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The following message was posted to: PharmPK
Dear all,
I am working on an in vitro/in vivo correlation and I have to use a
deconvolution method to calculate the absorption kinetics. I have choice
between numerical deconvolution and compartmental methods (Wagner-Nelson
and Loo-Riegelman), and I would like your point of view concerning
the most
appropriate method and why.
Thanks for your help,
A. Dunand
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I think it all depends on what the impulse disposition function you
have. If it is one compartment bolus, you can just use Wagner-
Nelson's. If it is a two-compartment bolus, you can use Loo-
Riegelman's. However, if the absorption rate of oral solution can
not be ignored for your drug, you will need to use deconvulution
method to deconv against the pk data from oral solution.
Best regards,
Sam Liao
Pharmax Research
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The following message was posted to: PharmPK
Dear Aude,
I fully agree with the reply of Sam Liao. In my opinion, numerical
deconvolution is in general the preferred choice, since it can be
applied in
all cases. The Wagner-Nelson method works only in case of one-
compartment
kinetics. The Loo-Riegelman method requires sufficient intravenous
data to
fit a two-compartment model, and it does not work if the reference
administration is given orally.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-at-.rug.nl
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The following message was posted to: PharmPK
Dears Dunand and Liao
Although the W-N and L-R methods intrinsically correspond to
deconvolution procedures, the underlying assumptions greatly depart
from a general linear systems analysis approach. For instance, to
correctly interpret a % unabsorbed plot constructed by the W-N
method, one must not forget that it was derived assuming a single
compartment disposition, first order elimination, complete absorption
and no lag time for absorption. So even a straight semi-log profile
may overestimate a first order absorption rate constant if those
assumptions are violated, or if pre-systemic elimination is relevant,
or there are parallel pathways for absorption, or bioavailability is
less than one, and so on. As for the L-R, although geniously
conceived as well, one needs to assess the validity of the
assumptions: naturally two compartment disposition, but also good
estimates of k10, k12, k21, not too large delta(t), particularly not
k21xdelta(t)>0.5 if fc<truncation. One can use the Wagner's exact Loo-Riegelman Equation
that does not require a Taylor series approximation and works for 3
compartments, but again good kij estimates are key.
So linear systems analysis (or convolution and deconvolution methods
as commonly refereed to) is much more than this. If one is willing to
pay the price of giving up the structural space-state insight (maybe
not that sound anyway), the reward is incomparably more flexibility
with fewer assumptions that may always be experimentally tested, such
as time invariance and linearity. In the context of drug absorption,
an input function does not need to be first order, or zero order, or
have an order at all. It's integral, the cumulative amount absorbed
may have significant characteristics relevant for drug development or
therapeutics which may be just filtered out by a too rigid set of
compartmental assumptions.
From the vast literature I may just recommend these to start the
trail for the interested reader:
'Noncompartmentally-based pharmacokinetic modeling' Veng-Pedersen P,
Adv.Drug Del.Reviews 48(2001)265-300
'Volterra series in pharmacokinetics and pharmacodynamics' Verotta D,
JPP 30(5)2003, 337-362
'A system-approach method for the adjustment of time-varying
continuous drug infusion in individual patients: A simulation study'
Durisova M, Dedik L, JPP 29(5/6)2003, 427-44
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.-a-.bos.mcphs.edu
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The following message was posted to: PharmPK
Sam Liao, Hans Proost, Luis Pereira gave the exactly definition. I
wrote a program on this topic in my master degree period. From a
practical viewpoint, W-N and L-R is best choice to immediate release,
while conv and deconv is best choice to some controlled release. When
use conv and deconv, you should pay more attention on your experiment
design. Conv and deconv also need more experimental resources.
Ma Guangli
Zhejiang University
glma.at.zju.edu.cn
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The following message was posted to: PharmPK
Dear Ma Guangli.
You wrote:
> From a
> practical viewpoint, W-N and L-R is best choice to immediate release,
> while conv and deconv is best choice to some controlled release.
Could you please be more specific? Why would W-N and L-R be best
choice to
immediate release?
> When
> use conv and deconv, you should pay more attention on your experiment
> design. Conv and deconv also need more experimental resources.
Again, please be more specific. I really do not understand what you mean
here with 'more experimental resources', and I don't see why one
should pay
more attention on experimental design using deconvolution. It would
be good
to hear your arguments.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.at.rug.nl
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Dear Hans Proost,
As my experience, W-N and L-R are the choice to immediate release
because
1) They are equivalent with Conv and Deconv, when compartment
assumption is available.
