Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development

Abstract

Understanding the relationship between hepatocellular carcinoma (HCC) and immunity is crucial for HCC immunotherapy. However, the existing research has solely focused on a novel population of primary tumor-induced non-leukocytes called Ter-cells and their circulating components in distant organs, neglecting the examination of immunity’s impact on cancer. In order to thoroughly examine the dynamics of Ter cells, HCC, and the known regulatory elements in the immunological milieu, we used a mathematical model in the form of a system of differential equations in this work. According to simulation studies, tumor cells cannot be completely eliminated by either the effective killing of HCC by cytotoxic T lymphocytes (CTL) or the inhibition of tumor cell proliferation. Nonetheless, continuous CTL activation and TGF-β-induced differentiation of CTL facilitated a transition from a high steady-state of HCC quantity to an unstable state, followed by a low state of HCC quantity, aligning with the three phases of the cancer immunoediting concept (escape, equilibrium, and elimination). Our survival study revealed that the ratio of CTL proliferation to CTL killing and relative TGF-β-induced differentiation of CTL have a significant impact on cancer-free survival. Sensitivity and bifurcation analysis of these parameters demonstrated that the rate of CTL proliferation, as well as the number of HCCs when the production rate reaches half of one, strongly affects the number of HCCs. Our findings highlight the critical role of immune system activation in cancer therapy and its potential impact on HCC treatment.