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
[email protected]
www.clinicalpharmacy.me
Time varying volume of distribution implementation
Hi Thorsten
We have done this in both paediatrics and pregnancy and you may find the
following paper useful.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4012043/
Changes in individual drug-independent system parameters during virtual
paediatric pharmacokinetic trials: introducing time-varying physiology into a
paediatric PBPK model.
Abduljalil K, et al. AAPS J. 2014.
Regards
Masoud
Quoted reply history
On 22 Apr 2016, at 22:34, Thorsten Lehr <[email protected]>
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
[email protected]
www.clinicalpharmacy.me
Natal van Riel presented on this topic in the context of large systems models
at a recent QSP meeting in Basel, see for example
http://www.ncbi.nlm.nih.gov/pubmed/23935478
Best,
Piet
Piet H. van der Graaf, PharmD PhD
Professor of Systems Pharmacology
Leiden Academic Centre for Drug Research (LACDR)
2333 CC Leiden
The Netherlands
Quoted reply history
From: M Jamei
Sent: Saturday, 23 April 2016 08:30
To: Thorsten Lehr
Cc: [email protected]
Subject: Re: [NMusers] Time varying volume of distribution implementation
Hi Thorsten
We have done this in both paediatrics and pregnancy and you may find the
following paper useful.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4012043/
Changes in individual drug-independent system parameters during virtual
paediatric pharmacokinetic trials: introducing time-varying physiology into a
paediatric PBPK model.
Abduljalil K, et al. AAPS J. 2014.
Regards
Masoud
On 22 Apr 2016, at 22:34, Thorsten Lehr
<[email protected]<mailto:[email protected]>>
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
[email protected]<mailto:[email protected]>
http://www.clinicalpharmacy.me
Thorsten,
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.
e.g.
$PK
POP_V=THETA(1)
POP_CL=THETA(2)
WT_ZERO=THETA(3)
WT_ALPHA=THETA(4)
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)
$DES
;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
DGRP_V=POP_V*DWT_T/70
DV=DGRP_V*PPV_V ; "individual" V at T using random effect for V
DGRP_CL=POP_CL*(DWT_T/70)**(3/4)
DCL=DGRP_CL*PPV_CL ; "individual" CL at T using random effect for CL
DADT(1)= -DCL*A(1)/DV
$ERROR
WT_T=WT_ZERO + WT_ALPHA*TIME ; fixed effect prediction of WT at the TIME of the current record
GRP_V=POP_V*WT_T/70
GRP_CL=POP_CL*(WT_T/70)**(3/4)
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
C=A(1)/V
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 fetus/child.
Best wishes,
Nick
Engle WA. Age terminology during the perinatal period. Pediatrics. 2004;114(5):1362-4.
Quoted reply history
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
> [email protected]
> www.clinicalpharmacy.me
--
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
email: [email protected]
http://holford.fmhs.auckland.ac.nz/
"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.
Dear Thorsten,
As suggested by other, implementing a time dependent covariate in $DES should be the way to go. A quick workaround could also be inserting dummy observations at regular intervals in your dataset e.g. when using ADVAN5.
Just out of scientific curiosity:
Are you investigating total (maternal + fetal) body weight as a covariate for volume of distribution? I would expect that both maternal body weight (water retention and increase in fat tissue) and placental-fetal-weight (growth, increase in volume of amniotic fluid) may increase during pregnancy and that depending on the drug (whether it penetrates the placenta) this has implications for your analysis.
Sincerely,
Rob
---
Dr. R. ter Heine, hospital pharmacist-clinical pharmacologist
Head of Clinical Trials Unit, Dept. of Pharmacy
Radboudumc
Quoted reply history
Van: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] Namens Thorsten Lehr
Verzonden: vrijdag 22 april 2016 23:34
Aan: nmusers_at_globomaxnm.com
Onderwerp: [NMusers] Time varying volume of distribution implementation
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
thorsten.lehr_at_mx.uni-saarland.de<mailto:thorsten.lehr_at_mx.uni-saarland.de>
http://www.clinicalpharmacy.me
Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het handelsregister onder nummer 41055629.
The Radboud university medical center is listed in the Commercial Register of the Chamber of Commerce under file number 41055629.
Dear Thorsten,
As suggested by other, implementing a time dependent covariate in $DES should
be the way to go. A quick workaround could also be inserting dummy observations
at regular intervals in your dataset e.g. when using ADVAN5.
Just out of scientific curiosity:
Are you investigating total (maternal + fetal) body weight as a covariate for
volume of distribution? I would expect that both maternal body weight (water
retention and increase in fat tissue) and placental-fetal-weight (growth,
increase in volume of amniotic fluid) may increase during pregnancy and that
depending on the drug (whether it penetrates the placenta) this has
implications for your analysis.