2) They are in simple mathematical form compared with Conv and
Deconv.
3) There is no strict limitation on experiment design for W-N and
L-R, while sampling time interval should be equal or well-arranged
for Conv and Deconv. Numerical Conv and Deconv algorithm restricts
time interval. If time intervals are unequal, there must be a
interpolation routine to run Conv and Deconv. But interpolation
routines make the results variable.
Conv and Deconv is the choice to some controlled release because
1)Failure of W-N and L-R methods for some controlled release. For
example, W-N or L-R often gets a value more than 100%.
But some attention should be paid for Conv and Deconv
1) Sampling time interval should be equal or well-arraged. -
experiment design. more sampling times (experimental resouces).
2) There is an immediate release or i.v. experment for calculation
of iteration component. (experimental resources).
They are my understanding, maybe wrong. I teached myself.
Best Regards
Ma Guangli
Ph.d. Candidate
Current reseach: ADME in silico
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The following message was posted to: PharmPK
Dear Ma Guangli,
Thank you for your reply. In general I agree with your
arguments, but I have a few comments:
> 1) They are equivalent with Conv and Deconv, when
> compartment assumption is available.
OK, but the advantage of Deconvolution is that this
assumption is not required.
> 2) They are in simple mathematical form compared with
>Conv and Deconv.
This is a matter of taste. In my opinion the convolution
integral is more simple than W-N and L-R. Perhaps you mean
that they are more easy to apply without a computer
program.
> 3) There is no strict limitation on experiment design
> for W-N and L-R, while sampling time interval should be
> equal or well-arranged for Conv and Deconv. Numerical
> Conv and Deconv algorithm restricts time interval. If
> time intervals are unequal, there must be a
> interpolation routine to run Conv and Deconv. But
> interpolation routines make the results variable.
Yes, with unequal time intervals interpolation routines
are required. But this can be done by simple methods, so I
don't see a clear limitation here. Interpolations based on
assumptions of a linear or exponential decline are
sufficiently accurate, and are not essentially different
from the assumptions in W-N and L-R.
Interpolations do not make the results variable. Perhaps
you mean that the results may be dependent on the rules
for interpolation. Yes, that is true, but by choosing
reliable rules the results are sufficiently accurate.
> Conv and Deconv is the choice to some controlled
>release because
> 1)Failure of W-N and L-R methods for some controlled
>release. For
> example, W-N or L-R often gets a value more than 100%.
This may happen also with Deconv, and, again, there is no
fundamental difference between the methods in this
respect.
> But some attention should be paid for Conv and Deconv
> 1) Sampling time interval should be equal or
>well-arraged. -
> experiment design. more sampling times (experimental
>resouces).
See above. Besides, a well-arranged sampling schedule is
preferred in any study!
> 2) There is an immediate release or i.v. experment for
> calculation of iteration component. (experimental
> resources).
I don't understand your point here. Perhaps you mean that
a reference is required for Deconv? But this is not
different from W-N and L-R. The nice feature of Deconv is
that the reference can be a solution or an immediate
release product, so that the calculated input reflects in
vivo drug release from the dosage form. This information
is valuable for in vitro-in vivo correlations.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.aaa.rug.nl
[Hans, the Deconv you mention, is that the MatLab library function? I
haven't looked but is that available in R or S (do I have that
spelling right ;-) thanks, db]
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The following message was posted to: PharmPK
Ma & Hans,
I held back as long as I could. . .
We believe that the most effective method of in vitro - in vivo
correlation
is through simulation of the absorption, pharmacokinetics, and resulting
plasma concentration-time in a science-based, mechanistic simulation
that
accounts for the various factors that affect
release/dissolution/precipitation/absorption/first pass extraction.
Our method is to first fit PK parameters from the best available data
(iv if
available, po if we must). Then with these PK parameters, fit an
absorption
model (if fitting is required) for immediate release data so that we
understand, as best we can, the regional dependencies of absorption
for the
drug. All methods require enough data to fit PK parameters and an
absorption
model - our method minimizes the simplifications for absorption and
allows
saturable (nonlinear) PK as well as saturable absorption and gut wall
metabolism.
