Re: kinetic interpolation and effect compartments

From sambol@itsa.ucsf.edu Tue Oct 1 17:51:32 1996 Subject: Re: kinetic interpolation and effect compartments Dear Rik, Some more comments regarding kinetic interpolation and effect compartments. We ran into the same problem (erratic conc.-time profile, but need to obtain predicted "effect site" concentrations to feed into PD model). We developed an empiric convolution method to obtain predictions of "effect site" concentration at time points corresponding to PD measurements. The method was used in the context of a population analysis (using NONMEM) of concentration vs. pain relief score of an analgesic. (Liu & Sambol, Pharm. Res., 12: 438-445, 1995; see also Liu & Sambol, Bulletin of the International Statistical Institute, 50: 716-717, 1995) Our goal is essentially the same as that which Lew described, but the implementation involves an explicit solution. The procedure involves a piecewise linear approximate to the concentration-time profile and convolution, carried out exactly, based on this approximate. The feature of this implemenation we like in particular is that it can be performed within $PRED. The general expression for this equation is provided in the paper cited above. An example of the relevant NONMEM code with time points 0=T0<T1<T2<T3 and observed plasma concentrations C1 and C3 (without C2, and with the desire to predict Ce at T2), is as follows: ------------ $PRED ... A1=0 B1=C1/T1 IF (TIME.LE.T1) THEN CE=KEO*(B1*(KEO*T1-1.0+EXP(-KEO*T1))/(KEO**2)) ENDIF IF(TIME.LE.T3.AND.TIME.GT.T1) THEN B2=(C3-C1)/(T3-T1) A2=C3-B2*T3 CE=B1*(KEO*TIME-1.0+EXP(-KEO*TIME))/(KEO**2) CE=CE+(A2-A1)*(1.0-EXP(-KEO*(TIME-T1)))/KEO CE=KEO*(CE+(B2-B1)*(KEO*T-1.0-(KEO*T1-1.0)*EXP(-KEO*(TIME-T1)))/(KEO**2)) ENDIF ... ------------- Note: Cn and Tn are data fields (read into NONMEM with either $DATA or verbatim code), although you don't need records for Tns and Cns where PK data are missing (i.e., measurements like C2 in the example). You also need a TIME field in $DATA with values corresponding to effect measurements. You can handle the fact that different individuals may have different numbers of concentration-time data points using "IF" statements. Finally, as you can imagine, if the distance between concentration observations is large (at certain locations), this method may not work so well. Chui Y Liu and Nancy Sambol Nancy C. Sambol, Pharm.D. Department of Biopharmaceutical Sciences University of California San Francisco San Francisco, CA 94143-0446 phone: 415-476-8884 fax: 415-476-9330