Back to the Top
The following message was posted to: PharmPK
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
Back to the Top
The following message was posted to: PharmPK
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]
Back to the Top
The following message was posted to: PharmPK
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.
Back to the Top
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
Back to the Top
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
Back to the Top
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
#
################################################################
Back to the Top
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)
Back to the Top
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]
Back to the Top
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
Back to the Top
The following message was posted to: PharmPK
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
Back to the Top
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.
Back to the Top
The following message was posted to: PharmPK
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
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)