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Dear All
I have come acrossed drug having double peak phenomenon. How will you
calculate the pharmacokinetic parameters for drugs which are giving
double peak phenomenon? Is it possible to calculate such parameters
using Winonlin?
Waiting for reply.
Thank you in advanced.
--
Prashant Musmade
Dept. of pharma Quality Assurance
Manipal
[Oh, as in enterohepatic recycling? I have a simple simulation
example at http://www.boomer.org/manual/EG/ehrc0/ehrc.html which may
be used for modeling if you have enough data - db]
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The following message was posted to: PharmPK
Dear Prashant,
Although you can fit a variety of equations to double peaks, I think
it's
more important to understand what is causing them.
What is the timing of the second peak? Is it about the time the dose
might
move from small intestine into colon? Was a meal given just before the
second rise? It might be enterohepatic circulation, but it can be due to
other factors as well, including increased hepatic blood flow in fed
state
affecting metabolism.
GastroPlus(tm) is used routinely to analyze such phenomenon in a
mechanistic
way. When you can model the mechanistic effects properly, you are
then able
to predict what will happen when you change dose, formulation, or other
factors.
Best regards,
Walt
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (AMEX: SLP)
42505 10th Street West
Lancaster, CA 93534-7059
U.S.A.
http://www.simulations-plus.com
Phone: (661) 723-7723
FAX: (661) 723-5524
E-mail: walt.at.simulations-plus.com
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The following message was posted to: PharmPK
I agree with Walt re the importance of understanding. Another possible
explanation is that there may be uptake via the lymphatic system (2nd
peak) as well as directly into blood (1st peak), in the case if highly
lipophilic molecules - see for example Ichihashi et al (1993) Pharm Res
11(4) pp508-512,
Kim Z Travis
Syngenta
[Are these discontinuous processes (like gall bladder dumping)? - db]
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Dear Prashant Musmade,
a good way how to explain the double peak phenomenon is to develop a
physiologically relevant model of the behavior of the drug in the
body, i.e. a model comprising approximations of processes which may
be cause this phenomenon.
Sincerely,
Diploma engineer Maria Durisova, DrSc (doctoral degree Math/Phys)
http://www.uef.sav.sk/advanced.htm
http://www.klinickafarmakologie.cz/pdfs/far/2003/03/02.pdf
http://www.klinickafarmakologie.cz/pdfs/far/2003/03/03.pdf
http://www.uef.sav.sk/
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The following message was posted to: PharmPK
Dear Prashant,
this problem could be solved. However, its solution depends on which
pharmacokinetic parameters and
which pharmacokinetic approach you are interested in. Few years ago I
wrote a Matlab code for
fitting of two consecutive 2-compartment population models (or any n-
compartmental model in its
integral, not differential form) with two "bumps" or even with the
lag-phase. In short, you need to
include Penalty function and and its argument - t(0) for every
emerging phase ("bump") in the
fitness function which makes a great problem to any standard
optimization algorithm (for example
BFGS). The problem is related to the numerous (infinite) number of
local minima. I used
least-squares fitness function. However, genetic algorithm hybridized
with some quasi-newton or
similar algorithm resolves this problem. Along with other population
pharmacokinetic parameters you
get t(0) for each new phase of release (or any other emerging
phenomenon). I wrote this code for the
drugs with biphasic release but it can be easily modified (if you are
allowed to do such changes).
Even the crossvalidation or bootstrap validation could be implemented
as a (correct) fitting quality
measure. If you want I could find and send to you the code in its
user-unfriendly form. In order to
do so send me a private e-mail request. Btw I was wondering if
someone is willing to compare/comment
other computational approaches to this problem with the one I described.
Zeljko Debeljak, PhD student
CROATIA
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I have come across drug having double peak phenomenon.
As some people have given opinion on this that verity of parameters
are there for calculating the pharmacokinetic. our aim is also to
study why there is double peak? But we want the method for
calculating pharmacokinetic parameters for drugs which they are gving
double peak. As it is different from single peak.
How will you calculate the pharmacokinetic parameters for drugs which
are giving double peak phenomenon? Is it possible to calculate such
parameters
using Winonlin ?
