6 min in
patients that were hyperventilated and 12.1 min in patients that were not hyperventilated.
Clearly, hyperventilation can shorten emergence time.
Higher PaCO2 during hyperventilation results in a shorter emergence time.(12)
Gopalakrishnan, et al. found that pigs woke up after desflurane anesthesia in 2.6 ± 0.9 min
54
Table 3.1
Patient demographics, including body mass index (BMI).
Isoflurane (n=20)
Sevoflurane (n=16)
Desflurane (n=16)
Without Device
M(7) F(3)
M(3) F(4)
M(3) F(5) Sex
(M=Male, F=Female) With
Device M(6) F(4)
M(2) F(7)
M(5) F(3)
Without Device 180 ± 8 171 ± 8 168 ± 10 Height
(cm) With Device 174 ± 13 172 ± 12 176 ± 10
Without Device 85 ± 19 83 ± 31 80 ± 26 Weight
(kg) With Device 70 ± 9 73 ± 18 100 ± 15
Without Device 35 ± 11 44 ± 12 42 ± 14 Age
(yrs) With Device 29 ± 9 33 ± 12 47 ± 14
Without Device 26 ± 5.1 31.2 ± 9.4 27 ± 6.6
BMI With Device 22.4 ± 1.8 25.8 ± 4.5 29.3 ± 1.0
55
Table 3.2
Duration of surgery and total dose of opioids admininstered (mean + SD).
Isoflurane (n=20)
Sevoflurane (n=16)
Desflurane (n=16)
Without Device 2.57 ± 0.37 2.28 ± 0.83 2.2 ± 0.63 Duration of
surgery (hrs) With
Device 2.53 ± 0.47 2.95 ± 1.7 2.93 ± 1.1
Without Device 1.8 ± 1.2 1.9 ± 0.4 1.8 ± 0.7 Total dose of
versed (mg) With
Device 1.6 ± 1.5 1.8 ± 0.6 1.8 ± 0.4
Without Device 203.8 ± 28.8 192.1 ± 24.5 200 ± 37.8 Total dose of
propofol (mg) With
Device 197.0 ± 24.5 186.0 ± 55.8 192.2 ± 43.5
Without Device * 214.3 ± 157.4 218.8 ± 128.0 Total dose of
fentanyl (µg) With
Device * 219 ± 199.9 327.8 ± 83.3
* fentanyl was not administered
56
Table 3.3
The table lists minute ventilation immediately before turning off the vaporizer (maintenance) and the end tidal CO2 concentration and minute ventilation at the time of tracheal extubation. The table also lists the average BIS 2 minutes prior to turning off the vaporizer and also the maximum BIS during emergence (mean + SD).
Isoflurane
Sevoflurane
Desflurane
Without Device 27.9±2.1 28.6 ± 3.9 30.5 ± 3.0 End tidal CO2 at
extubation (mmHg) With
Device 51.9±5.7 47.6 ± 4.5 53.9 ± 4.6
Without Device 7.2±1.7 6.8 ± 1.3 6.2 ± 0.5 Minute
ventilation during maintenance (L/min)
With Device 5.6±0.8 5.7 ± 1.6 6.9 ± 2.4
Without Device 11.6±3.1 9 ± 1.8 8.1 ± 1.6 Minute
ventilation at extubation (L/min)
With Device 14.0±0.7 13.9± 2.4 15.5 ± 1.5
Without Device 35.2±10.4 33.6±5.2 36.7±9.8 Pre-emergence
BIS With Device 37.6±9.0 43.6±10.8 38.6±6.7
Without Device 96.1±1.5 89.0±8.0 79.3±15.6 Maximum BIS
during emergence With Device 89.5±9.5 93.2±5.9 94.9±4.2
57
Table 3.4
The time between turning off the vaporizer and the time the patients opened eyes and mouth upon command and the time to tracheal extubation (mean + SD).
Isoflurane
Sevoflurane
Desflurane
Without Device 16.4 ± 4.1 12.2 ± 2.3 8.4 ± 1.4 Time to
open eyes (min) With
Device 6.2 ± 2.1 5.9 ± 1.5 2.9 ± 1.3
Without Device 16.9 ± 5.0 12.5 ± 1.7 8.6 ± 1.5 Time to
open mouth (min) With
Device 6.8 ± 2.2 5.8 ± 1.2 3.3 ± 1.4
Without Device 17.7 ± 4.7 12.6 ± 1.8 8.9 ± 1.7 Time to
extubation (min) With
Device 7.2 ± 2.1 6.1 ± 1.4 3.3 ± 1.4
58
Figure 3.2. Normalized BIS during emergence from 1 MAC of isoflurane, sevoflurane and desflurane anesthesia.
59
0.0
5.0
10.0
15.0
20.0
25.0
Without device With device
Tim
e to
Ext
ubat
ion
(min
± S
.D)
SEVOSEVOISO DES ISO DES
Figure 3.3. Time from turning off the vaporizer to tracheal extubation after 1 MAC of isoflurane, sevoflurane and desflurane anesthesia, with and without the device in use (mean + SD).
60
0.0
5.0
10.0
15.0
20.0
25.0
Without Device With Device
Tim
e to
Nor
mal
ized
BIS
to r
ise
to 0
.95
(min
± S
.D)
SEVOISO DES SEVOISO DES
Figure 3.4. Time from turning off the vaporizer to normalized BIS to rise to 0.95 after 1 MAC of isoflurane, sevoflurane and desflurane anesthesia, with and without the device in use (mean + SD).
61
during hypercapnia (EtCO2=55 mmHg) and 5.8 ± 2.4 min when hypocapnia(EtCO2=23
mmHg) was maintained during emergence, where all animals were hyperventilated at the
same level.(13) In response to hypercapnia, cerebral arterial smooth muscle dilates and
cerebral blood flow increases bye 6 % per mmHg increase in PaCO2.(14-15) The increase in
blood flow results in a more rapid clearance of volatile anesthetic from cerebral tissue,
especially when combined with hyperventilation to lower the arterial concentrations of the
volatile anesthetic agent and increase the cerebral capillary/tissue gradient.(12) Hypercapnia
increases blood flow and hyperventilation increases the diffusion gradient, thus both are
important in rapidly removing volatile agent from the brain.(16) In addition, hypercapnia
may initiate a sympathetically mediated release of catecholamine that may cause early
arousal as it raises MAC awake.
In the past, some anesthesia machines had a manual valve to bypass the CO2 absorber
and enable rebreathing of CO2(Ohio 18 Absorber, Ohio Medical Products, Madison WI)
(A100 Absorber, Penlon Limited, Abingdon, UK).(6) The amount of CO2 rebreathed and the
level of hypercapnia were controlled by adjusting the fresh gas flow to the breathing circuit.
The bypass option is not available on new anesthesia machines because of the risk of
inadvertently leaving the bypass active at the start of a case.(6) The CO2 absorber bypass is
of limited utility because high fresh gas flow is needed to clear exhaled anesthetic from the
breathing circuit, which reduces the amount of CO2 rebreathing and limits the rate at which
CO2 increases.(7-8)
Our device makes use of partial CO2 rebreathing as a convenient and safe way to
induce hypercapnia following anesthesia.(9, 17-18) The rebreathing hose is expanded or
contracted to control the amount of airway dead space and the amount of rebreathing. The
62
mixing that occurs within the corrugated rebreathing hose, as fresh gas mixes with the
exhaled gas trapped in the folds of the corrugated hose, results in partial rather than total CO2
rebreathing, even when the tidal volume equals the dead space. Total rebreathing is
undesirable because of the risk of inadequate oxygenation and slower nitrous oxide
elimination (N2O is not absorbed by charcoal). When the device is used, the tidal volumes
should be large enough to provide adequate oxygenation.
Activated charcoal adsorbs volatile anesthetic agent during inspiration, thereby
preventing rebreathing of the volatile agent. Advocates of closed circuit anesthesia have used
charcoal to absorb volatile anesthetics from the patient’s inspired gas, to rapidly lower the
inspired agent concentration, and to shorten emergence time.(19-20) They did not place
charcoal between the rebreathing volume and the patient to prevent rebreathing of the
anesthetic gases as we have done. Adsorption of water vapor exhaled by the patient could
reduce the surface area of activated charcoal and thus reduce the adsorption efficiency of the
device for anesthetic agent.(21) As an alternative approach, we added one way valves that
ensures that exhaled gas bypasses the activated charcoal while the inspired gas passes
through it. This alternative approach was used in four of the patients that received isoflurane
and in all the patients that received sevoflurane and desflurane. In our studies we found that
the inspired agent concentration stayed below 0.1 % during emergence showing that the
charcoal did not become saturated before trachea extubation occurred. Charcoal filters are
commonly found in safety respirators and gas masks where they prevent inhalation of large
volatile molecules that are toxic or irritating. These devices remove 100% of the large
volatile toxins from the inhaled gas. Our filter with valves showed similar efficiency in
removing inhaled anesthetics from the rebreathed gas following a volatile anesthetic.
63
This study has several limitations. The observer that measured the time when the
patients opened their eyes and mouth was not blinded as to the presence or absence of the
device. The decision as to when to perform tracheal extubation was based on the anesthetist’s
clinical judgment rather than on predefined criteria. Fortunately, the time to extubation
paralleled the times to open eyes and mouth, which are less subjective measures of
emergence time. Additionally, the differences in time for the normalized BIS to rise to 0.95,
which is a less subjective measure of emergence, was statistically significant for the three
agents tested and followed a trend similar to the times to open eyes and mouth (Figures 3.3
and 3.4). Since large differences in emergence parameters were observed and since
differences in the BIS rise times were statistically significant, we believe that similar
differences would have been obtained even with blinding.
