The linked article is for *SIAM News*, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

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## Mathematical Modeling Gains Days for Brain Cancer Patients

For *SIAM News*:

Glioblastoma, or glioblastoma multiforme, is a particularly aggressive and almost invariably fatal type of brain cancer. It is infamous for causing the deaths of U.S. Senators John McCain and Ted Kennedy, as well as former U.S. Vice President Joe Biden’s son Beau. Though glioblastoma is the second-most common type of brain tumor—affecting roughly three out of every 100,000 people—medicine has struggled to find effective remedies; the U.S. Food and Drug Administration has approved only four drugs and one device to counter the condition in 30 years of research. The median survival rate is less than two years, and only about five percent of all patients survive five years beyond the initial diagnosis.

Given these terrible odds, medical researchers strive for anything that can extend the effectiveness of treatment. The nature of glioblastoma itself is responsible for many obstacles; brain tumors are difficult to monitor noninvasively, making it challenging for physicians to determine the adequacy of a particular course of therapy.

Figure 1. Magnetic resonance imaging scan of the brain. Public domain image.

Kristin Rae Swanson and her colleagues at the Mayo Clinic believe that mathematical models can help improve patient outcomes. Using magnetic resonance imaging (MRI) data for calibration, they constructed the proliferation-invasion (PI) model — a simple deterministic equation to estimate how cancer cells divide and spread throughout the brain. Rather than pinpoint every cell’s location, the model aims to categorize the general behavior of each patient’s cancer to guide individualized treatment.