Thanking you
--
Prashant Musmade
Dept. of pharma Quality Assurance
Manipal, Karnataka, India
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The following message was posted to: PharmPK
Prashant
In compartmental terms, if you have rich data, you can consider two
separate inputs allowing a lagtime parameter and fraction of dose to
be estimated for the second (with WNL or any other nonlinear
regression package), which you may be able to interpret in terms of a
possible stomach emptying effect, enterohepatic circulation, or
intestinal Pgp efflux and secondary absorption, depending on how much
ancillary information you have.
If you have access to a reasonable unit impulse response estimate,
you can also try a deconvolution exercise (analytical or implicit)
(again with WNL or even Excel) choosing a bimodal input function
either to validate your mechanistic assumptions or to provide further
insight about the in vivo input (integrate and estimate
bioavailalibity, estimate MAT's, fractional areas, ...).
Plenty of room for modeling. Just keep in mind Walt's comment.
Luis
--
Luis M. Pereira, Ph.D.
Assistant Professor, Biopharmaceutics and Pharmacokinetics
Massachusetts College of Pharmacy and Health Sciences
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
Luis.Pereira.at.bos.mcphs.edu
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The following message was posted to: PharmPK
Dear Luis,
I am not WNL user, but I used many nonlinear regression packages
(Matlab and Mathematica regression
tools are my favourites). I must say that I am not aware of the
package that handles lags or
multiple phases of drug release in appropriate way i.e. I am not
aware of the package that can
easily CALCULATE the lagtime (t0 from my previous mail). Maybe I am
wrong, but Luis you are implying
that one needs to make an assumption about the lagtime. In other
words one needs to know t0 to
proceed with a "standard" regression calculations. If this is true,
then you should have sound
explanation that justifies the t0 selection (assumption). Only if one
predetermines t0 (treats t0 as
a user-defined variable) he could proceed with ANY regression
package. Otherwise, during the
regression one gets stuck, almost certainly in a well-known multiple
local minima optimization
problem. I should say that I am not a pharmacokineticist and I may be
terribly wrong. If so, please
point me to some regression package that could easily make fit
without previous knowledge about t0.
I have a feeling that this problem bothers Prashant. According to my
experience only a single-phase
release with lagtime could be appropriately fitted with "standard"
packages (with a bit of luck).
But if you have multiple release (more than one peak) fitting becomes
highly complex task. I assume
consecutive and independent n-compartment pharmacokinetic models.
Zeljko Debeljak, PhD student
CROATIA
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The following message was posted to: PharmPK
Prashant,
I believe that in a double peak situation, the most likely (though
not the
only) explanation is that the systemic pharmacokinetics are relatively
constant, but absorption is following a fast-slow-fast pattern.
If so, perhaps you could fit the first absorption phase with Ka1
(assuming
Ka is a constant - which it most assuredly is not), then the second
phase
with a Ka2, and the third with a Ka3, but with all phases using the
same Vc,
CL, K12, K21 (if 2-compartment), k13 and K31 (if 3-compartment). That
might
get you in the ballpark. This would work with either linear or saturable
clearance, as long as you're fitting the clearance parameter(s) (CL,
or Vmax
and Km if a single Michaelis-Menten equation is adequate) across all
three
phases simultaneously. I don't use the other tools mentioned earlier,
but I
imagine this can be done with one or more of them.
On the other hand, there is never a constant Ka, so the PK parameters
obtained in this way will be those that provide a minimized error
function
when Ka's are constant, not when they are time-variant. So you might
end up
with a pretty picture, but the PK parameters will have been
compromised to
fit the constant Ka assumption. This can work, but if you try to predict
what will happen when you change something more than a small amount, you
could also be seriously mislead. For example, suppose you fitted lag
times
for the 2nd and 3rd phases above. Should they be the same if you
change the
dose? What if you change the body weight? Or if you change from
fasted to
fed state?
We've seen a number of cases where the slope of the plasma
concentration-time curve between the first and second peak is so
steep that
it appears to be only clearing with no absorption at all, followed by a
second peak and subsequent slope at the last time points that is not as
steep as it was between peaks (so is it still absorbing?). We have to
ask
why this happens.