The anesthetist was not blinded as to the presence of the device during the maintenance
phase of the anesthetic case, and the use of supplemental opioids could have introduced bias.
With agent isoflurane, the study was more controlled in terms of opioid use and only opioid
administered during anesthesia maintenance was remifentanil and was discontinued ten
minutes prior to turning off the vaporizer. With sevoflurane and desflurane, opioid use,
except remifentanil was discontinued one hour before the anticipated end of the procedure.
The amount of opioid administered in both groups were comparable and we believe similar
differences would have been obtained had the anesthetist been blinded to the presence of the
device (Table 3.2).
Another limitation was the use of an older generation anesthesia machine where the
ventilator was not compensated for changes in fresh gas flow. When we increased the fresh
gas flow to 10 L/min, the delivered tidal volume increased and the patients where the device
64
was not used became slightly hypocapnic at the time of tracheal extubation (Table 3.3). This
may have biased the results in favor of the device.
Future studies are needed to define guidelines regarding the amount of hyperventilation
and hypercapnia to provide a safe and rapid emergence. The amount of each will likely be
dependent on the inhalation agent used, the depth and duration of the anesthetic, and the
patient’s physiologic state.(16) Hyperventilation with large tidal volumes can produce
barotraumas, lung injury and may decrease stroke volume or arterial pressure in critically ill
patients.(22-23) Hyperventilation with high respiratory rates (and short expiratory times)
may result in air trapping and alveolar over-distension in patients with restrictive airway
disease. Hypercapnia is associated with an increased risk of cardiac arrhythmias and is
contraindicated in patients who have pulmonary hypertension and in neurosurgical patients
where elevated cerebral blood flow may cause excessively high intracranial pressure.
However, PaCO2 levels are routinely kept at 65 mmHg in ICU patients where benefits
include higher tissue oxygen pressures.(24-25) Future studies are needed to measure
emergence times and other outcomes, including post-operative cognitive function, at CO2
levels above 55 mmHg.(26) Future studies are needed in the pediatric population, in patients
that are breathing spontaneously, and in patients receiving pressure support ventilation.
3.6 Conclusions
We found that emergence time after isoflurane, sevoflurane, and desflurane anesthesia
was shortened by 57% when hyperventilation was used to rapidly flush the agent from the
lungs and hypercapnia was induced using CO2 rebreathing. When it is important to provide a
rapid emergence following surgical procedures, hypercapnic hyperventilation should be
65
considered in those cases where it is important to maintain a high concentration of the
volatile anesthetic right up to the end of the procedure. Hypercapnic hyperventilation may be
useful to shorten emergence time when surgery end abruptly without warning.
3.7 References
1. Ide K, Eliasziw M, Poulin MJ. The relationship between middle cerebral artery blood velocity and end-tidal PCO2 in the hypocapnic-hypercapnic range in humans. J Appl Physiol 2003.
2. Razis PA. Carbon dioxide--a survey of its use in anaesthesia in the UK. Anaesthesia 1989;44:348-51.
3. Prys-Roberts C, Smith WD, Nunn JF. Accidental severe hypercapnia during anaesthesia. A case report and review of some physiological effects. Br J Anaesth 1967;39:257-67.
4. Sasano H, Vesely AE, Iscoe S et al. A simple apparatus for accelerating recovery from inhaled volatile anesthetics. Anesth Analg 2001;93:1188-91.
5. Vesely A, Fisher JA, Sasano N et al. Isocapnic hyperpnoea accelerates recovery from isoflurane anaesthesia. Br J Anaesth 2003;91:787-92.
6. Dorsch J, Dorsch, SE. Understanding Anesthesia Eequipment. Second ed. Baltimore, MD: Williams & Wilkins, 1985.
7. Bergman JJ, Eisele JH. The efficiency of partial soda-lime bypass circuits. Anesthesiology 1972;36:94-5.
8. Ivanov SD, Nunn JF. Methods of elevation of PCO2 after anaesthesia with passive hyperventilation. Br J Anaesth 1968;40:804.
9. Ivanov SD, Nunn JF. Methods of evaluation of PCO2 for restoration of spontaneous breathing after artificial ventilation of anaesthetized patients. Br J Anaesth 1969;41:28-37.
66
10. Haryadi DG, Orr JA, Kuck K et al. Partial CO2 rebreathing indirect Fick technique for non-invasive measurement of cardiac output. J Clin Monit Comput 2000;16:361-74.
11. Gopalakrishnan N SD, Orr JA, Westenskow DR. Evaluation of a Computer Controlled CO2 Infusion System for Speeding Emergence from Anesthesia. Proceeding 2005 BMES Annual Fall Meeting 2005;2005:P3.121.
12. Eger EI, 2nd, Saidman LJ. Illustrations of inhaled anesthetic uptake, including intertissue diffusion to and from fat. Anesth Analg 2005;100:1020-33.
13. Gopalakrishnan N OJ, Sakata DJ. Animal Evaluation of a Device to Speed Emergence from Desflurane Anesthesia. ASA Annual meeting proceedings 2005;2005:A795.
14. Brian JE, Jr. Carbon dioxide and the cerebral circulation. Anesthesiology 1998;88:1365-86.
15. Ito H, Kanno I, Ibaraki M et al. Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography. J Cereb Blood Flow Metab 2003;23:665-70.
16. Suwa K, Matsushita F, Ohtake K, Yamamura H. PaCO2 for optimum washout of inhalational anesthetics from the brain. A model study. Tohoku J Exp Med 1979;129:319-26.
17. Adler RH, Brodie SL. Postoperative rebreathing aid. Am J Nurs 1968;68:1287-9.
18. Jeretin S, Wandycz T. A variable-deadspace device for use with the Engstrom respirator. Anesthesiology 1971;34:576-7.
19. Ernst EA. Use of charcoal to rapidly decrease depth of anesthesia while maintaining a closed circuit. Anesthesiology 1982;57:343.
20. Romano E, Pegoraro M, Vacri A et al. Low-flow anaesthesia systems, charcoal and isoflurane kinetics. Anaesthesia 1992;47:1098-9.
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21. Maggs FA, Smith ME. Adsorption of anaesthetic vapours on charcoal beds. Anaesthesia 1976;31:30-40.
22. Donn SM, Sinha SK. Can mechanical ventilation strategies reduce chronic lung disease? Semin Neonatol 2003;8:441-8.
23. Dreyfuss D, Basset G, Soler P, Saumon G. Intermittent positive-pressure hyperventilation with high inflation pressures produces pulmonary microvascular injury in rats. Am Rev Respir Dis 1985;132:880-4.
24. Akca O, Doufas AG, Morioka N et al. Hypercapnia improves tissue oxygenation. Anesthesiology 2002;97:801-6.
25. Gosain A, Rabkin J, Reymond JP et al. Tissue oxygen tension and other indicators of blood loss or organ perfusion during graded hemorrhage. Surgery 1991;109:523-32.
26. Hovorka J. Carbon dioxide homeostasis and recovery after general anaesthesia. Acta Anaesthesiol Scand 1982;26:498-504.
CHAPTER 4
MODEL TO PREDICT EMERGENCE FROM INHALED ANESTHESIA 4.1 Abstract
Description of a physiological system in terms of a mathematical model allows us
to test a clinical intervention over a wide range of patient types and conditions. We
modified a mathematical model of inhaled anesthetic uptake, distribution and elimination
to predict emergence from inhaled anesthesia. Cerebral perfusion was altered with
changes in EtCO2 and the type of anesthetic agent used. The model was also modified to
simulate the use of a rebreathing device during emergence that allowed the simulated
patient to rebreathe CO2 while adsorbing volatile agent from the rebreathed gas.
A subset of the data collected from a study of 59 ASA Class I or II patients
undergoing 1 MAC of isoflurane (N=20), sevoflurane (N=16) or desflurane (N=23)
anesthesia was used to estimate the cerebral concentration of anesthetic at which the
patients opened their eyes in response to command. The patients excluded from the
calculation of cerebral awakening concentration were used to estimate the predictive
accuracy of the model when the calculated cerebral concentrations were used for
predicting emergence times. The process was repeated for three random selections of
patient subsets. For each agent, the average cerebral awakening concentration was used to
estimate the relative importance of hypercapnia and hyperventilation in decreasing
69
emergence time after 2 hours of anesthesia at 1 MAC for a simulated patient of height
1.83 m and weight 70 kg.
The average cerebral awakening concentration normalized to age adjusted MAC for
desflurane, sevoflurane and isoflurane for the entire patient dataset were 0.162 ± 0.044,
0.280 ± 0.058 and 0.356 ± 0.105 respectively. For three random selections of patient
subsets, the root means square of the performance error ranged from 10% to 24 %. The
model estimates that there will be at least a 56% reduction in emergence time with
hypercapnic hyperventilation. The three agents were found to behave very differently
during emergence with increasing EtCO2 especially with low minute volumes in the
range used in clinical practice.
4.2 Introduction
Recovery from anesthesia is a complex function of a number of factors like
alveolar minute ventilation, relative solubility of the agent in blood and the tissues,
duration of anesthesia, body mass index (BMI) of the patient, PaCO2 and variability in
patient response to the drug.(1-2) Modeling physiological systems in terms of
mathematical equations helps us to better understand the relative importance of each
factor in decreasing emergence time from anesthesia.
