A mathematical model has been developed for a two-step approach to cancer chemotherapy involving the use of targeted monoclonal antibody-enzyme conjugates for the selective activation of anti-cancer prodrugs. Theoretical analysis and numerical simulation are used to characterize critical parameters for intratumoral and systemic drug generation. The model suggests that the most important pharmacokinetic and clinical parameters for increased drug production in the tumor are the rate of prodrug clearance from the blood and the initial injected dose of prodrug. The physiological parameters with the most influence are the prodrug and drug permeability. The ratio of tumor to blood drug generation can best be improved by increasing the conjugate clearance from the blood and decreasing the rate at which prodrug is converted to active drug. Predictions from this model concerning intratumoral prodrug and drug levels are validated by comparison with experimental data. Finally, the effects of certain barriers to chemotherapeutic treatments including vascular heterogeneity and radially outward convection are studied. If vascular heterogeneity alone is considered, the model predicts that the highest drug levels will occur in the most poorly vascularized sections of the tumor. However, when the effects of convection directed radially outward is considered, the highest drug levels are seen in the semi-well vascularized regions. This implies that the rapidly growing periphery of the tumor and the semi-necrotic tumor interior will receive the least amount of drug. These mathematical model predictions can lead to improved treatment protocols for this two step approach to cancer chemotherapy.
Optimal control for a mathematical model for chemotherapy with pharmacometrics
