On the identification of a middle-large dynamic system for IN VIVO drug distribution and metabolism: comparison of three optimization routines

Abstract

To identify the fate of the allticancer drug daunomycin (DAU) in the rat the distribution of DAU and the formation of its metabolite daunomycinol (DOL) are described with first order processes in a double seven-compartment model. For DAU and DOL the compartments represent plasma; liver; spleen; well-perfused organs heart. kidneys. lungs. muscles in one “tissues.l” compartment; other tissues in a “tissues.2” compartment; and two excretion fluids. urine and bile. Anatomically determined pathways link the compartments. DAU and DOL concentrations are observed (high performance liquid chromatography (HPLC) method) in all compartments. except tissues.2. at various timepoints after a single i.v. injection of DAU. This input is modeled as an instantaneous loading of the plasma DAU compartment at time zero. Twenty-five rate constants that describe the dynamic system behaviour in terms of concentration-time histories are estimated by automatic optimization in the maximum likelihood (ML) sense. Three different optimization routines are described: 1) a modified Gauss-Newton method based on the solution of analytical sensivity differential equations (MGN); 2) a finite differences approach to the computation (FD); or 3) a direct determination of the gradient vector and the Hessian matrix of the log-likelihood function in the parameter space. again through finite differences (DEH). The performance of the three methods with respect to convergence characteristics. accuracy of results and speed of computation is compared. With proper precautions taken to prevent divergence the MGN method performs better than the DEH method. The FD approach may speed up computation only marginally. Revision of the assumption of first order kinetics seems necessary.