- On 23 Aug 2003 at 08:14:43, Vlase Laurian (vlase.at.email.ro) sent the message

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Hello

I have a WNL user-model (first order absorption, 2 comp, first order

elimination)

The WNL code I write is:

MODEL

remark ******************************************************

remark Developer:

remark Model Date: 08-24-2003

remark Model Version: 1.0

remark ******************************************************

remark

remark - define model-specific commands

COMMANDS

NFUNCTIONS 1

NDERIVATIVES 3

NPARAMETERS 6

PNAMES 'v', 'lag', 'k12', 'k21', 'k10', 'ka'

END

remark - define temporary variables

TEMPORARY

dose=con(1)

t=x

END

remark - define differential equations starting values

START

Z(1) = 0

Z(2) = 0

Z(3) = dose/v

END

remark - define differential equations

DIFFERENTIAL

DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)

DZ(2) = Z(1)*k12 - Z(2)*k21

DZ(3) = -ka*Z(3)

END

remark - define algebraic functions

FUNCTION 1

F= Z(1)

END

remark - define any secondary parameters

remark - end of model

EOM

Does anybody know how to introduce lag time calculation in WNL code?

Thank you!

Vlase Laurian

PhD Student

Dept. Pharm. Technol. & Biopharmaceutics

Faculty of Pharmacy

Cluj-Napoca

Romania - On 26 Aug 2003 at 23:13:28, Huadong Sun (hd.sun.aaa.utoronto.ca) sent the message

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It is tough or almost impossible to incorporate t(lag) in the

differential

equations. The solution is to try to solve the equations using Laplace

transform and linear algebra (you can facilitate this process using some

mathematic software like Maple (commercial available), Maxima(free

software)).

After you get the explicit form of concentration in every compartment,

express

the time "t" with "t-tlag" and fit your data. Hopefully you will get

t-lag.

314 Room, 19 Russell Street

Faculty of Pharmacy

University of Toronto

Toronto, Ontario M5S2S2

(Tel) 416-978-6996

(Fax)416-978-8511

[It is possible to incorporate an adjustable lag time with differential

equations using Boomer (and possibly other software) but fitting across

a discontinuity can be a problem not solved by using the integrated

form of the equation - or have I got that back to front ;-) - db] - On 27 Aug 2003 at 10:34:21, "A.Heydari" (MDP00AH.-a-.sheffield.ac.uk) sent the message

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Dear Valse Laurian

With respect to the WNL Differential equation model to introduce lag

time, you could use following instruction:

remark - define differential equations

DIFFERENTIAL

if x < tlag then

DZ(1) = 0

else

DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)

ENDIF

It would be interesting to hear comments on this topic

Thanks

Amir Heydari

PhD Student

Pharmacology Department

Royalle Halamshire Hospital

Sheffield

U.K. - On 27 Aug 2003 at 10:28:47, "Bonate, Peter" (pbonate.at.ilexonc.com) sent the message

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The following message was posted to: PharmPK

Actually lagtimes can be quite easily handled with differential

equations using a lag compartment. For example, to include a lag time

between the absorption compartment (X1) and central compartment (X3)

the DiffEqs would be

dX1/dt = -ka*X1

dX2/dt = ka*X1 - klag*X2

dX3/dt = klag*X2 - kel*X3

C = X3/V

The lag time is then 1/klag. The more lag compartments between X1 and

the central compartment the more all or none the lag time becomes.

The only price to this method is that as the number of compartments

increases the slower the fitting process.

Good luck,

Peter Bonate - On 27 Aug 2003 at 11:08:58, "Bonate, Peter" (pbonate.at.ilexonc.com) sent the message

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The following message was posted to: PharmPK

Amir Heydari writes:

"With respect to the WNL Differential equation model to introduce lag

time, you could use following instruction:

remark - define differential equations

DIFFERENTIAL

if x < tlag then

DZ(1) = 0

else

DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)

ENDIF

"

I wouldn't recommend this approach because the sum of squares response

surface is no longer a smooth quadratic function but a discontinuous

one, which may make fitting problematic.

Pete Bonate - On 27 Aug 2003 at 18:37:43, Jurgen Bulitta (bulitta.-at-.ibmp.osn.de) sent the message

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The following message was posted to: PharmPK

Dear Vlase,

it is quite straight forward to include lag time in

any kind of nonlin model. The code I attached should

work as it is. I would strongly recommend you to

watch all compartments you have defined. Thus I

included 3 functions, since otherwise sometimes

really funny mistakes in model specification

happen.

