Mathematical Modeling Offers New Insights into Alzheimer’s Disease Progression
A groundbreaking study leveraging advanced mathematics and data science is shedding light on the uneven spread of Alzheimer’s disease through the brain, potentially paving the way for more targeted treatments.
Mathematics may not be the first discipline that comes to mind when considering Alzheimer’s research, but for Dr. Pedro Maia, an assistant professor of mathematics and data science at The University of Texas at Arlington, analyzing the brain as a complex network is proving remarkably insightful. His latest work, developed in collaboration with researchers at the University of California–San Francisco’s Raj Lab, utilizes sophisticated mathematical modeling to explain why certain brain regions are more susceptible to damage from tau, a protein that disrupts normal brain cell function, while others demonstrate resilience.
The research, recently published in the prestigious journal Brain, represents a significant step forward in understanding this devastating neurological disorder. As one researcher explained, “What’s interesting is how mathematics, data methods and data science, and mathematical modeling can actually bring some advanced insights into Alzheimer’s disease.”
Untangling the Genetic Complexity of Alzheimer’s
Dr. Maia and his team created an extended network diffusion model – a mathematical tool that tracks the buildup and spread of tau protein throughout the brain’s interconnected regions. This model allows researchers to categorize genes into four distinct groups: those that amplify vulnerability based on brain network patterns, those that offer protection while following those same patterns, those that independently increase risk, and those that independently provide a protective effect.
This approach is helping to answer a long-standing question in Alzheimer’s research: why do some areas of the brain deteriorate rapidly while others remain relatively intact? According to Dr. Maia, the model “helps us untangle what was previously just a messy bag of genes.”
The core principle, he elaborated, is that the brain is not a homogenous structure. “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 said. “Regions that are more connected or closer to affected areas are more vulnerable. Isolated regions tend to be more resilient.”
Human Data Drives New Understanding
The study analyzed data from 196 participants, including 102 individuals with early-stage mild cognitive impairment, 47 with late-stage mild impairment, and 47 diagnosed with Alzheimer’s disease. This represents a shift from previous research by Dr. Maia and his colleagues, which primarily relied on controlled studies using animal 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,” Dr. Maia stated. “If we want to develop treatments that work in humans, we need data that comes from humans.”
The implications of this research are particularly poignant for states like Texas, which currently ranks fourth nationally in the number of Alzheimer’s cases – nearly half a million people – and second in Alzheimer’s-related deaths. The economic burden on the state is estimated at $24 billion annually, according to the Texas Department of State Health Services.
A Broader Shift in Mathematical Research
For Dr. Maia, applying his mathematical expertise to Alzheimer’s research is deeply fulfilling. He views this work as part of a larger trend within the field of mathematics itself.
“In the past century, physics was the big inspiration for mathematical research,” he observed. “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.”
This interdisciplinary approach underscores the growing recognition that complex biological problems often require innovative mathematical solutions, offering renewed hope in the fight against Alzheimer’s disease.
Source: University of Texas at Arlington
Journal reference: Anand, C., et al. (2025). Selective vulnerability and resilience to Alzheimer’s disease tauopathy as a function of genes and the connectome. Brain. doi.org/10.1093/brain/awaf179.
