Numerical simulation and fitting of tumor growth kinetics models using python

Abstract

Tumor growth kinetics may be mathematically described by ordinary differential equations. Fitting experimental data to different models often leads to non-convex functions optimization with multiple local minima. The aim of this paper is to present numerical methods for simulation and fitting of ordinary-differential-equation models of malignant tumors implemented in Python. The suggested protocol combines the generation of 1000 random initial parameter values with the Nelder-Mead simplex direct search for data fitting in order to escape from local minima. Sums of squared residuals obtained are compared with those achieved by the Levenberg-Marquardt method.