Mathematical modeling of tumor growth and treatment: Triple negative breast cancer

Abstract

In this study, a mathematical model of triple negative breast cancer (TNBC) with checkpoint inhibitor immunotherapy is proposed. The mathematical model includes interactions between tumor cells, innate and adaptive immune cells, programmed cell death protein 1 (PD-1), programmed death ligand 1 (PD-L1), and immune checkpoint inhibitor (ICI). The mathematical model exhibits two coexisting stable equilibria, representing the tumor-free and the large-tumor states. While the tumor-free equilibrium is locally unstable, mathematical analysis and numerical simulation prove that the model immune system is able to eliminate a tiny tumor, providing immune surveillance. Further simulation shows that natural kill (NK) cell response is able to effectively eliminate tumor cells and PD-L1 expression inhibits cytotoxic T lymphocyte (CTL) response. With immune checkpoint inhibitor, the simulated treatment is able to eliminate a larger tumor but the effectiveness is limited by the intrinsic immune response. Enhancing CTL response significantly improves the outcome of treatment. This suggests that a combination of checkpoint inhibitor and immune booster therapy can produce synergistic effect.