Some drug-resistant models for cancer chemotherapy. Part 1: Cycle-nonspecific drugs.

The pioneering mathematical analyses for describing the phenomenon of clonal selection, whereby cancer cells mutate and become resistant to treatment, were carried out by Goldie & Coldman (1979, 1983). The present analysis yields more generalized drug-resistant models arising in chemotherapy treatment when cycle-nonspecific (CNS) drugs (i.e. drugs which are toxic to cells irrespective of their position in the cell cycle) are deployed. This is accomplished by modifying models developed by Wheldon (1988) and Usher (1994) for investigating the effect of chemotherapy drugs on homogeneous cell populations (i.e. in the absence of drug resistance); both types of migration, of drug-sensitive cells to drug-resistant cells, and the possibility of a migration of drug-resistant cells to drug-sensitive cells, are incorporated into the models. Subsequently, drug concentrations are sought such that both the drug-resistant cell subpopulation and the drug-sensitive cell subpopulation either simultaneously decay or remain of constant size. The analysis reveals that the role played by the migration of drug-resistant cells to drug-sensitive cells is significant, if it occurs, when seeking appropriate drug concentrations. The qualitative results from these models provide further insight into the effective treatment of cancer by chemotherapy in the presence of drug resistance.