Sensitivity analysis of biomedical models using green’s function

Abstract

One of the important steps of analysis of any mathematical model is the sensitivity analysis. The most frequently used type of sensitivity analysis is the local parametric sensitivity analysis that answers the question how changes of model’s parameters influence the solution of the model. It is routinely used but it can be applied only for constant parameters. It cannot be applied for non-stationary parameters nor for varying in time external input signals. The full information about the sensitivity in such a case can be given by the sensitivity analysis using Green’s function. This work describes a toolbox written in MATLAB environment, which can be useful in sensitivity analysis of biomedical models described by system of ordinary differential equations. To illustrate this type of sensitivity analysis, we use the created tool to analyze a model of cell signaling pathway of p53 protein, which plays crucial role in the response of tumor and healthy cells to radiotherapy.