- On 9 Oct 1997 at 10:40:16, Keith_W_Ward.at.sbphrd.com sent the message

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To: PharmPK.at.pharm.cpb.uokhsc.edu.aaa.INET

cc:

From: Keith W Ward .-a-. SB_PHARM_RD

Date: 09-Oct-97 12:25:29 PM

Subject: Exponential Fitting vs. Compartmental Modeling

Categories:

PharmPKers:

In the course of a PK discussion recently, a colleague without much formal

PK background or training asked me to explain the functional/practical

difference between compartmental modeling of, say, a data set exhibiting

biexponential disposition, and simply fitting a biexponential function to

the data. For some reason, I've had a hard time formulating a cogent

response to this question. I'd appreciate any input and discussion on this

issue, especially relating to the difference in the recovered "parameters"

(either their numerical values or their real meaning) from both methods,

and the general utility of both methods. Thanks - I look forward to your

input.

Keith

--------------------------

Keith Ward

Investigator, DMPK

SmithKline Beecham Pharmaceuticals

UW2720; 709 Swedeland Road

King of Prussia, PA 19406

Keith_W_Ward.-a-.sbphrd.com - On 10 Oct 1997 at 14:51:02, "Robert D. Phair, Ph.D." (rphair.-at-.ix.netcom.com) sent the message

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Keith-

Your question is a classic one, and one that has received a lot of

attention from both theoreticians and experimentalists not only in PK/PD

but also in the broader field of biological and physiological modeling.

There is an excellent textbook treatment of the question in John Jacquez'

classic, Compartmental Analysis in Biology and Medicine. I believe the

third edition of his book has just been published.

But a short version of the answer might be given as follows. If you fit

your data set to a sum of two exponentials, you will recover four

parameters, the coefficients and the exponents of

A*exp(-a*t) + B*exp(-b*t)

If the data are sufficient, all four of these parameters will be

well-defined and the classical analyses of pharmacokinetics (AUC, etc.) can

be performed.

For more complicated systems or when mechanistic questions are important,

many investigators have found it useful to add compartmental modeling to

their arsenal of analytic tools. Most compartmental analysts will, in fact,

begin their analysis by fitting the data to a sum of exponentials, but

their goal is to determine how many compartments will be necessary to

adequately fit the data while still permitting estimation of the model's

parameter values with reasonable coefficients of variation. There is a

large body of published work in this sub-discipline, which has been called

Identifiability.

One of the advantages gained by including compartmental analysis in a suite

of tools used by pharmacokineticists, is the opportunity to assign

biological or physiological meaning to the rate constants or clearances

that characterize the compartmental model. To the extent that the model

structure reflects the real processes taking place in the cells, the

animals, or the human subjects, the corresponding model parameters will

serve to characterize the activity of those processes at the time the data

were collected. The reason this cannot be said of the parameters, A, a, B,

and b from the exponential fit is that all four of those parameters are

functions of all of the biological processes. This can be shown from first

principles. Occasionally, the numerical value of one of the exponents will

be dominated by a single biological process, but no R&D effort can afford

to make this assumption. There are too many circumstances, especially in

more complicated systems, in which you will be simply wrong.

The opportunity to determine compartmental rate constants or clearances

that characterize particular physiological processes is also the

opportunity to pursue studies of mechanism and even drug interactions.

These are both feasible and practical using the compartmental modeling

approach.

Compartmental analysis also has the potential to effectively address major

questions raised in the development and approval process for any new drug.

It is often the case that there is much more information in the

already-collected experimental data than can be extracted using classical

pharmacokinetic approaches. This, of course, is of no consequence for drugs

that sail through the approval process; classical PK is all you need. But

if you are faced with going back to do more experimental/clinical work in

order to answer a tough go/no-go development question or a tough approval

question, it seems obvious to me that you should first try to answer that

question using compartmental analysis of all the available data. The

savings in time and dollars and the resulting competitive advantage could

be enormous.

Regards,

Bob

----------

Robert D. Phair, Ph.D. rphair.-at-.bioinformaticsservices.com

BioInformatics Services http://www.bioinformaticsservices.com

12114 Gatewater Drive

Rockville, MD 20854 U.S.A. Phone: 1.301.315.8114

Partnering and Outsourcing for Computational Biology - On 10 Oct 1997 at 14:52:27, "Leon Aarons" (laarons.aaa.fs1.pa.man.ac.uk) sent the message

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My attitude to this has always been that when a multiexponential

model adequately describes a problem it is not necessary and, in a

sense it is preferable to use it rather than create an artificial

compartment model. The dangers of compartmental models have been stated

in the past and have to do with nonidentifiability and the tendency to

give physiological meaning to the parameters of the compartmental

model, particular the horrible micro rate constants.

However I have to qualify this position slightly. True physiological

models are compartmental models and their parameters do have a valid

physiological meaning. Also multiexponential models do not lend

themselves to situations of changing physiology (eg reduced renal

function) or dose dependent kinetics. For a drug which shows

biexponential disposition at low dose but has saturable elimination,

I know of no other way of handling this other than with a

2-compartmental model with Michaelis-Menten elimination from one of

the compartments (usually the first). One can describe a particular

dose by a sum of exponentials but this will not be predictive of

other doses. Maybe someone else knows of a noncompartmental

(predictive) method of doing this.

__________________________________________________

Leon Aarons

School of Pharmacy and Pharmaceutical Sciences

University of Manchester

Manchester, M13 9PL, U.K.

tel +44-161-275-2357

fax +44-161-275-2396

email l.aarons.at.man.ac.uk

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