Identifiability of mathematical models in medical biology

The analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling, and systems biology. The methods covered in this article can reduce the cost of experiments aimed at obtaining biological data. The problem of the identifiability of mathematical models in physiology, pharmacokinetics, and epidemiology is considered. The processes considered are modeled using nonlinear systems of ordinary differential equations. The mathematical modeling of dynamic processes is based on the use of the mass conservation law. The problem of estimating the parameters characterizing the process under study raises the question of nonuniqueness. When the input and output data are known, it is useful to perform an a priori analysis of the relevance of these data. The definition of the identifiability of mathematical models is considered. Methods for the analysis of the identifiability of dynamic models are reviewed. In this review article, the following approaches are considered: the transfer function method applied to linear models (useful for the analysis of pharmacokinetic data, since a large class of drugs is characterized by linear kinetics); the Taylor series expansion method applied to nonlinear models; the differential algebra methods (the structure of this algorithm allows it to be run on a computer); and a method based on graph theory (this method allows for the analysis of the identifiability of the model and finding a proper reparametrization reducing the initial model to an identifiable one). The need to perform a priori identifiability analysis before estimating the parameters characterizing any process is demonstrated with several examples. The examples of identifiability analysis of mathematical models in medical biology are presented.