Technical Brief

Effects of Residual Stress, Axial Stretch, and Circumferential Shrinkage on Coronary Plaque Stress and Strain Calculations: A Modeling Study Using IVUS-Based Near-Idealized Geometries

[+] Author and Article Information
Liang Wang

Mathematical Sciences Department,
Worcester Polytechnic Institute,
Worcester, MA 01609

Jian Zhu, Genshan Ma

Department of Cardiology,
Zhongda Hospital,
Southeast University,
Nanjing 210009, China

Habib Samady, David Monoly

Department of Medicine,
Emory University School of Medicine,
Atlanta, GA 30307

Jie Zheng

Mallinckrodt Institute of Radiology,
Washington University,
St. Louis, MO 63110

Xiaoya Guo

Department of Mathematics,
Southeast University,
Nanjing 210096, China

Akiko Maehara, Gary S. Mintz

The Cardiovascular Research Foundation,
Columbia University,
New York, NY 10022

Chun Yang

Network Technology Research Institute,
China United Network Communications Co., Ltd.,
Beijing 100140, China

Dalin Tang

Mathematical Sciences Department,
Worcester Polytechnic Institute,
Worcester, MA 01609;
Department of Mathematics,
Southeast University,
Nanjing 210096, China

1L. Wang and J. Zhu contributed equally to this paper.

2Corresponding author.

Manuscript received May 6, 2016; final manuscript received September 22, 2016; published online November 4, 2016. Assoc. Editor: C. Alberto Figueroa.

J Biomech Eng 139(1), 014501 (Nov 04, 2016) (11 pages) Paper No: BIO-16-1185; doi: 10.1115/1.4034867 History: Received May 06, 2016; Revised September 22, 2016

Accurate stress and strain calculations are important for plaque progression and vulnerability assessment. Models based on in vivo data often need to form geometries with zero-stress/strain conditions. The goal of this paper is to use IVUS-based near-idealized geometries and introduce a three-step model construction process to include residual stress, axial shrinkage, and circumferential shrinkage and investigate their impacts on stress and strain calculations. In Vivo intravascular ultrasound (IVUS) data of human coronary were acquired for model construction. In Vivo IVUS movie data were acquired and used to determine patient-specific material parameter values. A three-step modeling procedure was used to make our model: (a) wrap the zero-stress vessel sector to obtain the residual stress; (b) stretch the vessel axially to its length in vivo; and (c) pressurize the vessel to recover its in vivo geometry. Eight models were constructed for our investigation. Wrapping led to reduced lumen and cap stress and increased out boundary stress. The model with axial stretch, circumferential shrink, but no wrapping overestimated lumen and cap stress by 182% and 448%, respectively. The model with wrapping, circumferential shrink, but no axial stretch predicted average lumen stress and cap stress as 0.76 kPa and −15 kPa. The same model with 10% axial stretch had 42.53 kPa lumen stress and 29.0 kPa cap stress, respectively. Skipping circumferential shrinkage leads to overexpansion of the vessel and incorrect stress/strain calculations. Vessel stiffness increase (100%) leads to 75% lumen stress increase and 102% cap stress increase.

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Fig. 1

A human coronary plaque sample together with IVUS movie to determine vessel material properties: (a) stacked IVUS-VH contours showing 3D view of the plaque and (b) IVUS movie slices at a location corresponding to maximum and minimum pressure. Minimum circumference = 11.85 mm and maximum circumference = 12.53 mm.

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Fig. 2

Stress–stretch curves from Mooney–Rivlin models using parameter values determined from IVUS movie, 200% stiffness (2×in vivo), and ex vivo biaxial testing of human coronary plaques. Parameter values are listed in Table 2.

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Fig. 3

The IVUS slice and wrapping-up process: (a) the in vivo IVUS-VH image, (b) the segmented contour, (c) contour plot after smoothing and merging small lipid pools to a combined one; (d) overlapped contours at in vivo state (blue), no-load state (black), and stress-free state (magenta), circumferential shrinkage was applied; and (e) 3D view of the blood vessel geometry at no-load state and in vivo state

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Fig. 4

Stress/strain plots from M1 and M2 showing impact of residual stress. p = 130 mm Hg. (a) M1: stress-P1, (b) M2: stress-P1, (c) M1: strain-P1, and (d) M2: strain-P1.

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Fig. 5

Stress and strain plots from M1, M3, and M4 showing impact of axial stretch. p = 130 mm Hg. (a) M1: stress-P1, (b) M3: stress-P1, (c) M4: stress-P1, (d) M1: strain-P1, (e) M3: strain-P1, and (f) M4: strain-P1.

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Fig. 6

Stress and strain plots from M1, M5, and M6 showing impact of circumferential shrinkage. p = 130 mm Hg. (a) M1: stress-P1, (b) M5: stress-P1, (c) M6: stress-P1, (d) M1: strain-P1, (e) M5: strain-P1, and (f) M6: strain-P1.

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Fig. 7

Stress and strain plots from M1, M7, and M8 showing impact of material stiffness changes. p = 130 mm Hg. (a) M1: stress-P1, (b) M7: stress-P1, (c) M8: stress-P1, (d) M1: strain-P1, (e) M7: strain-P1, and (f) M8: strain-P1.

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Fig. 8

Stress and strain plots from M9 to M11 showing modeling results for a healthy vessel. p = 130 mm Hg. (a) M9: stress-P1, (b) M10: stress-P1, (c) M11: stress-P1, (d) M9: strain-P1, (e) M10: strain-P1, and (f) M11: strain-P1.

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Fig. 9

Stress and strain plots from M12 and M13 showing the impact of residual stress for an eccentric plaque case. p = 130 mm Hg. (a) in vivo geometry, (b) in vivo and open-up geometrics, (c)M12: stress-P1, (d) M12: strain-P1, (e) M13: stress-P1, and (f) M13: strain-P1.

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Fig. 10

Cut position has very modest impact on stress and strain calculations: (a) M1: stress-P1, (b) M14: stress-P1, (c) M1: strain-P1, and (d) M14: strain-P1




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