View
217
Download
0
Category
Preview:
Citation preview
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 1/83
PHARMACOKINETICSPHARMACOKINETICS
John Orton
Royal Oldham Hospital
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 2/83
What have the following got incommon?
V1V2
k12
k21
kel
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 3/83
What have the following got incommon?
V1V2
k12
k21
kel’
!
They
re allmo
dels
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 4/83
Models
Created to predict from limitedinformation what will happen in the realworld
Dependant of data Complexity can be at the cost of
accuracy
Often aims to predict in individualcircumstances from data obtained froma population
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 5/83
Why bother?
To adjust the dose of drug so that theresponse of the body is as much andfor as long as required
But...Problems measuring drug at biophaseDrug concentration may not correlate with
response
May not be possible to measure responseaccurately
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 6/83
Qualitative ApproachQualitative ApproachYou can get quite far without much maths
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 7/83
In (or uptake)
Intravenous Inhalational
main routes for anaesthesia
Intramuscular Oral
Bioavailability
○ Effective dose / Administered dose Transdermal
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 8/83
Around (or distribution)(Drug factors)
Lipid solubility Water solubility Molecular size pKa
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 9/83
Around (or distribution)(Tissue factors)
Lipid content○ Brain, CSF
Blood vessel content Highly perfused
○ Lung, kidney, spleen, thyroid, adrenal,brain
Poorly perfused○ Bone, fat
Variable○ Muscle, skin, gut
Tissue binding Tissue barriers
Blood brain barrier Placenta Glomerulus “Leaky Capillaries”
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 10/83
Around (or distribution)(Blood factors)
Plasma proteins Variable: depends on drug Effect is to slow down rate of diffusion Types
Albumin Acidic drugs Lipo- and GlycoproteinsBasic Drugs α 1 acid glycoprotein
Red blood cells Cardiac output Sequestration
Lungs and fentanyl StomachpH trap Muscle
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 11/83
Distribution: summary
Depends on: Molecular size
Ionisation Protein binding Tissue perfusion
eg Relaxants Low Protein binding
(<60%) so perfusion
affects distribution alot.
Highly ionised so tendto stay in ECF
BUT dTc undergoestissue binding, soVd is unexpectedlyhigher than ECF
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 12/83
“Diffusible Fraction”
Consists of: Drug unbound to plasma protein
which is also
Unionised
The more protein bound and ionised adrug is, the more it tends to stay in the
plasma.
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 13/83
Out (Metabolism, excretion andelimination) Liver
Lipid soluble drugs Kidney
Polar drugs Lung
Vapours and gases
Metabolism
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 14/83
Out (Liver)
First pass effectLipid soluble drugsOrally administered
HER = (Ca - Cv)/CaHER = 1
○ clearance is flow dependant○ liver has spare capacity
HER approx 0.3○ clearance is flow independant○ liver is working at maximum rate
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 15/83
A brief diversionA brief diversionNow for some maths
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 16/83
BASIC MATHS FORBASIC MATHS FOR
PHARMACOKINETIPHARMACOKINETI
CSCS
Its easy – honest!
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 17/83
10 + 10
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 18/83
+1 0 1 0
is 1 0 x 2
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 19/83
1 0 x 1 0
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 20/83
10 x 10
is102
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 21/83
10x10 x 10x10 is
102 x 102 is 104 10(2+2)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 22/83
103 x 106
is 10 +3 6
109
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 23/83
t3 x t6
is t +3 6
t9
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 24/83
tn x tm
is
t +n m
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 25/83
/10000 100
is
100
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 26/83
104 / 10 2
is
102
10000 / 100
is
100
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 27/83
10 -42
is
102
10000 / 100
is
100
104 / 102
is
102
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 28/83
t -42
is
t2
t4 / t2
is
t2
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 29/83
Logarithms
Multiply by adding the powers Divide by subtracting the powers
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 30/83
Logarithms
Any positive number can be expressed( )as a number usually 10 raised to
a power Eg
100 is 102
64 is 10 .1806
2 is 10 .0301
So how do you calculate 2 x 64 using
logarithms?
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 31/83
Logarithms
Any positive number can be expressed( )as a number usually 10 raised to
a power Eg
100 is 102
64 is 10 .1806
2 is 10 .0301
( )+ ( ) = .log 64 log 2 1 806+0.301 = 2.107 Antilog(2.107)=128 (ie 128 = 102.107 )
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 32/83
Wierdness
What is 10-1? 103/104 (103-4 ) [10 x 10 x 10] / [10 x 10 x 10 x 10] [10 x 10 x 10] / [10 x 10 x 10 x 10] 1/10 t-1 = 1/t
If t-n = y, 0<y<1 (y is between 0 and 1)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 33/83
Wierdness
What is 100.5 ? =√10 t0.5 = √t
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 34/83
Wierdness
What is 100? =1 t0 = 1
10 x 10 / 10 x 10 = 1 = 102/102=10(2-2)
=100!
