An MILP approach to cancer chemotherapy dose regime design

Cancer chemotherapy is a form of treatment in which both healthy and diseased tissues are adversely affected by dosing; this requires the clinician make decisions , which balance the effectiveness of treatment with toxicity effects, financial, and logistical constraints. This work presents a model-based approach for chemotherapy treatment scheduling that accounts for both drug toxicity constraints and the dosing constraints associated with clinical practice. A mixed-integer linear programming (MILP) approach is applied to a nonlinear system considered previously in an optimal control framework by Martin and Teo (1994). The nonlinearities in the pharmacodynamic PD model were eliminated by logarithmic transform and both the pharmacokinetic (PK) and PD models were converted into algebraic constraints by discretizing the system over the treatment window. This formulation also accounts for the toxicity constraints and allows for the easy incorporation of dosing constraints, which would be encountered during the course of treatment. MILP results are shown for three cases considered in R. Martin and K.L. Teo (1994): highly effective drug, moderately effective drug, and a drug with very little effect on the tumor. In the limit of the discretization timestep and delivery interval approaches zero, the MILP algorithm returns the optimal control solution. Like the optimal control solution, most of the drug is delivered at the end of the treatment cycle, which results in the minimal final cancer cell population. The MILP approach results in a problem which can be solved to optimality and can easily be augmented with constraints which give the problem more clinical relevance.