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

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.

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.

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.

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.