| Abstract:
Mathematical modeling, analysis and numerical simulation, combined with imaging and experimental validation, provide a powerful tool for studying various cardiovascular phenomena. This talk will address a couple of examples where such a synergy led to novel results. The first example concerns modeling of global properties of complex, multi-component structures, such as tissue-scaffolds, carbon nano-tubes, or endovascular stents, using mathematical theory of nonlinear hyperbolic nets. Our computational studies, motivated by the questions posed to us by cardiologists at the Texas Heart Institute, provided a novel insight into the mechanical properties of currently available coronary stents on the US market, and suggested optimal stent design for a novel application of stents in trans-catheter aortic valve replacement. The second example concerns a mathematical study of fluid-structure interaction in blood flow. Our novel computational method allows, for the first time, to capture longitudinal displacement and multi-layered structure of arterial walls and their interaction with pulsatile blood flow. As a result, we have been able to capture the recently observed large longitudinal displacements in high adrenaline stages of cardiac cycle, giving rise to the presence of substantial shear stress within the vessel wall. ?The role of these unexplored phenomena is unknown. This opens up a new field within cardiovascular research, revealing a previously unknown mechanism in the circulatory system.? (Ahlgren et al., Clin Phys Funct Imaging, 2009).
Results of the research presented in this talk were obtained in collaboration with: Dr. D. Paniagua (Texas Heart Institute), Dr. S. Little (Methodist Hospital, Houston), Prof. J. Tambaca (University of Zagreb, Croatia), Profs. A. Quaini and R. Glowinski (University of Houston), and PhD students M. Bukac, S. Mabuza, M. Kosor, and T. Kim.
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