Clamps. Scalpel. Sutures. Graphing calculator.
While research mathematicians may not be of much use in the operating room, they can be quite useful for increasing our understanding of the body and how it functions.
Mathematics associate professor Grady Wright is co-principal investigator on an interdisciplinary mathematical biology grant from the Division of Mathematical Sciences (DMS) at the NSF to study “Chemically-active Viscoelastic Mixture Models in Physiology: Formulation, Analysis, and Computation.” The award is part of the DMS Focused Research Group (FRG) program.
Other applied mathematicians and math biologists on the research team are from the University of Utah, University of California-Davis, and the Florida Institute of Technology. The total award is $1.1 million over three years, and Boise State will receive about $107,000 directly through an individual award to support undergraduate student research, summer salary, travel, and some modest computational equipment purchases.
Wright and collaborators will use mathematical and computational models to provide researchers with a better understanding of certain biological processes in the human body where viscoelastic fluid mixtures play a fundamental role. Viscoelastic fluids behave both like viscous fluids, where resistance to flow is governed by “internal friction” (think honey), and elastic materials , where there is some “memory” of a previous state (think stretched rubber band).
Human bodies are full of viscoelastic fluids, such as mucus, which line the lungs and stomach wall, cytoplasm in cells, and even blood. Pathologies in these basic components of the body are at the root of a variety of serious health problems. One example is cystic fibrosis, which involves a thick mucus layer in the lungs.
“Viscoelastic fluids found in the body are difficult to study experimentally,” Wright said. “The problem is that the behavior of these fluids can change rapidly and dramatically in response to external and internal stimuli, such as stresses or chemical activity, that are hard to recreate in vitro or experiment on in vivo. Mathematical modeling and simulation of these processes provide a powerful, cheap and harmless way to understand the dynamics, mechanics and function of these fluids.”
The project also will study cellular locomotion via blebbing (the process by where a cell forms a nodule and then shoots out a stream of its cytoplasm into the nodule), the dynamics of blood clot formation and its role in cerebral aneurysms, and mechanisms for protein trafficking and sorting by the Golgi Apparatus (pictured above).
While the biology of these processes differ quite dramatically, each involves a complex viscoelastic material mixture whose behavior is determined by the dynamic interplay of mechanics, flow, physical structure and chemistry. Through the use of sophisticated mathematical modeling, analysis and numerical simulation, researchers hope to get a clearer picture of how all of this works together.
“This is the beauty of mathematics,” said Wright. “These seem like disparate topics but in the end they can be linked by mathematical models.”
The project also involves a unique collaboration with experimentalists from the University of North Carolina School of Medicine, University of Washington School of Medicine, University of Pennsylvania School of Medicine, Colorado School of Mines, and the Max Planck Institute of Molecular Cell Biology and Genetics. The findings from the mathematical modeling and simulation will both be tested with what is known experimentally, and will be used to help guide future experiments.
This material is based upon work supported by the National Science Foundation under Grant No. DMS-1160379. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.