Optimization of an in Vitro Chemotherapy to Avoid Resistant Tumours

Chemotherapy use against solid tumours often results in the resistance of the cancer cells to the molecule used. In this paper, we will set up and analyse an ODE model for heterogeneous in vitro tumours, consisting of cells that are sensitive or resistant to a certain drug. We will then use this model to develop different protocols, that aim at reducing the tumour volume while preserving its heterogeneity. These drug administration schedules are determined through analysis of the system dynamics, and optimal control theory.