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 35/83
Wierdness
What is 100? =1 t0 = 1
10 x 10 / 10 x 10 = 1 = 102/102=10(2-2)
=100!
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 36/83
Summary
100 is 102
64 is 101.806
1 is 100
0.1 is 10-1
0.001 is 10-2
Notice you cannot express a negative as
a logarithm 100.5 is √10
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 37/83
eeWhat is it and where does it come from?
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 38/83
e
=2.718
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 39/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 40/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 41/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 42/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 43/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 44/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 45/83
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 46/83
As frequencyapproaches infinity thisbecomes e!(2.718)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 47/83
y = 10t
Simplify y = 10t
Use a logarithmic transform log y = t
Strictly speaking log10y = t
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 48/83
y = et
Simplify using logs to base e instead of base 10, ie loge instead of log10
y = et becomes loge(y) = t
Also written as ln instead of loge ie ln(y)=t
Natural logarithms
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 49/83
y = ek.t
Logarithmic transform: y = ek.t becomes Ln(y) = k.t
Logarithmic transform:
Ct = C0.e-k.t becomes Ln(Ct) = (Ln C0) - k.t
Ct = C0.e-k.t
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 50/83
y = mx + c
General eqation for a straight line graph m = slope of line c = intercept of y axis
y
x
m
c
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 51/83
Logarithmic transform
Lets you convert a complicated equation: Ct = C0e-tk
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 52/83
Logarithmic transform
Lets you convert a complicated equation: Ct = C0e-tk
Into a linear equation Ln(Ct) = Ln(C0)-t.k
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 53/83
Logarithmic transform
Into a linear equation Ln(Ct) = Ln(C0) - t . k
= – .y c x m
=y – . +m x c
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 54/83
pK a
Ka = [H+].[Drug-][H.Drug]
Since
log 1/[H+] = -log[H+] = pHandlog 1/Ka = -logKa = pKa
1 1 [Drug-][H+] Ka [H.Drug].=i.e
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 55/83
pK a
pH = pKa+log [Drug- / H.Drug] or
pH = pKa+log [Ionised / Unionised]
or pH = pKa+log [Proton acceptor / Proton Donor ]
If Ionised = Unionised
pH = pKa (since log(1)=0)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 56/83
pKa
So what? If pKa is near
physiological pHthen patients
condition willinfluence degreeof ionisation andtherefore clinical
effect cf local anaesthetics
% unionised at differentpH
Lignocaine pKa 7.9pH 7.0 11.2pH 7.4 24pH 7.8 44
Bupivacaine pKa 8.1pH 7.0 7pH 7.4 16pH 7.8 33
k h l l l l
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 57/83
Pk at the molecular levelDiffusion
Law of mass actionFlow along concentration
gradients
Major assumption in Pk models○ no active processes influencing
distribution
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 58/83
Rt α Ct
Or
Rt α Ct1
That is, elimination is proportional toconcentration raised to the first
power, hence ‘first order kinetics’
So…
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 59/83
But if….
Rt α Ct0 and Rt = k.Ct
0
Anything raised to the power of zero is 1
So Ct0
=1, therefore Rt α 1 Rt = k.1
So, Rt = k
In other words elimination is constant. Hence ‘zero order kinetics’.
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 60/83
Clearance, Vd, k, T1/2 and
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 61/83
Clearance
Rate of elimination (R) (mg.sec-1) Concentration (C) (mg.ml-1)
Law of mass action dictates:Rt α Ct
Rate of elimination at time t is proportional to concentration at time t
(assuming system isn’t saturated)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 62/83
Clearance
Rt α Ct
Rt = Ct.k, k=Rt/Ct
k is a constant – what sort of constant? Rt/Ct units are [mg].[sec]-1/ [mg].[ml] -1
Rearranging: [mg].[sec]-1.[mg]-1.[ml]
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 63/83
Rt α Ct
Rt = Ct.k
k is a constant – what sort of constant? Rt/Ct units are [mg].[sec]-1/ [mg].[ml] -1
Rearranging: [mg].[sec]-1.[mg]-1.[ml]
Cancelling out: ml.sec-1
It’s Clearance!
Clearance
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 64/83
Volume of Distribution (Vd)
Theoretical; rarely relates to aphysiological volume
After an IV bolus:
Dose (D)Concentration at time zero (C0)VVdd==
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 65/83
How to find C0CC00
C o n
c e
n t r a t i o
n
C o n c
e n
t ra t i o
n
TimeTime
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 66/83
Or...
