Biomedical Engineering and Bioengineering Commons^™

Stability Of A Microvessel Subject To Structural Adaptation Of Diameter And Wall Thickness, Alisha Sarang-Sieminski, John Geddes, Ilari Shafer, Rachel Nancollas, Morgan Boes

John B. Geddes

Vascular adaptation—or structural changes of microvessels in response to physical and metabolic stresses—can influence physiological processes like angiogenesis and hypertension. To better understand the influence of these stresses on adaptation, Pries et al. (1998, 2001a,b, 2005) have developed a computational model for microvascular adaptation. Here, we reformulate this model in a way that is conducive to a dynamical systems analysis. Using th ese analytic methods, we determine the equilibrium geometries of a single vessel under different conditions and classify its type of stability. We demonstrate that our closed-form solution for vessel geometry exhibits the same regions of stability as the …