Spring 2015
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: February 6, 2015
Speaker: Suncica Canic,
Cullen Distinguished Professor, Department of Mathematics,
University of Houston
Title: "Mathematical Methods for Cardiovascular Treatment"
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 examples where such a synergy led to novel results both in mathematics and in medical treatment. The focus will be on various fluid-structure interaction problems between blood flow and cardiovascular tissue. The cardiovascular applications motivating this research are related to the diagnosis and treatment of regurgitant heart valves, and the interaction between blood flow and arterial walls treated with vascular devices called stents. Stent is a mesh-like tube inserted into a vascular channel (i.e. coronary artery) to prop the arterial wall open and improve vascular flow. These problems were brought to our attention by our medical colaborators at the Texas Medical Center in Houston.
Mathematically, the focus is on the development of the mathematical theory and numerical simulations for fluid-structure interaction (FSI) problems with composite structures. No mathematical results exist so far that analyze solutions to fluid-structure interaction problems with composite structures. A composite structure in our application is the arterial wall, which consists of several layers, each with different mechanical characteristics and thickness. Additionally, arterial wall may hold a stent. This (stented) arterial wall interacts with blood flow, and gives rise to a nonlinear, fluid-composite structure interaction problem. In this talk we will discuss a recently developed partitioned numerical scheme and the mathematical well-posedness theory to study solutions of this class of nonlinear moving-boundary problems. Our theoretical results uncovered a new regularizng mechanism for this class of FSI problems: a thin fluid-structure interface with mass regularizes the dynamics of fluid-composite structure interaction. Numerical results motivated by the above-mentioned medical applications will be shown.
Collaborators include: M. Bukac (Notre Dame), B. Muha (U of Zagreb), Dr. S. Little and M. Jackson (The Methodist Hospital in Houston). Stent in Artery