Correct codes of modeling Michaelis-Menten elimination using concentration-time data

From: "Jiannguo Li" <LIJ4@gunet.georgetown.edu> Subject: Correct codes of modeling Michaelis-Menten elimination using concentration-time data Date: Fri, 29 Sep 2000 11:23:07 -0400 Dear NM users, In the NONMEM Users Guide -Part VIII (March, 1998, Page 321), the suggest code for modeling Michaelis-Menten elimination using concentration-time data for one compartment disposition should be: DADT(1)=3D-VM*(A(1)/S1)/(KM+A(1)/S1) (Equation 1) The S1 was defined in the $PK). If you use this code to model the alcohol data (Wilkinson PK et al (1976), "blood ethanol concentrations during and following constant-rate intravenous infusion of alcohol", Clinical Pharmacology and therapeutics, 19:213-223), the resulting parameter estimates (Vm and KM) were far from what reported in the paper for each of six subjects. However, a little bit change of the code: DADT(1)=3D-VM*A(1)/(KM+A(1)/S1) (Equation 2) (i.e. the amount A(1) in the numerator was not scaled by S1. The similar results of the parameter estimates were obtained. I think the amount A(1) in the numerator of M-M equation was implicitly scaled by S1 if S1 had been defined in $PK block, just like the case of defining a deferential equation for a first-order elimination ( DADT(1)=3D-Ke*A1(1)), it is incorrect to explicitly code A1(1) as A(1)/S1 if S1 had been defined in $PK. Consequently, the equation (2) should be the correct code. This is confirmed by simulation using the reported Vm and Km of the subject 1(Vm=3D0.253 mg/(ml*hr) , Km=3D0.108 (mg/ml, dose=3D79.6*79.6 (gm), infusion time=3D2 hours). The simulated predictions using equation 2 were coincident with those report in the paper for the subject 1. The data for the first subject and the control files of simulation using both equations 1 and 2 for the first subject are attached for inspections. Any comments are welcome. Jianguo Li, PhD Center for Drug Development Science Georgetown University filename=SIM103.CTL filename=SIM101.CTL filename=SUBJ1.prn