Mathematical modeling of tumor evolution and response to therapy

Abstract

Despite the availability and success of targeted therapies to treat diverse tumor types, treatment resistance remains a significant clinical challenge. Response to treatment and the emergence of resistance can be modeled quantitatively as an evolutionary process. These mathematical and statistical models can be used to identify optimal treatment administration schedules and facilitate optimal selection of targeted therapies. First, I develop a partial differential equations model describing the response to lapatinib therapy in glioblastoma patients. Second, I present an ordinary differential equations model that characterizes estrogen receptor positive breast cancer and the response to fulvestrant plus palbociclib combination treatment. Both models provide quantitative insights into the in vitro kinetics of tumor growth and enable the systematic comparison of treatment administration schedules. Third, I use patient and in vivo data to analyze the evolutionary pressures exerted on HER2 positive breast tumors by HER2 targeted therapy and provide insights into mechanisms of treatment resistance to HER2 targeted therapy. Lastly, I evaluate the effects of HER2 heterogeneity on response to T-DM1 plus pertuzumab combination therapy, and present a statistical model that can be used to predict pathologic response to T-DM1 plus pertuzumab.