Is absorption actually stopping for a while (for all practical
purposes)? If
so, is it because there is no drug in solution in the gut for a
while? Or
because the drug that is in solution is in a nonabsorbing region? Or
is the
drug getting absorbed but something (??) is causing it to be cleared
at an
extremely rapid rate for a while (but not before or after this time
interval)? Does the second peak begin shortly after mealtime (even
"fasted"
studies allow food at some point)? If so, is the second peak caused by
enterohepatic circulation - or perhaps by emptying of the caecum into
the
colon?
If you can't answer these questions with your model, how useful is it
going
forward?
So I repeat - it is more important to have a model that represents the
underlying mechanisms properly so that you can use it to predict what is
likely to happen under other conditions.
Walt
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (AMEX: SLP)
42505 10th Street West
Lancaster, CA 93534-7059
U.S.A.
http://www.simulations-plus.com
Phone: (661) 723-7723
FAX: (661) 723-5524
E-mail: walt.aaa.simulations-plus.com
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Dear Zeljko Debeljak,
If you only use nonlinear regression packages in Matlab,
Mathematica or any general mathematical platform, it is very
difficult to define and solve a model. It is because that nonlinear
regression is just a method to give you parameters and you should
transform your model from differential equations to analytic forms.
Anyway, Matlab, Mathematica, Maple, or MathCAD can define and sovle a
PKPD model. There is also a long study curve.
BM, SAAM and ADAPTII are good at ODEs and PKPD modeling.
These software packages are powerful to a pharmacokinetist.
Winnonlin and many many PK software packages are also choices.
But to a special problem such as aborption, I belive that the
software such as GastroPlus is a best choice. It can give you a deep
insight for a special problem such as double peaks.
Ma Guangli
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The following message was posted to: PharmPK
Dear Ma,
thank you for the response. Anyway, I am wondering which optimization
algorithm is implemented in
the SAAM, ADAPT etc? If one uses gradient based algorithms (greedy
search) and he is faced with
lagtime(s) he will almost ceratinly end up in singularity. This means
that he would not get any
model at all (Luis mentioned that one can use ANY regression tool - I
disagree on that). On the
other hand, if one uses simplex-based optimization approach multiple
minima problem would cause
problems related to fit quality (poor R2, RMSE, not to mention any
resampling statistics). The point
is that curves that are not smooth could not be easily modeled. One
way to solve this problem is to
use genetic algorithms (GA) or simulated annealing. These approaches
are very slow and they also
need parameter tuning. However, if you combine GA and some gradient
based approach, even with
default GA parameter values you'll get very nice fits within short
time. As far as I know commercial
packages that you mentioned use simplex-based methods to solve
problems related to the lagtime-curve
fitting. However, this approach could give you result which is far
from optimal. On the other hand,
implementation of pharmacokinetic equations in their differential
form and optimization of
pharmacokinetic parameters under such settings is not a great
problem, at least in Matlab (you need
to include a procedure for numerical integration such as some form of
Runge-Kutta algorithm). I do
not say that commercial packages designed for pharmacokinetic
purposes can not make fit. I am just
curious about the quality of the fit and conclusions drawn based on
(possibly) poor fitting.
Zeljko Debeljak, PhD student
CROATIA
[Interesting. I've been using boomer off and on to model 'adjustable'
lag-times with some apparent success. I set upper and lower bounds,
typically between data times points if that matters. I have a
facility in boomer that starts with a simplex optimization to get
close, then switches to a Gauss-Newton to finish the optimization. I
can also do repeated random simplex starts to rerun the problem
multiple times. Have I just been lucky or have I stumbled into an
approach that avoids the singularity problem? -db]
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The following message was posted to: PharmPK
Dear Zeljko
What you say is conceptually correct, but you're complicating things
too much. Of course I don't know what kind of data Prashant is trying
to model: whether they're too noisy, too sparse, with just a hump or
a well defined second peak. However, the initial query was about how
and which PK parameters to calculate and for that there are several
alternatives as other colleagues have suggested.
In a purely regression context, the dimension and irregularity of the
parameter space will always govern the optimization process. A good
optimizer, maybe derivative-free, and good initial estimates are
certainly paramount to successfully achieve a meaningful minimum
objective function (in nonlinear regression you always need initial
estimates of the adjustable parameters). But you don't need an
elephant gun to kill flies (although you certainly can). I've many
times used just the solver routine in Excel and a simple macro to
double check what other fancier packages are doing (you can also
write your own code with WNL or ADAPT and work out the ODE's directly).
