![Page 1: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/1.jpg)
Non-Compartmental PK Modelling “model independent” Distributed models
Transit/Residence distributions
Michael Weiss
Martin Luther University
Halle-Wittenberg
![Page 2: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/2.jpg)
)()(
tCCLdt
tdAe
Basic Equation
Rate of drug elimination = Clearance x Plasma concentration
(1)
dttCCLAdt
tdAe
e )()(
00
AUCCLDiv
Note: ive DA )( (nothing remains in the body)
Well-mixed plasma
compartment !
“ model independent “ or noncompartmental analysis)
![Page 3: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/3.jpg)
Estimation of Clearance (single dose)
AUC
DCL iv
AUC
C(t)
t
Single dose
Div dttCAUC
0
)(
!
Intravenous dose
Area Under the Curve
![Page 4: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/4.jpg)
Estimation of Clearance (infusion)
ssCCLSteady state after continuous
i.v. infusion DR
Output (elimination rate) = Input (dose rate, infusion rate)
t
C(t)
Css
DR
ssC
DRCL
Elimination rate
Dose rate
![Page 5: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/5.jpg)
Estimation of Bioavailability
dttCCLAe )(0
(cf. Eq. 1)
ivor
orivivor
AUCD
AUCDFDDif :
iv
or
iv
or
ive
ore
AUC
AUC
dttCCL
dttCCL
A
AF
)(
)(
0
0
,
, Assumption:
CL unchanged ! (13)
ncirculatiosystemicthereachesthatAmountAe
![Page 6: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/6.jpg)
Determinants of Clearance
Organ
QCin QCout
E = 1-F (extraction)
Cout = F Cin
F (availability)
)( otherRH CLCLCLCLhepatic renal
organorganorgan EQCL (4)
N
i
iiEQCL1
![Page 7: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/7.jpg)
Renal Clearance
2
1
21
)(
,
t
t
tteR
R
dttC
ACL
21
21
tt
tt
AUC
excretedamount
(5)
RH CLCLCLt1 t2
AUC
![Page 8: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/8.jpg)
Relative Bioavailability
Conor
Coniv
Treativ
Treator
Con
Treat
AUC
AUC
AUC
AUC
F
F
,
,
,
,
![Page 9: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/9.jpg)
D
tAtTtF e )(
Pr)(
If an amount of drug molecules (dose Div) is instantaneously injected intravenously,
each molecule will spend a random time T in the body until it is eliminated (the
disposition residence time of that molecule).
Residence Time Distribution
Residence time distribution, F(t), is defined by the fraction of molecules which have a
residence time less than t:
Ae(t) is the cumulative amount of drug
eliminated up to time t.
F(0) = 0 and F(∞) = 1
)()(
tCCLdt
tdAe
AUC
tC
dttC
tCtf
)(
)(
)()(
0
Density function
![Page 10: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/10.jpg)
0 0 0
)](1[)()(][ dttFdttFdtttfTEMRT
AUC
dtttC
MRT 0
)(
)(
)]()([
,
0
,,
Re
ReRe
A
dttAA
MRT
)()(
tCLCdt
tdAe
Weiss, Eur J Clin Pharmacol , 1992
Mean Residence Time
![Page 11: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/11.jpg)
][)( tTPtF Probability that residence time T of a molecule exceeds t.
