(526e) Modeling Cancer Dormancy and Recurrence with the Theory of Birth-Death Processes

Unfortunately, a significant number of patients treated for cancer suffer a recurrence of the disease. Although most recurrences occur within the first 5 years after treatment, 10-20% of patients suffer from late recurrences (more than 10 years after treatment), where relapse can occur even after decades. Our novel population balance model frames the mechanism for recurrence as a random walk with size-dependent parameters describing growth (mitosis), reduction (immunity and/or treatment), and metastasis generation and aims to gain new insights about the proposed recurrence mechanism.

We leverage the theory of birth-death processes to predict the probability of a recurrence for a tumor of any given initial size in a large population of tumors and, for those that recur, the expected dormancy time. We do the analogous calculation for the cure probability and expected cure time for tumors of any given initial size. Similar approaches have been applied to predict extinction times in population ecology models and the fate of cells in genetic drift models. We also illustrate how the sizes at which growth and reduction rates intersect are threshold values that determine the evolution of the distribution. When only one such crossover size exists, it allows for a small fraction of tumors not too far below the crossover size to escape immune surveillance. When multiple crossover sizes exist, it may allow a stable or growing population of metastases to arise that eventually promotes recurrences. Using the analytical approaches described in this study, we established a new framework for understanding how recurrences in cancer might occur.

For validation, we are using our own observations of melanoma growth and shrinkage in immunocompetent zebrafish to obtain a size-dependent clearance time distribution for tumors that are cured. Using measured size-dependent growth and reduction rates, our model enables the prediction of expected clearance times. In zebrafish melanoma, we have found only one crossover size, and it is far larger than most tumors that we observe. The model can predict what fraction of large tumors can escape beyond this crossover size and the expected time for this to happen. Understanding how slowly or quickly tumors of different sizes should respond to treatment as well as the likelihood and expected time of recurrence can have important ramifications in a clinical setting, e.g., when adjuvant therapy might yield little benefit and potentially, given host response issues, even be detrimental.