The role of cell density and intratumoral heterogeneity in multidrug resistance.

Recent data have demonstrated that cancer drug resistance reflects complex biologic factors, including tumor heterogeneity, varying growth, differentiation, apoptosis pathways, and cell density. As a result, there is a need to find new ways to incorporate these complexities in the mathematical modeling of multidrug resistance. Here, we derive a novel structured population model that describes the behavior of cancer cells under selection with cytotoxic drugs. Our model is designed to estimate intratumoral heterogeneity as a function of the resistance level and time. This updated model of the multidrug resistance problem integrates both genetic and epigenetic changes, density dependence, and intratumoral heterogeneity. Our results suggest that treatment acts as a selection process, whereas genetic/epigenetic alteration rates act as a diffusion process. Application of our model to cancer treatment suggests that reducing alteration rates as a first step in treatment causes a reduction in tumor heterogeneity and may improve targeted therapy. The new insight provided by this model could help to dramatically change the ability of clinical oncologists to design new treatment protocols and analyze the response of patients to therapy.