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Research Papers

Biomechanics of Porcine Renal Arteries and Role of Axial Stretch

[+] Author and Article Information
Pierre Badel

Ecole Nationale Supérieure des Mines
CIS-ENSMSE, CNRS:UMR5146
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.

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References

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Figures

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Fig. 1

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

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Fig. 2

Schematic of a network of fibers with two symmetric orientations

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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.

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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.

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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

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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

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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

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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

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