Physiological models describe the body as a system of compartments that mimic
human anatomy. Lerou, et al. developed and validated a model that described the body as
a system of 13 compartments. The model described the uptake of anesthetic from the
lung compartment and its subsequent distribution to well perfused tissues like brain,
70
kidney, heart and liver and less perfused tissues like muscle, connective tissue and
adipose tissue.(3)
Faster emergence and recovery profiles of newer anesthetic agents have made their
use very popular. However, the awakening and recovery profiles of slower anesthetic
agents could be significantly improved by using hyperventilation concomitantly with
hypercapnia. Hypercapnia during hyperventilation can be maintained using the
rebreathing adsorber device described in Chapters 2 and 3. The device allows the patient
to rebreathe CO2 while removing anesthetic agent from the inspired gas. During rapid
washout of anesthetic with hyperventilation, especially when accompanied by changes in
PaCO2, anesthetic concentration in the brain is believed to be a better indicator of
anesthetic depth when compared to the alveolar concentration. The cerebral vasculature
dilates with increase in PaCO2, thereby increasing blood flow to the brain and
accelerating clearance of anesthetic from the brain. Hyperventilation with a higher PaCO2
would thus lead to a faster emergence.
The diameter of the middle cerebral artery is unresponsive to changes in PaCO2 and
measurements of blood velocity with transcranial doppler has shown that relative changes
in blood velocity provide accurate estimates of relative changes in cerebral blood flow.(4)
For PaCO2 between 20 and 50 mmHg, an exponential function best describes the
relationship between middle cerebral artery blood velocity and PaCO2.(5) More recent
studies using positron emission tomography have measured changes in cerebral blood
flow and cerebral blood volume with changes in PaCO2.(6-8) Cerebral blood flow and
cerebral blood volume increased by 6% per mmHg and 1.8% per mmHg respectively
71
during hypercapnia. The increase in cerebral blood flow was greater than that in volume
indicating an increase in blood velocity.
Cerebral blood flow and cerebrovascular reactivity to CO2 are also modified by
anesthetic agents. Cerebrovascular reactivity to CO2 is preserved for desflurane,
sevoflurane and isoflurane concentrations less than or equal to 1 MAC. Cerebral
vasodilation and cerebrovascular reactivity to CO2 are comparable for isoflurane and
desflurane.(9-10) The direct vasodilatory effect produced by sevoflurane is less than that
produced by isoflurane or desflurane.(11-14) Agent concentrations of 1 MAC of
sevoflurane also reduce the cerebrovascular reactivity to changes in PaCO2. During
anesthesia with 1 MAC of agent, the percent increase in middle cerebral artery blood
velocity for every mmHg increase in PaCO2 was reported to be 5.7% for isoflurane and
2.1% for sevoflurane.(15) Mielck, et al. studied the effect of 1 MAC of sevoflurane and
desflurane on carbon dioxide reactivity using a modified Kety-Schmidt saturation
technique with argon as the tracer gas. Their study reported that 1 MAC of sevoflurane
and desflurane caused a 38% and 22% decrease in cerebral blood flow when compared to
the awake state.(16-17) The decrease is possibly due to a combination of a decrease in
cerebral metabolic rate and the counter acting effect of the vasodilation produced by the
anesthetic agent.
An increase in PaCO2 also affects the cardiovascular system. Cardiac output as
measured by the thermodilution technique was found to increase from 3.8 L/min to 4.2
L/min during anesthesia when PaCO2 was increased from 30 mmHg to 50 mmHg.(18)
Higher PaCO2 activates the central nervous system and evokes sympatho-adrenal
responses leading to an increase in cardiac output. Cullen, et al. studied cardiovascular
72
responses to CO2 in awake volunteers and reported a 32 % increase in cardiac output with
a 10 mmHg increase in PaCO2.(19)
The cerebral concentration of anesthetic agent which determines recovery is thus a
complex function of a number of parameters. Computer simulations could help us better
understand the relative importance of hypercapnia and hyperventilation in accelerating
clearance of anesthetic agent from the brain and help predict emergence times over a
wide range of conditions. This study attempts to use a mathematical model to estimate
the cerebral concentration of anesthetic agent at which patients responded to a command
to open eyes after 1 MAC of anesthesia with isoflurane, sevoflurane or desflurane. After
the predictive accuracy of the model was evaluated, the model was used to find optimal
combinations of EtCO2 and minute ventilation for speeding emergence from inhaled
anesthesia.
4.3 Methods
We implemented a computer model of anesthetic uptake, distribution and
elimination described by Lerou, et al. The model consists of 13 tissue compartments that
describes the transport of anesthetic in the arterial blood through each of the tissue groups
and to the venous blood (Figure 4.1).The lean body weight gives the sum of the weight of
all tissues excluding the adipose tissue.(20)
( ) ( )( )
( )maleH
BWBWLBW 2
2
1001281.1
××
−×= (4.1)
73
Figure 4.1. Schematic diagram of the compartments in the model.
74
( ) ( )( )
( )femaleH
BWBWLBW 2
2
10014807.1
××
−×= (4.2)
where LBW is the lean body weight in kg, BW is the body weight in kg and H is the
height of the patient in m.
The volume of each compartment was calculated as a fraction of the lean body
weight and the flow through each compartment was calculated as a fraction of the cardiac
output (Table 4.1).(21) The model uses arterial, venous and central blood pools to mimic
circulation times in the body. The tissue/blood partition coefficients and the blood gas
partition coefficients reported by Eger, et al. were used in the model (Table 4.2).(22) The
model was implemented in a computer program written in Borland C++ Builder v5.0
(Borland, Scotts Valley, CA). The model accepts the patient’s age, sex, weight and height
as inputs and allows the user to select the anesthetic gas type, vaporizer settings, fresh gas
flow, respiratory rate, tidal volume and the duration of anesthesia.
The anesthesia machine was modeled as three compartments consisting of an
inspiratory compartment, circuit compartment and expiratory compartment of volumes
1L, 4 L and 1 L respectively. A three compartmental model is able to provide a more
realistic simulation of washout of anesthetic from the circle system with increased fresh
gas flow when compared to a single compartmental anesthesia system used by Lerou.
Delayed rate of clearance of anesthetic from the circle system will lead to rebreathing of
anesthetic vapor which could lead to errors in predicted emergence time
The model was modified to simulate rebreathing of CO2 during emergence. The
modification allowed the simulated patient to inhale part of the gas stored in the
rebreathing hose from the previous breath. The model assumes that 85% of the volume of
75
Table 4.1
Volume and blood flows through the compartments
Tissue Volume* Blood flowϕ
Brain 0.0247 0.1600 Heart 0.0047 0.0500 Liver 0.0671 0.3000
Kidney 0.0047 0.2500 Muscle 0.5012 0.1300 Lung 0.0094 ----
Connective 0.3059 0.0600 Adipose ---- 0.0500
* Expressed as fractions of the lean body weight ϕ Expressed as fractions of the cardiac output
76
Table 4.2
Tissue/Blood partition coefficients (21,22) (Except for Blood/Gas partition coefficients)
Tissue Desflurane Sevoflurane Isoflurane
Blood/gas 0.45 0.65 1.40
Brain 1.22 1.69 1.57
Heart 1.22 1.69 1.57
Liver 1.49 2.00 1.86
Kidney 0.89 1.20 1.00 Muscle 1.73 2.62 2.57 Adipose 29.00 52.00 50.00
Lung 1.30 1.50 1.10 Connective 1.40 1.50 2.00
77
CO2 left in the hose from the previous breath is re-inhaled in the subsequent breath. The
model also assumes that activated charcoal in the device retains the entire anesthetic
exhaled by the patient so that no anesthetic is inhaled by the patient when the rebreathing
device is introduced into the circuit.
Exponential relationships were used to alter cerebral blood flow to changes in
EtCO2. The cerebral blood flow to EtCO2 relationship under 1 MAC of desflurane and
sevoflurane anesthesia are described by equations 4.1 and 4.2 respectively.(16-17)
20589.029. PaCODESFLURANE eCBF 4= (4.3)
20603.059.2 PaCOESEVOFLURAN eCBF = (4.4)
where CBF is cerebral blood flow in mlmin-1100g-1 and 2PaCO is the arterial partial
pressure of CO2 in kPa.
Desflurane and isoflurane have similar effects on cerebral blood flow and
preservation of cerebral reactivity to CO2.(10) The cerebral blood flow values obtained
by Ornstein, et al. for desflurane were comparable to that obtained by Mielck, et al.
Hence equation 4.1 was used to model cerebrovascular changes to CO2 for isoflurane.
Cardiac output was modeled as a function of PaCO2 using equation 4.3. Oxygen
tensions during anesthesia maintenance as well as during emergence were assumed to be
high enough to not affect cardiac output. A first order lag of 0.7 minutes was given to the
response and the constant k was calculated to be 0.15 to fit data for measurements of
cardiac output and PaCO2 during emergence.(23-24)
78
7.0
)35(*15.0 240 QPaCOQdtdQ −−+
= (4.5)
where Q is cardiac output, 40Q is the cardiac output at a PaCO2 of 40 mmHg.
