Are Geometrical and Structural Variations Along the Length of the Aorta Governed by a Principle of “Optimal Mechanical Operation”?

Abstract

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.