This Faculty Early Career Development (CAREER) grant will study the evolutionary dynamics of cancer. Cancer is thought to arise from a multi-step evolutionary process that transforms normal cells into highly motile cells with unchecked ability to proliferate and avoid programmed cell death signals. In the proposed work, we aim to use evolutionary principles to develop mathematically tractable, parametrized and validated stochastic models of several important processes during carcinogenesis and treatment. One important process in the evolution of cancer is the dissemination of tumor cells from the primary site to distant sites, i.e., metastasis. An important aspect of this grant is the study of anti-cancer treatment policies that minimize the risk of large metastatic burden. Another important process in cancer evolution is the recurrence of the disease following treatment. This work will also study the evolutionary dynamics of cancer recurrence following treatment. Of particular importance, are scenarios where cancers recur abnormally far away from their initial site of diagnosis. A common theme throughout this work is the mathematical study of rare events, where the evolution of the cancer cells behaves differently than expected. Courses will be developed at the undergraduate levels that introduce the use of operations research methodologies in medicine. In addition, there will be several opportunities to involve undergraduates in the research aspects of the project through research experiences for undergraduates (REU). Furthermore, classes will be developed at the graduate level that study the use of stochastic models and optimization in the treatment of cancer.
The work in this grant will introduce a number of new problems in the field of stochastic modeling and rare event simulation for stochastic particle systems. These types of processes have been used to model many biological processes at a variety of scales, from bacterial biofilms and tumor growth to migrating animal populations. Within these systems, rare stochastic events often drive important changes that lead to major evolutionary change. However, rare event simulation techniques for these types of models are largely undeveloped. The proposed work will establish new limit theorems for rare events in stochastic particle systems and develop new importance sampling algorithms for the estimation of their probabilities. Thus, this work makes advances to the field of rare event analysis and simulation. This work will benefit the biology and theoretical biology communities by providing tools to analyze biologically important rare events in similar models of other systems.
