PharmPK Discussion - AUC of a two compartment model with Michaelis Menten elimination kinetics

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On 28 Dec 2001 at 10:42:21, "Diederik Vansassenbroeck" (diederik.vansassenbroeck.at.rug.ac.be) sent the message


Dear,
we are currently working with gamma-hydroxybutyrate (GHB or liquid
XTC).  After an intravenous infusion in the rat, the plasma
concentration-time curve can be adequately described with a
two-compartment model with Michaelis-Menten elimination kinetics:

dC1/dt =3D R/Vc - Cld*C1/Vc + Cld*C2/Vc - Vmax*C1/(Km+C1)*Vc

where dC1/dt  is the rate of decline of drug concentration at time t,
VC the distribution volume of the central compartment, R the infusion
rate, Cld the intercompartmental clearance, C1 the concentration in
the central compartment, C2 the concentration in the peripheral
compartment, Vmax the theoretical maximum rate of the elimination and
Km the Michaelis-Menten constant.

We have two questions:
1. Does anybody know how to calculate the area under the curve from
Time 0 to infinity ?

2. After pre-treatment of rats with a drug, we find an increase in
Vmax of GHB treated rats (induction of the metabolism), but also an
increase in Km (decreased affinity). Does anybody have an explanation
for this ?

Sincerely yours,
Diederik

Dr. D. Van Sassenbroeck
Heymans Institute for Pharmacology
De Pintelaan 185
B-9000 Gent

TEL : +32 (0)9 240 33 56
FAX : +32 (0)9 240 49 88
e-mail : diederik.vansassenbroeck.-at-.rug.ac.be

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On 29 Dec 2001 at 12:51:42, "David M. Foster" (foster.at.saam.com) sent the message


The following message was posted to: PharmPK

In terms of the AUC, probably the best thing to do is estimate it.  To do
this, you need to solve your model (let it integrate) for longer than the
time of the experiment.  I use as an initial (ad hoc)guess three times the
inverse of the smallest rate constant.  Then what you have to do is let the
time increase until the value of the difference between two successive AUC's
is below some tolerable limit (usually .5 to 1%).

Of course in some nonlinear models, this may never happen.  In this case,
you should be okay.

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