Combination of anti-PD-L1 and radiotherapy in hepatocellular carcinoma: a mathematical model with uncertain parameters

Blockade of programmed death-ligand-1 (PD-L1) as a new method of immunotherapy for cancers has shown limited efficacy in hepatocellular carcinoma (HCC). The combination of anti-PD-L1 and radiotherapy (RT) enhances the antitumor effect in HCC cancer. The efficacy and interactions of these treatments can be addressed by a mathematical model. We developed a mathematical model using a set of ordinary differential equations (ODEs). The variables include cancer cells, cytotoxic T lymphocytes (CTLs), programmed cell death-1 (PD-1), PD-L1, anti-PD-L1, and ionizing radiation. The model is parameterized with imprecise data set of murine HCC model and the effect of parametric uncertainty is assessed by the fuzzy theorem. The global sensitivity analysis (GSA) is performed to assess model robustness against perturbation in parameters and to identify the most influential parameters on the dynamics of cells and proteins. In silico predictions are consistent with experimental data. The model simulation shows that anti-PD-L1 and RT have a synergistic effect. In silico assessment of treatments' efficacy in the fuzzy setting of parameters revealed that anti-PD-L1 therapy, RT, and combination treatment caused the uncertainty band of tumor cells to lead to lower populations. This model as a validated rigorous simulation framework can be used to deepen our understanding of tumor and immune cell interactions and helps clinicians to investigate the efficacy of different time schedules of anti-PD-L1, RT, and combination therapy. The fuzzy theorem in conjunction with the classical ODE model that is parameterized by imprecise data was used to predict reliable outcomes of treatment.