A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions.

This paper deals with the development of a mathematical model for the in vitro dynamics of malignant hepatocytes exposed to anti-cancer therapies. The model consists of a set of integro-differential equations describing the dynamics of tumor cells under the effects of mutation and competition phenomena, interactions with cytokines regulating cell proliferation as well as the action of cytotoxic drugs and targeted therapeutic agents. Asymptotic analysis and simulations, developed with an exploratory aim, are addressed to enlighten the role played by the biological phenomena under consideration in the dynamics of hepatocellular carcinoma, with particular reference to the intra-tumor heterogeneity and the response to therapies. The obtained results suggest that cancer progression selects for highly proliferative clones. Moreover, it seems that intra-tumor heterogeneity makes targeted therapeutic agents to be less effective than cytotoxic drugs and a joint action of these two classes of agents may mutually increase their efficacy. Finally, it is highlighted how targeted therapeutic agents might act as an additional selective pressure leading to the selection for the most fitting, and then most resistant, cancer clones.