A mathematical perspective on the paradox that chemotherapy sometimes works backwards

Abstract

Doctors are well aware that sometimes cancer treatments not only fail, but even work backwards, i.e. they make the treated tumor grow. In this work we present a mathematical perspective on this paradox in the case of chemotherapy, by studying a minimally parameterized mathematical model for the system composed of the tumor and the surrounding vasculature. To this end, we will use a system of two well-established nonlinear ordinary differential equations, which incorporates the cytotoxic (via the Norton-Simon hypothesis) and antiangiogenic effects of chemotherapy. Finally, we provide two theoretical ways to avoid these anomalies.