Math Models Showing Potential for Medical Research

When combating diseases, researchers have looked for solutions through new practices, such as Florida Tech mathematical sciences associate professor Jian Du.

Du is part of two medical research initiatives backed by national research organizations. His National Science Foundation-funded grant, “Collaborative Research: Blood Clotting at the Extreme — Mathematical and Experimental Investigation of Platelet Deposition in Stenotic Arteries,” is a four-year grant worth $149,999.

In the research, mathematical and computational scientists and bioengineers are studying the fundamental biophysical and biochemical mechanisms underlying the formation of blood clots within constricted arteries – the blood clots responsible for most heart attacks and many strokes. Understanding how they can form under the extreme physical conditions found in a narrow artery may lead to new techniques for preventing them.

So far, recent experiments suggest the importance of clot structure and specific flow-sensitive proteins in allowing platelets to quickly clump together in stenotic, or narrowed, arteries. Based on these findings, Du and colleagues have developed a novel and sophisticated multiphase computational model for arterial clot formation (thrombosis). Now they are using a combination of computer simulations and experiments to investigate the roles of clot permeability, elasticity and flow-induced platelet binding kinetics, a process that happens when process of platelets cohering to each other to form a clot.

While modeling will help in the ultimate goal of clot prevention, it will initially allow researchers to streamline their focus.

“With a math model, we can easily turn on or turn off certain biochemical reactions or receptor-ligand bindings, whereas the experimental process could be rather difficult,” Du said. “So, our simulation results can help the biologists to understand how exactly the individual component works together to initiate the process of arterial thrombosis.”

Du’s other research initiative, the National Institutes of Health-funded “Modeling Gastric Mucus Layer Physiology,” is a four-year, $1.48 million grant consisting of researchers from the University of Utah, Boston University and Montana State University in addition to Florida Tech. The team will look at how the stomach’s gastric mucus layer is maintained and how it responds to infecting bacteria and to changes in arrangement and size in gastric tissues.

The goals are to understand how this system maintains steady conditions, understand how the infectious Helicobacter pylori bacteria survives the stomach’s harsh environment to reside in the thin tissue cells, and determine whether gastric organoids can accurately model gastric mucus layer physiology and pathology, possibly providing new insight into new research on protection methods.

Current research has given insight into how the bacteria may pierce the protective mucus.

“Because of the mechanical properties of the gastric mucus layer, you can imagine the bacterium would have a hard time to move through it.  It turns out that H. pylori uses a clever biochemical strategy to raise the local PH value,” Du said. “This process can dissolve the mucin polymer and transfer it from a viscoelastic solid to a viscous fluid. So now the environment is more friendly for the bacteria to pass and penetrate through the mucous layer of the inner lining of our stomach, which causes infections.”

For Du and other researchers using modeling to work towards medical solutions, the past decade has seen rapid development in the collaboration between mathematics and biology and how the disciplines work together.

“It used to be the case that people collaborate, and biologists come to this math group and give a talk, and math majors go to the biology department and give a talk, and then everyone would go do their own work,” Du said. “With the development of more advanced modern computers and more powerful numerical algorithms, computational simulations of very complicated biological programs are now feasible.”


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