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I'm an experienced modeller, but new to modelling animal/human systems.
I'm
trying to understand the established conventions in PK modelling and
wonder
if anyone can help me gain this kind of overview. The types of models
I can
see so far are 1/ non-compartmental, 2/ compartmental and 3/
physiologically
based. But in reality many non-compartmental approaches use sums of
exponentials and so are equivalent to a compartmental model, so what is
the
real distinction here? I thought that the compartmental models would be
initially calibrated based on animal metabolism data showing amounts in
various organs over time, and then applied to blood-only datasets. But
in
reality blood seems often to be the only compartment that is used to
fit a
compartment model, and much of the software is not designed to fit to
any
other kind of data (except perhaps organ/blood partitioning
coefficients?).
This way of using a compartment model makes it barely less empirical
than a
non-compartmental approach. So are physiologically based models ones
where
data from multiple compartments is genuinely used, or are they just as
empirical, but with all sorts of standard organ blood flows and volumes
included to make them appear less empirical?
Perhaps these conventions have evolved due to the strong focus on man,
where
blood concentration profiles are all that is readily available. If so,
then
is there another different class of models/software used for rodents,
where
individual organ data are more readily obtainable? Even in man, urine
concentration profiles are readily obtainable, so sometimes a
simultaneous
fitting of a model to blood and urine data would make sense - is this
done
and if so then with what software?
Kim Travis
A puzzled newcomer to PK-land
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Dear Kim,
You can find examples of simultaneous fitting of plasma and urine data
in
"Pharmacokinetic and Pharmacodyamic Data Analysis: Concepts and
Applications" by Gabrielsson and Weiner
(http://www.pharsight.com/academic/aca_textbook.php). The book uses the
software WinNonlin. Innaphase (www.innaphase.com) also offers a
comprehensive PK-PD modeling software and they probably have relevant
examples of interest to you too.
There are a number of emerging companies offering tools to build
relatively
complex, mechanistic models, some designed to handle intracellular
processes. Most of the products provide links to databases providing the
opportunity to reference the estimates used in the model to the
information
source for the purpose of organizing your work. I don't know of a
specific
rodent model, most are focused on disease models and provide simulation
tools incorporating data from a range of sources. You can click on the
links
below for more information.
http://www.entelos.com/science/index.html
http://www.genomatica.com/science_technology.html
Sincerely,
Sarah
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The following message was posted to: PharmPK
Dear Kim,
> I'm an experienced modeller, but new to modelling animal/human systems.
> I'm trying to understand the established conventions in PK modelling
> and
> wonder if anyone can help me gain this kind of overview. The types of
models
> I can see so far are 1/ non-compartmental, 2/ compartmental and 3/
> physiologically based.
Two other approaches are as follows.
We use models in the form of linear differential equations
and the two approaches to modeling animal/human systems:
1) To build non-structured models we employ our traditional
approach which is based on the frequency
response method. This approach does not require a priori
information (or hypothesis) about the system under study
and is efficient even in situations when such information
is not available. Moreover, this approach starts
with a non-iterative method and thus:
a) it does not require initial estimates of model
parameters; b) it is very rapid.
2) To build models that exhibit physiologically interpretable
structures we use our new approach which is based on
a sequential simulation of those body systems which
play predominant role on the behavior of a biologically
active substance in the body.
For more information, please visit
the site http://www.uef.sav.sk/advanced.htm or
contact me.
With best regards,
Maria
Maria Durisova, PhD, DSc (Math/Phys),
Head of Department of Pharmacokinetics
and Scientific Secretary
Institute of Experimental Pharmacology
Slovak Academy of Sciences
841 04 Bratislava 4
Slovak Republic
Phone/Fax: +421 2 54775928
http://www.uef.sav.sk/durisova.htm
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The following message was posted to: PharmPK
To Kim Travis,
yes there are a number of different philosophies
regarding PK anlysis, compartmental models and
non compartmental models. Perhaps the best book
on the subject is " Investigating Biological Systems
Using Modeling - Strategies and Software. by Mery
E. Wastney, Blossom Patterson, Oscar A. Linares,
Peter C. Grief and Raymond C. Boston. Academic
Press. In this book, various modeling approaches
are discussed in detail and a number of kinetic
software programes are compared. Special
emphasis is given to WinSAAM (which can be
downloaded from WinSAAM.COM).
Note that with WinSAAM it is very easy to
simultaneously fit blood and urine data. Indeed, it is
easy to simultaneously fit data to many
compartments eg Blood, urine, feces and milk. In
the above book and in the help section in WinSAAM
many examples are given of fitting
multicompartment models (linear and non-linear
models).
Hope this helps,
Best wishes,
Peter Moate
Peter J. Moate
Research Associate
University of Pennsylvania,
School of Veterinary Medicine,
Biostatistics Section, Clinical Science,
New Bolton Center, 382 W. Street Road.
