Nonlinear least-squares regression analysis by a simplex method using differential equations containing Michaelis-Menten type rate constants.

Computer curve fittings were carried out to observed data as well as theoretically generated plasma concentrations of several drugs, using differential equations which contained nonlinear Michaelis-Menten type rate constants to discuss problems of initial parameter estimation in pharmacokinetic analysis. Calculation based on two different algorithms, each carried out by using SIMP (simplex method) and NONLIN (modified Gauss-Newton method) produced similar results. However, occasional divergence or unreasonable solutions occurred in a later case, when assumed values of Km and Vmax were used as initial parameters. A combined use of SIMP and NONLIN in which calculated values by SIMP were used as initial values for NONLIN, was shown to be effective to analyse plasma concentration data of indocyanine green bearing difficulty in estimating initial values. It is suggested that the successive method is useful for the curve fitting of plasma concentration with nonlinear pharmacokinetic rate processes.