Date: Fri, 02 Jul 1999 14:36:44 -0400 (EDT)

From: SRIRAM KRISHNASWAMI <Sriram.Krishnaswami@dupontpharma.com>

Subject: Drug-metabolite kinetics

Dear NM users

I am trying to simultaneously fit a drug and its metabolite concentrations. The drug can be modeled using a one-compartment model with 1st order absorption.

Can anybody give me suggestions as to how to model(syntax) the problem in NONMEM ?

Thanks

Sriram Krishnaswami

From: "Bachman, William" <bachmanw@globomax.com>

Subject: RE: Drug-metabolite kinetics

Date: Fri, 2 Jul 1999 15:21:19 -0400

One way to do this is to define a reasonable model using differential equations based on what you know about the drug and the metabolite. E.g., a one compartmental model for the parent and possibly interconversion of parent to metabolite (does metabolism occur in central compartment, is metabolism reversible?, does the metabolite also follow one compartment dispostion?) One then needs to define a CMT data item to specify which compartment the observation corresponds to (central for the parent, some other for the metabolite based on the metabolite portion of the structural model you are proposing.)

Code might look something like this:

$PROBLEM 1comp,rev.metab,both elim. 7/2/99 WJB

$INPUT ID DOSE=AMT TIME DV CMT

$DATA d:\vnmdata\TEST\TESTy.PRN IGNORE=C

$SUBROUTINE ADVAN8 TRANS1 TOL=5

$MODEL NPAR=7 NCOMP=3 COMP=(DEPOT,DEFDOSE) COMP=(PARENT) COMP=(METAB)

$PK

KA= THETA(1) ;KA

VP= THETA(2) ;VP central vol. parent

CL= THETA(3) ;CL clearance parent

VMT=THETA(4) ;VMT central vol. metab

KF= THETA(5) ;KF parent->metab. conversion

KB= THETA(6) ;KB metab.->parent conversion

CLM=THETA(7) ;CLM clearance metab.

S2=VP ;SCALING FACTOR FOR PARENT IN CENTRAL COMP

S3=VMT ;SCALING FACTOR FOR METAB. IN CENTRAL COMP

$DES

DADT(1)=-KA*A(1)

DADT(2)=KA*A(1)-KF*A(2)+KB*A(3)-CL*A(2)/VP

DADT(3)=KF*A(2)-KB*A(3)-CLM*A(3)/VMT

$ERROR

W1=1

W2=F

IPRED=F

IRES=DV-IPRED

IWRES=IRES/(W1+W2)

Y=F + W1*ERR(1) + W2*ERR(2)

$THETA (0,2.5) ;1 KA

$THETA (0,35) ;2 VP

$THETA (0,0.75) ;3 CL

$THETA (0,15) ;4 VMT

$THETA (0,0.1) ;5 KF

$THETA (0,0.05) ;6 KB

$THETA (0,2.0) ;7 CLM

$OMEGA (1)(0.1)

$ESTIMATION PRINT=5 MAXEVAL=9999

$TABLE ID TIME CMT NOPRINT FILE=TESTy.PAR

Code not guaranteed to be 100% error free, but, it will give you a starting point. note: this is coded for individual dated, add etas for population data.

hope this helps,

Bill

William J. Bachman, Ph.D.

GloboMax LLC

Senior Scientist

7250 Parkway Drive, Suite 430

Hanover, MD 21076

Voice (410) 782-2212

FAX (410) 712-0737

bachmanw@globomax.com

From: "BRUNO, Rene" <Rene.BRUNO@RP-RORER.FR>

Subject: RE: Drug-metabolite kinetics

Date: Mon, 5 Jul 1999 09:47:30 +0200

> Be careful I believe that this model may have identifiability problems. As

> it is written, CL (parent drug clearance should refer to clearance of all

> parent drug elimination routes except this particular metabolic route (it

> is accounted for by KF in the equation). In addition I don't think VMT is

> identifiable (as CLM) unless you know the fraction of parent drug

> converted to this particular metabolite (a problem similar for parent drug

> CL and VP in case of an oral drug, you need to know F, the absolute

> bioavailability).

>

An alternative code is this one (using ADVAN 6). The parent has 3 compartment IV route and the metabolite 2 compartments (compt 4 and 5) :

...

$SUBROUTINES ADVAN6 TRANS1 TOL=5

$MODEL

NCOMPARTMENTS=5 NPARAMETERS=10

COMP=(CENTRAL DEFDOSE NOOFF)

COMP=('PERIPH.' NOOFF)

COMP=('PERIPH.' NOOFF)

COMP=('METAB.' DEFOBS NOOFF)

COMP=('METAB.' NOOFF)

$PK

... ; parent parameters

TVK14=THETA(1)

K14=TVK14*EXP(ETA(1))

TVK45=THETA(2)

K45=TVK45*EXP(ETA(2))

TVK54=THETA(3)

K54=TVK54*EXP(ETA(3))

TVK40=THETA(4)

K40=TVK40*EXP(ETA(4))

K=CL/V ; K elimination for parent, all routes

S1=V ; Scaling for parent

S4=1 ; Scaling for the metabolite, should be V4 but it is unidentifiable since we don't know the fraction of parent CL accounted for by this metabolic route

$DES

DADT(1)=A(2)*K21+A(3)*K31-A(1)*(K12+K13+K) ; eq for parent

DADT(2)=A(1)*K12-A(2)*K21 ; eq for parent

DADT(3)=A(1)*K13-A(3)*K31 ; eq for parent

DADT(4)=A(1)*K14+A(5)*K54-A(4)*(K45+K40) ; eq for metabolite. As we fixed V4 = 1, then K14 estimate is actually K14/V4

DADT(5)=A(4)*K45-A(5)*K54 ; eq for metabolite

From: "Bachman, William" <bachmanw@globomax.com>

Subject: RE: Drug-metabolite kinetics

Date: Tue, 6 Jul 1999 07:44:37 -0400

The code originally given mostly likely DOES HAVE IDENTIFIABILITY PROBLEMS (see caveat added). However, its intent was mainly didactic -> how to code a parent-metabolite. The details, of course, are dependent on the usual modeling constraints: does it reflect what we know about the drug?, is it "reasonable"?, does the data we have allow identification of defined parameters?, etc. Also, choice of ADVAN 6, 8 or 9 is, in the end, what works for your data and model.

Bill

William J. Bachman, Ph.D.

GloboMax LLC

Senior Scientist

7250 Parkway Drive, Suite 430

Hanover, MD 21076

Voice (410) 782-2212

FAX (410) 712-0737

bachmanw@globomax.com

From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>

Subject: Re: Drug-metabolite kinetics

Date: Tue, 6 Jul 1999 13:29:38 +0100

Just a note.

Bill Bachman wrote:

>"reasonable"?, does the data we have allow identification

of defined

>parameters?, etc. Also, choice of ADVAN 6, 8 or 9 is, in

the end, what

>works for your data and model.

Don't rule out ADVAN 5 & 7 for linear PK models. I have often found them to be more "stable" than ADVAN 6 or 8 and quicker.

Regards

Steve

=====================

Stephen Duffull

School of Pharmacy

University of Manchester

Manchester, M13 9PL, UK

Ph +44 161 275 2355

Fax +44 161 275 2396