Durham, North Carolina, and University Park, Pennsylvania, November 22, 2023 — With Alzheimer’s disease expected to afflict 12.7 million Americans by 2050, researchers at Penn State University and Duke University Medical Center are advancing our understanding of the disease’s behavior in different people – making personalized, optimized treatment possible for the first time. And they’re doing it with math.

Their discovery – featured in SIAM News, a publication of Society for Industrial and Applied Mathematics (SIAM) – relies on a first-of-its-kind causal math model to accurately depict disease progression in individual patients, including the age at which the disease will present and the best course of treatment. According to the math, the disease onset and rate of progression varies on a case by case basis, meaning that some patients will be more likely to benefit from certain therapies than others.

“When you have enough data to draw from, it’s possible to simulate diseases on a computer with a very high degree of accuracy,” said Wenrui Hao, Associate Professor of Mathematics at Penn State University. “We’re at a point now where we can use this math to reliably suggest personalized, optimized regimens for Alzheimer’s disease, and that’s incredibly exciting.”


Wenrui Hao, Associate Professor of Mathematics at Penn State University

Hao is collaborating with Jeffrey Petrella – Professor of Radiology and Director of the Alzheimer Disease Imaging Research Lab at Duke University Medical Center – to advance the model, with funding from the National Science Foundation’s Mathematical Biology Program.

Jeffrey Petrella – Professor of Radiology and Director of the Alzheimer Disease Imaging Research Lab at Duke University Medical Center

The team’s model relies on clinical biomarkers for Alzheimer’s disease, including fluid markers for the amyloid protein that is responsible for plaque buildup in the brain, cognitive decline scores from pencil-and-paper testing, and MRI brain images. By using comprehensive, publicly-available data from the Alzheimer’s Disease Neuroimaging Initiative in the model, the researchers map individual disease progression simply by adjusting different biomarker parameters to match the real-world data – ultimately achieving a high degree of accuracy.

Petrella noted that the simulation’s biggest benefit is that it provides an unprecedented view of the disease’s complexity by removing the “black box” approach of other predictive tools and replacing it with a well-trained model that, in principle, can be informed by accumulated knowledge based on more than 100 years of prior research in the Alzheimer’s field.

“This model makes predictions from a place of understanding, telling us not only whether a patient is likely to develop the disease within five years, but here’s why and here’s what’s actually going on in their brain to explain that,” he said. “The most important benefit is that we now have an accurate model that we can use to perform virtual experiments with different types of interventions, quickly and digitally.”

Petrella first reached out to Hao in 2017 after discovering Hao’s original Alzheimer’s disease modeling research paper through a Google search. He’d always dreamed of combining math with medicine to help cure disease and was immediately impressed by Hao’s work. “I remember thinking ‘Wow! I wonder if we can combine models like this with real data to make predictions in actual patients,’” Petrella recalled.

Hao’s breakthrough approach applies a unique parameter estimation algorithm to ‘peel back’ the layers of disease trajectory and yield an initial condition. In this way, he can calibrate his model and introduce a disease progression score that explains the variations in disease onset for each patient.

“One patient may start off with a high risk of disease at 60 and develop Alzheimer’s five years later, whereas another patient aged 65 might take 10 years to develop symptoms,” he said. The model accounts for those disparities mathematically – allowing researchers to analyze the way in which different drug therapies work for different patients – and then predicts the outcome.

Earlier this year, the researchers and their collaborator, Suzanne Lenhart, Chancellor's Professor of Mathematics and Cox Professor at the University of Tennessee Knoxville, completed two in silico drug trials that used publicly available data to test a recently FDA-approved therapy, Aduhelm, an anti-amyloid therapy that removes plaque in the brain, as well as another similar drug in the pipeline, shown to slow the rate of cognitive decline. By simulating the drug’s performance in individual patients, they rapidly modeled the outcome of short-term (78 weeks) and long-term (10 years) treatments and discovered that when treatment begins by age 60, it’s possible to reduce cognitive decline by five percent. These findings closely matched the results of the corresponding real-life clinical trials.

Petrella explained that the benefits of the model are twofold. First, it paves the way toward personalized treatments of Alzheimer’s disease by serving as an expert assistant that helps a treating physician determine the best drug combination, dosage and regimen for each patient. Second, it provides pharmaceutical companies with a means of rapidly testing multiple drug therapies and patient scenarios. Using carefully selected ‘digital patients’ in place of humans, practitioners can run trials in minutes instead of years, increasing the rapidity with which drugs reach the market and markedly decreasing the cost of development, which can exceed a $1 billion for a single agent.

“The complexity of this disease is so high that it’s beyond any human’s intuition to be able to predict individual disease trajectories, whereas the model can integrate all known relationships and interactions and simulate an outcome,” said Petrella, who is excited about the model’s potential to transform clinical practice in the near future.

“Right now, the debate in the field is whether we keep patients on drugs like Aduhelm in perpetuity for their lifetime, or take them off once their brain is cleared of plaque,” he said. “With these in-silico simulations, we can model different scenarios in different patients to know what’s best for them. It reduces the guesswork.”

The researchers expect their model will be ready for use in a clinical setting within five years. To further refine it in the meantime, they are currently looking to collaborate with pharmaceutical companies to access more detailed patient data that pertains to individual biomarker trajectories. In the future, the model could also be applied to study other inflammatory diseases such as lupus, multiple sclerosis, and chronic pancreatitis, Hao said.

About Society for Industrial and Applied Mathematics (www.siam.org)
Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of 14,000 individual, academic and corporate members from 85 countries. SIAM helps build cooperation between mathematics and the worlds of science and technology to solve real-world problems through publications, conferences, and communities like chapters, sections and activity groups. Learn more at siam.org.