Predicting Efficacy of 5-Fluorouracil Therapy via a Mathematical Model with Fuzzy Uncertain Parameters.

Abstract

Background: Due to imprecise/missing data used for parameterization of ordinary differential equations (ODEs), model parameters are uncertain. Uncertainty of parameters has hindered the application of ODEs that require accurate parameters.

Methods: We extended an available ODE model of tumor-immune system interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. The fuzzy ODE (FODE) model assigns a fuzzy number to the parameters, to capture parametric uncertainty. We used the FODE model to predict tumor and immune cell dynamics and to assess the efficacy of 5-fluorouracil (5-FU) chemotherapy.

Result: FODE model investigates how parametric uncertainty affects the uncertainty band of cell dynamics in the presence and absence of 5-FU treatment. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and natural killer cells, and decreasing that of myeloid-derived suppressor cells. The global sensitivity analysis was proved model robustness against random perturbation to parameters.

Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient/imprecise experimental data in the field of mathematical oncology and can predict cell dynamics uncertainty band.