With an increased cardiac output with a higher PaCO2, significant differences were
observed by Sawai, et al. between thermodilution and transesophageal methods of cardiac
output measurement. This is perhaps due to an increase in cerebral perfusion with higher
CO2 and because the descending aortic blood flow measured by doppler is less dependent
on changes in PaCO2. With an increase in cerebral perfusion with a higher PaCO2, the
difference the difference between the cardiac output and cerebral blood flow was
distributed amongst the various tissues in the proportions described in Table 4.1.
4.3.1 Study protocol
After IRB approval and obtaining written informed consent, we collected data from
59 ASA Class I or II patients undergoing anesthesia with 1 MAC of isoflurane(N=20),
sevoflurane(N=16) or desflurane(N=23) anesthesia. The patients that received isoflurane
underwent anterior cruciate ligament repair surgery. They were premedicated with 1-2
mg of midazolam and received a femoral nerve block before the surgery. Induction
commenced with 150 mcg of remifentanil, 2.0 mg/kg of propofol and 1.0 mg/kg of
succinylcholine. A continuous infusion of remifentanil was titrated to meet the patient’s
needs beyond 1 MAC of the inhaled agent.
79
The 39 patients that received sevoflurane or desflurane underwent general
anesthesia lasting longer than one hour. Each patient was premedicated with 1-2 mg of
midazolam. Anesthesia was maintained with either 2% sevoflurane (1 MAC) or 6%
desflurane (1 MAC) for the duration of the procedure. Up until one hour before the end
of the procedure, the clinicians gave what they considered to be therapeutic amounts of
opioids to meet the patient’s needs beyond 1 MAC of inhaled agent. During the hour
before the end of the case, opioids were limited to remifentanil. Remifentanil infusion
was discontinued 10 minutes before the vaporizer was turned off.
For all patients, respiratory rate was set at 8 breaths/minute and tidal volume was
adjusted to maintain EtCO2 at 33mmHg (Narkomed II, North American Drager, Telford,
PA). A gas analyzer (Datex AS/3, Datex-Ohmeda, Helsinki, Finland) measured the
inspired agent and end tidal CO2 and anesthetic agent concentrations. We kept the expired
agent concentration at 1 MAC until the end of the case, without decreasing the
concentration in anticipation of the case ending. Nitrous oxide was not used for
maintaining anesthesia.
When the surgeon applied the first adhesive wound closure strip we increased the
fresh gas flow to 10 L/min and turned off the vaporizer. In the group where the device
was not used, the tidal volume was left unchanged. In the group where the device was
used, the patients were emerged at hypercapnic CO2 during hyperventilation by inserting
the device in the airway with the rebreathing hose fully distended to 665 ml and doubling
the respiratory rate to16 breaths/minute. To prevent the EtCO2 from rising higher than 55
mmHg, we adjusted the length of the rebreathing hose. The patients that did not receive
the device were emerged at mildly hypocapnic EtCO2 during mild hyperventilation. We
80
recorded the time from when the vaporizer was turned off until the patient opened their
eyes in response to command.
For desflurane, 15 patients were emerged at hypercapnic CO2 during
hyperventilation and 8 patients at mildly hypocapnic EtCO2. 10 patients in the group that
received isoflurane and 7 patients that received sevoflurane were emerged at mildly
hypocapnic CO2 during mild hyperventilation. The remaining 10 patients that received
isoflurane anesthesia and 9 that received sevoflurane anesthesia were emerged at
hypercapnic CO2 during hyperventilation. 3 patients that received isoflurane and 3 that
received sevoflurane had to be excluded from the data analysis either because our
program failed to record the data files or because data collection was started a few
minutes before emergence due to non availability of personnel responsible for recording
data.
4.3.2 Estimation and validation of awakening brain concentration
Random selection of a subset of the data collected for each agent was used to
estimate the cerebral concentration of anesthetic agent at which the patients responded to
a verbal command to open eyes. The patients were selected using a random number
generator in Matlab. Data from the patients that were not used in calculating the cerebral
awakening concentration was used to estimate the predictive accuracy of the model using
the calculated cerebral concentration. The process of random selection and validation was
performed three times for three random selections of patient subsets. For isoflurane, the
validation subset included random selection of 3 patients at hypercapnic and 3 at
hypocapnic EtCO2. For sevoflurane and desflurane the validation data set included
81
random selection of 2 subjects each at hypocapnic EtCO2 and 3 and 5 subjects
respectively at hypercapnic EtCO2.
For estimating the cerebral awakening concentration of anesthetic agent, the
patient’s age, height and weight obtained from the anesthesia records were used to
calculate model parameters for each patient. The recorded inspired agent concentration,
EtCO2, respiratory rate and minute ventilation were used as inputs to the simulation. The
patient was simulated for the duration of anesthesia and during emergence when the
vaporizer was turned off. The modeled concentration of anesthetic in the brain at the time
when the actual patient (from the clinical study) opened eyes in response to command
was calculated for each patient. The cerebral awakening concentration was normalized by
the age adjusted MAC of the patient to make the concentration comparable amongst
different agents.(25)
For validating the estimated cerebral concentration, the model was used to predict
emergence times for patients that were not used in estimating the cerebral awakening
concentration. For each simulated patient, patient specific parameters (age, height, weight
and sex), inspired agent concentration, EtCO2 and minute ventilation were given as input
to the model. The patient was simulated for the duration of anesthesia. The time from
when the vaporizer was turned off until the cerebral concentration agent concentration
normalized to the MAC dropped to the cerebral awakening threshold was calculated for
each patient in the validation data set. This process was repeated for the three validation
data sets using the three cerebral awakening concentrations estimated from the patients
who were excluded from the validation data set. The emergence times estimated by the
82
model were then compared to the actual emergence times recorded from the operating
room.
4.3.3 Performance analysis
To evaluate the predictive performance of the model we used the methods
described by Varvel, et al.(26) The performance error (PE) for each patient was
calculated as
( )
100×−
=p
pm
EEE
PE (4.6)
where Em is the measured emergence time and Ep is the emergence time predicted by the
model for each patient. The performance error was calculated as a percentage of the
predicted time because that is the information available when the model is being used.
The following variables were calculated from the performance error.
• Median absolute performance error (MDAPE) gives an estimate of the
inaccuracy of the model. It is given by the median of the absolute value of the
PE for each trial of random selection of patients. The median gives a better
estimate when compared to the mean especially in situations where there is
asymmetrical distribution of data.
{ } NjPEmedianMDAPE j ,....,1, == (4.7)
83
where N is the number of patients.
• Median prediction error (MDPE) is a signed value and represents the direction
of the performance error rather than the size and thus gives an estimate of
bias.
{ } NjPEmedianMDPE j ,....,1, == (4.8)
• Root mean squared error (RMSE) gives an estimate of gross error and is not
influenced by the sign of the prediction errors. It can be decomposed into a
bias and scatter term.
∑=
=N
jjPE
NRMSE
1
21 (4.9)
• Bias is the average of the prediction error and is a measure of systematic
component of error. It is a signed value and gives information about over or
under prediction by the model but does not provide information about the size
of the prediction error.
∑=
=N
jjPE
NBIAS
1
1 (4.10)
84
• Scatter (SC) gives a measure of the prediction errors around the mean
( )∑=
−=N
jj BIASPE
NSC
1
21 (4.11)
The performance measures listed above were calculated for three trials of random
selection of subjects.
4.3.4 Total agent uptake over different durations of anesthesia
The average cerebral concentration obtained from the entire data set for each agent
was used to simulate emergence times from anesthesia for a 40 year old male patient of
height 1.83 m and weighing 70 kg. Anesthesia durations of 0.5, 2 and 8 h with 1 MAC of
isoflurane, sevoflurane or desflurane were simulated. A constant metabolic CO2
production was assumed depending on the body weight of the patient. The minute
ventilation was adjusted to maintain an EtCO2 of 33 mmHg at a respiratory rate of 8
breaths/min during anesthesia maintenance. The vaporizer setting was adjusted to
maintain expired concentration of 1 MAC of agent. Fresh gas flow was set to 1.5 L/min
during anesthesia maintainenance. Fresh gas flows of 10 L/min were used during the first
10 minutes of anesthesia and during emergence. For each simulation, three emergence
protocols were simulated.
• EtCO2 was increased gradually from 33 to 52 mmHg by rebreathing of
CO2. The patient was hyperventilated by doubling the respiratory rate.
85
• Minute ventilation was increased so that EtCO2 falls to hypocapnic
level (~25mmHg)
• Respiratory rate and tidal volume remained unchanged after turning
off the vaporizer to maintain an EtCO2 of 33 mmHg.
For each simulation, we calculated the time from when the vaporizer was turned off
to the time when the cerebral anesthetic concentration normalized to age adjusted MAC
decreased below the threshold for emergence for agent’s isoflurane, sevoflurane and
desflurane. The total anesthetic uptake by the patient for each simulation as well as the
total amount of agent exhaled by the patient during emergence was calculated.
4.3.5 Relative importance of hyperventilation and hypercapnia
We simulated emergence from 2 hours of anesthesia at 1 MAC of isoflurane,
sevoflurane or desflurane for a 40 year old male patient of height 1.8 m and weighing 70
kg. Anesthesia was maintained at 1 MAC of agent during maintenance with a fresh gas
flow of 1.5 L/min and respiratory rate of 8 breaths/min. The tidal volume during
anesthesia maintenance was adjusted to maintain an EtCO2 of 33 mmHg.
