Understanding stochasticity in cancer recurrence timing

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Mutation-induced drug resistance represents a major obstacle in cancer treatment and often causes the failure of therapies and tumor recurrence. The time at which cancer recurrence occurs (i.e., survival benefit of therapy) is governed by a complex balance between many factors such as initial tumor size, mutation rates, the type/number of resistance mechanisms, and drug efficacy and schedule. This research aims to develop a comprehensive mathematical understanding of how these factors conspire to control the temporal dynamics of the evolutionary processes driving cancer recurrence, using branching process models of tumor growth. The first part of the work will focus on developing a detailed understanding of the temporal dynamics of cancer recurrence, under the basic assumptions that tumor cell populations are ?well-mixed? in a constant selective environment. The analysis will characterize both mean dynamics and fluctuations in the system due to both demographic stochasticity and random mutational fitness changes. In the second part of the work, the investigators will relax these basic assumptions to quantify and compare the effects of additional factors that may significantly impact recurrence dynamics. These additional factors include temporally varying selective environments, spatial structure and inhomogeneity, and hierarchical population structure. All of these investigations will be performed using stochastic process models of escape from extinction, and both analytical and computational tools will be utilized to study recurrence dynamics. This research will lead to a better understanding of the mechanisms driving variability in patterns of cancer progression following acquired resistance to treatment. The results can eventually aid in the development of better statistical tools for prognosis, evaluating drug efficacy, and improving treatment strategies. For example, an understanding of how the timing of cancer recurrence reveals information about the composition or prior genetic history of the tumor can aid in determining optimal treatment strategies post-recurrence. In addition, this project will contribute to a general mathematical understanding of the dynamics of escape from population extinction. Thus, the theory developed will be broadly applicable, with minimal extension, to understanding similar issues in evolution, health (e.g. bacterial and viral drug resistance), and ecology. This project will support for trainees at the undergraduate, graduate and postdoctoral levels in research at the interface of mathematics, biology, and medicine.