Analysis and simulation of a model for intracellular drug accumulation in tumors

We consider a spatio-temporal mathematical model describing drug accumulation in tumors. The model is a free boundary problem for a system of partial differential equations governing extracellular drug concentration, intracellular drug concentration and sequestered drug concentration. The balance between cell proliferation and death generates a velocity field. The tumor surface is a moving boundary. We study the model using analytical methods and numerical methods. The analytical methods involve proving existence and uniqueness of model solutions and yielding an explicit condition, in terms of model parameters, for which tumor eradication may be achieved. The numerical results illustrate the effect of parameter variation on the system behavior and the profiles of the drug concentrations in three compartments. The effect of multiple rounds of treatment is also numerically studied.