Modeling Adaptive Cancer Chemotherapy

Abstract

Adaptive therapies show promising early results in patients presenting metastatic castration-resistant prostate cancer (mCRPC). The goal of this work is to apply patient-specific modeling to mCRPC trial data to simulate the efficacy of adaptive therapy. We employ Lotka-Volterra equations of interspecific competition to model a two-population mCRPC system of cells sensitive and resistant to abiraterone acetate chemotherapy. Cancer populations are coupled to prostate-specific antigen (PSA) concentrations through a source-decay relaxation dynamic and fit to biomarker trial data from the standard-of-care (SoC) cohort in pilot study NCT02415621 [1]. We follow a biologically-motivated heuristic approach to inform initial parameter guesses and then utilize the Nelder-Mead simplex search algorithm as a local optimization method to extract best-fit parameter values for each patient. Of the fifteen patients we consider from the small-cohort study, twelve are examined for modeling due to data concerns, and seven produce models that successfully meet criteria for biological feasibility. We then simulate an adaptive therapy protocol using the model parameters found in the fitting process. Time to progression (TTP) and fraction of total treatment time spent on abiraterone are reported and compared to the SoC for each of the seven patients. We explore both an ideal treatment scenario wherein clinicians are omniscient of PSA levels throughout the simulation, as well as a stochastic scenario wherein observational frequency and measurement error are introduced as state variables. Though findings are limited by the small cohort size, we demonstrate a universal improvement in TTP under adaptive therapy, on average 34.36% (-1.90% to 70.61% at 95% confidence) better than SoC treatment in the ideal scenario. Stochastic scenarios yield similar outcomes. Notably, results appear bimodal and entirely dependent on patient-specific parameters: two of the seven patients saw increases in TTP of 89.94% and 119.35%, while the other five improved only by a mean 6.24% (1.85%-10.63%). Additionally, all patients required significantly less abiraterone as a fraction of total treatment time, averaging 43.87% (27.95%-59.78%) compared to 100% in the SoC.