A Nonlinear Model Predictive Control Algorithm for Breast Cancer Treatment

Abstract

A nonlinear model predictive control (NMPC) algorithm was developed to dose the chemotherapeutic tamoxifen to mice bearing breast cancer xenografts. A novel saturating rate cell-cycle model (SCM) was developed to capture unperturbed tumor growth dynamics, and a bilinear tumor kill term was included in the G-phase to account for the cycle-specific nature of tamoxifen and its active metabolite. Drug pharmacokinetics were modeled using a three-compartment linear model, which successfully approximated parent compound and metabolite (4-hydroxytamoxifen) plasma concentrations as a function of time. Using daily tumor measurements, the model predictive control algorithm successfully reduced tumor volume along a specified reference trajectory over a period of 4 months. A more clinicallyrelevant implementation using weekly or biweekly tumor measurements, and a prediction horizon seven days beyond the measurement interval, also led to reduced tumor volumes. In the mismatch case, a controller based on the simpler linear cell-cycle model (LCM) was unable to track desired reductions in tumor volume. Controllers based on a lumped-parameter saturating Gompertz model (GM), however, can yield similar performance to those using the more complex saturating rate cell-cycle model. This performance was dependent on the cellcycle phase of drug effect, with poorer results for M-phase targeted drugs. Overall, NMPC is a suitable algorithm for the class of chemotherapy problems with daily drug dosing, and the algorithm developed here may be adaptable to the clinical setting for the treatment of human breast cancer patients.