Research Papers

Biomechanics of Porcine Renal Arteries and Role of Axial Stretch

[+] Author and Article Information
Pierre Badel

Ecole Nationale Supérieure des Mines
Saint-Etienne F-42023, France

Mohamed Gabr

Biomedical Engineering Program,
School of Medicine,
University of South Carolina,
Columbia, SC 29208

Michael A. Sutton

Biomedical Engineering Program,
School of Medicine,
Department of Mechanical Engineering,
University of South Carolina,
Columbia, SC 29208

Susan M. Lessner

Biomedical Engineering Program,
Department of Cell Biology and Anatomy,
School of Medicine,
University of South Carolina,
Columbia, SC 29208

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 24, 2012; final manuscript received May 18, 2013; accepted manuscript posted May 30, 2013; published online June 12, 2013. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 135(8), 081007 (Jun 12, 2013) (10 pages) Paper No: BIO-12-1510; doi: 10.1115/1.4024685 History: Received October 24, 2012; Revised May 18, 2013; Accepted May 30, 2013

It is known that arteries experience significant axial stretches in vivo. Several authors have shown that the axial force needed to maintain an artery at its in vivo axial stretch does not change with transient cyclical pressurization over normal ranges. However, the axial force phenomenon of arteries has never been explained with microstructural considerations. In this paper we propose a simple biomechanical model to relate the specific axial force phenomenon of arteries to the predicted load-dependent average collagen fiber orientation. It is shown that (a) the model correctly predicts the authors' experimentally measured biaxial behavior of pig renal arteries and (b) the model predictions are in agreement with additional experimental results reported in the literature. Finally, we discuss the implications of the model for collagen fiber orientation and deposition in arteries.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Hu, J. J., Fossum, T. W., Miller, M. W., Xu, H., Liu, J. C., and Humphrey, J. D., 2007, “Biomechanics of the Porcine Basilar Artery in Hypertension,” Ann. Biomed. Eng., 35(1), pp. 19–29. [CrossRef] [PubMed]
Humphrey, J. D., Eberth, J. F., Dye, W. W., and Gleason, R. L., 2009, “Fundamental Role of Axial Stress in Compensatory Adaptations by Arteries,” J. Biomech., 42, pp. 1–8. [CrossRef] [PubMed]
Van Loon, P., Klip, W., and Bradley, E. L., 1977, “Length–Force and Volume–Pressure Relationships of Arteries,” Biorheology, 14, pp. 181–201. [PubMed]
Weizsacker, H., Lambert, W. H., and Pascale, K., 1983, “Analysis of the Passive Mechanical Properties of Rat Carotid Arteries,” J. Biomech., 16, pp. 703–715. [CrossRef] [PubMed]
Cardamone, L., Valentín, A., Eberth, J. F., and Humphrey, J. D., 2009, “Origin of Axial Prestretch and Residual Stress in Arteries,” Biomech. Model. Mechanobiol., 8(6), pp. 431–446. [CrossRef] [PubMed]
Gleason, R. L., Wilson, E., and Humphrey, J. D., 2007, “Biaxial Biomechanical Adaptations of Mouse Carotid Arteries Cultured at Altered Axial Extension,” J. Biomech., 38(6), pp. 766–776. [CrossRef]
Holzapfel, G. A., Gasser, T. C., and Ogden, R. W., 2000, “A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models,” J. Elast., 61, pp. 1–48. [CrossRef]
Humphrey, J. D., and Rajagopal, K. R., 2003, “A Constrained Mixture Model for Arterial Adaptations to a Sustained Step Change in Blood Flow,” Biomech. Model. Mechanobiol., 2, pp. 109–126. [CrossRef] [PubMed]
Rachev, A., 2000, “A Model of Arterial Adaptation to Alterations in Blood Flow,” J. Elast., 61, pp. 83–111. [CrossRef]
Gleason, R. L., and Humphrey, J. D., 2005, “Effect of a Sustained Extension on Arterial Growth and Remodeling: A Theoretical Study,” J. Biomech., 40(4), pp. 1255–1261. [CrossRef]
KarîsajI., and Humphrey, J. D., 2012, “A Multilayered Wall Model of Arterial Growth and Remodeling,” Mech. Mater., 44, pp. 110–119. [CrossRef] [PubMed]
Avril, S., Badel, P., and Duprey, A., 2010, “Anisotropic and Hyperelastic Identification of In Vitro Human Arteries From Full-Field Measurements,” J. Biomech., 43, pp. 2978–2985. [CrossRef] [PubMed]
Brossollet, L. J., and Vito, R. P., 1995, “An Alternate Formulation of Blood Vessel Mechanics and the Meaning of the In Vivo Property,” J. Biomech., 28, pp. 679–687. [CrossRef] [PubMed]
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress, and Growth, Springer, New York.
Humphrey, J. D., 2002, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer, New York.
Sacks, M. S., 2000, “Biaxial Mechanical Evaluation of Planar Biological Materials,” J. Elast., 61, pp. 199–246. [CrossRef]
Van de Geest, J., Sacks, M. S., and Vorp, D., 2004, “Age Dependency of the Biaxial Biomechanical Behavior of Human Abdominal Aorta,” J. Biomech. Eng., 126(6), pp. 815–822. [CrossRef] [PubMed]
Van de Geest, J., Sacks, M. S., and Vorp, D., 2006, “A Planar Biaxial Constitutive Relation for the Luminal Layer of Intraluminal Thrombus in Abdominal Aortic Aneurysms,” J. Biomech., 39(13), pp. 2347–2354. [CrossRef] [PubMed]
McGilvray, K., Sarkar, C. R., Nguyen, K., and Puttlitz, C. M., 2010, “A Biomechanical Analysis of Venous Tissue in Its Normal and Post-Phlebitic Conditions,” J. Biomech., 43(15), pp. 2941–2947. [CrossRef] [PubMed]
Valentín, A., Cardamone, L., Baek, S., and Humphrey, J. D., 2009, “Complementary Vasoactivity and Matrix Remodeling in Arterial Adaptations to Altered Flow and Pressure,” J. R. Soc. Interface, 6, pp. 293–306. [CrossRef] [PubMed]
Baek, S., Gleason, R. L., Rajagopal, K. R., and Humphrey, J. D., 2007, “Theory of Small on Large: Potential Utility in Computations of Fluid–Solid Interactions in Arteries,” Comput. Methods Appl. Mech. Eng., 196, pp. 3070–3078. [CrossRef]
Masson, I., Boutouyrie, P., Laurent, S., Humphrey, J. D., and Zidi, M., 2008, “Characterization of Arterial Wall Mechanical Behavior and Stresses From Human Clinical Data,” J. Biomech., 41, pp. 2618–2627. [CrossRef] [PubMed]
Badel, P., Avril, S., Lessner, S., and Sutton, M., 2012, “Mechanical Identification of Layer-Specific Properties of Mouse Carotid Arteries Using 3D-DIC and a Hyperelastic Anisotropic Constitutive Model,” Comput. Methods Biomech. Biomed. Eng., 15(1), pp. 37–48. [CrossRef]
Haskett, D., Johnson, G., Zhou, A., Utzinger, U., and van de Geest, J., 2010, “Microstructural and Biomechanical Alterations of the Human Aorta As a Function of Age and Location,” Biomech. Model. Mechanobiol.9, pp. 725–736. [CrossRef] [PubMed]
Holzapfel, G. A., 2006, “Determination of Material Models for Arterial Walls From Uniaxial Extension Tests and Histological Structure,” J. Theor. Biol., 238, pp. 290–302. [CrossRef] [PubMed]
Hill, M. R., Duan, X., Gibson, G. A., Watkins, S., and Robertson, A. M., 2012, “A Theoretical and Non-Destructive Experimental Approach for Direct Inclusion of Measured Collagen Orientation and Recruitment Into Mechanical Models of the Artery Wall,” J. Biomech., 45(5), pp. 762–771. [CrossRef]
Hariton, I., deBotton, G., Gasser, T. C., and Holzapfel, G. A., 2007, “Stress-Driven Collagen Fiber Remodeling in Arterial Walls,” Biomech. Model. Mechanobiol., 6, pp. 163–175. [CrossRef] [PubMed]
Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, “Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations,” J. R. Soc. Interface, 3(6), pp. 15–35. [CrossRef] [PubMed]
Kim, J. H., Avril, S., Duprey, A., and Favre, J. P., 2012, “Experimental Characterization of Rupture in Human Aortic Aneurysms Using a Full-Field Measurement Technique,” Biomech. Model. Mechanobiol., 11(6), pp. 841–854. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic of the cylindrical segment of artery and the loading system (in dotted lines, schematic of the helically arranged fibers)