Several emergence scenarios using different combinations of EtCO2 varying from
20 mmHg to 60 mmHg and minute ventilation ranging from 4 L/min to 18 L/min were
simulated. For this simulation, we assumed that EtCO2 instantaneously reaches the set
EtCO2 value during emergence. The average cerebral concentration (from all patients
studied for each drug) at emergence normalized to age adjusted MAC was used as the
threshold for emergence. For each combination of minute ventilation and EtCO2 we
calculated the time from when the vaporizer was turned off until the cerebral anesthetic
concentration dropped below the threshold for emergence. The emergence time for each
86
combination of minute ventilation and EtCO2 was then used to create contour lines that
show the combination of minute ventilation and EtCO2 for achieving a particular
emergence time for each agent used.
4.4 Results
For agent desflurane, the average cerebral concentration of agent normalized to age
adjusted MAC at which the patients responded to a command to open eyes for three
random selection of 13 patients were 0.156 ± 0.045, 0.158 ± 0.046 and 0.173 ± 0.043.
The emergence times estimated by the model for the patients that were excluded from
calculating the concentration using the respective brain concentration for each trial are
shown in Figure 4.2. The estimated cerebral awakening concentrations normalized to age
adjusted MAC were 0.269 ± 0.061, 0.286 ± 0.066, 0.282 ± 0.054 for sevoflurane and
0.361 ± 0.147, 0.367 ± 0.116, 0.354 ± 0.113 for isoflurane. The average cerebral
awakening concentration normalized to age adjusted MAC for desflurane, sevoflurane
and isoflurane (for all the patients) were 0.198 ± 0.054, 0.280 ± 0.058 and 0.356 ± 0.105
respectively. The emergence times estimated by the model and the actual emergence
times obtained from the clinical study for sevoflurane and isoflurane are shown in Figure
4.3 and 4.4 respectively. Table 4.3 lists the performance measures for three random trials
each for desflurane, sevoflurane and isoflurane.
Table 4.4 lists the emergence times estimated by the model from 1 MAC of
isoflurane, sevoflurane or desflurane for a 70 kg, 40 year old adult male patient after 0.5,
2 and 8 hours of anesthesia during hypercapnic hyperventilation(rebreathing), hypocapnia
during hyperventilation and when ventilation settings during emergence was the same as
87
that during maintainenance. Table 4.4 also lists the total amount of agent inhaled during
anesthesia maintenance and exhaled by the patient during each emergence scenario
tested.
Figures 4.5, 4.6 and 4.7 show the emergence times estimated by the model for
different combinations of minute ventilation from 4 to18 L/min and EtCO2 from 20 to 60
mmHg.
4.5 Discussion
We used a modified version of the model of inhaled anesthetic uptake, distribution
and elimination described by Lerou, et al. to estimate the cerebral awakening
concentration of anesthetic agent (normalized to age adjusted MAC) during emergence
from 1 MAC of desflurane, sevoflurane or isoflurane. The model was then used to find
optimal combinations of minute ventilation and EtCO2 for accelerating recovery from
each anesthetic agent.
We performed three random trials in which part of the data set was used for
estimating cerebral anesthetic concentration and the remaining patient data was used for
validating the estimated cerebral anesthetic concentration. The maximum value obtained
for the median absolute performance error (MDAPE), which gives the magnitude of
prediction error was 19%, 16% and 17% for desflurane, sevoflurane and isoflurane
respectively. The median performance error ranged from -15% to 7% for the three agents.
Swinhoe, et al. described the acceptable limits for a target controlled infusion system as
88
Trial one (Brain Conc = 0.156)
0
2
4
6
8
10
12
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial two (Brain Conc = 0.158)
0
2
4
6
8
10
12
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial three (Brain Conc = 0.173)
0
2
4
6
8
10
12
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Figure 4.2. Predicted and measured emergence times from 1 MAC of desflurane anesthesia in 7 subjects. The three cerebral concentrations were estimated from random selection of 13 subject and the 7 subjects shown above were not used in estimating cerebral awakening concentration.
89
Trial one (Brain Conc = 0.269)
0
5
10
15
20
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial two (Brain Conc = 0.286)
02468
10121416
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial three (Brain Conc = 0.282)
02468
10121416
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Figure 4.3. Predicted and observed measured times for 1 MAC of sevoflurane anesthesia in 5 subjects. The 3 cerebral concentrations were estimated from random selection of 11 subject and the 5 subjects shown above were not used in estimating cerebral awakening concentration
90
Trial one (Brain Conc = 0.361)
02468
101214161820
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial two (Brain Conc = 0.367)
02468
101214161820
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Trial three (Brain Conc = 0.354)
02468
101214161820
Tim
e to
ope
n ey
es (m
in)
Measured Predicted
Figure 4.4. Predicted and measured emergence times from 1 MAC of isoflurane anesthesia in 5 subjects. The 3 cerebral concentrations were estimated from random selection of 13 subject and the 5 subjects shown above were not used in estimating cerebral awakening concentration.
91
Table 4.3
Performance measures of the model during emergence
from 1 MAC of isoflurane, sevoflurane or desflurane anesthesia
Agent Trial MDAPE (%)
MDPE (%)
RMSE (%)
BIAS (%)
SC (%)
1 13.66 -12.50 19.64 -11.21 16.16 2 19.05 -10.00 19.28 -7.86 17.63 Desflurane 3 15.38 5.79 24.60 11.37 22.08
1 8.74 -8.74 14.76 -8.68 10.75 2 11.97 7.00 9.48 3.11 12.93 Sevoflurane 3 15.83 -13.90 20.86 -1.83 25.39
1 10.00 0.11 18.64 4.30 22.50 2 10.11 7.00 14.44 5.09 17.70 Isoflurane 3
16.51
-14.48
19.65
0.89
22.70
92
Table 4.4
Estimated emergence times after 0.5, 2 and 8 hours of
anesthesia with 1 MAC of isoflurane, sevoflurane or desflurane.
Time to Open Eyes (min)
Agent Duration (hours)
Hyperventilation (EtCO2=25
mmHg)
Maintenance Ventilation (EtCO2=33
mmHg)
Hyperventilation with
Rebreathing (EtCO2=55
mmHg)
0.5 17.33 14.42 6.75 2 21.75 19.58 8.00 Isoflurane 8 28.42 31.17 10.33
0.5 14.33 11.08 5.25 2 16.08 12.50 5.58 Sevoflurane 8 17.50 13.75 5.83
0.5 8.50 7.17 3.75 2 9.17 7.83 3.92 Desflurane 8 9.58 8.17 4.00
93
Table 4.5
Total agent inhaled and exhaled
by the patient after 0.5, 2 and 8 hours of anesthesia with 1 MAC of isoflurane, sevoflurane or desflurane.
Exhaled Agent (L)
Agent Duration (hours)
Inhaled Agent (L)
Hyperventilation(EtCO2=25
mmHg)
Maintenance Ventilation (EtCO2=33
mmHg)
Hyperventilation with
Rebreathing (EtCO2=55
mmHg) 0.5 0.78 0.20 0.17 0.15
Isoflurane 2 1.95 0.32 0.27 0.20 8 3.95 0.49 0.46 0.29 0.5 0.62 0.19 0.16 0.14
Sevoflurane 2 1.47 0.27 0.22 0.17 8 2.93 0.34 0.27 0.19 0.5 1.39 0.43 0.37 0.32
Desflurane 2 3.10 0.54 0.46 0.37 8 5.77 0.61 0.52 0.40
94
Figure 4.5. Estimated emergence times for a 40 year old, 70 kg, 1.83 m adult male patient after 2 hours of desflurane anesthesia at 1 MAC. A normalized cerebral awakening concentration of 0.162 was used for the simulation.
95
Figure 4.6. Estimated emergence times for a 40 year old, 70 kg, 1.83 m adult male patient after 2 hours of sevoflurane anesthesia at 1 MAC. A normalized cerebral awakening concentration of 0.280 was used for the simulation.
96
Figure 4.7. Estimated emergence times for a 40 year old, 70 kg, 1.83 m adult male patient after 2 hours of isoflurane anesthesia at 1 MAC. A normalized cerebral awakening concentration of 0.356 was used for the simulation.
97
MDPE less than 10-20% and MDAPE less than 20-40%.(27) Our results with this model
lie within these limits.
Scatter (SC) gives the magnitude of the prediction error around the mean. The
largest value of SC from the three trials was 22%, 25% and 22 % for desflurane,
sevoflurane and isoflurane respectively. BIAS had both positive as well as negative signs
indicating underprediction as well as over prediction by the model. The maximum root
mean square error in the performance error (calculated as a percent of the predicted
emergence time) was 25%.
The average cerebral awakening concentration normalized to age adjusted MAC
estimated from the entire patient data was 0.280±0.058 and 0.356 ± 0.105 respectively
for sevoflurane and isoflurane. The cerebral awakening concentration to MAC reported
by Katoh, et al. using a one compartment brain model was 0.3 ± 0.07 and 0.26 ± 0.07
respectively for sevoflurane and isoflurane.(28) Their model however assumed a constant
cerebral blood flow as a fraction of the cardiac output and did not take into account the
changes in cerebral blood flow with different PaCO2 or the anesthetic agents used.
Hyperventilation and rebreathing shortened emergence from all the inhaled
anesthetic agents. Modeling suggests a somewhat larger benefit for the more soluble
agents especially over longer durations of anesthesia. The amount of agent exhaled when
hypercapnic hyperventilation is used was similar to that obtained with a slower
emergence during hyperventilation alone. This leads us to believe that there is no risk for
re-sedation due to the residual anesthetic agent left in the patient when the rebreathing
adsorber device is used. Additionally the patients emerged with hypercapnic
hyperventilation would have higher arterial PaCO2 at the time of extubation which will
98
provide a greater respiratory stimulus and drive to breathe more vigorously and excrete
more anesthetic during the early post-extubation period.
