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]
