Rachev Alexander, Greenwald Stephen, Shazly Tarek
Biomedical Engineering Program, College of Engineering and Computing, University of South Carolina, Columbia, SC 29208, USA.
J Biomech Eng. 2013 Aug;135(8):81006. doi: 10.1115/1.4024664.
It is well-documented that the geometrical dimensions, the longitudinal stretch ratio in situ, certain structural mechanical descriptors such as compliance and pressure-diameter moduli, as well as the mass fractions of structural constituents, vary along the length of the descending aorta. The origins of and possible interrelations among these observed variations remain open questions. The central premise of this study is that having considered the variation of the deformed inner diameter, axial stretch ratio, and area compliance along the aorta to be governed by the systemic requirements for flow distribution and reduction of cardiac preload, the zero-stress state geometry and mass fractions of the basic structural constituents of aortic tissue meet a principle of optimal mechanical operation. The principle manifests as a uniform distribution of the circumferential stress in the aortic wall that ensures effective bearing of the physiological load and a favorable mechanical environment for mechanosensitive vascular smooth muscle cells. A mathematical model is proposed and inverse boundary value problems are solved for the equations that follow from finite elasticity, structure-based constitutive modeling within constrained mixture theory, and stress-induced control of aortic homeostasis, mediated by the synthetic activity of vascular smooth muscle cells. Published experimental data are used to illustrate the predictive power of the proposed model. The results obtained are in agreement with published experimental data and support the proposed principle of optimal mechanical operation for the descending aorta.
有充分文献记载，降主动脉的几何尺寸、原位纵向拉伸比、某些结构力学描述符（如顺应性和压力-直径模量）以及结构成分的质量分数沿降主动脉长度方向存在变化。这些观察到的变化的起源以及可能的相互关系仍然是悬而未决的问题。本研究的核心前提是，考虑到沿主动脉变形内径、轴向拉伸比和面积顺应性的变化受血流分布和降低心脏前负荷的全身需求支配，主动脉组织基本结构成分的零应力状态几何形状和质量分数符合最佳机械运作原理。该原理表现为主动脉壁圆周应力的均匀分布，确保有效承受生理负荷，并为机械敏感的血管平滑肌细胞提供有利的力学环境。提出了一个数学模型，并针对有限弹性、约束混合物理论中基于结构的本构建模以及由血管平滑肌细胞合成活性介导的应力诱导的主动脉稳态控制所产生的方程，求解了反边值问题。已发表的实验数据用于说明所提出模型的预测能力。获得的结果与已发表的实验数据一致，并支持所提出的降主动脉最佳机械运作原理。
