Parameter Identifiability of Nonlinear Biological Systems

Parameters characterizing the internal behaviour of biological and physiological systems are usually not directly accessible to measurement. Their measurement is usually approached indirectly as a parameter estimation problem. A dynamic model describing the internal structure of the system is formulated and an input-output experiment is designed for model identification. Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. Recently, differential algebra tools have been applied to study the identifiability of nonlinear dynamic systems described by polynomial equations, however very few results have been obtained. Given that biological/physiological systems are usually characterized by nonlinear dynamics, e.g. threshold processes, and that the identification experiments are often performed on systems started from known (equilibrium) initial conditions, our purpose was to develop a new differential algebra algorithm, which tests a priori identifiability of nonlinear models with given initial conditions. The algorithm is presented together with an example.