Understanding stochasticity in cancer recurrence timing

突变导致的耐药性是癌症治疗的主要障碍，经常导致治疗失败和肿瘤复发。癌症复发的时间(即治疗的生存益处)取决于许多因素之间的复杂平衡，如初始肿瘤大小、突变率、耐药机制的类型/数量以及药物疗效和方案。这项研究的目的是利用肿瘤生长的分支过程模型，对这些因素如何协同控制推动癌症复发的进化过程的时间动力学进行全面的数学理解。这项工作的第一部分将侧重于在肿瘤细胞群体混合良好的基本假设下，对癌症复发的时间动力学进行详细的理解。在一个不断选择的环境中。该分析将表征由于人口随机性和随机突变适应度变化而导致的系统中的平均动态和波动。在这项工作的第二部分，研究人员将放松这些基本假设，以量化和比较可能显著影响复发动力学的其他因素的影响。这些附加因素包括时间变化的选择性环境、空间结构和不均质性以及等级种群结构。所有这些研究都将使用逃脱灭绝的随机过程模型进行，并将利用分析和计算工具来研究复发动力学。这项研究将有助于更好地理解获得性耐药后癌症进展模式中驱动变异的机制。这些结果最终可以帮助开发更好的统计工具来预测预后、评估药物疗效和改进治疗策略。例如，了解癌症复发的时间如何揭示有关肿瘤成分或先前遗传史的信息，有助于确定复发后的最佳治疗策略。此外，该项目还将有助于从数学上对逃脱种群灭绝的动态进行一般的理解。因此，开发的理论将广泛适用于理解进化、健康(例如细菌和病毒耐药性)和生态学中的类似问题。该项目将支持本科生、研究生和博士后在数学、生物和医学方面的研究。

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.