Dear nmusers,
I'm working on the pharmacokinetics of an antiCD20 mAb; I suspect the
clearance of this mAb should be time dependent as rituximab’s clearance do.
I tried to model this behavior but I’m not sure if the ODEs are correct.
Please can you help? I share part of the code.
$SUBROUTINE ADVAN13 TOL=9
$MODEL COMP=(CENTRAL) COMP=(PERIPH1)
$PK
;---- STRUCTURAL PARAMETERS ------
TVCL1 = THETA(2) ; system-nonspecific clearance
TVV1 = THETA(3)
TVQ = THETA(4)
TVV2 = THETA(5)
TVKDES = THETA(6) ; rate constant of the specific clearance decay
TVCL2 = THETA(7) ; time varying clearance at time zero
;---- MU_TRANSFORMATION ------
MU_1 = LOG(TVCL1)
MU_2 = LOG(TVV1)
MU_3 = LOG(TVQ)
MU_4 = LOG(TVV2)
MU_5 = LOG(TVKDES)
MU_6 = LOG(TVCL2)
;---- INDIVIDUAL PARAMETERS ------
CL1 = EXP(MU_1+ETA(1))
V1 = EXP(MU_2+ETA(2))
Q = EXP(MU_3+ETA(3))
V2 = EXP(MU_4+ETA(4))
KDES = EXP(MU_5+ETA(5))
CL2 = EXP(MU_6+ETA(6))
S1 = V1
;---- INITIAL CONDITIONS ------
A_0(1) = 0
A_0(2) = 0
CL2_TIME = CL2*EXP((-KDES)*(TIME))
CL_TOTAL = CL2_TIME + CL1 ; total clearance
;---- DES ------
$DES
CONC = A(1)/V1
DADT(1) =-(CL_TOTAL/V1)*A(1)-(Q/V1)*A(1)+(Q/V2)*A(2)
DADT(2) = (Q/V1)*A(1)-(Q/V2)*A(2)
;----$ERROR ------
CONC1 = A(1)/V1
IPRED=-3
IF(CONC1.GT.0) IPRED=LOG(CONC1)
W = THETA(1)
Y = IPRED+W*EPS(1)
IRES=DV-IPRED
IWRES=IRES/W
Thank you,
Niurys
MSc Niurys de Castro Suárez
Assistant Professor of Pharmacometrics
Assistant Research
Pharmacy Department
Institute of Pharmacy and Food,
University of Havana
Cuba
Help with ODEs for a time varying clearance
Definition of CL should be moved inside the DES block; other than that, looks fine:
;---- DES ------
$DES
CL2_TIME = CL2*EXP(-KDES*T)
CL_TOTAL = CL2_TIME + CL1 ; total clearance
...
Thanks
Leonid
Quoted reply history
On 7/22/2021 3:30 PM, Niurys.CS wrote:
> Dear nmusers,
>
> I'm working on the pharmacokinetics of an antiCD20 mAb; I suspect the clearance of this mAb should be time dependent as rituximab’s clearance do. I tried to model this behavior but I’m not sure if the ODEs are correct. Please can you help? I share part of the code.
>
> $SUBROUTINE ADVAN13 TOL=9
> $MODEL COMP=(CENTRAL) COMP=(PERIPH1)
> $PK
> ;---- STRUCTURAL PARAMETERS ------
> TVCL1 = THETA(2) ; system-nonspecific clearance
> TVV1 = THETA(3)
> TVQ = THETA(4)
> TVV2 = THETA(5)
> TVKDES = THETA(6) ; rate constant of the specific clearance decay
> TVCL2 = THETA(7) ; time varying clearance at time zero
> ;---- MU_TRANSFORMATION ------
> MU_1 = LOG(TVCL1)
> MU_2 = LOG(TVV1)
> MU_3 = LOG(TVQ)
> MU_4 = LOG(TVV2)
> MU_5 = LOG(TVKDES)
> MU_6 = LOG(TVCL2)
> ;---- INDIVIDUAL PARAMETERS ------
> CL1 = EXP(MU_1+ETA(1))
> V1 = EXP(MU_2+ETA(2))
> Q = EXP(MU_3+ETA(3))
> V2 = EXP(MU_4+ETA(4))
> KDES = EXP(MU_5+ETA(5))
> CL2 = EXP(MU_6+ETA(6))
> S1 = V1
> ;---- INITIAL CONDITIONS ------
> A_0(1) = 0
> A_0(2) = 0
> CL2_TIME = CL2*EXP((-KDES)*(TIME))
> CL_TOTAL = CL2_TIME + CL1 ; total clearance
> ;---- DES ------
> $DES
> CONC = A(1)/V1
> DADT(1) =-(CL_TOTAL/V1)*A(1)-(Q/V1)*A(1)+(Q/V2)*A(2)
> DADT(2) = (Q/V1)*A(1)-(Q/V2)*A(2)
> ;----$ERROR ------
> CONC1 = A(1)/V1
> IPRED=-3
> IF(CONC1.GT.0) IPRED=LOG(CONC1)
> W = THETA(1)
> Y = IPRED+W*EPS(1)
> IRES=DV-IPRED
> IWRES=IRES/W
>
> Thank you,
> Niurys
>
> MSc Niurys de Castro Suárez
> Assistant Professor of Pharmacometrics
> Assistant Research
> Pharmacy Department
> Institute of Pharmacy and Food,
> University of Havana
> Cuba
Dear Niurys,
I have not checked the whole code, but something I spotted as incorrect is the
use of TIME.