Continuous infusion: Mass dA which entered the body in the time interval [t-dt,t] which
remains in the body at time t is given by:
dttFDR )(
dttFDRtA
t
0
)()( dttFDRAAss
0
)()(
MDRTDRAss
CLMDRTC
MDRTDR
C
AV
ssss
ssss
Weiss, J Pharm Sci , 1991
![Page 12: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/12.jpg)
1. Disposition Curves (Bolus Injection)
Clearance CL
Volume of distribution at steady state Vss
Mean Disposition Residence Time MDRT
CL
VMDRT ss
(14)
![Page 13: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/13.jpg)
Mean Disposition Residence Time
A(t)
t
Div
10 % of Div
t 90%
Bolus injection
t 90%
Continuous infusion
t
90 % of Css
Css
C(t)
2/1%90 4 ttMDRTt 7.3%90(15)
Weiss, J Pharmacokin Biopharm, 1986
![Page 14: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/14.jpg)
Multiple Dosing
ssC
C(t)
Dor Dor Dor Dor Dor Dor Dor Dor
dosing interval
maintenance dose
average
concentration
dose rate orFD
Dor = Dm
![Page 15: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/15.jpg)
C(t)
Dor Dor Dor Dor Dor Dor Dor Dor
Cmax
increasing
toxicity
decreasing
efficacy
Cmin
Therapeutic Drug Monitoring (TDM)
![Page 16: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/16.jpg)
C(t)
Dor Dor Dor Dor Dor Dor Dor Dor
AUC
AUCss
AUCAUCss
MDRT
doseemaintenanc
statesteadyatbodyinamount
ssC
CL
FD
CL
DRC m
ss
![Page 17: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/17.jpg)
CL determines maintenance dose Dm
V determines loading dose DL
MDRT determines time to steady state t90%
and dosing interval
Basic Pharmacokinetic Parameters
![Page 18: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/18.jpg)
n
i
t
iivieBtC
1
)( fit to data, estimate Bi and i (i= 1..n)
n
i i
i
iv
B
DCL
1
n
i i
iBAUCdttC
10
)(
Parametric Curve Model
n
i i
i
n
i i
i
iv
iv
iv
iv
B
B
AUC
AUMC
dttC
dtttC
MDRT
1
12
0
0
)(
)(
MDRTCLVss
![Page 19: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/19.jpg)
Mean Residence Time after Oral and Intravenous Administration
Absorption
Disposition
C(t)
Dissolution
Dor
Div
Mean Dissolution
Time
Mean Absorption
Time
Mean Disposition Residence
Time
Mean Input Time
Mean Body Residence Time
MBRT = MDT + MAT + MDRT
![Page 20: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/20.jpg)
Mean Body Residence Time MBRT
or
or
or
or
AUC
AUMC
dttC
dtttC
MBRT
0
0
)(
)(
Mean Disposition Residence Time MDRT
iv
iv
iv
iv
AUC
AUMC
dttC
dtttC
MDRT
0
0
)(
)(
![Page 21: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/21.jpg)
Mean Input Time MATMDTMIT
Oral Administration
Dissolution
Absorption
SolutionTablet MBRTMBRTMDT
MDRTMBRTMAT Solution
MAT
Dor
FDor
. . . . . . . . . . . . . . . . . . . . MDT
Systemic
Circulation
MDTin vitro
MDTin vivo
![Page 22: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/22.jpg)
C(t) after extravascular (oral) administration
0
)( AUCdttC0
)( AUMCdtttCand
by numerical integration Trapezoidal rule
C(t)
ti ti+1
Ci
Ci+1
tN
,NtAUC
![Page 23: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/23.jpg)
Trapezoidal rule
,,0
2111
1
1
)1
()(2
1
NN tt
zz
NNiiiiii
N
i
AUMCAUMC
tCttCtCtAUMC
,,0
11
1
1
)(2
1
NN tt
z
Niiii
N
i
AUCAUC
CttCCAUC
ti+1 ti
)(2
111 iiii ttCC
![Page 24: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/24.jpg)
Reactor: Turbulent mixing
Transit time dispersion in microcirculatory network:
mixing
How to describe mixing/distribution kinetics ?
