Mathematical modeling of blood clotting and physiological gels. Computational Fluid Dynamics, Development of Numerical Methods for Partial Differential Equations.
- PhD, Mathematics, Courant Institute of Mathematical Science, New York University
I have been a faculty member at the University of Utah since 1986 after earning my Ph.D. at the Courant Institute of Mathematical Sciences of New York University and Postdocs at the University of California, Berkeley and the Courant Institute. I am a Professor of Mathematics, Adjunct Professor of Biomedical Engineering, and was Associate Dean for Research of the College of Science in the period 2014-17.
My mathematical interests are in modeling biological processes, fluid dynamics, and computational methods for partial differential equations. My research has focused on developing mathematical models (and appropriate numerical methods with which to study the model equations) of several important aspects of the blood clotting process. Clotting is an extremely complex process with physical, chemical, and cell biological components which is essential to maintaining the integrity of our circulatory system. When it malfunctions the consequences can be dire, including heart attack and stroke. Clotting is subject to intense research by laboratory and medical scientists but its complexity makes it very difficult to think through how it works or to make predictions about how well medical interventions to treat clotting problems will work.
That is where mathematics and the work I do comes in. Mathematics is ideally suited to describing and exploring complex, multi-faceted dynamic processes and to eliciting quantitiative information about them. Our modeling has led to a number of novel predictions of how clotting is regulated (which have subsequently been validated experimentally) and to the proposal of possible mechanisms underlying mysterious aspects of clotting observed experimentally. Very recently, we used one of our models to identify how normal variations in the amount of a specific protein in the blood could modify the liklihood of major bleeding episodes for severe hemophliacs. Others of our models are used by biomedical engineers to study dangerous clot formation in cardiovascular devices.
My research has been supported by the National Science Foundation and/or the National Institutes of Health continuously since 1982.