Three-Dimensional Contractile Mechanics of Artery Accounting for Curl of Axial Strip Sectioned from Vessel Wall

Abstract

Purpose: It is well known that a sliced ring of arterial wall opens by a radial cut. An axial strip sectioned from arterial wall also curls into an arc. These phenomena imply that there exist residual strains in the circumferential and axial directions. How much do the axial residual strains affect the stress distributions of arterial wall? The aim of the present study is to know stress distributions of arterial wall with the residual strains under the passive and constricted conditions.

Methods: We analyzed the stress distributions under passive and constricted conditions with considering a Riemannian stress-free configuration. In the analysis, we used strain energy functions to describe the passive and active mechanical properties of artery.

Results: The present study provided distributions of stretch ratio with reference to the stress-free state (Riemannian stress-free configuration) and stress with and without the curl of axial strip of a homogenous cylindrical arterial model under the passive and constricted smooth muscle conditions. The circumferential and axial stresses with activated smooth muscle (noradrenaline 10^-5 M) at the intraluminal pressure 16 kPa and the axial stretch ratio 1.5 with reference to the unloaded vessel decreased by 3.5 and 13.8% at the inner surface with considering the axial residual strain, respectively.

Conclusions: We have shown that the Riemannian stress-free configuration is appropriate tool to analyze stress distributions of arterial wall under passive and activated conditions with the residual stresses.

Keywords: Arteries; Residual strains; Smooth muscle constriction; Stress distributions.