Steady-state → transient state
Circulation without dispersion: no mixing
![Page 25: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/25.jpg)
Residence time sytem
Transit time sytem
Disposition
curve
Outflow
curve
Transit time dispersion Rate of distribution
Mean transit time Extent of distribution
![Page 26: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/26.jpg)
Normalized (dimensionless) variance
Relative Dispersion of Disposition Residence Time Distribution
2
2
MDRT
VDRTRDD
n
i
t
iivieBtC
1
)(
n
ij
i
ij
j
BjdttCtm
11
0
!)(
2
0
1
0
2
m
m
m
mVDRT
0
1
m
mMDRT
![Page 27: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/27.jpg)
t
Div Weiss, Pharm Res , 2007
Closed (noneliminating) system (CL = 0)
t
Div
Rate of Distribution: Mixing Clearance
21
2
DM
iv
MRD
CL
AUC
DCL)1(
2
1 2
DM RD
AUC
AUC
Well-mixed system (1-compartment model)
12
DRD Exponential distribution
dtCtCAUCM
0
)()(
ss
iv
V
DC )(
V
DC iv)0(
)()()(
0 CtCCLdt
tdCV M
![Page 28: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/28.jpg)
AUCM: Circulatory Transit Time
AUCM
C( )
t
Div
Closed
(noneliminating)
system (CL = 0)
Weiss & Pang, J Pharmacokin Biopharm, 1992
)1(2
1 2
civ
M RDQ
DAUC
VCTMCT
)1(1 22
cD RDQ
CLRD
![Page 29: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/29.jpg)
From Flow-to Diffusion-Limited Distribution Kinetics A Continuous Transition
Cardiac Output (l/min)
Antipyrine
Inulin
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
Dis
trib
uti
on
Cle
aran
ce (
l/m
in) flow-limited
diffusion -limited
Deff~ 7*Dinulin Sorbitol
Thiopental
Weiss et al, Pharm Sci, 2007
![Page 30: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/30.jpg)
5 6 7 8 9 10 11
0
1
2
3
CLM
(l/min)
Q (l/min)
Slope 0.26 ± 0.07, P < 0.05; R = 0.84
Distribution Kinetics of Alfentanil
Data from: Henthorn et al., Clin Pharmacol Ther, 1992
4
1
)(i
t
iivieBtC
4
11
!i
j
i
i
j
Bjm
![Page 31: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/31.jpg)
Thiopental: heterogeneity of residence time distribution increases with obesity
Weiss , Pharmacokin Pharmacodyn, 2008
![Page 32: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/32.jpg)
Brain
Heart
Kidney
Testes
Fat
Gut
Carcass
Vei
ns
Art
erie
s
Lung
Pancreas
Spleen
Skin
Liver
Muscle
Pulmonary
Circulation
Systemic
Circulation
Minimal Circulatory PK Model
Heterogeneous subsystems
Transit time distributions
© Weiss 2005
![Page 33: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/33.jpg)
Why are they relevant?
Less than 0.1% of PK models used in literature are circulatory models
2) First-principles modeling of distribution kinetics
Role of cardiac output, convective dispersion and intratissue diffusion
(ICG, inulin, antipyrine, thiopental, rocuronium)
Modeling of slow tissue binding (digoxin)
Use of the multiple indicator approach in parameter estimation
1) Description of initial mixing kinetics (2 min after bolus injection)
Front-end kinetics of short acting iv anesthetics
![Page 34: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/34.jpg)
Circulatory minimal model
Pulmonary Circulation
Systemic Circulation
Div
Cardiac
Output, Q
Arterial
Sampling
Transit Time
Density
MTT=V/Q, RD
Elimination
CL = EQ
tMTTRD
MTTt
tRD
MTTtf IG
2
)(exp
2)(
2
3
Extraction
E © Weiss 2005
Weiss et al., Br J Clin Pharmacol ,1996
![Page 35: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/35.jpg)
)(ˆ)(ˆ)1(1
)(ˆ)(ˆ
sfsfE
sfsf
ps
p
circ
)(ˆ)( 1 sfQ
DLtC circ
Recirculatory PK Model
Numerical inverse Laplace Transformation
Q
CLE Extraction (probability of elimination in one passage through systemic
circulation)
Schalla & Weiss, Eur J Pharm Sci, 1999
![Page 36: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/36.jpg)
Hemodynamic Influences on Sorbitol Kinetics in Humans Inverse Gaussian Transit Time Density