If you are not satisfied with the speed of optimization,

it is also possible to compile such nonlin models, what

accelerates things by approximately a factor of ~ 10.

Hope this helps.

Best regards

Juergen Bulitta

================================================================

=

= Please find the nonlin model here

MODEL

remark ******************************************************

remark Developer:

remark Model Date: 08-24-2003

remark Model Version: 1.0

remark ******************************************************

remark

remark - define model-specific commands

COMMANDS

NFUNCTIONS 3

NDERIVATIVES 3

NPARAMETERS 6

NCON 1

PNAMES 'v', 'TLAG', 'k12', 'k21', 'k10', 'ka'

END

remark - define temporary variables

TEMPORARY

dose=con(1)

T = X

END

remark - define differential equations starting values

START

Z(1) = 0

Z(2) = 0

Z(3) = dose/v

END

remark - define differential equations

DIFFERENTIAL

IF T GE TLAG THEN

DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)

DZ(2) = Z(1)*k12 - Z(2)*k21

DZ(3) = -ka*Z(3)

else

DZ(1) = 0.0

DZ(2) = 0.0

DZ(3) = 0.0

endif

END

remark - define algebraic functions

FUNCTION 1

F= Z(1)

END

FUNCTION 2

F= Z(2)

END

FUNCTION 3

F= Z(3)

END

remark - define any secondary parameters

remark - end of model

EOM

=

================================================================

################################################################

#

# Your data file should look like:

# Please note, you need at least one non-missing value

# for each function. I would recommend the time point at 0.0h

# BQL is my code for Missing value. Any other is also fine.

Time Conc Function

0 0 1

0.5 BQL 1

1 BQL 1

1.5 BQL 1

2 BQL 1

2.5 BQL 1

3 BQL 1

3.5 BQL 1

4 BQL 1

4.5 BQL 1

5 BQL 1

5.5 BQL 1

6 BQL 1

0 0 2

0.5 BQL 2

1 BQL 2

1.5 BQL 2

2 BQL 2

2.5 BQL 2

3 BQL 2

3.5 BQL 2

4 BQL 2

4.5 BQL 2

5 BQL 2

5.5 BQL 2

6 BQL 2

0 0 3

0.5 BQL 3

1 BQL 3

1.5 BQL 3

2 BQL 3

2.5 BQL 3

3 BQL 3

3.5 BQL 3

4 BQL 3

4.5 BQL 3

5 BQL 3

5.5 BQL 3

6 BQL 3

#

################################################################ - On 28 Aug 2003 at 12:01:30, fabrice_nollevaux.at.sgs.com sent the message

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Vlase Laurian wrote:

"I have a WNL user-model (first order absorption, 2 comp, first order

elimination)"... "Does anybody know how to introduce lag time

calculation in WNL code?"

Why do you build a user-model since this model is part of the WNL

internal library of pharmacokinetic models ?

-> Model 12 (micro-constants) or Model 14 (macro-constants) in

WinNonlin 4.0

Fabrice Nollevaux, MSc

Senior Biostatistician

Biometrics Department

SGS Biopharma SA,

Vieux Chemin du Poete 10

B-1301 Wavre (Belgium) - On 29 Aug 2003 at 11:57:54, Jurgen Bulitta (bulitta.-a-.ibmp.osn.de) sent the message

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The following message was posted to: PharmPK

Dear Dr. Bonate, dear all,

I totally agree with Dr. Peter Bonate's comment

that using tlag without a lag compartment may

have severe disadvantages on the sum of square surface.

It often turns out that tlag is the worst of all fit

parameters and that tlag often converges at a point

where is should not. One of the reasons is that the

absorption process is often not mirrored by a simple

first order process.

To slightly improve the technical situation during fitting:

- It is often helpful to define a cutoff value for tlag,

setting tlag to zero if the first estimate is below say 1-3 min.

- One should take time in getting realistic initials for tlag.

- One should apply rather narrow boundaries on tlag.

Does 1/klag or tlag become a much well behaved parameter, if

one specifies a lag compartment? And is it still advisable to

use those three improvement suggestions as proposed above?

Thanks for any comments.

Best regards

Juergen Bulitta

Pharmacokineticist

Institute for Biomedical

and Pharmaceutical Research

Germany

[I agree, setting realistic limits on tlag seem to help - db] - On 1 Sep 2003 at 16:58:31, "Hans Proost" (j.h.proost.at.farm.rug.nl) sent the message

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The following message was posted to: PharmPK

Dear Peter Bonate and Juergen Bulitta,

The suggestion of Peter Bonate to replace lagtimes by a delay using an

additional compartment is very good. Using the traditional concept of an

abrupt change in absorption rate, results in problems in finding the

best

fitting value, as was stated correctly. I have a few comments:

> The lag time is then 1/klag. The more lag compartments between X1 and

> the central compartment the more all or none the lag time becomes.