When the computer model was used to predict the relative importance of
rebreathing and cerebral blood flow with regard to emergence time, the model estimates
that the ideal choice of minute ventilation and EtCO2 for a rapid emergence from
anesthetic would be different for the three agents.
With low minute volumes and a high EtCO2, the three agents were found to behave
very differently. The decrease in cerebral concentration of the agent in this case is limited
by the decreased clearance of anesthetic from the blood stream by ventilation. Once the
anesthetic concentration in the brain approaches that of the blood flowing into the brain,
further decrease in emergence times are only possible by decreasing the blood agent
concentration by increased ventilation. Hence no further decrease in emergence times
would be possible with increasing CO2 while maintaining the same minute ventilation for
these agents. With isoflurane, this effect is seen with minute ventilation less than 8 L/min
and increasing EtCO2 beyond 45 mmHg. For desflurane increasing EtCO2 beyond 55
mmHg with minute volumes less than 6 L/min does not seem to decrease emergence time
further. With sevoflurane this effect is seen only with very low minute volumes of 2
L/min which are not clinically relevant.
When sevoflurane is used for maintaining anesthesia, cerebrovascular reactivity to
CO2 is decreased due to the effect of sevoflurane and perhaps the cerebral concentration
might still be higher than the blood concentration even at low minute volumes due to the
decreased flow to the brain. From the model, it appears that further decrease in
99
emergence times would thus be possible with sevoflurane by increasing the cerebral
perfusion with a higher PacO2 even when minute volumes are small.
For desflurane it appears that short emergence times would be possible by using a
high EtCO2 along with mild hyperventilation. The model suggests that a faster emergence
from isoflurane would require larger amount of hyperventilation along with a high
EtCO2. For sevoflurane it appears that moderate hyperventilation along with an EtCO2 of
about 50 mmHg would yield a rapid emergence. For sevoflurane and desflurane it
appears that a large amount of hyperventilation does not yield significant reduction in
emergence times and could be avoided. With isoflurane, hyperventilation plays a more
important role and a fast emergence would require minute ventilations in the range of 10
to 14 L/min.
Nitrous oxide, which is often used in combination with volatile anesthetic agents is
not adsorbed by activated charcoal used in the rebreathing device. The optimal choice of
minute ventilation and EtCO2 should also take into account rebreathing of nitrous oxide
especially when a larger rebreathing efficiency is used to increase PaCO2. The optimum
percent rebreathing should thus provide adequate oxygenation, nitrous oxide removal and
increase in PaCO2 for faster emergence without compromising nitrous oxide removal and
arterial oxygenation.
The iso emergence curves generated by the model are to be interpreted with
caution. The cerebral concentrations used for the predictions were obtained from data for
hypercapnic hyperventilation and mild hypocapnia during hyperventilation. The
validation of the iso emergence lines would require emergence data at different
100
combinations of minute ventilation and CO2 which were not available from our clinical
study.
As in most computer models, this simulation does not account for inter patient
variability. For example, patients with chronic obstructive pulmonary disease and
chronically elevated PaCO2 may not have the increase in cerebral blood flow as the
PaCO2 rises. The model assumes a constant metabolic production of CO2 determined by
the patients body weight and was not altered during anesthesia nor increased during
emergence. The effect of the anesthetic agents on cardiac output was not modeled. The
emergence times recorded from our clinical study could have been affected by the
variable amount of pain stimuli in the patients which the model does not account for.
Although the use of opioids other than remifentanil was discontinued one hour before the
end of the procedure, there could still have been some residual amount of opioid effect,
which could have influenced emergence time independent of the amount of inhaled
anesthetic in the brain. The model does not take into account the opioid-agent interaction
effects on emergence time.
Sevoflurane depresses cerebrovascular CO2 reactivity and the cerebral blood flow
is also altered with change in the concentration of anesthetic agent. The cerebrovascular
reactivity for the agents and the cerebral blood flow was not altered during emergence
towards that of a normal awake human with decreasing concentration of the agent.
4.6 Conclusions
The cerebral concentration of agent at which patients respond to a command to
open eyes was estimated for isoflurane, sevoflurane and desflurane. Using the calculated
101
concentrations, the model predicts a 56% decrease in emergence time with hypercapnic
hyperventilation. The predictions regarding the relative importance of EtCO2 and minute
ventilation in decreasing emergence time might prove useful to the clinician using the
rebreathing adsorber to pick an optimal combination for a fast emergence.
4.7 References
1. Eger EI 2nd L. Anaesthetic solubility in blood and tissues: values and signficance. Br J Anaesth 1964;36:140-4.
2. Wiesner G, Wild K, Merz M, Hobbhahn J. [Rates of awakening, circulatory parameters and side-effects with sevoflurane and enflurane. An open, randomized, comparative phase III study]. Anasthesiol Intensivmed Notfallmed Schmerzther 1995;30:290-6.
3. Lerou JG, Dirksen R, Beneken Kolmer HH et al. A system model for closed-circuit inhalation anesthesia. II. Clinical validation. Anesthesiology 1991;75:230-7.
4. Bishop CC, Powell S, Rutt D, Browse NL. Transcranial Doppler measurement of middle cerebral artery blood flow velocity: a validation study. Stroke 1986;17:913-5.
5. Ide K, Eliasziw M, Poulin MJ. The relationship between middle cerebral artery blood velocity and end-tidal PCO2 in the hypocapnic-hypercapnic range in humans. J Appl Physiol 2003.
6. Ito H, Kanno I, Fukuda H. Human cerebral circulation: positron emission tomography studies. Ann Nucl Med 2005;19:65-74.
7. Ito H, Kanno I, Ibaraki M et al. Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography. J Cereb Blood Flow Metab 2003;23:665-70.
8. Rostrup E, Knudsen GM, Law I et al. The relationship between cerebral blood flow and volume in humans. Neuroimage 2005;24:1-11.
102
9. Matta BF, Mayberg TS, Lam AM. Direct cerebrovasodilatory effects of halothane, isoflurane, and desflurane during propofol-induced isoelectric electroencephalogram in humans. Anesthesiology 1995;83:980-5; discussion 27A.
10. Ornstein E, Young WL, Fleischer LH, Ostapkovich N. Desflurane and isoflurane have similar effects on cerebral blood flow in patients with intracranial mass lesions. Anesthesiology 1993;79:498-502.
11. Bedforth NM, Hardman JG, Nathanson MH. Cerebral hemodynamic response to the introduction of desflurane: A comparison with sevoflurane. Anesth Analg 2000;91:152-5.
12. Matta BF, Heath KJ, Tipping K, Summors AC. Direct cerebral vasodilatory effects of sevoflurane and isoflurane. Anesthesiology 1999;91:677-80.
13. Summors AC, Gupta AK, Matta BF. Dynamic cerebral autoregulation during sevoflurane anesthesia: a comparison with isoflurane. Anesth Analg 1999;88:341-5.
14. Holmstrom A, Akeson J. Sevoflurane induces less cerebral vasodilation than isoflurane at the same A-line autoregressive index level. Acta Anaesthesiol Scand 2005;49:16-22.
15. Nishiyama T, Matsukawa T, Yokoyama T, Hanaoka K. Cerebrovascular carbon dioxide reactivity during general anesthesia: a comparison between sevoflurane and isoflurane. Anesth Analg 1999;89:1437-41.
16. Mielck F, Stephan H, Weyland A, Sonntag H. Effects of one minimum alveolar anesthetic concentration sevoflurane on cerebral metabolism, blood flow, and CO2 reactivity in cardiac patients. Anesth Analg 1999;89:364-9.
17. Mielck F, Stephan H, Buhre W et al. Effects of 1 MAC desflurane on cerebral metabolism, blood flow and carbon dioxide reactivity in humans. Br J Anaesth 1998;81:155-60.
18. Sawai T, Nohmi T, Ohnishi Y et al. Cardiac output measurement using the transesophageal Doppler method is less accurate than the thermodilution method when changing PaCO2. Anesth Analg 2005;101:1597-601.
103
19. Cullen DJ, Eger EI, 2nd. Cardiovascular effects of carbon dioxide in man. Anesthesiology 1974;41:345-9.
20. Hallynck TH, Soep HH, Thomis JA et al. Should clearance be normalised to body surface or to lean body mass? Br J Clin Pharmacol 1981;11:523-6.
21. Lerou JG, Dirksen R, Beneken Kolmer HH, Booij LH. A system model for closed-circuit inhalation anesthesia. I. Computer study. Anesthesiology 1991;75:345-55.
22. Eger EI, 2nd, Saidman LJ. Illustrations of inhaled anesthetic uptake, including intertissue diffusion to and from fat. Anesth Analg 2005;100:1020-33.
23. Einarsson SG, Cerne A, Bengtsson A et al. Respiration during emergence from anaesthesia with desflurane/N2O vs. desflurane/air for gynaecological laparoscopy. Acta Anaesthesiol Scand 1998;42:1192-8.
24. Einarsson S, Cerne A, Bengtsson A et al. Should nitrous oxide be discontinued before desflurane after anaesthesia with desflurane/N2O? Acta Anaesthesiol Scand 1997;41:1285-91.
