Anti-Cancer Treatment and the Cell Cycle: Cellular-Level Mathematical Models

Abstract

This dissertation presents a collection of mathematical models for cellular response to the most common forms of anti-cancer therapy (radiation and chemotherapy) and the role of the cell cycle in this response. These models have application to improving cancer therapy through: optimization of dose and scheduling of agents already in clinical use; better predictive methods for selecting the most promising among new drug candidates or candidate combinations; and combination therapy with newer agents that target the cell cycle or cellular metabolism. The cellular pharmacodynamic models are based on the key concept of "cellular damage" that results from exposure to therapy and has distinct kinetics from cell kill. Damage is lethal only if it exceeds a cell's tolerance threshold at one or more checkpoints in the cell cycle (for apoptosis) or at any time point (for necrosis). This is the "peak damage" model. Each mechanism of cell kill, each agent in combination therapy, and each cycle in fractionated therapy increases the damage function (the "additive damage" model). The overall framework is termed the "peak additive damage model." This model framework is first tested on 128 independent in vitro dose-response data sets for radiation alone. It outperforms previously proposed models, including the widely-used linear-quadratic model. The peak additive damage model is then applied to radiochemotherapy. Its performance is superior to the previously proposed independent cell kill model when tested with 218 data sets for fixed-schedule exposure against. For varying-schedule exposures, cell heterogeneity and cycle asynchrony necessitate a cell-cycle-phase-structured model that divides the population into cohorts with different responses, still determined for each cohort by the peak additive damage model, that are then averaged. This model simultaneously predicts dose-response and cell cycle distribution data, and is tested with such data from the literature. Finally, a first step is taken towards allowing for microenvironmental input into cellular response, by developing a model for the cell cycle that is driven by metabolic inputs and external growth factors. Overall, the models presented here have great flexibility to be extended to complex schedules, any number of agents, and agents with metabolic or cell-cycle targets.