Title: Mathematical Methods for Cardiovascular Treatment

Suncica Canic, Cullen Distinguished Professor, Director, Center for
Mathematical Biosciences, Department of Mathematics, University of
Houston

Abstract:
Mathematical modeling, analysis and numerical simulation, combined
with imaging and experimental validation, provide a powerful tool for
studying various aspects of cardiovascular treatment and diagnosis.
This talk will address two examples where such a synergy led to novel
results. The first example concerns a mathematical study of
fluid-structure interaction (FSI) in blood flow with clinical
application to 2D and 3D Doppler assessment of mitral regurgitation
(MR). Our computational studies, performed in collaboration with
several experts in echocardiography, addressed current imaging
challenges in Doppler assessment of MR, which led to refinement and
reinforcement of the emerging 3D echocardiographic applications. The
second example concerns a novel dimension reduction/multi-scale
approach to modeling of endovascular stents as 3D meshes of 1D curved
rods forming a 3D network of 1D hyperbolic conservation laws. Our
computational studies, motivated by the questions posed to us by
cardiologists at the Texas Heart Institute, provided novel insight
into the mechanical properties of 4 currently available coronary
stents on the US market, and suggested optimal stent design for a
novel application of stents in transcatheter aortic valve replacement.
The applications discussed above gave rise to new mathematical
problems whose solutions required a development of sophisticated
mathematical ideas. They include a design of a novel unconditionally
stable, loosely coupled partitioned scheme for numerical simulation of
solutions to FSI in blood flow, and the development of the theory and
numerics for nonlinear hyperbolic nets and networks arising in
dimension reduction of the stent problem. An overview of the basic
mathematical ideas associated with this research, and application to
the two related problems in cardiovascular diagnosis and treatment,
will be presented. This talk will be accessible to a wide scientific
audience.

Speaker Bio: Suncica Canic earned her Ph.D. in 1992 in the area of
nonlinear hyperbolic conservation laws from the Department of Applied
Mathematics and Statistics at SUNY Stony Brook. Upon her move to the
University of Houston in 1999, she began collaborating with various
medical specialists at the Texas Medical Center in Houston on problems
related to cardiovascular treatment and diagnosis. Canic is the
founder of the Center for Mathematical Biosciences at the University
of Houston, which fosters interdisciplinary research at the interface
between mathematics, engineering, biology, and medicine. She was
honored for her research by the National Science Foundation as
Distinguished MPS Lecturer in 2007, and received the US Congressional
Recognition for Top Women In Technology in 2006. Her research received
local and national media attention, and was featured in several
publications by NSF, NIH, and AMS. In December 2011 she gave a
Congressional Briefing on Capitol Hill discussing the importance of
mathematics in real-world problems.