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# The Effect of Longitudinal Pre-Stretch and Radial Constraint on the Stress Distribution in the Vessel Wall: A New Hypothesis

Wei Zhang1,2, Carly Herrera1, Satya N. Atluri1, Ghassan S. Kassab2,3

Department of Mechanical and Aerospace Engineering and
Department of Biomedical Engineering, University of California, Irvine, CA, USA.
Corresponding author. Ph: (949) 824-9490; Fax: (949) 824-9932; E-mail: gkassab@uci.edu.

Molecular & Cellular Biomechanics 2005, 2(1), 41-52. https://doi.org/10.3970/mcb.2005.002.041

## Abstract

It is well known that blood vessels shorten axially when excised. This is due to the perivascular tethering constraint by side branches and the existence of pre-stretch of blood vessels at the \textit {in situ} state. Furthermore, vessels are radially constrained to various extents by the surrounding tissues at physiological loading. Our hypothesis is that the axial pre-stretch and radial constraint by the surrounding tissue homogenizes the stress and strain distributions in the vessel wall. A finite element analysis of porcine coronary artery and rabbit thoracic aorta based on measured material properties, geometry, residual strain and physiological loading is used to compute the intramural stresses and strains. We systematically examined the effect of pre-stretch and external radial constraint in both vessels. Our results show that both stretching in the axial direction and compression in the radial direction lead to a more homogeneous strain and stress state in the blood vessel wall. A uniform biaxial strain'' hypothesis is proposed for the blood vessel wall and the ramifications are discussed.

## Keywords

Zhang, W., Herrera, C., Atluri, S. N., Kassab, G. S. (2005). The Effect of Longitudinal Pre-Stretch and Radial Constraint on the Stress Distribution in the Vessel Wall: A New Hypothesis. Molecular & Cellular Biomechanics, 2(1), 41–52.

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