Using Mathematics to Study Cancer and Much More

Laura Beaudin '07, Mathematics major, and
Dr. Joanna Ellis-Monaghan, Associate Professor of Mathematics
Dr. Greta Pangborn, Assistant Professor of Computer Science

Senior Laura Beaudin knew she could have spent the summer of 2006 working a “boring” job, but instead decided to pursue a research project. “It would challenge me intellectually and help me use what I learned throughout the year,” she said.

Supported by a grant from the Vermont Genetics Network, Beaudin studied the Potts Model, a mathematical model that is used to predict what’s going to happen in a given complex system. Beaudin perused research materials on the topic and produced a paper that provides an in-depth look at the crunching of the numbers used in the model’s application.

Potts Model“A lot of people allude to the mathematics [of the model], but don’t give them, so I wanted to give some concrete applications,” Beaudin said.

In addition to a careful development of the mathematical details of the model, Beaudin researched Potts Model applications in a variety of fields. For example, Beaudin analyzed a documented tumor simulation to explain how the Potts Model can be used to determine the likelihood of tumor growth, and the spread of cancer, in actual cases. This can be done through calculating the probabilities of different cells becoming infected, depending on various internal and external factors, Beaudin said.  She also explained the mathematics of the Potts Model in relation to human demographic interactions as well as it application to foam flows used in firefighting.   

Beaudin has been presenting her findings at conferences. Dr. Joanna Ellis-Monaghan, assistant professor of mathematics and one of Beaudin’s research advisors, said that the field of mathematics involving the application of the Potts Model is rapidly developing. “Laura’s work really contributes to an understanding of the mathematics that drive these models,” she said.

Her research experience has persuaded Beaudin to continue studying mathematics at the graduate school level.

“To know that I can use mathematics to make a difference is a powerful thing for me,” Beaudin said.