Simulating Cancer Recurrence Patterns From Post-Treatment Viable Tumor Burden Distributions

PURPOSE Ordinary differential equation mathematical models of tumor volume dynamics can accurately describe tumor growth and treatment response. Here, we extend such continuous models to also simulate outcomes. We conceptualize post-treatment viable tumor burden distributions across a treatment population and a novel model of tumor regrowth that can simulate population-level recurrence patterns. METHODS We use a mathematical model of tumor regrowth dynamics that is attenuated by a minimum viable tumor burden threshold (ε V ) below which the tumor will be cured. Tumor regrowth is simulated until the tumor burden exceeds a detection threshold (ω d ), which allows for the modeling of Kaplan-Meier curves. RESULTS We then explore the effect of the different model parameters and growth laws on the shapes of simulated Kaplan-Meier curves and demonstrate how this model can be used to further our understanding of clinical trial results. We also present qualitative fitting of this model to real-world recurrence data from a clinical trial comparing different radiation therapy protocols in head and neck cancer (RTOG 9003). CONCLUSION The theoretical framework described in this brief report provides a means to connect models of tumor dynamics to recurrence patterns. We foresee that it will also provide a new methodology for interpreting the shapes of Kaplan-Meier curves and provide insights as to why particular clinical trials failed and guide how to redesign them for success.