Kennett Square, PA 19348
Phone: 610-444-5800 Ext. 2146
Fax: 610-925-8123
Work Email: Moate.aaa.cahp2.nbc.upenn.edu
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The following message was posted to: PharmPK
Dear Kim,
Perhaps I can offer an overview of PBPK models for you, based on my
experience and previous training in their use at a CSU Workshop.
You ask:
“So are physiologically based models ones where
data from multiple compartments is genuinely used, or are they just as
empirical, but with all sorts of standard organ blood flows and volumes
included to make them appear less empirical?
In their purest form, PBPK models are based entirely on physiological
data derived from independent experiments – in this sense, they are
based on experimental data. In contrast, the PK models try to estimate
a set of parameters by their fit to a set of observed curves. Inasmuch
as the parameters are not directly related to anatomical or
physiological entities – the process is more analytical than
experimental.
Thus, conceptually the PBPK models are diametrically opposed to the PK
models. The PBPK models predict – the PK models fit. In practice, it
may happen that due to lack of some experimental data the PBPK model
must fit one or two parameters, but this should be regarded as a
temporary measure, or could be considered as a calibration to predict
the next set of data. In the PBPK world, a model is considered feasible
if it behaves reasonably close to the observed data and is tested by
how well it can be extrapolated to the next data set. If the mechanisms
in the model appear to be feasible, the model can be scaled
appropriately to the next individual or even to the next species.
It was emphasized during the CSU workshop that one of the first PBPK
models (Teorell, 1937 ) intended for drug distribution studies, had to
be abandoned for the time being due to the fact that it could only be
solved numerically. While preparing a presentation on PBPK models, I
noticed that as each new generation of computer arrived, attempts were
made to revive an interest in the PBPK approach. Jacquez, Bellman,
Kalaba (1960) for mainframes, and Bischoff, Brown and Deidrick (1973)
for minicomputers. The PBPK models seemed to be more favourably
received in the environmental health sector probably because of their
potential to predict the effect of toxic trace elements.
On the pharmaceutical side, now that sufficient computing power is
easibly accessible, the PBPK approach appears to be more acceptable.
There are many numerical packages on the market (e.g. ACSL – very
powerful, very expensive; SCoP – more than adequate, reasonably priced)
that can routinely solve the set of stiff differential equations that
are sometime encountered with the PBPK models. An excellent
presentation of the current potential of the PBPK approach in the
pharmaceutical industry can be found at this website:
http://cdds.georgetown.edu/conferences/PBPK2002.html.
At least two presentations at this conference make the argument that
PBPK models are the only serious way to describe drug action and
disposition.
Personally, as someone with a physiological & mathematical background,
I find the PBPK models to be more satisfying since they are based on
real organs, real blood flows, real anatomical topology and real
biochemical experiments. With these constraints to reality and one or
more feasible mechanisms (based on experiment), the modeller can
predict the next set of data, plan the next experiment, and convince
the government regulators of the soundness of his/her conclusions. But
why listen to me? Please see the presentations in the Georgetown
Conference and draw your own conclusions. I would be interested in
hearing your opinions.
Edmond Edwards, Ph.D.,
EDIT Research
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The following message was posted to: PharmPK
Dear Kim:
Since I have similar backgroud as yours, maybe I can offer some help to
you.
I was trained in Chemical Engineering, and had worked on process
analysis and
modeling before I switched to pharmacokinetic modeling when I started
to worked
for Dr. Bischoff. Then I have worked in enviromental toxicology and
pharmaceutical indursty.
There are four different appraoches in PK modeling:
1 noncompartmental modeling
2 classical compartmental modeling (people just call it as
compartmental
analysis)
3 PBPK modeling
4 population PK modeling
2~4 belong to compartmental modeling. Each approach has its advantages
and
limitations. In fact, noncompartmental modeling is a special case of
compartmental modeling: linear PK and one compartment. You can derive
all
results from noncompartmental modeling by compartmental modeling
assuming
linear pk and one compartment model. Therefore, from the assumption,
you can
see the limitation of this approach. However, it has advantages. just
from
numerical aspect, noncompartmental modeling is much simpler than
compartmental
modeling. the former calculates the AUC (intergration, which usually
offsets
the error), and the later is an optimization on either differential
equations
or integrate equations, where the error has more impact on the final
outputs.
In addition, AUC, Cmax provides information on safety and efficacy
required by
FDA. Therefore, approximately 80% of study analysis in drug
development only
needs noncompartmental analysis, which is quick and simple.
The difference between classical compartmental analysis and PBPK is in
that in
classical compartment modeling, the compartments and the parameters
have no
clear physiological meaning, while in PBPK modeling, the compartments
and the
parameters have clearer physiological meaning. However, mathematical
approaches are the same. The advantages of PBPK modeling were stated
by Dr.
Edwards in his response. Here I would only mention another advantages
of PBPK
approach towards population PK modeling.
