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Technical Briefs

Non-Euclidean Stress-Free Configuration of Arteries Accounting for Curl of Axial Strips Sectioned From Vessels

[+] Author and Article Information
Keiichi Takamizawa

e-mail: ktaka@ncvc.go.jp

Yasuhide Nakayama

Department of Biomedical Engineering,
National Cerebral and Cardiovascular Center
Research Institute, 5-7-1 Fujishirodai,
Suita, Osaka 565-8565, Japan

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received February 20, 2013; final manuscript received August 16, 2013; accepted manuscript posted September 6, 2013; published online September 26, 2013. Assoc. Editor: Stephen M. Klisch.

J Biomech Eng 135(11), 114505 (Sep 26, 2013) (5 pages) Paper No: BIO-13-1091; doi: 10.1115/1.4025328 History: Received February 20, 2013; Revised August 16, 2013; Accepted September 06, 2013

It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.

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Figures

Grahic Jump Location
Fig. 1

Schematic drawing of the circumferential stress-free sectors and the axial stress-free arcs, the unloaded segments for adventitia and media-intima, and the unloaded intact segment

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Fig. 2

Residual stretch ratios (a) and residual stresses (b) based on one-layer model accounting for circumferential opening sector and axial arc dissected from a porcine common carotid artery. Radius denotes that of the unloaded configuration.

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Fig. 3

Stretch ratio (a) and stress (b) distributions under a physiological load accounting for circumferential opening sector and axial arc dissected from a porcine common carotid artery. Radius denotes that of the physiologically loaded configuration.

Grahic Jump Location
Fig. 4

Residual stretch ratios (a) and residual stresses (b) based on two-layer model accounting for circumferential sectors and axial arcs of media-intima and adventitia dissected from a human common carotid artery. Radius denotes that of the unloaded intact configuration.

Grahic Jump Location
Fig. 5

Stretch ratio (a) and stress (b) distributions under a physiological load accounting for circumferential opening sectors and axial arcs of media-intima and adventitia dissected from a human common carotid artery. Radius denotes that of the physiologically loaded configuration.

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