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Re: [NMusers] Time varying volume of distribution implementation

From: Nick Holford <>
Date: Sat, 23 Apr 2016 10:43:07 +0200


Time varying V is no different from time varying CL (or any other
parameter). You should use the variable T in $DES, not TIME, in order to
have the time at the instant the DEQ solver evaluates $DES. T may occur
anywhere in the interval between the previous record TIME and the
current record TIME. TIME in $PK, $DES and $ERROR is the time at the end
of the $DES solution interval.

The other thing that you may wish to do is to assign the random effect
expression for V and CL in $PK so that you can estimate the random
variability after accounting for the fixed effect variability in WT. An
expression involving ETA() cannot be used in $DES so it has to be
assigned in $PK.


PPV_V=EXP(ETA(1)) ; random effect for V (PPV_V=population parameter
variability for V)
PPV_CL=EXP(ETA(2)) ; random effect for CLT (PPV_CL=population parameter
variability for CL)

;Variable names e.g. DWT_T are used in $DES because the same variable
names cannot be assigned in both $DES and in $ERROR

DWT_T=WT_ZERO + WT_ALPHA*T ; fixed effect prediction of WT at T

; Biology requires V and CL must both be functions of WT
DV=DGRP_V*PPV_V ; "individual" V at T using random effect for V

DCL=DGRP_CL*PPV_CL ; "individual" CL at T using random effect for CL

DADT(1)= -DCL*A(1)/DV


WT_T=WT_ZERO + WT_ALPHA*TIME ; fixed effect prediction of WT at the TIME
of the current record


V=VT*PPV_V ; "individual" V at the TIME of the current record
CL=GRP_CL*PPV_CL ; "individual" CL at the TIME of the current record


You may, of course, add random effects to WT_ZERO and/or WT_ALPHA as
well as having random effects on V and CL.

BTW You should consider using the term postmenstrual age rather than
gestational age. Gestational age is a single value defined at the time
of delivery according to the American Academy of Pediatrics (Engle et al
2004). Postmenstrual age is a continuous variable which may be used
during pregnancy and after birth to represent the biological age of the

Best wishes,


Engle WA. Age terminology during the perinatal period. Pediatrics.

On 22-Apr-16 23:34, Thorsten Lehr wrote:
> Dear NMusers,
> I'm modeling a compound where body weight has a known impact on the
> volume of distribution. This compound is investigated in pregnant
> women over a long period (from gestational age of 8 weeks until they
> give birth). Consequently, the body weight changes over time and I
> have a decent formula to describe the individual body weight change.
> The PK model has to be coded by ODEs. Does anyone has experience how
> to integrate a time varying volume of distribution if differential
> equations are used?
> Best regards
> Thorsten
> --
> Thorsten Lehr, PhD
> Junior Professor of Clinical Pharmacy
> Saarland University
> Campus C2 2
> 66123 Saarbrücken
> Germany
> Office: +49/681/302-70255
> Mobile: +49/151/22739489

Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(6)62 32 46 72

"Declarative languages are a form of dementia -- they have no memory of events"

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.
Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol. 2015;79(1):18-27.

Received on Sat Apr 23 2016 - 04:43:07 EDT

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