Identifiability of mathematical models in medical biology

Abstract

Analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling and systems biology. The methods covered in this article could reduce the cost of experiments for biological data. The problem of identifiability of mathematical models in physiology, pharmacokinetics and epidemiology is considered. The processes considered are modeled using nonlinear systems of ordinary differential equations. Math modeling of dynamic processes is based on the use of the mass conservation law. While addressing the problem of estimation of the parameters characterizing the process under the study, the question of nonuniqueness arises. 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 identifiability of mathematical models is considered. Methods for analysis of 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 analysis of pharmacokinetic data, since a large class of drugs is characterized by linear kinetics); the Taylor series expansion method applied to nonlinear models; a method based on differential algebra theory (the structure of this algorithm allows this to be run on a computer); a method based on graph theory (this method allows for analysis of the identifiability of the model as well as finding a proper reparametrization reducing the initial model to an identifiable one). The need to perform a priory identifiability analysis before estimating parameters characterizing any process is demonstrated with several examples. The examples of identifiability analysis of mathematical models in medical biology are presented.

Keywords

• identifiability
• mathematical models in medical biology
• system of ordinary differential equations
• pharmacokinetic
• epidemiology
• physiology
• differential algebra