Back to the Top
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
Back to the Top
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
Back to the Top
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
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)