# PharmPK Discussion - WNL alternative model problem

PharmPK Discussion List Archive Index page
• On 18 Dec 2003 at 21:16:06, Laurian Vlase (vlaselaur2.at.yahoo.com) sent the message

Hello,
I have one PK model (extravascular dose, 1 comp.) written in two ways
(WNL) : absorbtion as differential equation (model A) and absorbtion as
algebraic equation (model B)

When I fitted both models for the same data, all the parameters were
identical except volume of distribution (greater in model 2 than in
model 1).
I do not understand why, as time the both models are for the same
kinetic process and I start the calculations from the same dose value !

Thank you!

Vlase Laurian

Data:

time/conc

1 1.76
1.25 3.12
1.5 4.15
1.75 4.92
2 5.47
2.25 5.86
2.5 6.10
3 6.29
3.5 6.21
4 5.97
4.5 5.63
5 5.25
5.5 4.85
6 4.46
6.5 4.08
7 3.73
7.5 3.39
8 3.08
8.5 2.80
9 2.54
9.5 2.30
10 2.08
10.5 1.89
11 1.71
11.5 1.55
12 1.40

model A

Model 1
remark   ******************************************************
remark   Developer:
remark   Model Date: 12-05-2003
remark   Model Version: 1.0
remark   ******************************************************
remark
remark - define model-specific commands
COMMANDS
NFUNCTIONS 1
NDERIVATIVES 2
NPARAMETERS 4
PNAMES  'vd', 'k01', 'k10', 'tlag'
Initial 80, 0.5, 0.15, 1
upper 200, 5, 1.5, 2
lower 50, 0.2, 0.01, 0
END
remark - define temporary variables
TEMPORARY
t=x
END
remark - define differential equations starting values
START
Z(1) = 1000
Z(2) = 0
END
remark - define differential equations
DIFFERENTIAL
If  t<= tlag then
DZ(1) = 0
DZ(2) = 0
else
DZ(1) = -K01*Z(1)
DZ(2) = K01*Z(1)-k10*Z(2)
endif
END
remark - define algebraic functions
FUNCTION 1
F= Z(2)/Vd
END
remark - define any secondary parameters
remark - end of model
EOM

model B

Model 1
remark   ******************************************************
remark   Developer:
remark   Model Date: 12-05-2003
remark   Model Version: 1.0
remark   ******************************************************
remark
remark - define model-specific commands

remark - dose is 1000

COMMANDS
NFUNCTIONS 1
NDERIVATIVES 1
NPARAMETERS 4
PNAMES  'vd', 'k01', 'k10', 'tlag'
Initial 110, 0.75, 0.15, 1
upper 200, 5, 1.5, 2
lower 50, 0.2, 0.01, 0
END
remark - define temporary variables
TEMPORARY
t=x
END
remark - define differential equations starting values
START
Z(1) = 0
END
remark - define differential equations
DIFFERENTIAL
If  t <= tlag then
input=0
DZ(1) = 0
else
input=1000*dexp(-k01*(t-tlag))
DZ(1) = input-k10*Z(1)
endif
END
remark - define algebraic functions
FUNCTION 1
F= Z(1)/Vd
END
remark - define any secondary parameters
remark - end of model
EOM

Vlase Laurian Univ. Med. & Pharmacy "I. Hatieganu" Dept. of
Pharmaceutical Technology and Biopharmaceutics Cluj-Napoca Romania

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• On 19 Dec 2003 at 20:12:38, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

The following message was posted to: PharmPK

Laurian,

You are using different initial estimates for the two models. This can
influence the final value. Try starting from identical initial
estimates.

The data is clearly simulated without residual error. Which method is
giving you estimates closer to the parameters used for simulation?

Nick

> model A
>
> PNAMES 'vd', 'k01', 'k10', 'tlag'
> Initial 80, 0.5, 0.15, 1
> upper 200, 5, 1.5, 2
> lower 50, 0.2, 0.01, 0
> END
>
> model B
>
> Model 1
> PNAMES 'vd', 'k01', 'k10', 'tlag'
> Initial 110, 0.75, 0.15, 1
> upper 200, 5, 1.5, 2
> lower 50, 0.2, 0.01, 0
> END

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

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• On 19 Dec 2003 at 09:46:29, "Hans Proost" (j.h.proost.at.farm.rug.nl) sent the message

The following message was posted to: PharmPK

Dear Laurian,

If I understand your problem correctly, the error is in model B:

> input=1000*dexp(-k01*(t-tlag))
> DZ(1) = input-k10*Z(1)

'input' is here the amount of drug at the site of absorption.
The absorption rate is k01 * 'input', so the second equation should be
written:

DZ(1) = k01*input-k10*Z(1)

I hope this helps.

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

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• On 19 Dec 2003 at 10:48:29, "vgcasabo" (vicente.casabo.-a-.uv.es) sent the message

The following message was posted to: PharmPK

Hi Vlase,
You have in model 2
> input=1000*dexp(-k01*(t-tlag))
this is amount remaining in absorption compartment, not input rate.
Input rate is k01*amount

Try
Input=k01*1000*dexp(-k01*(t-tlag))

Vicente G. Casabo

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• On 21 Dec 2003 at 22:53:38, "Kazimierz H. Kozlowski" (khkoz.-a-.czd.waw.pl) sent the message

The following message was posted to: PharmPK

=======================
input=1000*dexp(-k01*(t-tlag))
DZ(1) = input-k10*Z(1)
=======================
I think that:
Input=A*EXP(-k01*t)=concentration in absorption compartment--> plese
change on
input rate
or use algebraic CP=A*(EXP(-k10*(t-tlag))-EXP(-k01*(t-tlag)))
sincerely
Kazimierz H. Kozlowski
Laboratory of Pharmacokinetics
The Children's Memoria Health Institute
04-736 Warsaw, Poland
khkoz.-a-.czd.waw.pl

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