CAREER: Stochastic Models of Cancer Evolution

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This project will develop rigorous mathematical frameworks for understanding cancer initiation from healthy tissue, and the role of the tumor microenvironment on the evolution of resistance to anti-cancer therapies. In its first phase, this project will build stochastic models describing the evolutionary processes of reproduction, death and mutation in a spatially structured population, using stochastic interacting particle systems and mesoscopic approximations of these processes. These models will be analyzed to investigate how spatial population structure impacts the cancer initiation process and resulting genetic heterogeneity of the tissue. In its second phase, this project will develop mathematical models of the feedback between the evolving tumor cell population and its environment, using non-Markovian branching processes. These models will be analyzed to help elucidate the role of the tumor environment in the evolution of drug resistance. The PI will collaborate with cancer biologist to parametrize and validate these models a lung cancer experimental system. This research investigates how cancer evolution is shaped by environmental pressures and spatial population structure. This research can lead to the development of better statistical tools for assessment of cancer risk from premalignant fields, survival prediction, evaluation of treatment efficacy, and improved design of treatment regimens to prevent or delay drug resistance. The mathematical frameworks developed in this proposal will also be broadly applicable to understanding similar issues in ecology and disease dynamics, e.g. emergence of antibiotic resistance in bacterial or viral populations, or the geographic spread of invasive plant species and pesticide resistant weeds. An education goal of this project is to increase the representation of women in mathematics, with an emphasis on recruitment into the mathematical biology and medicine. A week-long summer program will be held each year at the University of Minnesota for local high school girls with the theme of "Mathematics in Biology and Medicine." In addition, a workshop will be held to bring together early career women in mathematical biology with the aim of sharing research and discussing emerging areas of the field, and undergraduate students will be integrated into the proposed research efforts for year-long projects. These programs will be linked through the development of an online community to provide support, networking and guidance to alumni, as they continue pursuing their goals beyond these programs.