Pla
sma
So
rbit
ol
(µg
/ml)
0 5 10 15 20 25 30 35
Time (min)
0
50
100
150
200
Control
Orciprenaline
(10 µg/min)
Sorbitol
0.8 g, 1min
RDs + 27 %
CLM + 44 %
CL + 24 %
Weiss et al., Br J Clin Pharmacol,1996
Q + 53%
![Page 37: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/37.jpg)
0
20
40
60
80
100
0 5 10 15 20 25 300
40
80
120
160
200
0 2 4 6 8 100 2 4 6 8 10
0
40
80
120
160
200
Physiological (recirculatory)
vs. Compartmental (biexponential)
Time (min)
simulated
fitted
Art
eria
l co
nce
ntr
atio
n
5 min
Infusion 1 min
simulated
predicted
Pul circ
Sys circ Central
Peripheral
![Page 38: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/38.jpg)
0
40
80
120
160
200
0 2 4 6 8 100 2 4 6 8 10
0
40
80
120
160
200
0 2 4 6 8 10
0
40
80
120
160
200
0 2 4 6 8 10
0
40
80
120
160
200
0
40
80
120
160
200
0 2 4 6 8 100 2 4 6 8 10
0
40
80
120
160
200
0 2 4 6 8 10
0
40
80
120
160
200
0
10
20
30
40
50
0 10 20 30 40 50 600 10 20 30 40 50 60
0
10
20
30
40
50
Time (min)
Conce
ntr
atio
n
1 min 15 min
Arterial vs. peripheral venous sampling
CA(t)
CV(t)
![Page 39: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/39.jpg)
First-principles modeling of distribution kinetics
Advective transport
Advective dispersion Vascular mixing
Permeation (Capillary uptake)
Diffusion (Extravascular)
Tissue Binding
![Page 40: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/40.jpg)
Extraction, E
Pulmonary Circulation
Systemic Circulation
Div
Cardiac
Output, Q
Drug+vascular marker (ICG)
ICG (vascular marker)
Drug
fs(s)
fp(s)
Div
1. Simultaneous injection, ICG+drug
2. Fit of ICG data (IG model)
3. Fixing of ICG parameters
in drug model
4. Fit of drug data
Arterial Sampling
![Page 41: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/41.jpg)
Q
VB,p VT,p
VB,s VT,s Intravenous
injection
C(t)
Arterial
sampling Dose
Cardiac output
Pulmonary blood and tissue volume
Systemic
Extravascular diffusion
CL
d
![Page 42: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/42.jpg)
Intravascular
mixing
(vascular marker)
Microcirculatory network
Tissue
distribution
Microscopic volume element
vascular
tissue
phase
Dif
fusi
on
Vp
VT
Capillary
flow
Systemic circulation: Advection-diffusion model Stochastic model of transit time distribution
Weiss & Roberts, J Pharmacokin Biopharm, 1996
![Page 43: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/43.jpg)
Extravascular Diffusion Kinetics Rocuronium (+ICG as vascular marker)
Systemic
Circulation
Q )(ˆ sf p
)(ˆ sfs
Vp 2
pRDQ
d VT,s
VB,s
vascular
ISF
Cell
extravascular
2
,sBRDVB,s
ssv
sfsf dd
d
sIGs tanhˆ)(ˆ
B
T
V
Vv
eff
dD
L2
![Page 44: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/44.jpg)
)(ˆ, sf pIG
0 2 4 6 8 10
0
5
10
15
100 1017 8 2 3 4 5 6 7 8 2 3
100
101
78
2
3
4
5
6
78
2
3
ICG
conce
ntr
atio
n(µ
g/m
l)
Pre
dic
ted
co
nce
ntr
atio
n (
µg/m
l)
Time (min)
Observed concentration (µg/ml)
Vascular Mixing Kinetics Vascular Marker (ICG) in Patient
VB,p
VB,s
2
, pBRD
2
,sBRD
Q
E
Relative dispersion -> Intravascular mixing
)(ˆ, sf sIG
2
, pBRD 0.09 12
0.37 21
Population
Mean
Interpatient
CV(%)
Pulmonary circulation
Systemic circulation
Q (L/min) Cardiac output 3.52 20
2
,sBRD
TT dispersion
Time (min)
Weiss et al.,
J Pharmacokin
Pharmacodyn, 2011
![Page 45: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/45.jpg)
101
102
103
104
105
0 50 100 150 200 2500 50 100 150 200 250
101
102
103
104
105
0 1 2
0
2
4
6
8
10
12
14
Ro
curo
niu
m c
on
cen
trat
ion
(n
g/m
l)
Time(min)
89 (37) 50(62)
2.66(97) 115 (61)
Distribution kinetics of rocuronium
Interstitial diffusion, time constant
Interstitial volumes
d (min)
VT,p (L))
VT,s (L)
Population Mean
(%RSE)
Interpatient %CV
(%RSE)
14.2 (30) 29 (96)
Individual estimates of ICG parameters were
used as fixed parameters in fitting rocuronium data.
