- On 6 Apr 2006 at 13:02:19, aude.dunand.-a-.pierre-fabre.com sent the message

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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 - On 6 Apr 2006 at 17:01:52, sliao.aaa.pharmaxresearch.com sent the message

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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 - On 7 Apr 2006 at 08:44:25, "Hans Proost" (j.h.proost.at.rug.nl) sent the message

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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 - On 7 Apr 2006 at 12:08:27, "Pereira, Luis" (Luis.Pereira.-a-.mcphs.edu) sent the message

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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 - On 8 Apr 2006 at 09:59:04, "Long Wang" (wangl78.-at-.hotmail.com) sent the message

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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 - On 10 Apr 2006 at 08:30:07, "Hans Proost" (j.h.proost.at.rug.nl) sent the message

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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 - On 11 Apr 2006 at 10:16:49, "Ma Guangli" (guanglima.at.gmail.com) sent the message

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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 - On 11 Apr 2006 at 08:37:12, "J.H.Proost" (J.H.Proost.at.rug.nl) sent the message

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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] - On 11 Apr 2006 at 14:34:07, "Walt Woltosz" (walt.-at-.simulations-plus.com) sent the message

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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 - On 11 Apr 2006 at 20:30:14, "Pereira, Luis" (Luis.Pereira.at.mcphs.edu) sent the message

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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 - On 12 Apr 2006 at 11:23:22, "Ma Guangli" (guanglima.at.gmail.com) sent the message

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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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