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Dear Group,
Is it possible / valid to incorporate microconstants in a physiologically
based pharmacokinetic model (PBPK) to get a distribution phase. I have an
equation set for a simple PBPK model as follows:
V(liver)*C(liver)'=Q*C(blood)-Q*C(liver)-CLint*C(liver)
V(blood)*C(blood)'=Q*C(liver)-Q*C(blood)
where ' indicates differentials.
This equation with the flow and volume parameters simulates into a typical
"one-compartment model". Is it valid to incorporate microconstants to get:
a biexponential profile using the following:
V(blood)*C(blood)'=Q*C(liver)-Q*C(blood)-k12*C(blood)+k21*C(tissue)
V(tissue)*C(tissue)'=k12*C(blood)-k21*C(tissue).
If so, how are these microconstant values related to the microconstant
values obtained by a compartmental fitting?
Any suggestion is gratefully appreciated.
Thanks
Raj
Nelamangala V. Nagaraja
S110/T5-1, Pre-Clinical DMPK
DuPont Pharmaceuticals
Ph: 302-366-6342 (W)
302-738-3529 (H)
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The following message was posted to: PharmPK
Dear Raj,
It might be worthwhile considering additional tissues where the drug is
possibly distributing. Perhaps, these tissues have slower blood flow rates
or different binding mechanisms. Such additional compartments should provide
the flexibility you were looking for. The true value of PBPK models comes
from their ability to extrapolate using established physiological constants.
Rate constants will limit this value.
Regards,
Joga Gobburu,
Pharmacometrics,
CDER, FDA
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The following message was posted to: PharmPK
Dear Dr. Nagaraja,
I am certainly not an expert in PBPK, and therefore I cannot
answer your question. However, I have a comment on your
question.
You proposed to use the following equations:
> V(blood)*C(blood)'=Q*C(liver)-Q*C(blood)-k12*C(blood)+k21*C(tissue)
> V(tissue)*C(tissue)'=k12*C(blood)-k21*C(tissue).
These equations are wrong, as can be seen from the dimensions:
k12 and k21 cannot be rate contants with dimension 1/time.
Written in this form, k12 and k21 are intercompartmental
clearances.
In classical compartmental modeling, differential equations are
written in terms of amounts, and in that case rate constants are
used.
Best regards,
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-at-.farm.rug.nl
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The following message was posted to: PharmPK
Dear Raj,
It is possible to incorporate micro rate constants as well as the organs
flows and volumes into PBPK models. Please see for example the cyclosporin
model in Kawai R. Mathew D. Tanaka C. Rowland M."Physiologically based
pharmacokinetics of cyclosporine A: extension to tissue distribution
kinetics in rats and scale-up to human." Journal of Pharmacology &
Experimental Therapeutics. 287(2):457-68, 1998.
The logic is to have two compartments per organ (as required). Thus what we
measure as organ concentrations is the sum of two kinetically distinct
(although not physiologically identifiable) compartments, corresponding to
rapidly (dC6R) and slowly (dC6S) equilibrating parts of the organ. I
personally visualise this as an internal diffusion plus non-specific tissue
binding process. The style of equations used is exemplified as:
dC6R = Q6*(CA - C6o)/V6 - KA6*C6R + KD6*C6S
dC6S = KA6*C6R - KD6*C6S
C6U=C6R/KP6
C6P=C6U/FU
C6B=C6U*(NSB+NPB/(C6U+KDB))
C6o=C6P*(1-H)+C6B*H
where CA=arterial blood concentration, C6o=concentration leaving the organ,
Q6=blood flow, V=organ volume, H=haematocrit, U=unbound, KP=partition
coefficient to the rapid compartment, KA and KD the association and
dissociation rate constants for the slowly equilibrating compartment. It is
assumed that the volume for both the rapidly (dC6R) and slowly (dC6S)
equilibrating parts of the organ is common to both compartments. There is
also non-linear blood cell binding in this particular example, hence the
separation of plasma from the blood cells and the non-specific (NSB),
maximal (NPB) and half-maximal (KDB) binding for blood cells. This is for a
non-eliminating organ which does not receive multiple flow inputs.
I hope this helps.
Best regards, Phil.
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The following message was posted to: PharmPK
Dear Dr. Lowe,
With respect to your message of 27 Sept I have the following
comments.
1. The way you wrote the differential equations may be correct in
your particular case (I did not check that), but it is at least a
dangerous approach. Both classical compartmental and PBPK
modeling are based on mass balance. In order to be sure that
mass balance is maintained, differential equations should be
written in terms of amount (amount/time) at the left side. At the
right side, concentrations should be used; as a result the
corresponding constants are defined in terms of flow or clearance
(volume/time), which is understandable in terms of physiology and
anatomy, and apply to both perfusion and diffusion processes.
Alternatively, one may use amounts at the right side, in which case
the constants are rate constants.
In practice, it is most useful to write the equations at the left side in
terms of concentration multiplied by the volume of the
compartment, thus converting concentrations to amounts. Writing
differential equations in this way, mass balance is guaranteed.
2. What do you mean with 'association and dissociation rate
constants for the slowly equilibrating compartment'.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.aaa.farm.rug.nl
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