Rocuronium Kinetcs in Patients
Weiss et al.,J Pharmacokin Pharmacodyn, 2011
![Page 46: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/46.jpg)
2.5 3.0 3.5 4.0 4.5 5.0
0.25
0.30
0.35
0.40
0.45
Rel
ativ
e S
yst
emic
D
isp
ersi
on
Cardiac Output (L/min)
Fig. 3
Systemic transit time heterogeneity of ICG decreases linearly with cardiac output (P< 0.005)
2.5 3.0 3.5 4.0 4.5 5.0
1.4
1.6
1.8
2.0
2.2
2.4
Cardiac Output (L/min)
Pulm
onar
y B
lood V
olu
me,
VB
,p(L
)
Fig. 4
Central blood volume increases linearly with cardiac output (P<0.01)
Weiss et al.,J Pharmacokin Pharmacodyn, 2011
![Page 47: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/47.jpg)
The validity of a model is determined
by the modeling objectives
Minimal PBPK models are relevant for explaining -Initial intravascular mixing (blood volumes, TT dispersion, role of the lungs) -Tissue distribution kinetics (permeation,diffusion,binding)
-Effect of obesity (highly lipid-soluble drugs) -Effect of cardiac output and hemorrhagic shock -Hemodynamic drug interactions -Hepatic function in vivo (ICG)
Model selection and experimental design are strongly interrelated: Frequent early blood sampling and multiple indicator method
Conclusions
![Page 48: Non-Compartmental PK Modelling - University of Warwick · Non-Compartmental PK Modelling “model independent” Distributed models Transit/Residence distributions Michael Weiss Martin](https://reader036.vdocument.in/reader036/viewer/2022070721/5ee206c9ad6a402d666caeb0/html5/thumbnails/48.jpg)
References
Henthorn, T., T. Krejcie, et al. (2008). "Early drug distribution: a generally neglected aspect of
pharmacokinetics of particular relevance to intravenously administered anesthetic agents."
Clin Pharmacol Ther 84(1): 18-22.
Henthorn, T. K., T. C. Krejcie, et al. (1992). "The relationship between alfentanil distribution
kinetics and cardiac output." Clin Pharmacol Ther 52(2): 190-196.
Schalla, M. and M. Weiss (1999). "Pharmacokinetic curve fitting using numerical inverse Laplace
transformation." European journal of pharmaceutical sciences 7(4): 305-309.
Weiss, M. (1986). "Generalizations in linear pharmacokinetics using properties of certain classes of
residence time distributions. I. Log-convex drug disposition curves." Journal of
pharmacokinetics and biopharmaceutics 14(6): 635-657.
Weiss, M. (1991). "Nonidentity of the steady-state volumes of distribution of the eliminating and
noneliminating system." Journal of pharmaceutical sciences 80(9): 908-910.
Weiss, M. (1992). "The relevance of residence time theory to pharmacokinetics." European journal
of clinical pharmacology 43(6): 571-579.
Weiss, M. (2007). "Residence time dispersion as a general measure of drug distribution kinetics:
Estimation and physiological interpretation." Pharmaceutical research 24(11): 2025-2030.
Weiss, M. (2008). "How does obesity affect residence time dispersion and the shape of drug
disposition curves? Thiopental as an example." Journal of pharmacokinetics and
pharmacodynamics 35(3): 325-336.
Weiss, M., G. Hübner, et al. (1996). "Effects of cardiac output on disposition kinetics of sorbitol:
recirculatory modelling." British journal of clinical pharmacology 41(4): 261-268.
Weiss, M. and K. S. Pang (1992). "Dynamics of drug distribution. I. Role of the second and third
curve moments." Journal of pharmacokinetics and biopharmaceutics 20(3): 253-278.
Weiss, M., M. Reekers, et al. "Circulatory model of vascular and interstitial distribution kinetics of
rocuronium: a population analysis in patients." Journal of pharmacokinetics and
pharmacodynamics 38(2): 165-178.
Weiss, M. and M. S. Roberts (1996). "Tissue distribution kinetics as determinant of transit time
dispersion of drugs in organs: application of a stochastic model to the rat hindlimb." Journal
of pharmacokinetics and biopharmaceutics 24(2): 173-196.