Department of Biomedical Engineering
January 29, 2013
Computational Modeling of Vascular Adaptation: Applications from Aneurysms and Tissue Engineering
Phenomenological models of the mechanical behavior of the arterial wall continue to play important roles in vascular mechanics. Indeed, such models revealed the importance of residual stresses in homogenizing the transmural distribution of stress in normalcy, which in turn led to one of the most important hypotheses in vascular mechanobiology – the existence of a mechanical homeostasis. Nevertheless, classical models are not able to exploit the rapidly increasing information on the different mechanical properties and rates and extents of turnover of different structurally significant constituents within the arterial wall. To address this need, we have proposed a structurally-motivated, materially nonuniform model of the arterial wall based on a theory of constrained mixtures. Key features of this model include the ability to prescribe individual stored energy functions for different structurally significant constituents that are constrained to move together within the overall wall while being allowed to possess individual evolving natural (stress-free) configurations, and the ability to prescribe separate stress-mediated constitutive relations for constituent production and removal. Such models promise to provide increased insight into diverse problems in vascular biology and surgery, including rational design of tissue engineered grafts, understanding better the progression of diseases, designing surgical procedures, and predicting long-term responses of vessels to implanted devices.