RE: Duration of Absorption Time From Depot (Gut) as Covariate

Hi Paul In your first email you mentioned: “... data that suggest a dependence of AUC and Cmax upon transit time in the gut. The elimination rates for the one compartment model are quite similar, suggesting that the variability lies in bioavailability. Preliminary data suggest that the absorption of this drug from the gut is transporter-limited, and may be dependent upon the duration of time that the drug is exposed to a specific portion of the duodenum or jejunum.” Based on these indications, if you manage to obtain reliable predictions for the Weibull distribution function and the time mapping parameter [THETA(IVIVC)] these parameters embody a mixture of dissolution transformation (in vitro to in vivo), interplay of transporters and gut enzymes, drug permeability in different segments of the gut and the gut physiology and anatomy e.g. small intestine transit time, duodenum length, etc. Also the related inter-individual variability values and covariates may not provide consistent explanation of the observed variability. In such cases application of (semi) physiologically-based models facilitates incorporation of extra information such as any physicochemical, in vitro or imaging data as well as physiological knowledge in the model which can give better understanding of the drug behaviour in the body, please see: http://www.pkuk.org.uk/ContentImages/KiyohikoSugano.pdf http://www.pkuk.org.uk/ContentImages/MartinBergstrand.pdf http://www.pkuk.org.uk/ContentImages/MasoudJamei.pdf. Regards Masoud *From:* [email protected] [mailto:[email protected]] *On Behalf Of *Paul Hutson *Sent:* 16 December 2009 21:18 *Cc:* [email protected] *Subject:* Re: [NMusers] Duration of Absorption Time From Depot (Gut) as Covariate Leonid: Thank you very much for your clear and helpful answer. May I suggest that the Weibull distribution function might be more clearly written: B= IVIVC*PAR1 WDER=(GAMA1/B)*((T/B)**(GAMA1-1))*EXP(-(T/B)**GAMA1) Be well. Paul Leonid Gibiansky wrote: Paul, No, this is not a correct way to introduce drug to depot. The idea was: Step 1. Fit Weibull or something similar to the dissolution data: time t = 0, 1, 2,... fraction absorbed: f = 0, 0.1, 0.5 .. Use model: f(t)=1-exp(t/to)^gamma Using observed dissolution data, finds t0 and gamma that would provide good fit of the dissolution data If needed, add extra parameter f(t)=A*(1-exp(t/to)^gamma) Step 2: Assume some IVIVC model, for example: in-vivo dissolution is the same as in vitro: FF=1-exp(t/to)^gamma or in-vivo dissolution is faster/slower then in vitro: FF=1-exp(t/(THETA(IVIVC)*t0))^gamma where THETA is estimated or some other model Step 3: put drug to depot, but it should be in the $DES block, and it should be a derivative of FF, not FF itself: $DES B=THETA(IVIVC)*t0 WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM) DADT(1)=F1*DOSE*WDER-KA*A(1) Here t0 and GAMM are fixed (from in-vitro data fit) while THETA(IVIVC) corresponds to IVIVC and need to be estimated from the data. If you would like to stop dissolution at some time TMAX, you can use: $DES B=THETA(IVIVC)*t0 WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM) IF(T.GT.TMAX) WDER=0 DADT(1)=F1*DOSE*WDER-KA*A(1) If you would like to stop absorption at some time TMAX, you can use: $DES B=THETA()*t0 WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM) IF(T.GT.TMAX) KA=0 DADT(1)=F1*DOSE*WDER-KA*A(1) Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Paul Hutson wrote: Leonid & Jeroen: Thank you for your suggestions. I incorporated Jeroen's suggestion of using MTIME below, with a slight modification (KA = TVKA *(1-MPAST(1))), since I want to turn KA off, not on, at TOFF. I try below to use Leonid's suggestion of a Weibull distribution to describe the dissolution of the oral product, rather than using multiple AMT & RATE inputs corresponding to the dissolution data for the product. My fit deteriorates both by OBj Func and VPC. Does the code below appear to be appropriate for introducing the oral drug in A(1) using a Weibull distribution? Thanks very much Paul $SUBROUTINES ADVAN6 TOL=3 $MODEL COMP=(DEPOT, DEFDOSE) COMP=(CENTRAL, DEFOBS) $PK callfl=-2 CL=THETA(1)*EXP(ETA(1)); CLEARANCE V2=THETA(2)*EXP(ETA(2)); V2 TOFF=THETA(3)*EXP(ETA(3)); DURATION OF PRESENCE IN ABSORPTION SEGMENT K=CL/V2 AUC=AMT/CL S2=V2/1000 ;CLOSE ABSORPTION AFTER SOME TIME TOFF TVKA=THETA(4)*EXP(ETA(4)) MTIME(1)=TOFF KA=TVKA*(1.001-MPAST(1)); MPAST(1) = O UNTIL MTIME(1)(TOFF) IS REACHED, THEN IS 1 ;DRUG APPEARANCE PAR1=THETA(5); SCALING CONSTANT FOR TIME GAMA1=THETA(6); SLOPE FUNCTION FOR WEIBULL WB1=1-EXP(-((TIME/PAR1)**GAMA1)) RAT1 = AMT*WB1 $DES DADT(1) = RAT1 - A(1)*KA DADT(2) = A(1)*KA - A(2)*CL/V2 $ERROR IPRE = F W1=F DEL = 0 IF(IPRE.LT.0.001) DEL = 1 IRES = DV-IPRE; NEGATIVE TREND IS OVERESTIMATING IPRED WRT DV IWRE = IRES/(W1+DEL) Y=F*(1+ERR(1))+ERR(2) $THETA (0.1,1.23, 50); CL $THETA (0.10,97.8,1000); V2 $THETA (0.1,86.5,1000); TOFF $THETA (0.0001, .7, 4); KA $THETA 176.1 FIXED; PAR1 $THETA 1.033 FIXED ; SLOPE $OMEGA 0.5; CL $OMEGA 0.3; V2 $OMEGA 0.6; TOFF $OMEGA 0.3; ka $SIGMA .5; SIG1 $SIGMA .1; SIG2 $ESTIMATION METH=1 INT SIGDIGITS=3 MAXEVAL=9999 PRINT=10 NOABORT Elassaiss - Schaap, J. (Jeroen) wrote: Leonid, Paul, Alternatively one may use the MTIME function in NM6 so the algebraic solutions in eg. ADVAN2 are still applicable: $PK .... MTIME(1)=TOFF KA=TVKA*MPAST(1) Best regards, Jeroen Jeroen Elassaiss-Schaap, PhD Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) Early Clinical Research and Experimental Medicine Schering-Plough Research Institute T: +31 41266 9320