Grahic Jump Location
Fig. 2

Schematic of a network of fibers with two symmetric orientations

Grahic Jump Location
Fig. 4

Pictures of the experimental test performed on the segments of artery. (a) Environmental chamber in Bose test bench and vertically oriented camera. (b) Representative example of porcine renal artery attached to barbed Luer fixtures inside environmental chamber for mechanical testing. Scale bar in mm.

Grahic Jump Location
Fig. 3

Diagram defining the opening angle. It is known that the “traction-free” state in which the artery is excised from the body is not a stress-free state. Thus the arterial ring springs open when cut in a radial direction. It is assumed that the open sector is the undeformed stress-free reference configuration. No axial deformation is assumed to occur during radial separation, so that the axial stretch between the stress-free to traction-free state is approximated to 1.

Grahic Jump Location
Fig. 5

F-P curves obtained on two different specimens (experiment and model): (a) RRA on pig ID 5, coefficient of determination R2 = 0.59 and (b) LSA2 on pig ID 3, coefficient of determination R2 = 0.87

Grahic Jump Location
Fig. 6

P versus λθ curves obtained on two different specimens (experiment and model): (a) RRA on pig ID 5, coefficient of determination R2 = 0.65 and (b) LSA2 on pig ID 3, coefficient of determination R2 = 0.7

Grahic Jump Location
Fig. 7

σzz versus λz curves obtained on two different specimens (experiment and model): (a) RRA on pig ID 5, coefficient of determination R2 = 0.96 and (b) LSA2 on pig ID 3, coefficient of determination R2 = 0.85

Grahic Jump Location
Fig. 8

Qualitative comparison between experimental data obtained for a pig basilar artery [5] and our model for the same artery: (a) Experimental force versus pressure curves obtained for a pig basilar artery [5] and (b) theoretical force versus pressure curves obtained with Eq. (11) for the same artery



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