Sincerely,
Rob
---
Dr. R. ter Heine, hospital pharmacist-clinical pharmacologist
Head of Clinical Trials Unit, Dept. of Pharmacy
Radboudumc
Quoted reply history
Van: [email protected] [mailto:[email protected]] Namens
Thorsten Lehr
Verzonden: vrijdag 22 april 2016 23:34
Aan: [email protected]
Onderwerp: [NMusers] Time varying volume of distribution implementation
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
[email protected]<mailto:[email protected]>
http://www.clinicalpharmacy.me
Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het
handelsregister onder nummer 41055629.
The Radboud university medical center is listed in the Commercial Register of
the Chamber of Commerce under file number 41055629.
Dear Nick, Thorsten and others,
Nick's example is very good.
He models WT so that it increases linearly with TIME:
DWT_T=WT_ZERO + WT_ALPHA*T
where WT_ZERO and WT_ALPHA are thetas.
It occurs to me that some users may not have a model for WT vs. T,
but have only observed values of WT at fixed points.
In this case, WT can be interpolated within the $DES block.
Here is a small example of code that can be used to interpolate WT
between values that are recorded on the data records.
All the code in $PK to compute OLDTIME and OLDWT and SLOPE, and
the code for D_WT in $DES, could be copied to user's control stream.
Other code (for integrating D_WT in $DES and the analytic solution in
$ERROR)
is for testing and would not be part of the user's control stream.
Here is the control file:
$PROB INTERPOLATE WT IN $DES
; this example shows how to interpolate WT in $DES.
; it is assumed that WT is recorded on every data record.
; As a test, the value of D_WT in $DES is integrated to obtain AUC of WT
VS. T
; This is also calculated analytically in $ERROR.
$INPUT ID TIME WT DV
$DATA desinterp.dat
$SUBROUTINES ADVAN6 TOL=5
$MODEL
COMP=(AUC_WT DEFOBS)
$PK
; initialize OLDTIME and OLDWT
IF (NEWIND.LE.1) THEN
OLDTIME=TIME
OLDWT=WT
ENDIF
; calculate the slope for $DES
DELTA_TIME=TIME-OLDTIME
DELTA_WT=WT-OLDWT
IF (DELTA_TIME>0) THEN
SLOPE=DELTA_WT/DELTA_TIME
ELSE
SLOPE=0.
ENDIF
; save wt and time for next $PK record
OLDTIME=TIME
OLDWT=WT
$DES
D_WT=OLDWT+SLOPE*(T-OLDTIME) ; D_WT is the value of WT at time T
DADT(1)=D_WT ; compute AUC of D_WT as a test
$ERROR
Y=F+ETA(1)+EPS(1)
; Compute analytic solution as a test.
; Does not use compartment amounts.
; Uses only the values of WT and TIME on event records.
; Suppose WT vs T looks like this:
;
;
; WT
; |
; | w3 w4
; | w2 w5
; | w1
; |
; --------------------------------> TIME
; t1 t2 t3 t4 t5
;
; at t2, the contribution to the sum is
; the rectangle w1 x (t2-t1)
; plus the triangular piece
; (w2-w1)/(t2-t1) / 2
;
; w2
; /|
; / |
; /__|
; w1 |
; | |
; | |
; ------------
; t1 t2
IF (NEWIND.LE.1) THEN
PREV_WT=WT ; Initialize WT from previous data record
SUM=0
ELSE
SUM=SUM+PREV_WT*DELTA_TIME+DELTA_WT*DELTA_TIME/2
ENDIF
PREV_WT=WT ; save WT from previous data record
$OMEGA 1
$SIGMA 1
$TABLE ID TIME WT PRED=AUC_WT SUM FILE=desinterp.tbl NOPRINT NOAPPEND
; The following two values should always be equal:
; PRED (which is the AUC of WT obtained by integrating WT)
; SUM (which is the analytic solution) computed in $ERROR
Here is the data file for the first subject. Note that WT
sometimes is constant and sometimes decreases:
1 0. 10 0
1 1. 20 0
1 2. 35 0
1 2. 35 0
1 4. 45 0
1 5. 40 0
Here is the table file:
TABLE NO. 1
ID TIME WT AUC_WT SUM
1.0000E+00 0.0000E+00 1.0000E+01 0.0000E+00 0.0000E+00
1.0000E+00 1.0000E+00 2.0000E+01 1.5000E+01 1.5000E+01
1.0000E+00 2.0000E+00 3.5000E+01 4.2500E+01 4.2500E+01
1.0000E+00 2.0000E+00 3.5000E+01 4.2500E+01 4.2500E+01
1.0000E+00 4.0000E+00 4.5000E+01 1.2250E+02 1.2250E+02
1.0000E+00 5.0000E+00 4.0000E+01 1.6500E+02 1.6500E+02
Quoted reply history
On Sat, Apr 23, 2016, at 01:43 AM, Nick Holford wrote:
> Thorsten,
>
> 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.
