CAREER: Branching Processes on Graphs Inform Early Detection of Colorectal Cancer

在美国，结直肠癌是癌症死亡的第二大常见原因，在转移扩散之前及早发现，对于降低结直肠癌死亡率至关重要。分析血液样本中的无细胞DNA是早期非侵入性检测癌症的一条有希望的途径，因为癌症患者的无细胞DNA通常含有携带肿瘤特异性突变的DNA片段。这项研究的目的是通过分析患者血液样本中的无细胞DNA，为早期发现结直肠癌提供最佳策略。这将通过开发结直肠癌演变过程中无细胞DNA脱落的新的数学和计算模型来实现，并使用它们来评估早期检测的不同策略。这项工作背后的一个共同的数学主题将是研究图形上的随机演化。将这项研究纳入本科生和研究生的应用数学课程，将使学生接触到数学生物学的最新研究课题。此外，还将开发一本互动教科书，让学生和研究人员亲身体验癌症的数学模型。此外，还将组织一系列关于癌症数学建模的现场直播虚拟研讨会，包括研究生、博士后研究员和教师在内的不同演讲者，并向世界各地的公众提供录音。这一职业奖将研究图表上的分支过程，并将其应用于结直肠癌的早期发现问题。具体地说，它将开发一种概率方法，用于研究图形上分支过程的有限时间特性，建立结直肠癌进化过程中无细胞DNA脱落的随机模型，以及评估无细胞DNA策略以早期发现结直肠癌的计算方法。这项工作中开发的数学框架将适用于应用概率、进化、流行病建模和微生物疗法抗药性等领域，以及癌症研究。该项目由DMS的数学生物学计划和CBET的生物医学系统工程计划联合支持。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Colorectal cancer is the second most common cause of cancer deaths in the US, and early detection, before metastatic dissemination, is critical for reducing colorectal cancer mortality. Analysis of cell-free DNA from blood samples is a promising avenue for early non-invasive detection of cancer, as cell-free DNA from patients with cancer often contains DNA fragments carrying tumor-specific mutations. The goal of this research is to inform optimal strategies for early detection of colorectal cancer using analysis of cell-free DNA from patient blood samples. This will be achieved through developing novel mathematical and computational models of cell-free DNA shedding during colorectal tumor evolution, and using them for evaluating diverse strategies for early detection. A common mathematical theme underlying this work will be the study of stochastic evolution on graphs. Incorporating this research into the undergraduate and graduate applied mathematics curriculum will result in students’ exposure to the most recent research topics in mathematical biology. In addition, an interactive textbook will be developed, allowing students and researchers hands-on experience with mathematical models of cancer. Furthermore, a live-streamed virtual seminar series on mathematical modeling of cancer will be organized, featuring diverse speakers including graduate students, postdoctoral fellows and faculty, with recordings accessible to the world-wide public.This CAREER award will investigate branching processes on graphs and apply them to the problem of early detection of colorectal cancer. Specifically, it will develop a probabilistic methodology for the study of finite time properties of branching processes on graphs, a stochastic model of cell-free DNA shedding during colorectal tumor evolution, as well as computational methodology for evaluating cell-free DNA strategies for early detection of colorectal cancer. The mathematical frameworks developed in this work will be applicable to the fields of applied probability, evolution, modeling of epidemics and resistance to microbial therapies, in addition to the study of cancer.The project is supported jointly by the Math Biology program in DMS and the Engineering of Biomedical Systems program in CBET.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.