Title: An Inverse Problem to Recover Sensitivity to Treatment in Prostate Cancer Tumors
Abstract: Resistance to prostate cancer treatment is a serious concern in modern oncology due to the risk it poses for poor patient outcomes. A key facet of treatment resistance is that traditional therapies can select for resistant cells. Understanding the heterogeneity of sensitivity to treatment in heterogeneous tumors is key to predicting and delaying the time to treatment resistance. We construct a novel random differential equation (RDE) model that incorporates sensitivity to treatment, then use inverse problem methods to recover the distribution of sensitive and resistant cells from noisy simulated data. We use the Akaike Information Criteria (AIC) to pinpoint the optimal mesh for the recovered distribution, which can help optimize individual treatment plans.