25. Nickalls RW, Mapleson WW. Age-related iso-MAC charts for isoflurane, sevoflurane and desflurane in man. Br J Anaesth 2003;91:170-4.
26. Varvel JR, Donoho DL, Shafer SL. Measuring the predictive performance of computer-controlled infusion pumps. J Pharmacokinet Biopharm 1992;20:63-94.
27. Swinhoe CF, Peacock JE, Glen JB, Reilly CS. Evaluation of the predictive performance of a 'Diprifusor' TCI system. Anaesthesia 1998;53 Suppl 1:61-7.
28. Katoh T, Suguro Y, Kimura T, Ikeda K. Cerebral awakening concentration of sevoflurane and isoflurane predicted during slow and fast alveolar washout. Anesth Analg 1993;77:1012-7.
CHAPTER 5
SUMMARY AND CONCLUSIONS
5.1 Project Overview
The concept that hypercapnic hyperventilation speeds emergence from inhaled
anesthesia is not new. In 1923 White, et al. reported a decrease in emergence time from
ether anesthesia from 75 min to 14 min by introducing carbon dioxide into the breathing
gas mixture and hyperventilating with minute volumes around 25-35 L/min.(1) Infusion
of CO2 to speed emergence from anesthesia was very common amongst the
anesthesiologists in the United Kingdom in 1980’s. However they were also concerned
about the risks of accidental hypercapnia leading to hypoxia. Majority of them also
considered limiting the flow of CO2 to less than 1 L/min to improve safety.(2-4) The use
of hypercapnia to speed emergence was never applied to clinical practice in the United
States and later discontinued in the United Kingdom due to the risk of inadvertent
hypercapnia.(3)
Hypercapnia increases cerebral blood flow during hyperventilation, thus
accelerating the clearance of anesthetic from the brain resulting in a rapid emergence.
Increase in PaCO2 also increases the oxygen available to the tissues by a rightward shift
in the oxyhemoglobin dissociation curve and a decrease in the systemic vascular
resistance. Carbon dioxide also produces an increase in cardiac output due sympathetic
105
activation. CO2 in the range of 20 to 60 mmHg has a stimulatory effect on the cardiac
output while PaCO2 greater than 70 mmHg causes myocardial depression. Increased
cerebral blood flow due to a high CO2 also increases the intra cranial pressure, which
may result in impaired cerebral perfusion.
The issues of safety with hypercapnia could be reduced by using feedback
controlled infusion of CO2 as described in our study. The controller can monitor the
capnogram and stop infusion of CO2 if the concentration of CO2 in the inspired gas
mixture exceeds a safe limit or if the inspired oxygen concentration delivered to the
patient decreases below safe limits. Monitoring of EtCO2 and inspired oxygen
concentration is a part of standard clinical practice today. A controller could be built
using the existing sensors used in the operating room. However due to the wide range of
monitoring equipment available by different manufacturers such a solution may not be
practical unless the controller has its own sensors, which would increase the cost of the
device. An ideal solution would be to have the controller built into the anesthesia
machine. The controller provides the advantage of leaving the clinicians attention to
managing the patient instead of monitoring the EtCO2 and oxygen saturation.
Perhaps a much simpler method of maintaining hypercapnia during
hyperventilation is by using the rebreathing adsorber described in our study. The
rebreathing device uses rebreathing of CO2 to increase PaCO2 and activated charcoal to
remove anesthetic agent from the rebreathed gas. The maximum CO2 that can be
achieved is limited by the rebreathing efficiency and the volume of CO2 exhaled by the
patient. The device does not require complex circuitry or CO2 tanks, thus making the
device very cost effective. However the clinician has to monitor the patients EtCO2 and
106
adjust the length of rebreathing hose to target a desired EtCO2. When the device is used,
the minute ventilation should be at least doubled to ensure adequate oxygen delivery to
the patient and prevent oxygen desaturation incidents. The safety of the device could
probably be improved by limiting the rebreathing volumes by using a rebreathing hose of
shorter length. This however limits the maximum EtCO2 that can be attained during
hyperventilation.
The performance of the rebreathing device and the feedback controller in
speeding emergence from 2 hours of anesthesia with 2 MACPIG of isoflurane, sevoflurane
or 1 MACPIG of desflurane was evaluated in an animal study with each animal serving as
its own control. Emergence times during hypercapnic hyperventilation (55mmHg) and
hypocapnic hyperventilation (22 mmHg) were compared. Emergence time from
isoflurane and sevoflurane anesthesia was shortened by 65% with rebreathing or with the
CO2 controller (p< 0.05).
The performance of the rebreathing device in decreasing emergence time was
evaluated in a clinical study of fifty two surgical patients undergoing 1 MAC of
isoflurane, sevoflurane or desflurane anesthesia. Fresh gas flows were raised to 10 L/min
during emergence. The patients that received the device were hyperventilated by
doubling the minute ventilation and EtCO2 was raised to 55 mmHg by extending the
rebreathing hose. The patients that did not receive the device were mildly hyperventilated
due to the increased fresh gas flow and were emerged at mildly hypocapnic EtCO2 (29
mmHg). The time between turning off the vaporizer and the time when the patients
opened their eyes and mouth, the time of tracheal extubation and the time for normalized
BIS to rise to 0.95 were faster whenever hypercapnic hyperventilation was maintained
107
using the rebreathing adsorber (p< 0.05). The time to tracheal extubation was shortened
by an average of 57%.
We modified a multi compartmental model of cerebral anesthetic uptake,
distribution and elimination to alter cerebral perfusion with changes in PaCO2 and predict
emergence time from inhaled anesthetic agents. The model was modified to simulate the
use of the rebreathing adsorber by allowing the simulated patient to rebreathe 85% of the
exhaled CO2. A subset of the data collected from the clinical study was used to estimate
the cerebral concentration of anesthetic (normalized to age adjusted MAC) at which the
patients opened their eyes in response to command. The data from the remaining patients
was used to evaluate the predictive accuracy of the model. The model was used to
estimate the relative importance of hypercapnia and hyperventilation to speed emergence
from inhaled anesthesia.
The average awakening brain concentrations normalized to age adjusted MAC for
desflurane, sevoflurane and isoflurane from all the patients were 0.162 ± 0.044, 0.280 ±
0.058 and 0.356 ± 0.105 respectively. The model estimates that there will be at least a
56% reduction in emergence time with hypercapnic hyperventilation. The root mean
square error in the performance error ranged from 10% to 24%. The model predicts that
the three agents behave differently for different combinations of hyperventilation and
CO2 and that higher minute ventilation would be required to speed emergence from
isoflurane anesthesia.
108
5.2 Conclusions
Hypercapnic hyperventilation significantly speeds up emergence times from all
the inhaled agents studied. A reduction in emergence time by at least 56% is possible by
the use of the rebreathing device. The results from our animal study indicate that the
emergence times using the rebreathing device were similar to that obtained from an
optimally tuned CO2 controller which was able to maintain very accurate CO2 values
during emergence. Accuracy of maintaining a steady value is not important but it is
important is that it should be high enough and never too high to pose a safety risk to the
patient. The optimal EtCO2 used is thus a compromise between achieving a faster
emergence and reducing the side effects and safety issues associated with a high PaCO2.
From our simulation results (Chapter 4), it appears that EtCO2 of approximately 50
mmHg would be sufficient to speed emergence from all the inhaled agents.
The rebreathing adsorber device is much simpler to use compared to the devices
described in the literature. Perhaps a rotary switch that varies the dead space might make
the device more convenient to use instead of compressing/expanding the rebreathing
hose. Sasano, et al. used a complex system of a tank containing a mixture of 6% CO2 and
oxygen, a demand based regulator and a modified resuscitation bag to maintain isocapnia
during hyperventilation. Use of their device in dogs after anesthesia with 1.7 MAC of
isoflurane decreased emergence time by 63%.EtCO2 when their device was used was
fixed and was determined by the proportion of CO2 and oxygen in the tank.
To achieve a reduction in the time to extubation from 12.1 min to 3.6 min from
1.1% of isoflurane-nitrous oxide anesthesia, Veseley, et al. used average minute volumes
of 12.1 L/min.(5) However, the minute ventilation reported for a typical patient ranged
109
from 6 L/min to 33 L/min. Results from our simulations indicate that for a patient of
70kg, 1.83 m increase in minute ventilation beyond 10-12 L/min at an EtCO2 in the range
of 50 to 55 mmHg does not yield further decrease in emergence times. Use of very large
tidal volumes to speed emergence could result in stretch induced lung injury. A faster
emergence might be possible by using a combination of moderate hyperventilation along
with a higher EtCO2, thus avoiding the risks associated with ventilator associated lung
injury.
5.3 Limitations of the study
Although we developed an accurate feedback controller we did not make good
use of it in understanding the relative contribution of different levels of hypercapnia in
speeding emergence. With the animal experiments, we only studied emergence times
with isoflurane, sevoflurane and desflurane at two EtCO2 levels (55 and 23 mmHg)
during the same amount of hyperventilation. Perhaps we should also have tested different
combinations of EtCO2 and minute ventilation in each animal to see if similar emergence
times are possible with a lower EtCO2 and with the minimal amount of hyperventilation.
In the animal study, only 30 min of anesthesia was maintained between the first
and second emergence and the second and third emergence tested. The tissue depots of
anesthetic depleted during emergence may not have been completely restored in the 30
min period. The sample size for desflurane was too small to show statistical significance
between emergences at hypercapnic and hypocapnic emergences.
