Modeling the chemotherapy-induced selection of drug-resistant traits during tumor growth

The emergence of drug-resistance is a major challenge in chemotherapy. In this paper we develop a mathematical model to study the dynamics of drug-resistance in solid tumors. Our model follows the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug. The equation for the tumor density is written as a reaction-diffusion equation with a pressure term that depends on the local cell density. The model incorporates the dynamics of nutrients and two different types of drugs: a cytotoxic drug, which directly impacts the death rate of the cancer cells, and a cytostatic drug that reduces the proliferation rate. This model successfully integrates the phenotype structured drug-resistance approach with an asymmetric tumor growth model in space. Through analysis and simulations we study the impact of spatial and phenotypic heterogeneity on the tumor growth under chemotherapy. We demonstrate that heterogeneous cancer cells may emerge due to the selection dynamics of the environment. Our model predicts that under certain conditions, multiple resistant traits emerge at different locations within the tumor. We show that a higher dosage of the cytotoxic drug may delay a relapse, yet, when this happens, a more resistant trait emerges. Moreover, we estimate the expansion rate of the tumor boundary as well as the time of relapse, in terms of the resistance trait, the level of the nutrient, and the drug concentration. Finally, we propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait. By combining the cytotoxic and cytostatic drugs, we demonstrate that the resistant cells can be eliminated.