What is the lag time in case of n compartments with rate constants

klag? Is

it n/klag?

> The only price to this method is that as the number of compartments

> increases the slower the fitting process.

The model using an additional compartment is a different model

resulting in

a different absorption profile and a different plasma concentration

profile

(unless the number of lag compartments is very high). Therefore the

results

cannot be compared, and lagtimes will be somewhat different from those

using

the traditional abrupt change in absorption rate.

Juergen Bulitta wrote:

> One of the reasons is that the absorption process is often not

> mirrored

by a

> simple first order process.

Yes, one might argue that the absorption profile described by a few lag

compartments (small n) is more realistic than the abrupt change of the

traditional lag time concept; in fact, the latter is rather

unrealistic: a

zero absorption rate after ingestion of a drug formulation, and then an

abrupt change to the maximum absorption rate, declining

monoexponentially.

Ever seen this in practice?

> - One should apply rather narrow boundaries on tlag.

This may indeed avoid getting unrealistic values for tlag, but what to

do if

the estimated lag time reaches the bounderies (usually asumptotically,

depending of the software)? Bounderies do not guarantee correct results.

A further comment: be careful if the first measurable concentration is

relatively low compared to the next one or to the peak concentration.

Such

values may affect the fitting considerably, and are actuallly

incompatible

with the traditional lag time approach. I think that Peter Bonate's lag

compartments will give much better results in such cases, which are not

uncommon in my experience.

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.farm.rug.nl - On 6 Sep 2003 at 22:43:09, Jurgen Bulitta (bulitta.-a-.ibmp.osn.de) sent the message

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Dear Dr. Proost, dear Dr. Bonate, dear all,

I believe the discussion about lag time has gone to a point

where we should reconsider the final goal. Is it

a) to define the absorption phase as precisely as possible trying

to interpret all possible effects of influence.

b) to find a reasonable input function that allows drawing

conclusions on any disposition or PK/PD issue.

The lag-compartment approach is certainly an elegant and much

smoother way to describe the absorption phase. For solid oral

dosage forms the following processes may influence the kinetics

of drug absorption:

- disintegration

- dissolution

- local pH changes along the GI-tract

- de-/protonation equilibria according to local pH

- gastric emptying time

- different rate constants of drug absorption between stomach and

duodenum etc. due to physiological differences

- first pass metabolism, possibly saturable

- and sometimes enterohepatic recirculation (as a source for

additional drug up-take)

What one hopes during modelling with a single rate constant ka is,

that one of these processes is predominant. This is most often

untrue.

What I would like to say is: If one is really interested in all

those processes, he/she might possibly better use deconvolution

or Wagner Nelson, Loo-Riegelman etc. to study the absorption

phase in detail. This can usually only reliably be done with an

(intraindividual) iv reference.

As one usually is not in the rich situation to have an

intraindividual iv reference, I guess the following

solutions apply:

1) introducing lag time (as a rough approximation)

2) specifying absorption rate constant as a function of time

3) introducing lag compartments (as a better approximation)

4) specifying direct input functions like a Weibull function.

To 1) As you asked what to do, if Tlag reaches its boundaries.

It may be feasible to adjust the boundaries from run to run, so

that the minimum distance between fitted Tlag and its e.g. upper

boundary is at least 0.5 h, factor 2 x estimate (or whatever).

This also helps for other fitting parameters. If it is no longer

necessary to adjust any boundaries, self-convergence of the

parameters is achieved. This technique is often used in quantum

chemistry.

To 2) As Hans Proost proposed, this approach is certainly much

more realistic and often observed in (part of) the subjects'

profiles. Whether one uses ka(t) or zero-order followed by

first order depends on the situation. So this approach may really

help, but often suffers from interindividual variability and it

is sometimes difficult to fit the switch-time (--> error surface

issue), if one uses a stepwise function for ka. It may happen,

that some subjects show a switch while others do not have any

information about a switch.

To 4) Specifying the input as function of time (not as a

differential term) may sometimes be a big improvement

during fitting.

All these approaches are subject to the following practical

problems:

A) I seldom saw that there was one solution applicable to all

subjects, although the lag-compartment approach may be the most

robust in this case.