Nitrous oxide is often used in combination with inhaled agents. Activated
charcoal used in the rebreathing device however does not adsorb nitrous oxide at low
110
partial pressures. The elimination of nitrous oxide with the rebreathing device was not
studied. However since the corrugated rebreathing hose allows only 85% rebreathing, we
believe that nitrous oxide would be eliminated during hyperventilation with the device.
However, this needs to be further studied to see if there is a better alternative than 85%
rebreathing that allows faster nitrous oxide elimination, while providing adequate
oxygenation and ability to raise the PaCO2.
The control subjects in the clinical study were mildly hyperventilated because we
used older generation anesthesia machines that did not compensate for the increased fresh
gas flows during emergence and because anesthesia was maintained at an EtCO2 of 33
mmHg. As a result the control subjects were emerged at mildly hypocapnic EtCO2 which
could have increased the difference in emergence times with and without the rebreathing
device. A major flaw in our study design was that the observer that recorded the time to
movement of multiple limbs in the animal study and the time to open eyes in the clinical
evaluation was not blinded to the presence or absence of the device.
The model for emergence from anesthesia was based on data obtained at two
different levels of EtCO2 at two levels of hyperventilation. Emergence times with other
combinations of EtCO2 and minute ventilations are required for proper validation of the
model.
5.3 Future work
This study was focused on evaluating the decrease in emergence times obtained
during hyperventilation with the rebreathing adsorber and when mild hyperventilation
was used without the device. Although a significant decrease in emergence time was
111
observed, a faster emergence need not necessarily improve the overall quality of
recovery. Further studies are required to see if an early emergence by hypercapnic
hyperventilation translates into a faster emergence from the PACU, faster return of
airway protection reflex and decreased post operative pain scores due to faster transit
through stage II of anesthesia. Maintainenance of mild hypercapnia during anesthesia
maintenance and hypercapnia during emergence might also improve cognitive function
especially in the elderly population. However further studies are required to evaluate post
anesthesia outcomes.
Further studies are required to ascertain if there is a better choice than 85%
rebreathing that allows optimal washout of anesthetic, ability to increase PaCO2 to a
desired level and provide adequate oxygen to the patient.
The relative contribution of hypercapnia and hypocapnia in speeding emergence
from anesthesia has been estimated only from a modeling approach. Further clinical
studies at different levels of EtCO2 and minute ventilation would be needed to validate
the isoemergence time curves generated by the model.
5.4 References 1. White J. Deetherization by means of carbon dioxide inhalations. Arch Surg
1923;7:347-70.
2. Shipton EA, Roelofse JA, van der Merwe CA. Accidental severe hypercapnia during anaesthesia. Case reports and a review of some physiological effects. S Afr Med J 1983;64:755-6.
3. Prys-Roberts C, Smith WD, Nunn JF. Accidental severe hypercapnia during anaesthesia. A case report and review of some physiological effects. Br J Anaesth 1967;39:257-67.
112
4. Razis PA. Carbon dioxide--a survey of its use in anaesthesia in the UK. Anaesthesia 1989;44:348-51.
5. Vesely A, Fisher JA, Sasano N et al. Isocapnic hyperpnoea accelerates recovery from isoflurane anaesthesia. Br J Anaesth 2003;91:787-92.
APPENDIX
EQUATIONS USED IN THE MATHEMATICAL MODEL A.1 Symbols
1. A Age (years).
2. BW Body weight (kg).
3. aC Fractional concentration of agent in blood leaving arterial pool.
4. 'aC Fractional concentration of agent in blood exposed to alveolar gas.
5. ''aC Fractional concentration of agent in the blood entering arterial pool.
6. AC Fractional concentration of agent in the alveolar gas.
7. CC Fractional concentration of agent in the central anesthetic circuit.
8. EC Fractional concentration of agent in the expiration section of circuit.
9. IC Fractional concentration of agent in the inspiration section of circuit.
10. _v
C Fractional concentration of agent in the blood leaving central venous pool.
11. '
_v
C Fractional concentration of agent in the blood leaving central venous pool.
12. vpaC Fractional concentration of agent in the blood leaving adipose tissue venous
pool
114
13. 'vpaC Fractional concentration of agent in the blood entering adipose tissue venous
pool
14. vplC Fractional concentration of agent in the blood entering lean tissue venous pool.
15. 'vplC Fractional concentration of agent in the blood leaving lean tissue venous pool.
16. vpvC Fractional concentration of agent in the blood entering viscera tissue venous
pool.
17. 'vpvC Fractional concentration of agent in the blood leaving viscera tissue venous
pool.
18. i
Cω Fractional concentration of agent in venous blood draining tissue i.
19. sf Shunt fraction of cardiac output.
20. FRC Functional residual capacity.(L)
21. H Height.(m)
22. iQ⋅
Blood flow through tissue i.
23. leakQ⋅
Anesthetic agent lost as vapor at BTPS through leaks.(L/min)
24. t Time.(min)
25. ⋅
AV Alveolar ventilation at BTPS.(L)
26. blV Total blood volume.(L)
27. ablV , Blood volume in arterial pool.(L)
28. vblV , Venous blood volume.(L)
29. CV Volume of anesthetic circuit at BTPS.(L)
115
30. DV Volume of dead space at BTPS.(L)
31. EV Volume of expiratory section of anesthesia circuit.(L)
32. iV Volume of tissue i.(L)
33. IV Volume of inspiratory section of anesthesia circuit.
34. LV Lung volume into which anesthetic is distributed.(L)
35. leakV⋅
Gas volume lost from the closed circuit.(L/min)
36. TV Tidal volume at BTPS.(L)
37. vpaV Blood volume of the adipose tissue venous pool.(L)
38. vpcV Blood volume of the central venous pool.(L)
39. leakV⋅
Gas volume lost from the closed circuit.(L/min)
40. TV Tidal volume at BTPS.(L)
41. vpaV Blood volume of the adipose tissue venous pool.(L)
42. vpcV Blood volume of the central venous pool.(L)
43. vplV Blood volume of the lean tissue venous pool.(L)
44. vpvV Blood volume of the viscera venous pool.(L)
45. ZV )(LVV DZ +
46. bλ Blood-gas partition coefficient.
47. iλ Tissue-blood partition coefficient for tissue i.
116
A.2 Relationship between the variables
( ) )(090.1009.0340.265.0 manAHFRC −+= (A.1)
( ) )(000.1001.0240.265.0 womanAHFRC −+= (A.2)
DCZ VVV += (A.3)
BWVbl 07.0= (A.4)
blabl VV 2.0, = (A.5)
blvbl VV 8.0, = (A.6)
BWVD 002.0= (A.7)
lungbTL BWVFRCV λλ008.05.0 ++= (A.8)
blvblvpc VVV 101.0126.0 , == (A.9)
blvblvpl VVV 291.0364.0 , == (A.10)
117
blvblvpv VVV 3191.0399.0 , == (A.11)
blvblvpa VVV 009.0111.0 , == (A.12)
A.3 Description of model compartments
A.3.1 Anesthesia circuit
The following equations describe the rate of change in anesthetic concentration in
the three compartments that describe the anesthesia machine.
( )
I
ICAI
VVVV
dtdC −
=
.
(A.13)
( )
C
leakCAEAC
V
QVapFGFCVCFGFV
dtdC
⋅⋅⋅−+−
−=
% (A.14)
( )
E
EAAE
VVVV
dtdC −
=
.
(A.15)
118
A.3.2 Lung compartment
For the lung compartment, the rate of change in the alveolar concentration of the
agent
( )( )
L
VAbs
ACL
AA
V
CCfQCC
VV
dtdC
−−
−−=_1
.. λ
(A.16)
Since 'aAb CC =λ ,
( ) sv
saa fCfCC _1''' +−= (A.17)
A.3.3 Arterial pool and tissue groups
The rate of change of the arterial concentration of the agent is
( )aaap
a CCVQ
dtdC
−= ''
.
(A.18)
The rate of change in concentration of agent in the venous blood draining tissue group i
(i
Cω ) is
( )i
i CCVQ
dtdC
aii
iω
ω
λ−=
.
(A.19)
119
A.3.4 Venous pool
The concentration of agent in the venous blood draining the viscera is given by
∑= +++
=4
1.
43
.
1
.
1
.
.
i
ivpv
QQQQ
QCC iω (A.20)
The rate of change in the concentration of agent in the venous pool of viscera is
( )'.
43
.
1
.
1
.'
vpvvpvvpv
vpv CCV
QQQQdt
dC−
+++= (A.21)
The concentration of agent in the venous blood draining the lean tissue is given by
∑= +
=6
56
.
5
.
.
i
ivpl
QCC iω (A.22)
The rate of change in the concentration of agent in the venous pool of lean tissue is
( )'6
.
5
.'
vplvplvpl
vpl CCV
QQdt
dC−
+= (A.23)
120
The concentration of agent in the venous blood draining the adipose tissue
7ωCCvpa = (A.24)
The rate of change in the concentration of agent in the venous pool of the adipose tissue
( )'77
.'
vpavpa
vpa CCVQ
dtdC
−= (A.25)
The concentration of agent in the central venous pool is
.8
.
.7
.
'.6
.
5
.
'.
.
43
.
1
.
1
.
''
_
Q
QC
Q
QC
Q
QQC
Q
QQQQCC avpavplvpv
v++
++
+++= (A.26)
The rate of change in the concentration of agent in the central venous pool
−= __
_
'
.
VVvpc
v CCVQ
dt
dC (A.27)