CC00
L o
g
C o
n c
e n t r
a t i o
n
L o
g
C o
n c e
n t r a t
i o n
TimeTime
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 67/83
Vd and Cl
Rate of drug elimination is constantlychanging
But…
Percentage (or fraction) eliminated in unittime is constant (k)actually it’s
the natural log (ln) of the fraction ln{ C 0 / C t }
where t=1 Units are min-1
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 68/83
k = Cl / Vd
Another way of looking at k The fraction of Vd cleared of drug in unit
time
i.e. Cl / Vd
k = Clearance expressed as a fraction of Volume of Distribution
k is the Rate Elimination Constant
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 69/83
k, T1/2 and With k, the denominator is unit time
(minute, second, hour, whatever), thevariable is the fraction
With T1/2 , the denominator is a fraction(which in this case is 1/2), the variableis time
But T1/2 is not 1/k (or not exactly)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 70/83
k, T1/2 and
Ct =C0e-k.t (basic decay function)
Ct/C0 =e-k.t
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 71/83
k, T1/2 and
Ct/C0 =e-k.t
When Ct/C0 =0.5(C has dropped to half original conc)
e-k.t =0.5
Ln{e-k.t } = Ln{0.5} = -k.t
Ln{0.5 } = -0.693 k.t = 0.693, k=0.693 / t Since t=T1/2 , k = 0.693 / T1/2
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 72/83
k, T1/2 and
τ is the time constant
It is the time taken for to reach zero if rate of fall were constant or the time taken for Ct to fall to 1/e
(instead to 1/2)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 73/83
k, T1/2 and
Ct/C0 =e-k.t
When t=τ , Ct/C0 =1/e e-k.t
=1/e
Ln{e-k.t } = -k.t
Ln{1/e } = -1 k.t = 1 or k=1 / t
Since t=τ , k = 1/τ
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 74/83
k, T1/2 and
Since k = 1/τ And since k = 0.693 / T1/2
0.693 / T1/2 = 1/τ
T1/2 = τ x 0.693
= τ x ln(2)
V k Cl T
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 75/83
Vd k elCl T1/2
Vd volume of distribution
○ If <5L corresponds to vascular space○ If >15L corresponds more to ECF (or an organ is
concentrating the drug)
kel proportion of drug eliminated in unit time (or more
precisely the logarithm: ln(Ct / Co)
Cl Clearance, ml/second
T1/2 Time taken for drug concentration to change by 1/2 T1/2 = 0.693 / kel
Cl = Vd.ke = Total Dose / AUC
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 76/83
Different Vd
Vd
VdssSteady state
Vdβ
elimination phase
Infusion Kinetics
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 77/83
Infusion KineticsHow to calculate rate of infusion to achieve a given blood
concentration
Assume that at steady statein = outi.e. rate of infusion = rate of elimination
Rate of elimination = Clearance x Concentration Concentration you know Clearance you either look up or calculate from
Cl = Vd.k For an infusion you will require Vdss (not ordinary Vd from a
bolus) Calculate this by doing an actual study, infusing at a constant
rate to steady state and measuring blood levels (see nextslide)
Vd
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 78/83
Vdss
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 79/83
Exponential Change(decay in this example)
Ct=C0e-kt
Universal process
Where something changes according to its own magnitude
l d l
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 80/83
Compartmental Modelsand some basic Pk terms
One compartmentRapid bolusRapid mixingOpen (ie drug leaves as 1st order process)
D
Central CompartmentVd
k elCl
Estimation of Pk parameters
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 81/83
Estimation of Pk parameters
in a one compartment model
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
Time
0.001
0.01
0.1
1
10
100
Drug Concentration
Drug Concentration
(Log plot)
Co
Co
Gradient = k el
Ct = Coe-k el
.t
Drug Concentration Ct Drug concentration (Log Axis)
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 82/83
Two Compartment Model
0.01
2.01
4.01
6.01
8.01
10.01
12.01
14.01
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Co = Ae-α t
+ Be-β t
V1
V2
k12
k21
k10
Drug Concentration (Log plot:: looks flattish because of log transform)t
8/6/2019 PK all 2011
http://slidepdf.com/reader/full/pk-all-2011 83/83
TwoCompartment
ModelLogarithmic Plot
• NB α and β (calledhybrid rate
constants) are notk 12 , k 21 , k 10 in the
model
•They are hybrids of k 12 , k 21 and k 10
0.001
0.01
0.1
1
10
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
g ( g p g )
A (Distribution)
B (Elimination)
C- t -β
o = Aeα
+ Bet
A
B
Gradient = βBe-
β t Gradient = α
Ae-
α t
V1V2
k12
k21
kel
Recommended