Theory & Experiment for Tumor Growth, Regression & Metastasis

This paper posits a new mathematical model and complementary experiments for tumor evolution. Rather than focusing only on the how the mean tumor size evolves or on how the tumor size distribution changes due only to logistic growth and metastasis, as have been done in the literature, we model the effects of tumor growth, response to immunity and/or therapy and mitosis on the entire tumor distribution. These are chemical engineering methods that come from polymer modeling. The interaction of growth and immunity/ therapy leads to a novel diffusive term in tumor-size space that exhibits potentially patient-relevant new behavior. We will describe a fluorescent-melanoma-tumors-in-transparent-zebrafish model and planned experiments that should allow us to measure (possibly gender-dependent) model parameters for the fish system and to test model predictions to further our understanding of the fundamental science of tumor population progression. Insights from this integrated mathematical/ experi­mental program may help explain confounding human patient cohorts, suggest sources of gender disparities in melanoma and potentially lead to new treatment strategies.