B) Even intra-individually there is sometimes large variation

in the absorption process especially for sustained release products.

C) Specifying the input as a function of time may severely

influence the disposition parameters. The same applies to

specifying ka as a function of time.

Therefore, if one is not primarily interested in the absorption

process, it might be a reasonable choice simply using ka and Tlag.

These parameters are often highly correlated with each other and

they tend to be imprecise and difficult to fit, but they might

influence the disposition parameters not as much as all

other approaches.

Our problem is that the window of watching the

absorption process - plasma concentrations - is pretty late. So

one should really ask, how many parameters do I want to spend on

the absorption process and do (all) my profiles contain enough

information for my preferred model, at least if one applies

individual PK?

I would be interested, if anyone has successfully applied the ka

as a function of time approach for a set of say > 10 subjects

and how much inter-/intra-individual variability was involved there.

Has anyone experience with Pop-PK and such extended absorption

models?

Thanks very much in advance.

Best regards

Juergen Bulitta - On 6 Sep 2003 at 21:28:41, "Michael B. Bolger" (bolger.-a-.usc.edu) sent the message

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I've been meaning to weigh in on the lag time compartment issue for a

while now. Juergen Bulitta has nicely defined most of the

characteristics that should be accounted for in properly considering

absorption modeling. A lag time compartment does not shed any light on

the physiological and biochemical processes involved in absorption, not

the least of which is saturable gut metabolism and transport. See

references below:

The lag-compartment approach is certainly an elegant and much

smoother way to describe the absorption phase. For solid oral

dosage forms the following processes may influence the kinetics

of drug absorption:

- disintegration

- dissolution

- local pH changes along the GI-tract

- de-/protonation equilibria according to local pH

- gastric emptying time

- different rate constants of drug absorption between stomach and

duodenum etc. due to physiological differences

- first pass metabolism, possibly saturable

- and sometimes enterohepatic recirculation (as a source for

additional drug up-take)

Please check the following references that describe applications of the

Advanced Compartmental Absorption and Transit (ACAT) model to the

simulation of almost all of the factors described above. We have not

published on enterohepatic recirculation (EhRc) yet, but the latest

version of our software "GastroPlus" has an implementation of EhRc.

Agoram B, Woltosz WS, and Bolger MB: (2001) Predicting the impact of

physiological and biochemical processes on oral drug bioavailability.

Adv. Drug. Deliv. Rev. 50:S41-S67.

Hendriksen BA, Sanchez MF, and Bolger MB: (2003) The Composite

Solubility Versus pH Profile and its Role in Intestinal Absorption

Prediction. AAPS Pharm. Sci. 5(1):Article 4, 2003

(http://www.aapspharmsci.org/view.asp?art=ps050104).

Bolger MB, Gilman TM, Fraczkiewicz R, Steere B, and Woltosz W: (2002)

“Predicting drug absorption by computational methods.” In “Cell Culture

Models of Biological Barriers: In-vitro test systems for Drug

Absorption and Delivery“, ed. C.M. Lehr, Saarbrücken, Germany; by

Taylor & Francis, London, UK.

Bolger MB, Agoram B. Fraczkiewicz R, and Steer B: (2002) “Simulation of

absorption, metabolism, and bioavailability.” In “Drug

Bioavailability. Estimation of Solubility, Permeability and

Bioavailability, for the Series Methods and Principles in Medicinal

Chemistry “, ed. Han van de Waterbeemd , published by Wiley

Publishers 2002.

Bolger MB, Woltosz WS, Chittenden J, Fraczkiewicz G (2003) Accurate

Simulation of the Non-linear Dose Dependence for Absorption of

Valacyclovir and Amoxicillin: Influence of PepT1 and HPT1

Intestinal Distribution. AAPS Drug Transport Meeting, Peachtree City,

GA, February 2003.

Michael B. Bolger, Ph.D.

USC School of Pharmacy and Simulations Plus, Inc. - On 8 Sep 2003 at 09:34:20, JELASSAI.at.PRDBE.jnj.com sent the message

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Dear Juergen,

[...Has anyone experience with Pop-PK and such extended absorption

models?...]

Please look at the NonMem news archive:

http:/gaps.cpb.uokhsc.edu/nm/5may0895.html [if you can't open it,

google to

"nonmem absorption", than look in "cached"]

and

http://www.cognigencorp.com/nonmem/nm/98oct042001.html

The combination of zero-order and first-order rates makes for a

flexible fit

to the absorption phase.

Best regards,

Jeroen

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