A theoretical study of the implications of resource competition for adaptive therapy of castration-resistant prostate cancer

Abstract

The standard method for therapy against cancer is to administer cytotoxic drugs at the Maximum tolerated dose (MTD). This however, leads to competitive release of the drug-resistant cells and the tumour becomes unresponsive to further therapy. Adaptive therapy aims to maintain a steady population of drug-sensitive and prevent such competitive release by administering the drug at lower and fluctuating doses.

The success and failure of this method wholly rests on the competition between the sensitive and resistant cells, and the ability of the sensitive cells to suppress the resistant cells as a result. This competition is driven primarily by their shared requirement for limited resources in the tumour micro-environment. Based on this premise, we have developed a mathematical model of castration-resistant prostate cancer (CRPC) consisting of a system of ODEs (ordinary differential equations) that describe three kinds of tumour cells along with two resource variables, oxygen and testosterone. Close investigation of this model shows that resource dynamics could play a controlling role in outcomes of competition, over other variables like cell-intrinsic doubling times. This is then further extended to add mechanistic insights to the competitive processes between tumour cells, and eventually to the outcomes of adaptive therapy.