Graduate student Kristin Swanson has always been intrigued by mathematics. And she's been determined to use her math skills to benefit others. No problem there: her current research project may lead to more effective treatment of brain tumors.

	Kristin Swanson's mathematical models help predict the spread of certain brain tumors, which may lead to more effective treatments. Photo by Mary Levin.

Swanson, a student in applied mathematics, has been studying gliomas--a type of brain cancer that lacks well-defined boundaries, making treatment particularly difficult. Her project has been to create a computer model that can predict how glioblastoma multiforme, which Swanson describes as "a worst case scenario of a glioma," grows and spreads in the brain. Her hope is that the model will eventually serve as a guide for treatment.

"We usually think of tumors as solid, like a fist," explains Swanson. "But gliomas are never fists. They are diffuse. The tumor cells get up and run around." There is usually an area of high concentration that is visible with a CT scan, says Swanson, but the tumor cells that travel to other areas of the brain--individually or in small concentrations--go undetected. That means that removal of the visible tumor and the surrounding area will not eradicate all the cancer. After surgery, the remaining tumor cells develop into a ring of new tumors encircling the area that has been removed.

"It's somewhat like a forest fire that spreads out in a circular pattern," says Swanson. "Firefighters don't go to the point of origin to stop it, but rather they try to get in front of it and stop it at the outside edges. The same idea holds for gliomas. The goal is to surround and capture them."

Easier said than done when many of the tumor cells are not visible with current technology. That's where Swanson's computer model comes in. Working closely with Dr. Ellsworth Alvord, head of neuropathology at University Medical Center, and Applied Mathematics Professor James Murray, Swanson has created a mathematical model of the brain that predicts where a glioma visible on a CT scan is likely to have migrated and grown. The model considers multiple factors, including the location of grey and white matter in the brain. (It turns out that gliomas migrate more slowly in grey matter, where neurons are located, than in white matter, the site of neurons' long axon tails.)

"First we did simulations with rat brains, watching how this type of cancer spreads in white and grey matter," says Swanson. "Then we used a database, recently created at McGill University, that defines where white and grey matter are in the human brain. With this information, plus information from old CT scans of glioma patients, we were able to develop detailed estimates of diffusion and growth."

Using the mathematical model, physicians can place a tumor anywhere in the "virtual" human brain and predict the tumor's path and response to treatment. The model has been quite accurate, based on comparisons with CT scans of past glioma patients taken at various intervals. The next step is a clinical trial that will use Swanson's mathematical model to suggest treatment options for current patients.

"We are not thinking that we can eliminate all of the tumor, given the present technology," admits Swanson. "With this type of cancer, there are likely to be some cancer cells remaining no matter what you do. But our hope is that enough of the cancer can be removed that the body itself can do some 'self help' and attack the diffuse individual cells that remain. Our hope is that it will allow patients to live longer and better lives."

[Summer 1999 - Table of Contents]