PDF file - 2179K, Supplementary details on the mathematical model. Supplementary details concerning numerical results. Table S1. Range and biological interpretation of variables and parameters. Table S2. Simulation details of all variables and parameter values plotted in all figures. Table S3. Simulation details of Figure S2. Table S4. Dynamics with variations in the percentage of cells altered. Figure S1. Drug efficacy as a function of the dose and resistance level. Figure S2. Dynamics with variations in the mutation rates over time with/without drugs.
ARTICLE ABSTRACTRecent 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. Cancer Res; 73(24); 7168–75. ©2013 AACR.