As always we need to exercise good judgment which in this case starts
by looking at the concentration-time profile, hopefully sufficiently
informative as I said before (and this is an important if). In that
case, the onset of the second peak ought to be a good hint for a time-
shift parameter related only to a second absorption phase (an
adjustable parameter, not a 'user-defined variable'); the magnitude
of that peak should guide about the fraction of the dose being
absorbed and the interpretation of the results.
If convergence problems still arise, one may start fixing the
disposition parameters to reduce the parameter space and facilitate
the optimization (releasing them later). Statistical significance and
parameter identifiability may certainly be emergent problems but
again all depends on the amount of information being conveyed by the
data.
Please notice that multiple inputs do not mean multiple 'compartment
pharmacokinetic models'. You're just splitting the administered dose
and phasing it apart, using the same disposition model. If structural
modeling fails or looks fishy, I again advise a system analysis
approach by deconvolution, maybe just to put everything back together
at the end.
Hope this helps and we may soon hear from Prashant about his efforts.
Luis
--
Luis M. Pereira, Ph.D.
Assistant Professor, Biopharmaceutics and Pharmacokinetics
Massachusetts College of Pharmacy and Health Sciences
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
Luis.Pereira.at.bos.mcphs.edu
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The following message was posted to: PharmPK
Dear All
For the sake of correctness I must say that there is no theoretical
justification to say that estimating lag-time(s) 'will almost
certainly end up in a singularity'. Non-convergence or parameter non-
identifiability are not issues proprietary to lag-time(s). Given a
well dimensioned model with sufficiently informative data, ANY
regression tool providing an optimizer choice (Gauss-Newton,
Levenberg-Marquard, Nelder-Mead, etc...) will have a good chance to
converge to a solution.
Even in the case of a very bumpy parameter landscape versus an
objective function, singularities (meaning infinite slopes, normally
associated to stiff differential equations) are seldom seen in common
daily observed experimental data. But even if Prashant is dealing
with such (interesting) data, usually a reparameterization of the
initial problem provides a different parameter space to work with
still using ANY nonlinear regression tool.
The issue of multiple local minima is common to essentially every
optimization procedure. And parameter identifiability and
interpretation must not be confounded with goodness of fit. A serious
regression exercise should never end after the first convergence, but
rather test the effect of different initial estimates, parameter
constraints and relaxation, different optimization (minimization)
algorithms, internal validation, until a consistent and admissible
narrow parameter space is identified. Variance-covariance matrices
should be looked at, serial correlation should be investigated,
information criteria should be calculated, and on, and on.
It's very dangerous to say that 'curves that are not smooth could not
be easily modeled' since this is absolutely not true (remember
interrupted iv infusion?). A genetic algorithm or a simulated
annealing procedure, or any other farfetched methodology, will add
nothing to a single subject data problem for which the data are
simply not informative. Ockham's razor still rules.
Luis
--
Luis M. Pereira, Ph.D.
Assistant Professor, Biopharmaceutics and Pharmacokinetics
Massachusetts College of Pharmacy and Health Sciences
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
Luis.Pereira.aaa.bos.mcphs.edu
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Dear Zeljko Debeljak,
Most of pharmacokinetic softwares are based on Gauss-Newton
like algorithms (Gauss-Newton, Hartly, LM) and SIMPLEX. SA or GA is
also employed in some software package.
I am sorry that I do not understand the relationship between
lagtime and singularty. According to my experience, singularty
appears when a data set is too small to some algorithm.
Unfortunately, most of gradient based algorithms need more data
points to avoid singularity but LM. So the problem maybe is that
your algorithm did not match your data set. I believe that what Luis
want to express was that lagtime problem is not different with other
PK problems from a computational viewpoint.
You have a good understanding about optimization algorithms. But
in practice, SIMPLEX is used to estimated initial values of
parameters for gradient based algorithms. I also like to combine a
grid search to a gradient based algorithm. I use GA or SA
independently for nonlinear regression problems.
There are several open-source packages based on Matlab or Maple
for PK. But somebody wants to control these, he/she will spend more
time than other softwares.
I agree with you abslutely. Poor fitting should be avoid. :)
Best regards,
Ma Guangli
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