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 (εV) below which the tumor will be cured. Tumor regrowth is simulated until the tumor burden exceeds a detection threshold (ωd), 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.