Understanding stochasticity in cancer recurrence timing

突变诱导的耐药性代表了癌症治疗的主要障碍，并且经常导致治疗失败和肿瘤复发。 癌症复发发生的时间（即，治疗的存活益处）由许多因素之间的复杂平衡控制，所述因素例如初始肿瘤大小、突变率、耐药机制的类型/数量以及药物功效和时间表。这项研究旨在利用肿瘤生长的分支过程模型，对这些因素如何合谋控制推动癌症复发的进化过程的时间动态进行全面的数学理解。 第一部分的工作将集中在发展一个详细的了解时间动态的癌症复发的基本假设下，肿瘤细胞群是？混合均匀？在一个不断选择的环境中。该分析将表征由于人口统计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。在研究的第二部分，研究人员将放宽这些基本假设，以量化和比较可能显著影响复发动态的其他因素的影响。这些额外的因素包括随时间变化的选择性环境，空间结构和不均匀性，以及层次种群结构。所有这些研究将使用逃避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dynamics.This研究将导致更好地理解的机制驱动的变化模式的癌症进展后获得性耐药治疗。 这些结果最终可以帮助开发更好的统计工具，用于预后，评估药物疗效和改善治疗策略。 例如，了解癌症复发的时间如何揭示有关肿瘤的组成或先前遗传史的信息，可以帮助确定复发后的最佳治疗策略。 此外，该项目将有助于从种群灭绝中逃逸的动力学的一般数学理解。 因此，开发的理论将广泛适用，以最小的扩展，以理解进化，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、研究生和博士后级别的受训人员在数学、生物学和医学的接口进行研究。

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.