Pharmacokinetics in nonlinear and partially compartmentalized systems

The pharmacokinetics of complex systems both linear and nonlinear, compartmentalized, distributed, and partially compartmentalized are reviewed. The two problems considered are: 1) the prediction of concentration or pharmacological effects, and 2) the determination of the input (absorption, dosage schedule) from a given set of measured or desired concentrations. These problems are solved using the super-position integral in linear time-invariant systems by i) integration and ii) deconvolution respectively. Time-varying systems are dealt with by using tracer methods. Nonlinear systems are defined as systems with concentration-dependent parameters. The examples of Michaelis-Menten kinetics, tissue binding, and threshold effects are considered. Approaches to solutions of these problems are generally model-dependent and achieved through i) system identification (parameter estimation), ii) linearization for limiting cases, and iii) tracer techniques. Tracer techniques effectively linearize a nonlinear system so that some variable-dependent parameters can be measured. It is suggested that some of the more general techniques used in the study of metabolic systems may be useful in pharmacokinetics.