From: "Bonate, Peter, Quintiles" <pbonate@qkcm.quintiles.com>

Subject: flip-flop kinetics

Date: Fri, 2 Apr 1999 10:23:52 -0600

I have never had occassion to model a drug with flip-flop kinetics before. I understand that if you model a one-compartment system as C=A*exp(-alpha*t)+B*exp(-beta*t) then you have to assume that Ka>Kel. But what if you model a system as a series of differential equations:

dX1/dt = -Ka*X1

dX2/dt = Ka*X1 - Kel*X2

with scaling parameter C=X2/V? Are the output rate constants from such a fit really the right values? The standard errors are quite precise and the fit appears excellent.

Unfortunately, I do not have iv data. Any comments on this would be appreciated. Thanks.

PETER L. BONATE, PhD.

Clinical Pharmacokinetics

Quintiles

POB 9708 (L4-M2828)

Kansas City, MO 64134

phone: 816-767-6084

fax: 816-767-3602

From: "Nick Holford" <n.holford@auckland.ac.nz>

Subject: Re: flip-flop kinetics

Date: Sat, 3 Apr 1999 09:07:56 +1200

Yes (well at least within the usual caveat of all models being wrong). The closed form solution parameterised in A,alpha,B,beta is obtained by integrating the DEs and hiding the DE parameterisation. The hiding of the parameters is part of the legacy of having mathematicians rather than biologists think about how to express the model. It does not change the solution. However, reparameterisation can change the final solution if the obj function minimum is not well defined because the search depends on the parameterisation. Any differences in the model prediction are usually small. If they are big something is wrong with the way the model is coded or the data is very poor for identifying the model parameters.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html

From: ABoeckmann <alison@c255.ucsf.edu>

Date: Fri, 2 Apr 1999 16:04:23 -0800 (PST)

Subject: flip-flop kinetics

I agree with Nick's comments on Peter's question. I'd like to add that I know of no reason why flip-flop should be any more or less likely when one uses an analytic solution (ADVAN2) vs. a numerical solution (integrating differential equations in ADVAN6). But the predictions from the two ADVAN's will inevitably have tiny numeric differences, and the estimation step *might* follow a slightly different path to the minimum, which *might* lead to a flip-flop with

one or both methods.

To avoid flip-flop, you can include observations of the drug in the depot (absorption) compartment. Probably you do not have this data.

Or, model your parameters so that KA>K

E.g., KA = K + a term that must be positive

This can be done with both ADVAN2 and ADVAN6.