RE: Changing Clearance over time : Enzyme auto-induction

From: "Mats Karlsson" Subject: RE:[NMusers] Changing Clearance over time : Enzyme auto-induction Date: Mon, August 9, 2004 3:23 am Dear Partha, I agree with Johan that a more physiological model is often preferable. Taking it one step further is to make the magnitude of induction graded. It may be reasonable to make it dependent on the plasma drug concentration. Code for such a model is given below. Also, there may be both inducible and uninducible pathways of elimination for a drug. If you have metabolite data you need to take this into account. We used such a model in: Hassan M et al.. A mechanism-based pharmacokinetic-enzyme model for cyclophosphamide autoinduction in breast cancer patients. Br J Clin Pharmacol. 1999 Nov;48(5):669-77. With this model, you don't need to make any assumption about relative rates of drug and enzyme turn-over. If it takes some time before the induction is becoming apparent, it can be modeled with a lagtime, but on the other hand, a lagtime is not particularly physiological. One solution that Toufigh Gordi and I have used is to include a precursor into the chain of events (ie drug induces production of precursor which in turn increases the rate of enzyme production), the turn-over of the precursor will determine the delay in appearance of observable induction. Best regards, Mats $PROBLEM Cyklophosfamid induction (drug + metabolite) $INPUT DROP ID TIME DV NEWA AMT RATE CMT FLAG DURA $DATA cp11.dta IGNORE=# $SUBROUTINES ADVAN9 TOL=6 $MODEL COMP=CENTRAL COMP=PERI COMP=4OH COMP=ENZ $PK CLUI = THETA(1)*EXP(ETA(1)) CLI = THETA(2) V1 = THETA(3)*EXP(ETA(2)) Q = THETA(4)*EXP(ETA(3)) V2 = THETA(5)*EXP(ETA(4)) CLOH = THETA(6)*EXP(ETA(5)) VOH = THETA(7) EMAX = THETA(8)*EXP(ETA(6)) EC50 = THETA(9) KENZ = THETA(10) S1 = V1 S3 = VOH K10 = CLUI /V1 K12 = Q /V1 K13 = CLI /V1 K21 = Q /V2 K30 = CLOH /VOH $DES CP = A(1)/V1 DADT(1)=-A(1)*(K10+K12+K13*A(4)) + K21*A(2) DADT(2)= A(1)* K12 - K21*A(2) DADT(3)= A(1)*A(4)* K13 - K30*A(3) DADT(4)= KENZ*(1+EMAX*CP/(CP+EC50)-A(4)) $THETA (0,1.14 ) ;CLUI (0,1.76 ) ;CLI (0,9.75 ) ;V1 (0,12.6 ) ;Q (0,21.5 ) ;V2 (0,300) ;CLOH (0,30 ) ;VOH (0,306) ;EMAX (0,5540 ) ;EC50 (0,.0279 ) ;KENZ (0,1.38 ) ;ADD ERROR (0,.0642 ) ;PROP ERROR (0,.03) ;ADD ERROR (0.05,.13) ;PROP ERROR $OMEGA .0556 .267 .41 .219 .06 .232 $ERROR W = 1 IF(F.GT.0) W= SQRT(THETA(11)**2+THETA(12)**2*F**2) IF(F.GT.0.AND.CMT.EQ.3) W= SQRT(THETA(13)**2+THETA(14)**2*F**2) IPRED = F IRES = DV-IPRED IWRES = IRES / W Y = IPRED+EPS(1)*W $SIGMA 1 FIX ;RESIDUAL ERROR $ESTIMATION MAXEVALS=9990 METH=1 INTER PRINT=1 MSFO=msfb99 $COV $TABLE ID TIME IPRED IWRES ONEHEADER NOPRINT FILE=sdtab99 $TABLE ID FLAG TIME IPRED IWRES ONEHEADER NOPRINT FILE=mutab99 $TABLE ID CLUI CLI V1 Q V2 CLOH VOH EMAX ONEHEADER NOPRINT FILE=patab99 $TABLE ID ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ONEHEADER NOPRINT FILE=mytab99 -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se _______________________________________________________