blood vessel adaptation with fluctuations in capillary flow distribution血管适应波动在毛细管流动分布.pdfVIP

Blood Vessel Adaptation with Fluctuations in Capillary Flow Distribution 1 2,3 4 Dan Hu *, David Cai , Aaditya V. Rangan 1 Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China, 2 Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China, 3 Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York, United States of America, 4 Courant Institute of Mathematical Sciences, New York University, New York, New York, United States of America Abstract Throughout the life of animals and human beings, blood vessel systems are continuously adapting their structures – the diameter of vessel lumina, the thickness of vessel walls, and the number of micro-vessels – to meet the changing metabolic demand of the tissue. The competition between an ever decreasing tendency of luminal diameters and an increasing stimulus from the wall shear stress plays a key role in the adaptation of luminal diameters. However, it has been shown in previous studies that the adaptation dynamics based only on these two effects is unstable. In this work, we propose a minimal adaptation model of vessel luminal diameters, in which we take into account the effects of metabolic flow regulation in addition to wall shear stresses and the decreasing tendency of luminal diameters. In particular, we study the role, in the adaptation process, of fluctuations in capillary flow distribution which is an important means of metabolic flow regulation. The fluctuation in the flow of a capillary group is idealized as a switch between two states, i.e., an open-state and a close-state. Using this m