The variable TIME only changes in a discrete way with the time of events in the
dataset (e.g. doses or samples).
If you want something truly "continuous" you need to use the variable T and
define inside the $DES block all the variables that depend on T (and are
therefore time varying).
In your case, you should move the equations calculating the CL to $DES and use
T instead of TIME.
...
;---- DES ------
$DES
CL2_TIME = CL2*EXP((-KDES)*(T))
CL_TOTAL = CL2_TIME + CL1 ; total clearance
...
For more info, I'd google TIME vs T DES Nonmem, I think there is a tutorial by
Nick about this.
I hope this helps.
Good luck!
Paolo
Quoted reply history
On 22 July 2021 21:41:43 "Niurys.CS" <[email protected]> wrote:
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Dear nmusers,
I'm working on the pharmacokinetics of an antiCD20 mAb; I suspect the clearance
of this mAb should be time dependent as rituximab’s clearance do. I tried to
model this behavior but I’m not sure if the ODEs are correct. Please can you
help? I share part of the code.
$SUBROUTINE ADVAN13 TOL=9
$MODEL COMP=(CENTRAL) COMP=(PERIPH1)
$PK
;---- STRUCTURAL PARAMETERS ------
TVCL1 = THETA(2) ; system-nonspecific clearance
TVV1 = THETA(3)
TVQ = THETA(4)
TVV2 = THETA(5)
TVKDES = THETA(6) ; rate constant of the specific clearance decay
TVCL2 = THETA(7) ; time varying clearance at time zero
;---- MU_TRANSFORMATION ------
MU_1 = LOG(TVCL1)
MU_2 = LOG(TVV1)
MU_3 = LOG(TVQ)
MU_4 = LOG(TVV2)
MU_5 = LOG(TVKDES)
MU_6 = LOG(TVCL2)
;---- INDIVIDUAL PARAMETERS ------
CL1 = EXP(MU_1+ETA(1))
V1 = EXP(MU_2+ETA(2))
Q = EXP(MU_3+ETA(3))
V2 = EXP(MU_4+ETA(4))
KDES = EXP(MU_5+ETA(5))
CL2 = EXP(MU_6+ETA(6))
S1 = V1
;---- INITIAL CONDITIONS ------
A_0(1) = 0
A_0(2) = 0
CL2_TIME = CL2*EXP((-KDES)*(TIME))
CL_TOTAL = CL2_TIME + CL1 ; total clearance
;---- DES ------
$DES
CONC = A(1)/V1
DADT(1) =-(CL_TOTAL/V1)*A(1)-(Q/V1)*A(1)+(Q/V2)*A(2)
DADT(2) = (Q/V1)*A(1)-(Q/V2)*A(2)
;----$ERROR ------
CONC1 = A(1)/V1
IPRED=-3
IF(CONC1.GT.0) IPRED=LOG(CONC1)
W = THETA(1)
Y = IPRED+W*EPS(1)
IRES=DV-IPRED
IWRES=IRES/W
Thank you,
Niurys
MSc Niurys de Castro Suárez
Assistant Professor of Pharmacometrics
Assistant Research
Pharmacy Department
Institute of Pharmacy and Food,
University of Havana
Cuba
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Thanks Niurys for revisiting this.
It was discussed quite a lot before.
Using T in $DES, as Paolo suggested, is what I always do.