>
> e.g.
>
> $PK
> POP_V=THETA(1)
> POP_CL=THETA(2)
> WT_ZERO=THETA(3)
> WT_ALPHA=THETA(4)
> 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)
>
> $DES
> ;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
> DGRP_V=POP_V*DWT_T/70
> DV=DGRP_V*PPV_V ; "individual" V at T using random effect for V
>
> DGRP_CL=POP_CL*(DWT_T/70)**(3/4)
> DCL=DGRP_CL*PPV_CL ; "individual" CL at T using random effect for CL
>
> DADT(1)= -DCL*A(1)/DV
>
> $ERROR
>
> WT_T=WT_ZERO + WT_ALPHA*TIME ; fixed effect prediction of WT at the TIME
> of the current record
>
> GRP_V=POP_V*WT_T/70
> GRP_CL=POP_CL*(WT_T/70)**(3/4)
>
> 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
>
> C=A(1)/V
>
> 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
> fetus/child.
>
> Best wishes,
>
> Nick
>
> Engle WA. Age terminology during the perinatal period. Pediatrics.
> 2004;114(5):1362-4.
>
>
> 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
> > [email protected]
> > www.clinicalpharmacy.me
>
> --
> 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
> email: [email protected]
> http://holford.fmhs.auckland.ac.nz/
>
> "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.
>
--
Alison Boeckmann
[email protected]
The code cannot be used when any WT values are missing.
In order to interpolate appropriately in $DES, WT should be present
on every event record.
$PK sees only the current and previous record.
If WT is missing from the current record, $PK has no way of knowing
what WT will be on the next record.
The code in NONMEM 7.3 help file INFN_INTERPOLATION EXAMPLE 2
(infn2.exa)
can be used to fill in missing WT values in the event records.
The idea is that the $INFN block does two passes through the data set.
After the first pass, it knows what the WT values are on all the event
records, so that it can interpolate to fill in a missing WT.
The finedata utility (fine1.exa) can also be used to fill in
the missing values, and performs interpolation if necessary.
BTW, the code for $PK and $DES will be a new help item in
Nonmem 7.4 INTERPOLATION IN $DES (desinterp.exa)
Quoted reply history
On Wed, May 11, 2016, at 04:18 AM, SIMON Nicolas wrote:
> Dear Alison,
>
> Perhaps I miss something but is it possible to use your code for
> interpolating WT when some WT are missing in the dataset for an
> individual?
>
> Best regards
> Nicolas
>
>
> -----Message d'origine-----
> De : [email protected] [mailto:[email protected]]
> De la part de Alison Boeckmann
> Envoyé : mardi 10 mai 2016 20:06
> À : Nick Holford; nmusers; [email protected]
> Objet : Re: [NMusers] Time varying volume of distribution implementation
>
> Dear Nick, Thorsten and others,
>
> Nick's example is very good.
> He models WT so that it increases linearly with TIME:
> DWT_T=WT_ZERO + WT_ALPHA*T
> where WT_ZERO and WT_ALPHA are thetas.
>
> It occurs to me that some users may not have a model for WT vs. T, but
> have only observed values of WT at fixed points.
> In this case, WT can be interpolated within the $DES block.
>
> Here is a small example of code that can be used to interpolate WT
> between values that are recorded on the data records.
> All the code in $PK to compute OLDTIME and OLDWT and SLOPE, and the code
> for D_WT in $DES, could be copied to user's control stream.
> Other code (for integrating D_WT in $DES and the analytic solution in
> $ERROR)
> is for testing and would not be part of the user's control stream.
>
> Here is the control file:
>
> $PROB INTERPOLATE WT IN $DES
> ; this example shows how to interpolate WT in $DES.
> ; it is assumed that WT is recorded on every data record.
> ; As a test, the value of D_WT in $DES is integrated to obtain AUC of WT
> VS. T ; This is also calculated analytically in $ERROR.
>
> $INPUT ID TIME WT DV
> $DATA desinterp.dat
>
> $SUBROUTINES ADVAN6 TOL=5
> $MODEL
> COMP=(AUC_WT DEFOBS)
>
> $PK
> ; initialize OLDTIME and OLDWT
> IF (NEWIND.LE.1) THEN
> OLDTIME=TIME
> OLDWT=WT
> ENDIF
>
> ; calculate the slope for $DES
> DELTA_TIME=TIME-OLDTIME
> DELTA_WT=WT-OLDWT
>
> IF (DELTA_TIME>0) THEN
> SLOPE=DELTA_WT/DELTA_TIME
> ELSE
> SLOPE=0.