Population PK modeling is based on classical PK modeling. Since
parameters in
classical PK model are lumped factors, it cannot explain the
interindividual
variability. For example, volume of distribution is the lumped factors
of body
weight, body composition, etc. for different individual, this
parameter will
be different. Population PK builds the correlation between individual
information (called covariates) to the parameter (called covariate
model), so
that the difference between different individual can be explained (if no
covariate model, the distribution of the interindividual variability
can be
estimated). For example, rather just giving the different values of
the volume
of distribution in classical PK modeling, popPK also provides you with
the
information on why volume of distribution for each individual is
different, and
how to estimate the volume of distribution for different individuals.
At this stage, the covariate model in popPK is built largely on
statistical
analysis. Since PBPK model has physiological meaning and the
parameters has
clearer physiological meanings, ideally PBPK model can interpret
interindividual variability. Due to the limitation of available data,
it is
difficult to apply PBPK modeling to drug development. However, applying
PBPK
modeling and lumping can help us build the covariate model through
mechanistic
process rather than pure statistical analysis.
I would like to suggest you some references:
Gibaldy and Perrier, pharmacokinetics, 2nd ed. With this book, you
will know
more or less about classical compartment modeling and noncompartmental
analysis.
FDA guidlines: you will know why noncompartmental analysis dominate 80%
of data
analysis in drug development
Bischoff and Brown (1965), you can see what a critical assumption
Bischoff and
Brown was made, so the problem that stopped Bellman, et al, was solved.
Bischoff and Dedrick's late 60s and early 70s work established the
foundation
of PBPK modeling, and species extrapolation through PBPK modeling.
Andersen and Clewell applied PBPK modeling to enviromental toxicology,
risk
assessment. They have done a tremandous work on species
exptrapolation, dose
extrapolation by applying PBPK modeling..
Sheiner and Beal's publications on population PK modeling.
From those references, you will be able to find which approach will
benifit to
your study.
with regards,
xiaofeng wang
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Ed:
Your comments on the importance of using physiological principles in
the develpment of models (Yes, Virginia, Physiology still exists) are
very important.
What needs to be reemphasized is that models are not an end in itself:
they are simplified representations of events in a living system, and
their importance is directly proportional to the extent that they
either clarify the mechanism of action of a drug or allow better
decision making on how to optimize the use of that drug.
The problem until now with physiologically based models was in the
limitation of the available data. Measuring drug levels in organs and
tissues using the classical methods that are being used to measure drug
levels in blood and other accessible body fluids is simply not
possible. You may be able to get an occasional biopsy, or measure drug
levels in surgical specimens or post-mortem, but that gives you a very,
very limited number of time points.
Noninvasive methods, on the other hand, can give you many time points.
Indeed, in many of our studies, we drown in data!. And because such
methods are noninvasive (e.g,, they do not perturb the system that is
being studied) they can be repeated and the subject is his/her own
control.
The approach we use is somewhat different from the classic
Bischoff-Dedrick method, which uses a complete model. We use the
simplest model that is predictive of the action of the drug, and we use
only data gleaned from that one subject. It is likely that at some
point in time, when there has been a sufficient amount of noninvasive
data measured in patients with different diseases, drugs, age, etc, we
may also be able to use a population modeling approach.
Professor Walter Wolf, Ph.D. President, Correlative Imaging Council,
Society of Nuclear Medicine
Distinguished Professor of Pharmaceutical Sciences
Director, Pharmacokinetic Imaging Program
Department of Pharmaceutical Sciences, School of Pharmacy
University of Southern California 1985 Zonal Ave., Los Angeles, CA
90089-9121
E-Mail: wwolfw.at.usc.edu
Telephone: 323-442-1405
Fax: 323-442-9804
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The following message was posted to: PharmPK
Dear Kim,
it was very interesting to follow the discussion that you initiated
with your
question. I fully agree that the use of the same term "modeling" for
very
different concepts is quite confusing for a newcomer in PK.
As it was already pointed out by others, the different methods are
useful for
different purposes. Classical "PK-modelling" approaches, particularly
non-compartmental modeling, are in first instance methods to analyse
experimental data rather than modeling methods. They generate numbers
which
characterize measured concentration curves and are useful and important
to
compare different results. However, there are methods available which
use these
numbers to make extrapolations to not investigated scenarios what is of
course
some kind of modeling and therefore justifies the naming.
PBPK-modeling on the other hand is a "real" modeling method in the
sense that it
tries to describe the physical and physiological processes which
determine the
pharmacokinetics of a substance with mathematical models and make
predictions of
what will happen in reality. However, there is one important aspect
that has not
been mentioned in the discussion hitherto. Because a large part of the
above
mentioned physical processes are influenced by the physical or chemical
properties of a substance, PBPK-modeling allows to make the connection
between
PK and such less complex properties. Therefore PBPK-modeling is the
method of
choice to really interpret and understand pharmacokinetic behavior in
terms of
substance properties. By this it can be a very helpful tool to better
assess a
new compound in drug research and find out how to optimize it in terms
of its
ADME properties.
More about this last aspect you can read at www.pk-sim.com.
There you also find a universal solution that is able to contradict the
opinion
that PBPK-modeling needs lots of data and information and is therefore
hardly
applicable for daily problems.
Best Regards
Walter Schmitt
Bayer Technology Services
Biophysics
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)