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

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.