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. Once cancer has reached detectable sizes ($10^{6}$ cells or 1 mm$^3$), it is assumed to have spread throughout the body, and a systemic form of treatment is needed. Chemotherapy treatment is commonly used, and it effects both healthy and diseased tissue. This creates a dichotomy for clinicians who need develop treatment schedules which balance toxic side effects with treatment efficacy. Nominally, the optimal treatment schedule --- where schedule is defined as the amount and frequency of drug delivered --- is the one found to be the most efficacious from the set evaluated during clinical trials. In this work, a model based approach for developing drug treatment schedules was developed. Cancer chemotherapy modeling is typically segregated into drug pharmacokinetics (PK), describing drug distribution throughout an organism, and pharmacodynamics (PD), which delineates cellular proliferation, and drug effects on the organism. This work considers two case studies: (i) a preclinical study of the oral administration of the antitumor agent 9-nitrocamptothecin (9NC) to severe combined immunodeficient (SCID) mice bearing subcutaneously implanted HT29 human colon xenografts; and (ii) a theoretical study of intravenous chemotherapy from the engineering literature.Metabolism of 9NC yields the active metabolite 9-aminocamptothecin (9AC). Both 9NC and 9AC exist in active lactone and inactive carboxylate forms. Four different PK model structures are presented to describe the plasma disposition of 9NC and 9AC: three linear models at a single dose level (0.67 mg/kg 9NC); and a nonlinear model for the dosing range 0.44 -- 1.0 mg/kg 9NC. Untreated tumor growth was modeled using two approaches: (i) exponential growth; and (ii) a switched exponential model transitioning between two different rates of exponential growth at a critical size. All of the PK/PD models considered here have bilinear kill terms which decrease tumor sizes at rates proportional to the effective drug concentration and the current tumor size. The PK/PD model combining the best linear PK model with exponential tumor growth accurately characterized tumor responses in ten experimental mice administered 0.67 mg/kg of 9NC myschedule (Monday-Friday for two weeks repeated every four weeks). The nonlinear PK model of 9NC coupled to the switched exponential PD model accurately captured the tumor response data at multiple dose levels. Each dosing problem was formulated as a mixed--integer linear programming problem (MILP), which guarantees globally optimal solutions. When minimizing the tumor volume at a specified final time, the MILP algorithm delivered as much drug as possible at the end of the treatment window (up to the cumulative toxicity constraint). While numerically optimal, it was found that an exponentially growing tumor, with bilinear kill driven by linear PK would experience the same decrease in tumor volume at a final time regardless of when the drug was administered as long as the {it same amount} was administered. An alternate objective function was 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 two different objectives above 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. This solution also attempted to administer as much drug as possible at the end of the treatment interval. The problem was then posed as a receding horizon trajectory tracking problem. Once again, a more clinically relevant objective returned promising results; the tumor burden was rapidly eliminated.