Tumor dynamics modeling based on formalreaction kinetics

Abstract

Modeling the effect of therapeutic drugs on tumor dynamics is a fundamental step that leads to the optimization of cancer therapy using mathematical tools. We discuss three tumor dynamics models starting from a minimalist model describing the effect of bevacizumab based on experiments where the measurements can be defined with one parameter exponential curves, and finally discussing a more complex model that describes the effect of pegylated liposomal doxorubicin (PLD) based on measurements with richer dynamics. The differential equations are created with the analogy of formal reaction kinetics, enabling universal interpretation of the modeled phenomena. Parametric identification is carried out based on measurements to prove the efficacy of the models. The results of the parametric identification show that the discussed models can sufficiently describe the experimental results. The between-subject variability of the model parameters is given which highlights the parameters that may change the most in a virtual patient set.