Research by the numbers: math students at Centre contribute to lung disease research
Though they don’t work in a laboratory or collect samples from the field, mathematics students at Centre College are still making important strides in lung disease research. This summer Chang He ’16 and Matt McCurdy ’15 have been working with Assistant Professor of Mathematics Ellen Swanson to model mathematically the movement of fluid in the lungs—specifically, when driven by surfactant.
Surfactant is a viscous substance found naturally in the lungs that keeps the alveoli from collapsing by reducing surface tension. He and McCurdy have been solving equations that model the movement of surfactant over a thin layer of fluid.
“Understanding how fluid moves within the lung is pertinent to developing more effective treatments for diseases such as cystic fibrosis,” explains Swanson (pictured below, far right).
The team anticipates that their models will be used in future medical research to test medications that use surfactant’s ability to spread fluids outward in order to coat a larger region of the lung.
To advance the real-world applications of their findings, Swanson, He and McCurdy are also in collaboration with a team of researchers at Harvey Mudd College, led by Associate Professor of Mathematics Rachel Levy. While Swanson’s students are mathematically modeling the movement of surfactant over a horizontal surface or on an incline, Levy’s team is physically testing these movements with experiments.
“Soon we will be able to compare our numerical solutions to what Levy’s team is seeing experimentally,” says Swanson.
He and McCurdy have been tackling partial differential equations for these models, which include derivatives with respect to both space and time, and by writing a computer program that approximately solves the equations, they have been able to generate and graph solutions.
Though their work is challenging, He and McCurdy agree that their prior math coursework at Centre has amply prepared them for this research.
Yet for He, charting unknown territory is much different and more exhilarating than a normal math class.
“In class, we’re given a problem and asked to solve it,” she says. “But right now we have to solve problems on our own. There is no answer until I find it.”
One of Swanson’s primary goals for the student researchers has been to foster this sense of ownership of their work.
“I want them to experience the feeling of accomplishment when they figure something out that nobody else in the world knows,” she says. “They are becoming experts.”
But becoming an expert in anything takes perseverance, according to McCurdy.
“Hitting sticking points is something I’ve learned to deal with,” he explains. “The first couple of weeks I was making so much progress, but I’ve gotten stuck since then.”
“For research, the most important thing to have is tenacity,” agrees He.
Swanson believes the joys and frustrations of research are all part of the experience.
“They are also developing problem-solving skills,” she adds. “Even if they’re stuck, they can figure out things to test and question. I’m definitely seeing them do it.”
McCurdy, a mathematics major, and He, a mathematics and economics double major, both plan to attend graduate school and are confident this intensive research experience will pay off.
“We both would have been doing math this summer, but it wouldn’t have been at this caliber,” says McCurdy.
by Caitlan Cole
July 22, 2014