Tracer experiment design for unique identification of nonlinear physiological systems

Abstract

The design of tracer kinetic experiments, the purpose of which is to elucidate uniquely the internal couplings of a nonlinear dynamic system, is considered for a practical class of models of physiological systems. The extent of information about the real system contained in tracer kinetic data is a central issue. Criteria for determining whether nonlinear model parameters can be estimated from small-signal, "linearizing" tracer experiments are developed and illustrated by examples. The concept of "structural identifiability" is employed in this analysis to determine which model parameters can be and which cannot be determined "uniquely" from given input-output data; a step-by-step procedure based on an extension of this concept is presented for adapting the overall approach to the experimental design problem. Estimation of unmeasurable endogenous inputs and system state variables, problems that are intimately related to parameter estimation for physiological systems, are also considered.