As far as your code / model file is concerned, I somehow like it as long as
you will be able to explain in simpler terms to non-pharmacometricians and
Physicians what the values mean and implications on situations.
Thanks,
Simba
Quoted reply history
On Thu, Jul 22, 2021, 4:37 PM Leonid Gibiansky <[email protected]>
wrote:
> PK block is executed only once per record so CL(TIME) is constant
> between records, while in the DES block T (time) changes continuously,
> thus implementing time dependence CL(T) exactly rather than
> approximately. The rest is fine.
> Thanks
> Leonid
>
> On 7/22/2021 4:19 PM, Niurys.CS wrote:
> > Dear Leonid,
> > Thanks for yor suggestion. I've never thought in that possibility.
> > However, I have two questions:
> > 1-Why must I write those equations inside $DES?
> > 2-Do you think the ODE that I proposed are Ok?
> >
> > Thank you very much
> >
> > MSc Niurys de Castro Suárez
> > Assistant Professor of Pharmacometrics
> > Assistant Research
> > Pharmacy Department
> > Institute of Pharmacy and Food,
> > University of Havana
> > Cuba
> >
> > El 22/07/2021 16:04, "Leonid Gibiansky" <[email protected]
> > <mailto:[email protected]>> escribió:
> >
> > Definition of CL should be moved inside the DES block; other than
> > that, looks fine:
> > ;---- DES ------
> > $DES
> > CL2_TIME = CL2*EXP(-KDES*T)
> > CL_TOTAL = CL2_TIME + CL1 ; total clearance
> > ...
> >
> > Thanks
> > Leonid
> >
> >
> > On 7/22/2021 3:30 PM, Niurys.CS wrote:
> >
> > Dear nmusers,
> > I'm working on the pharmacokinetics of an antiCD20 mAb; I
> > suspect the clearance of this mAb should be time dependent as
> > rituximab’s clearance do. I tried to model this behavior but I’m
> > not sure if the ODEs are correct. Please can you help? I share
> > part of the code.
> >
> > $SUBROUTINE ADVAN13 TOL=9
> > $MODEL COMP=(CENTRAL) COMP=(PERIPH1)
> > $PK
> > ;---- STRUCTURAL PARAMETERS ------
> > TVCL1 = THETA(2) ; system-nonspecific clearance
> > TVV1 = THETA(3)
> > TVQ = THETA(4)
> > TVV2 = THETA(5)
> > TVKDES = THETA(6) ; rate constant of the specific clearance
> decay
> > TVCL2 = THETA(7) ; time varying clearance at time zero
> > ;---- MU_TRANSFORMATION ------
> > MU_1 = LOG(TVCL1)
> > MU_2 = LOG(TVV1)
> > MU_3 = LOG(TVQ)
> > MU_4 = LOG(TVV2)
> > MU_5 = LOG(TVKDES)
> > MU_6 = LOG(TVCL2)
> > ;---- INDIVIDUAL PARAMETERS ------
> > CL1 = EXP(MU_1+ETA(1))
> > V1 = EXP(MU_2+ETA(2))
> > Q = EXP(MU_3+ETA(3))
> > V2 = EXP(MU_4+ETA(4))
> > KDES = EXP(MU_5+ETA(5))
> > CL2 = EXP(MU_6+ETA(6))
> > S1 = V1
> > ;---- INITIAL CONDITIONS ------
> > A_0(1) = 0
> > A_0(2) = 0
> > CL2_TIME = CL2*EXP((-KDES)*(TIME))
> > CL_TOTAL = CL2_TIME + CL1 ; total clearance
> > ;---- DES ------
> > $DES
> > CONC = A(1)/V1
> > DADT(1) =-(CL_TOTAL/V1)*A(1)-(Q/V1)*A(1)+(Q/V2)*A(2)
> > DADT(2) = (Q/V1)*A(1)-(Q/V2)*A(2)
> > ;----$ERROR ------
> > CONC1 = A(1)/V1
> > IPRED=-3
> > IF(CONC1.GT.0) IPRED=LOG(CONC1)
> > W = THETA(1)
> > Y = IPRED+W*EPS(1)
> > IRES=DV-IPRED
> > IWRES=IRES/W
> >
> > Thank you,
> > Niurys
> >
> > MSc Niurys de Castro Suárez
> > Assistant Professor of Pharmacometrics
> > Assistant Research
> > Pharmacy Department
> > Institute of Pharmacy and Food,
> > University of Havana
> > Cuba
> >
>
>