> ENDIF
>
> ; save wt and time for next $PK record
> OLDTIME=TIME
> OLDWT=WT
>
> $DES
> D_WT=OLDWT+SLOPE*(T-OLDTIME) ; D_WT is the value of WT at time T
> DADT(1)=D_WT ; compute AUC of D_WT as a test
>
> $ERROR
> Y=F+ETA(1)+EPS(1)
>
> ; Compute analytic solution as a test.
> ; Does not use compartment amounts.
> ; Uses only the values of WT and TIME on event records.
> ; Suppose WT vs T looks like this:
> ;
> ;
> ; WT
> ; |
> ; | w3 w4
> ; | w2 w5
> ; | w1
> ; |
> ; --------------------------------> TIME
> ; t1 t2 t3 t4 t5
> ;
> ; at t2, the contribution to the sum is
> ; the rectangle w1 x (t2-t1)
> ; plus the triangular piece
> ; (w2-w1)/(t2-t1) / 2
> ;
> ; w2
> ; /|
> ; / |
> ; /__|
> ; w1 |
> ; | |
> ; | |
> ; ------------
> ; t1 t2
> IF (NEWIND.LE.1) THEN
> PREV_WT=WT ; Initialize WT from previous data record
> SUM=0
> ELSE
> SUM=SUM+PREV_WT*DELTA_TIME+DELTA_WT*DELTA_TIME/2
> ENDIF
> PREV_WT=WT ; save WT from previous data record
>
> $OMEGA 1
> $SIGMA 1
>
> $TABLE ID TIME WT PRED=AUC_WT SUM FILE=desinterp.tbl NOPRINT NOAPPEND ;
> The following two values should always be equal:
> ; PRED (which is the AUC of WT obtained by integrating WT) ; SUM (which
> is the analytic solution) computed in $ERROR
>
> Here is the data file for the first subject. Note that WT sometimes is
> constant and sometimes decreases:
> 1 0. 10 0
> 1 1. 20 0
> 1 2. 35 0
> 1 2. 35 0
> 1 4. 45 0
> 1 5. 40 0
>
> Here is the table file:
> TABLE NO. 1
> ID TIME WT AUC_WT SUM
> 1.0000E+00 0.0000E+00 1.0000E+01 0.0000E+00 0.0000E+00
> 1.0000E+00 1.0000E+00 2.0000E+01 1.5000E+01 1.5000E+01
> 1.0000E+00 2.0000E+00 3.5000E+01 4.2500E+01 4.2500E+01
> 1.0000E+00 2.0000E+00 3.5000E+01 4.2500E+01 4.2500E+01
> 1.0000E+00 4.0000E+00 4.5000E+01 1.2250E+02 1.2250E+02
> 1.0000E+00 5.0000E+00 4.0000E+01 1.6500E+02 1.6500E+02
>
> On Sat, Apr 23, 2016, at 01:43 AM, Nick Holford wrote:
> > Thorsten,
> >
> > 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.
> >
> > e.g.
> >
> > $PK
> > POP_V=THETA(1)
> > POP_CL=THETA(2)
> > WT_ZERO=THETA(3)
> > WT_ALPHA=THETA(4)
> > 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)
> >
> > $DES
> > ;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
> > DGRP_V=POP_V*DWT_T/70
> > DV=DGRP_V*PPV_V ; "individual" V at T using random effect for V
> >
> > DGRP_CL=POP_CL*(DWT_T/70)**(3/4)
> > DCL=DGRP_CL*PPV_CL ; "individual" CL at T using random effect for CL
> >
> > DADT(1)= -DCL*A(1)/DV
> >
> > $ERROR
> >
> > WT_T=WT_ZERO + WT_ALPHA*TIME ; fixed effect prediction of WT at the
> > TIME of the current record
> >
> > GRP_V=POP_V*WT_T/70
> > GRP_CL=POP_CL*(WT_T/70)**(3/4)
> >
> > 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
> >
> > C=A(1)/V
> >
> > 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 fetus/child.
> >
> > Best wishes,
> >
> > Nick
> >
> > Engle WA. Age terminology during the perinatal period. Pediatrics.
> > 2004;114(5):1362-4.
> >
> >
> > 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
> > > [email protected]
> > > www.clinicalpharmacy.me
> >
> > --
> > 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
> > email: [email protected]
> > http://holford.fmhs.auckland.ac.nz/
> >
> > "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.
> >
>
>
> --
> Alison Boeckmann
> [email protected]
--
Alison Boeckmann
[email protected]