A mathematical model of the effects of drug resistance in cancer chemotherapy

A mathematical model is proposed relating tumor responce under repeated doses of a single cytotoxic agent to the presence and accumulation of phenotypic drug resistance. The latter is assumed to comprise two elements: that present at diagnosis and that acquired in responce to and during treatment. New analytic expressions are presented for quantities such as the fractional tumor reduction effected by each dose, the minimum tumor size achieved under therapy, the changing composition of the tumor, and the number of doses before apparent clinical resistance (the nadir) is observed. A similar model accommodates the sequential delivery of different drugs between which there is some degree of cross-resistance, and it is shown how competing treatment strategies can be simulated and compared.