Model-based design of cancer chemotherapy treatment schedules

Cancer is the name given to a class of diseases characterized by an imbalance in cell proliferation and apoptosis, or programmed cell death. Upon detection, cancer is assumed to have metastasized, requiring a systemic form of treatment. Chemotherapy is commonly used, and it affects both healthy and diseased tissue. This creates a dichotomy for clinicians who need to develop treatment schedules which balance toxic side effects with treatment efficacy. The optimal treatment schedule is the most efficacious schedule evaluated during clinical trials. In this work, a model-based approach for drug treatment schedule design was developed. Cancer chemotherapy modeling is typically segregated into drug pharmacokinetics (PK) and pharmacodynamics (PD). This work considers two case studies: (i) the oral administration of the antitumor agent 9-nitrocamptothecin (9NC) to severe combined immunodeficient mice bearing subcutaneously implanted HT29 human colon xenografts; and (ii) a theoretical study of intravenous chemotherapy from the engineering literature.; Two different PK/PD models were developed to describe the anticancer effects of 9NC. These were then used to formulate dosing problems as mixed-integer linear programs (MILP), which guarantees globally optimal solutions. Objective functions were selected to minimize tumor volume along a trajectory. This is more clinically relevant in that it better represents the objective of the clinician (eliminate the diseased tissue as rapidly as possible). This resulted in a treatment schedule which eliminated the tumor burden more rapidly, and this schedule can be evaluated recursively at the end of each cycle for efficacy and toxicity, as per current clinical practice.; The second case study consists of an intravenously administered drug with first order elimination treating a tumor under Gompertzian growth. This system was also formulated as a MILP, and the different objectives were considered. The first objective was minimizing the tumor volume at a final time---the objective the original authors considered. The MILP solution was qualitatively similar to the solutions originally found using control vector parameterization techniques. The problem was then reposed as a receding horizon trajectory tracking problem. Once again, a more clinically relevant objective returned promising results; the tumor burden was rapidly decreased.