Mathematics offers new clues in the fight against Alzheimer's

Mathematics may not be the first thing people associate with Alzheimer's disease research. But for Pedro Maia, an assistant professor of mathematics and data science at The University of Texas at Arlington, analyzing how different parts of the brain interact like a network is revealing new insights into one of the world's most devastating brain disorders.

Dr. Maia's latest breakthrough-developed in collaboration with colleagues at the University of California–San Francisco's Raj Lab-uses advanced mathematical modeling to help explain why Alzheimer's disease spreads unevenly through the brain. Their work reveals why certain brain regions are more vulnerable to damage from tau, a protein that accumulates in brain cells and disrupts their normal function, while other areas remain more resilient.

The study was recently published in Brain, a leading journal in clinical neurology.

What's interesting, is how mathematics, data methods and data science, and mathematical modeling can actually bring some advanced insights into Alzheimer's disease."

Dr. Pedro Maia, assistant professor of mathematics and data science, The University of Texas at Arlington

Maia and his UCSF colleagues created a mathematical tool-called an extended network diffusion model-that tracks how tau protein builds up and spreads through the brain's network of interconnected regions. Using this model, researchers can classify genes into four categories: those that follow the brain's network patterns and increase vulnerability; those that follow the patterns and provide protection; those that act independently but raise risk; and those that act independently and help protect the brain.

It's a significant step in advancing Alzheimer's research, helping to answer a question that has baffled researchers for years: Why do some brain regions deteriorate rapidly while others remain largely intact?

The model, as Maia said, "helps us untangle what was previously just a messy bag of genes."

"The idea is that the brain isn't uniform-different regions are made up of different kinds of cells and genes, and they're connected differently too," he continued. "Regions that are more connected or closer to affected areas are more vulnerable. Isolated regions tend to be more resilient."

The study used data from 196 people. Of those participants, 102 had been diagnosed with early-stage mild cognitive impairment, 47 with late-stage mild impairment and 47 with Alzheimer's disease. Previous research by Maia and his colleagues relied on more controlled studies using rodent models.

"Human data, even though it is more challenging to work with given the variables involved, gives us direct insight into how Alzheimer's progresses in real people," Maia said. "If we want to develop treatments that work in humans, we need data that comes from humans."

In Texas, nearly half a million people live with Alzheimer's disease as the state ranks fourth in the nation for Alzheimer's cases and second in Alzheimer's-related deaths. That results in an estimated $24 billion expense for the state annually, according to the Texas Department of State Health Services.

For Maia, applying his mathematics background to Alzheimer's research has been especially rewarding. He sees it as part of a broader shift in how the field of mathematics is evolving.

"In the past century, physics was the big inspiration for mathematical research," he said. "Today, biology-especially the brain-is becoming the big source of inspiration. If you're willing to chat in multidisciplinary settings, you'll see that math modeling still has a big role to play."