From: Paul Hutson <prhutson@pharmacy.wisc.edu>
Subject: 2cmp MM

Date: Mon, 07 Dec 1998 09:03:38 -0600

Has anyone any code or suggestions for a two compartment model with michaelis-menton elimination? I can't seem to find it on the Palo Alto VA site. Thanks

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From: R.Port@DKFZ-Heidelberg.DE (Ruediger Port)
Subject: 2 comp MM

Date: Fri, 11 Dec 1998 10:33:25 +0100

Hi everybody,

a control file for a two-compartment model with MM elimination was posted a few days ago where the expression for the MM clearance in \$DES is somewhat unusual in that VM, as it stands there, will have dimension concentration/time (e.g. (mg/L)/min) whereas it is usually understood to have dimension amount/time (e.g. mg/min). I thought if someone uses this code he or she should be aware of this distinction.

The proposed control file has this code:
S2=V1/1000 ;SCALING FACTOR FOR CENTRAL COMP

\$DES

By defining C2 = A(2)/V1 and C3 = A3/V2 one could rewrite DADT(2) like this:
DADT(2) = KA*A(1) - Q1*C1 + Q2*C2 - CL*C1 - VM*A(2)/(KM + C2)

The ratio A(2)/(KM + C2) in the last term on the right-hand side has dimension amount/(amount/volume), i.e. volume. If the entire term, VM*A(2)/(KM + C2), defines a change of amount per time, VM must have dimension (amount/time)/volume, or concentration/time.

The following modification will produce a VM parameter having dimension amount/time (e.g. mg/min):
DADT(2) = KA*A(1) - Q1*C1 + Q2*C2 - CL*C1 - VM*C2/(KM + C2)

Ruedi
------------------------------------------------------------------------------
R.E. Port, Dept. 0420, German Cancer Research Center
P.O. Box 10 19 49, D-69009 Heidelberg
phone: x49-6221 42-3385
-3347
fax: -3382
e-mail: r.port@dkfz-heidelberg.de

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From: "Bonate, Peter, HMR/US" <Peter.Bonate@hmrag.com>
Subject: 2 compartment MM

Date: Fri, 11 Dec 1998 07:10:37 -0600

Speaking of things users should be aware of. If a 2-compartment model with elimination from both the central and peripheral compartments, regardless of whether elimination is linear or nonlinear, is used and only samples are collected from the central compartment, then the parameter estimates will be unidentifiable. Only when samples are collected from both the central and peripheral or metabolite compartment will the parameter estimates be unique and identifiable.

PETER L. BONATE, PhD.
Population Pharmacokinetics
Hoechst Marion Roussel
POB 9627 (F4-M3112)
Kansas City, MO 64134
phone: 816-966-3723
fax: 816-966-6999

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From: "Bachman, William" <bachmanw@globomax.com>
Subject: RE: 2 compartment MM

Date: Fri, 11 Dec 1998 09:15:42 -0500

Dr. Bonate is correct, of course, with repsect to "mathematical identifiability" of the parameters of parallel elimination models from central & peripheral compartments. (In the model code distributed, both elimination paths are from the central compartment). Physiologically, it is not uncommon to have more than one elimination route, one of which is nonlinear. (e.g. a metabolic path & renal elimination. The question is - does your data support your model? (and does your model accurately describe your data) In practice, I have found that it's often less difficult to fit the parallel model to data than a nonlinear only model. For an example, see:

Bachman, W. J., and DeLap, R. J., "Population Pharmacokinetics of High-Dose Zidovudine in a Phase I Cancer Study", Drug Invest., 8(3), pp. 134-142 (1994).

With respect to the comments on the parameterization of Vm & Km (R.E. Port), yes, there is more than one way to parameterize Michaelis-Menten kinetics. I find the one I use more intuitive (to me). One should just be consistant (and aware) of which you are using.

William J. Bachman, Ph.D.
GloboMax LLC
Senior Scientist
7250 Parkway Drive, Suite 430
Hanover, MD 21076
Voice (410) 782-2212
FAX (410) 712-0737
bachmanw@globomax.com

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From: "Nick Holford" <n.holford@auckland.ac.nz>
Subject: Re: 2 comp MM
Date: Fri, 11 Dec 1998 09:30:03 -0800

My 2c on parameterization of capacity limited elimination models (aka MM, saturable, non-linear):

If Vmax is parameterized as conc/time instead of amount/time then it is necessarily confounded with the volume of distribution. This is similar to the problem of parameterizing a model in terms of a half-life or rate constant. When describing the concs in an individual the parameterization is irrelevant but when trying to estimate population model parameters the conc/time parameterization of Vmax will introduce covariance between Vmax and volume that is a consequence of the parameterization rather than reflecting some underlying biology that one might be interested in exploring.

As Bill Bachman has pointed out it is a matter of personal preference ("intuitiveness") which one uses but I am on the side of amount/time as well as the CL, V [Q,Vss] parameterizations instead of half-lives, micro-constants and God Forbid A,B,alpha and beta (Watch out Kinetica!). My rational, as opposed to intuitive, argument is to try and have parameters reflect independent properties of the underlying biology and avoid confounding if possible.

-- Nick Holford,
Dept Neurology,L226 OHSU,
3181 SW Sam Jackson Park Rd,
Portland,OR 97201,USA
email:n.holford@auckland.ac.nz
tel:+1(503)494-7228
fax:494-7242
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm