Analysis program based on finite element method, MULTI(FEM), for evaluation of dose‐dependent local disposition of drug in liver

Abstract

A curve‐fitting program based on the Finite Element Method, MULTI(FEM), was developed to model nonlinear local disposition of a drug in the liver under non‐steady‐state conditions. The program was written in FORTRAN on an IBM‐compatible personal computer. The validity of MULTI(FEM) was confirmed by analyzing the outflow kinetics of oxacillin (a model drug) following a pulse input to isolated, perfused rat livers, according to both linear and nonlinear dispersion models. Four dose levels (300, 1000, 3000, and 5000 µg) of oxacillin were administered to observe the dose‐dependency in the hepatic local disposition. First, the individual outflow time‐profiles at the same dose were averaged, and the average time‐profile was analyzed by MULTI(FEM) based on linear dispersion models to yield a single curve fit. The fitted parameters at each dose level were compared with parameters estimated using MULTI(FILT), a program based on fast inverse Laplace transform, to analyze linear pharma‐cokinetics. The estimated parameters by MULTI(FEM) were in good agreement with those by MULTI(FILT). The apparent elimination rate constant (ke) decreased with an increase in dose, whereas other parameters showed no discernible dependency on an increase of dose. Second, the average outflow time‐profiles at the four dose levels were simultaneously analyzed by MULTI(FEM) based on dispersion models featuring Michaelis–Menten elimination. The outflow time‐profiles of oxacillin were well approximated by a two‐compartment dispersion model with central Michaelis–Menten elimination. The maximum elimination rate constant (Vmax) and the Michaelis constant (Km) were estimated to be 1520 µg/mL/min and 41.3 µg/mL, respectively. Thus, the capability of MULTI(FEM) was demonstrated in evaluating capacity‐limited local disposition in the liver.