From: Partha Nandy partha.nandy@bms.com Subject:[NMusers] Changing Clearance over time : Enzyme auto-induction Date: Fri, August 6, 2004 2:46 pm Hi All, I am trying to model the kinetics of a drug that exhibits enzyme auto-induction. From the data it seems that for the first few days there is no effect on the enzyme, as evidenced from the accumulation factor. But slowly the induction sets in. To model the change in clearance, I am using a Emax model for CL; CL=CL0+CLmax*t/t50+t. I have used appropriate hill function as well, but my predicted concentrations are systematically lower than those observed at the earlier time points. Can any one help me with modeling the CL where the CL value will remain constant up to a time 'X', the critical time (preferably expressed as THETA) after which the non-linear function will kick-in. Your help is greatly appreciated. Regards, Partha Partha Nandy Clinical Discovery BMS-Lawrenceville, NJ _______________________________________________________ From: "Bhattaram, Atul" BhattaramA@cder.fda.gov Subject: RE:[NMusers] Changing Clearance over time : Enzyme auto-induction Date: Fri, August 6, 2004 3:01 pm Hello Partha Did you refer to this link? It has a reference which could help you. http://www.cognigencorp.com/nonmem/nm/97may142001.html Venkatesh Atul Bhattaram Pharmacometrics DPE-1, OCPB, FDA _______________________________________________________ From: Leonid Gibiansky lgibiansky@emmes.com Subject: RE:[NMusers] Changing Clearance over time : Enzyme auto-induction Date: Fri, August 6, 2004 3:11 pm Have you tried straightforward: NewT = T-theta(*) CL = CL0 IF(NewT.GT.0) THEN CL = CL0 + CLmax*NewT/(t50+NewT) ENDIF Leonid _______________________________________________________ From: Johan.Gabrielsson@astrazeneca.com Subject: RE:[NMusers] Changing Clearance over time : Enzyme auto-induction Date: Mon, August 9, 2004 1:59 am Dear Partha, Leonid et al, Interesting discussion. May I propose a first-order induction function (since often enzyme reactions can be approximated to that) as an alternative to the previously proposed models. Namely, CL = CLinduced -(CLinduced - CLpre)*exp(-kout*(t-Tlag)) where kout corresponds to the fractional turnover rate of the induced enzyme, CLpre the pre-induction clearance (your CL0 I suppose), CLinduced the clearance at steady-state post-induction, and Tlag the lag-time for induction to occur (I suppose your NewT parameter). I have personally applied this relationship (taken from the textbook of Gibaldi and Perrier 1982, pgs. 304-305) at several occassions. The nice thing about the model is that it gives you some info about the apparent fractional turnover-rate (and turnover time) of the inducing enzyme, provided the rate limiting step is the change of the amount of enzyme rather than the half-life of the drug (T1/2kout >> T1/2K(drug)) and that the turnover rate (production) rather than the fractional turnover rate (loss) of enzyme is affected. I have some documented practical examples of simultaneous pre-, peri- and post-induction modelling after repeated dosing (p.o. and i.v.), that I'll be happy to share if you are interested. :-) Johan _______________________________________________________ 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 _______________________________________________________