Design optimality for models defined by a system of ordinary differential equations.

Many scientific processes, specially in pharmacokinetics (PK) and pharmacodynamics (PD) studies, are defined by a system of ordinary differential equations (ODE). If there are unknown parameters that need to be estimated, the optimal experimental design approach offers quality estimators for the different objectives of the practitioners. When computing optimal designs the standard procedure uses the linearization of the analytical expression of the ODE solution, which is not feasible when this analytical form does not exist. In this work some methods to solve this problem are described and discussed. Optimal designs for two well-known example models, Iodine and Michaelis-Menten, have been computed using the proposed methods. A thorough study has been done for a specific two-parameter PK model, the biokinetic model of ciprofloxacin and ofloxacin, computing the best designs for different optimality criteria and numbers of points. The designs have been compared according to their efficiency, and the goodness of the designs for the estimation of each parameter has been checked. Although the objectives of the paper are focused on the optimal design field, the methodology can be used as well for a sensitivity analysis of ordinary differential equation systems.