Research Papers

Residual Shear Deformations in the Coronary Artery

[+] Author and Article Information
Ruoya Wang

George W. Woodruff
School of Mechanical Engineering,
Georgia Institute of Technology,
315 Ferst Drive, 2305 IBB,
Atlanta, GA 30332
e-mail: r.wang@gatech.edu

Rudolph L. Gleason, Jr.

George W. Woodruff
School of Mechanical Engineering
Wallace H. Coulter
Department of Biomedical Engineering
Parker H. Petit
Institute for Bioengineering
and Bioscience,
Georgia Institute of Technology,
315 Ferst Drive, 2305 IBB,
Atlanta, GA 30332
e-mail: rudy.gleason@gatech.edu

Manuscript received November 10, 2013; final manuscript received March 19, 2014; accepted manuscript posted April 2, 2014; published online April 21, 2014. Assoc. Editor: Kristen Billiar.

J Biomech Eng 136(6), 061004 (Apr 21, 2014) (6 pages) Paper No: BIO-13-1525; doi: 10.1115/1.4027331 History: Received November 10, 2013; Revised March 19, 2014; Accepted April 02, 2014

Quantifying arterial residual deformations is critical for understanding the stresses and strains within the arterial wall during physiological and pathophysiological conditions. This study presents novel findings on residual shear deformations in the left anterior descending coronary artery. Residual shear deformations are most evident when thin, long axial strips are cut from the artery. These strips deform into helical configurations when placed in isotonic solution. A residual shear angle is introduced as a parameter to quantify the residual shear deformations. Furthermore, a stress analysis is performed to study the effects of residual shear deformations on the intramural shear stress distribution of an artery subjected to pressure, axial stretch, and torsion using numerical simulation. The results from the stress analyses suggest that residual shear deformations can significantly modulate the intramural shear stress across the arterial wall.

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Fig. 4

Theoretical representation of residual strains in an artery. The stress-free configuration consists of a series of infinitesimally thin cylindrical shells that vary in axial lengths and radii (a) and (b). Circumferential and longitudinal residual strains are induced when the shells are axially and circumferentially stretched and assembled into a continuous, but residually stressed, tube (c). Residual shear strains are induced when each shells undergoes a shearing axial twist prior to the assembly (d).

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Fig. 3

Template for measuring the residual shear angle. A representative helical section is superimposed with an angle measurement template. Angles β1→4 were used to calculate the mean residual shear angle (ωi). Note that these angles are measured at the intimal surface.

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Fig. 2

Two helical configurations exhibiting negative (a) and positive (b) shearing directions. The asterisk denotes the ink-labeled adventitial surface of the proximal end, which is used as a reference marker for determining the shearing direction.

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Fig. 1

Destructive cutting protocol developed to reveal residual shear deformations in the coronary artery. (a) A single straight cut down the length of the artery is made. (b) The artery is laid flat and a parallel strip is stamped down the center. (c) The arterial strip is placed in isotonic saline where it immediately deforms into a tortuous shape. (d) The final configuration is reached following further sectioning into approximate thirds.

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Fig. 5

Experimental measurements of the residual shear angles. The residual shear angles are given relative to the section numbers. Each artery was divided into three segments denoted by S1, S2, and S3, with S1 being the most proximal section. All sections exhibited residual shear deformations. Both magnitude and direction of the RSD varied greatly along the length of the artery. Each symbol represents measurements from a single artery.

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Fig. 6

Predicted intramural residual stresses. (a) Intramural residual shear stress gradients increase with increasing magnitudes of residual shear angles (ωi). (b) Radial (solid line), circumferential (square markers), and longitudinal (dashed line) residual stresses for residual shear angle ωi = 20 deg. Note that the radial boundary condition was not completely satisfied using parameters from the literature (the radial stress at outer wall should be zero).

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Fig. 7

Intramural shear stresses predicted using different combinations of residual shear angles and loaded axial twists. The magnitudes of the angles are within the bounds of experimental and physiological measurements. The intramural shear stress distribution can be greatly affected by different combinations of both the magnitude and direction of the residual shear and axial twist angles.



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