Research Papers

Tensile Stability of Medial Arterial Tissues

[+] Author and Article Information
Alan J. Levy

Department of Mechanical and
Aerospace Engineering,
Syracuse University,
263 Link Hall,
Syracuse, NY 13244-1240
e-mail: ajlevy@syr.edu

Xinyu Zhang

Department of Mechanical and
Aerospace Engineering,
Syracuse University,
263 Link Hall,
Syracuse, NY 13244-1240

1Corresponding author.

Manuscript received January 7, 2016; final manuscript received February 17, 2016; published online March 17, 2016. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 83(5), 051013 (Mar 17, 2016) (7 pages) Paper No: JAM-16-1014; doi: 10.1115/1.4032858 History: Received January 07, 2016; Revised February 17, 2016

Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Walsh, M. T. , Cunnane, E. M. , Mulvihill, J. J. , Akyildiz, A. C. , Gijsen, F. J. H. , and Holzapfel, G. A. , 2014, “ Uniaxial Tensile Testing Approaches for Characterization of Atherosclerotic Plaques,” J. Biomech., 47(4), pp. 793–804. [CrossRef] [PubMed]
Hutchinson, J. W. , and Neale, K. W. , 1977, “ Influence of Strain-Rate Sensitivity on Necking Under Uniaxial Tension,” Acta Metall., 25(8), pp. 839–846. [CrossRef]
Hutchinson, J. W. , and Obrecht, H. , 1977, “ Tensile Instabilities in Strain Rate Dependent Materials,” International Conference on Fracture (ICF4), Waterloo, ON, Canada, June 19–24, pp. 101–116.
Levy, A. J. , 1986, “ The Tertiary Creep and Necking of Creep Damaging Solids,” Acta Metall., 34(10), pp. 1991–1997. [CrossRef]
Levy, A. J. , 1987, “ Tensile Instability in Creep Damaging Solids,” Acta Metall., 35(10), pp. 2583–2592. [CrossRef]
Clark, J. M. , and Glagov, H. , 1985, “ Transmural Organization of the Arterial Media. The Lamellar Unit Revisited,” Arterioscler., Thromb., Vasc. Biol., 5(1), pp. 19–34. [CrossRef]
Wolinsky, H. , and Glagov, S. , 1967, “ A Lamellar Unit of Aortic Medial Structure and Function in Mammals,” Circ. Res., 20(1), pp. 99–111. [CrossRef] [PubMed]
Carew, T. E. , Vaishnav, R. N. , and Patel, D. J. , 1968, “ Compressibility of the Arterial Wall,” Circ. Res., 23(1), pp. 61–68. [CrossRef] [PubMed]
Hoeve, C. A. J. , and Flory, P. J. , 1974, “ The Elastic Properties of Elastin,” Biopolymers, 13(4), pp. 677–686. [CrossRef] [PubMed]
Gundiah, N. , Ratcliffe, M. B. , and Pruitt, L. A. , 2007, “ Determination of Strain Energy Function for Arterial Elastin: Experiments Using Histology and Mechanical Tests,” J. Biomech., 40(3), pp. 586–594. [CrossRef] [PubMed]
Blatz, P. J. , Chu, B. M. , and Wayland, H. , 1969, “ On the Mechanical Behavior of Elastic Animal Tissue,” Trans. Soc. Rheol., 13(1), pp. 83–102. [CrossRef]
Valanis, K. C. , and Landel, R. F. , 1967, “ The Strain Energy Function of a Hyperelastic Material in Terms of the Extension Ratios,” J. Appl. Phys., 38(7), pp. 2997–3002. [CrossRef]
Yin, F. C. P. , and Fung, Y. C. , 1971, “ Mechanical Properties of Isolated Mammalian Ureteral Segments,” Am. J. Physiol., 221, pp. 1484–1493. [PubMed]
Garikipati, K. , Goktepe, S. , and Miehe, C. , 2008, “ Elastica-Based Strain Energy Functions for Soft Biological Tissue,” J. Mech. Phys. Solids, 56(4), pp. 1693–1713. [CrossRef]
Lally, C. , Reid, A. J. , and Prendergast, P. J. , 2004, “ Elastic Behavior of Porcine Coronary Artery Tissue Under Uniaxial and Equibiaxial Tension,” Ann. Biomed. Eng., 32(10), pp. 1355–1364. [CrossRef] [PubMed]
Ludwik, P. , 1909, Elemente der Technologischen Mechanik, Springer Verlag, Berlin.
Hollomon, H. , 1945, “ Tensile Deformation,” Trans. Am. Inst. Min., Metall. Pet. Eng., 162, pp. 268–290.
Faury, G. , Maher, G. M. , Li, D. Y. , Keating, M. T. , Mecham, R. P. , and Boyle, W. A. , 1999, “ Relation Between Outer and Luminal Diameter in Cannulated Arteries,” Am. Physiol. Soc., 277(5), pp. 1745–1753.
Glagov, S. , and Wolinsky, H. , 1963, “ Aortic Wall as a Two Phase Material,” Nature, 199(4893), pp. 606–608. [CrossRef]
Cox, R. H. , 1978, “ Passive Mechanics and Connective Tissue Composition of Canine Arteries,” Am. J. Physiol., 234(5), pp. H533–H541. [PubMed]


Grahic Jump Location
Fig. 1

Idealized model of a single MEF: C—collagen, E—elastin, and M—smooth muscle

Grahic Jump Location
Fig. 2

(a) stretch versus nominal stress and (b) areal stretch versus nominal stress. χ is the nominal stress normalized by the elastic modulus of elastin.

Grahic Jump Location
Fig. 3

(a) Initial geometrical imperfection: stretch imperfection growth versus nominal stress and (b) areal stretch imperfection growth versus nominal stress

Grahic Jump Location
Fig. 4

(a) Initial material imperfection: stretch imperfection growth versus nominal stress and (b) areal stretch imperfection growth versus nominal stress

Grahic Jump Location
Fig. 5

Geometrical imperfection growth rate versus nominal stress for arterial tissue and constituents and elastin with a decaying power law stiffness



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In