With the estimated PK and regional absorption fixed, we then use the in
vitro release-time curve as the first estimate for in vivo release.
If the
prediction is not adequate, we assume that the majority of the
unexplained
error is because the in vivo release was different from the in vitro
profile, and we then fit an in vivo release profile to produce the best
match to Cp-time. This can be done for individual subjects, for
population
means or medians, or a best average release profile can be fitted across
multiple subjects' Cp-time data.
The fitted in vivo release profile can then be compared directly to
the in
vitro release profile. This is a _direct_ in vitro - in vivo
correlation -
i.e., we directly correlate release-time with release-time. We
believe this
is much more useful and enlightening to the formulation scientist than a
traditional F(t) correlated with in vitro release-time.
As Hans has noted, with a computer, there is no need for the
simplifications
that were practical necessities in the past. That includes the
assumption
that absorption is modeled with a constant Ka, which we now know that
it is
not a constant, but a time-varying coefficient (Amidon, et al).
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.-a-.simulations-plus.com
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The following message was posted to: PharmPK
Dear Ma and Hans
For the sake of correctness the only assumptions required for a
deconvolution exercise are linearity and time-invariance with respect
to the response under consideration. There's no theoretical
requirement about equally spaced observations, or (as some times is
reported) same observation times for both the response and the unit
impulse response or the input function.
I must stress again that different modeling strategies should be
perceived as concurrent rather than strictly alternative. So the
choice doesn't really depend on whether immediate or sustained
release occurs, but rather on the true characteristics of drug
absorption in face of the modeling assumptions. An immediate release
formulation with a noisy input function due maybe to enterohepatic
circulation and second peak phenomena, stomach emptying effects, pre-
systemic elimination, enteric absorption windows, nonlinear
absorption, food interactions, or anything else, will gain from a
more flexible modeling approach. Conversely, a sustained release
formulation that really performs in vivo as a zero order input
perhaps just preceded by an identifiable burst effect can perfectly
be modeled under the set of assumptions of W-N or L-R methods. My
recommendation is always to conduct both analyses (and maybe also a
moment analysis on the side) and at the end gather all the
information. If all the different assumptions are reasonably complied
with, then the strategies validate each other since they start from
different premises. If the results are contradictory, normally good
insights can be gathered as to identify the biases and the underlying
causes. For instance, it was mentioned that an intercept larger than
100% may be obtained for the fraction unabsorbed at time zero and
therefore a deconvolution strategy should be chosen. In fact this can
happen if a significant lag time for absorption exists and it may be
estimated this way by looking at the time when 100% is reached, and
further confidence intervals may be calculated around that estimate
to see it they exclude zero and therefore is significant. But if a
deconvolution strategy is chosen that does not contemplate a lagtime
for the input function the result can only be perhaps even more biased.
Essentially deconvolution can be worked out analytically (having
properly characterized functional forms for the response, the
distribution function and the unit impulse), numerically (by any of
the available finite difference methods) or implicitly (aka
deconvolution through convolution) making use of regression and
statistical inference while estimating the parameter assigned to the
input function. Again the references are numerous and the
implementations likewise.
The flexibility required by the anticipated absorption process should
dictate the choice of drug absorption modeling strategy.
Regards
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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Dear Hans, Walt Woltosz, and Luis,
Thanks for the deep discussion. I am totally with yours.
W-N, L-R, and convolution/deconvolution are based on simple
assumptions. There must be many restrictions as Walt Woltosz and Luis
mentioned.
The future of oral absorption, IVIVC, dosage form design, and
pharmaceutical optimization is mechanism based. As I know, advanced
compartment and transit (ACAT) is a leading model for this purpose.
Luis's deep thought could be found in ACAT model.
Back to W-N, L-R, and convolution/deconvolution. Luis gave the full
range description and Hans added the critical points. I am so happy
to read these lines which I am agree with and do not know how to
express.
But theoretical problems are different from practical ones. As Hans
said, if there is an available computer program, computation is not a
problem. But what I faced 3 or 4 years ago is how to design the
program. Integration routines and interpolation routines make
convolution and decovolution more difficult than W-N, L-R. So I am
sensitive about this. It is not very important from a pharmaceutical
viewpoint.
Hans, its my habit to call convolution and deconvolution as Conv and
Deconv. Yes, matlab and other software name the routines like this.
Best Regards
Ma Guangli
Ph.d. Candidate, Zhejiang University, China
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)