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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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References

Loree, H. M. , Kamm, R. D. , Stringfellow, R. G. , and Lee, R. T. , 1992, “ Effect of Fibrous Cap Thickness on Peak Circumferential Stress in Model Atherosclerotic Vessels,” Circ. Res., 71(4), pp. 850–858. [CrossRef] [PubMed]
Richardson, P. D. , 2002, “ Biomechanics of Plaque Rupture: Progress, Problems, and New Frontiers,” Ann. Biomed. Eng., 30(4), pp. 524–536. [CrossRef] [PubMed]
Tang, D. , Kamm, R. D. , Yang, C. , Zheng, J. , Canton, G. , Bach, R. , Huang, X. , Hatsukami, T. S. , Zhu, J. , Ma, G. , Maehara, A. , Mintz, G. S. , and Yuan, C. , 2014, “ Image-Based Modeling for Better Understanding and Assessment of Atherosclerotic Plaque Progression and Vulnerability: Data, Modeling, Validation, Uncertainty and Predictions,” J. Biomech., 47(4), pp.834–846. [CrossRef] [PubMed]
Stone, P. H. , Saito, S. , Takahashi, S. , Makita, Y. , Nakamura, S. , Kawasaki, T. , Takahashi, A. , Katsuki, T. , Nakamura, S. , Namiki, A. , Hirohata, A. , Matsumura, T. , Yamazaki, S. , Yokoi, H. , Tanaka, S. , Otsuji, S. , Yoshimachi, F. , Honye, J. , Harwood, D. , Reitman, M. , Coskun, A. U. , Papafaklis, M. I. , and Feldman, C. L. , 2012, “ Prediction of Progression of Coronary Artery Disease and Clinical Outcomes Using Vascular Profiling of Endothelial Shear Stress and Arterial Plaque Characteristics: The Prediction Study,” Circulation, 126(2), pp. 172–81. [CrossRef] [PubMed]
Wang, L. , Zheng, J. , Maehara, A. , Yang, C. , Billiar, K. L. , Wu, Z. , Bach, R. , Muccigrosso, D. , Mintz, G. S. , and Tang, D. , 2015, “ Morphological and Stress Vulnerability Indices for Human Coronary Plaques and Their Correlations With Cap Thickness and Lipid Percent: An IVUS-Based Fluid-Structure Interaction Multi-Patient Study,” PLoS Comput. Biol., 11(12), p. e1004652. [CrossRef] [PubMed]
Tang, D. , Teng, Z. , Canton, G. , Yang, C. , Ferguson, M. , Huang, X. , Zheng, J. , Woodard, P. K. , and Yuan, C. , 2009, “ Sites of Rupture in Human Atherosclerotic Carotid Plaques are Associated With High Structural Stresses: An In Vivo MRI-Based 3D Fluid-Structure Interaction Study,” Stroke, 40(10), pp. 3258–3263. [CrossRef] [PubMed]
Samady, H. , Eshtehardi, P. , McDaniel, M. C. , Suo, J. , Dhawan, S. S. , Maynard, C. , Timmins, L. H. , Quyyumi, A. A. , and Giddens, D. P. , 2011, “ Coronary Artery Wall Shear Stress is Associated With Progression and Transformation of Atherosclerotic Plaque and Arterial Remodeling in Patients With Coronary Artery Disease,” Circulation, 124(7), pp.779–788. [CrossRef] [PubMed]
Teng, Z. , Brown, A. J. , Calvert, P. A. , Parker, R. A. , Obaid, D. R. , Huang, Y. , Hoole, S. P. , West, N. E. , Gillard, J. H. , and Bennett, M. R. , 2014, “ Coronary Plaque Structural Stress Is Associated With Plaque Composition and Subtype and Higher in Acute Coronary Syndrome: The BEACON I (Biomechanical Evaluation of Atheromatous Coronary Arteries) Study,” Circ. Cardiovasc. Imaging, 7(3), pp. 461–470. [CrossRef] [PubMed]
Finet, G. , Ohayon, J. , and Rioufol, G. , 2004, “ Biomechanical Interaction Between Cap Thickness, Lipid Core Composition and Blood Pressure in Vulnerable Coronary Plaque: Impact on Stability or Instability,” Coronary Artery Dis., 15(1), pp. 13–20. [CrossRef]
Hetterich, H. , Jaber, A. , Gehring, M. , Curta, A. , Bamberg, F. , Filipovic, N. , and Rieber, J. , 2015, “ Coronary Computed Tomography Angiography Based Assessment of Endothelial Shear Stress and Its Association With Atherosclerotic Plaque Distribution In-Vivo,” PLoS One, 10(1), p. e0115408. [CrossRef] [PubMed]
Fung, Y. C. , 1994, A First Course in Continuum Mechanics, Prentice Hall, Englewood Cliffs, NJ, Chap. 13.
Fung, Y. C. , and Liu, S. Q. , 1992, “ Strain Distribution in Small Blood Vessel With Zero-Stress State Taken Into Consideration,” Am. J. Physiol., 262(2), pp. H544–H552. http://ajpheart.physiology.org/content/262/2/H544 [PubMed]
Delfino, A. , Stergiopulos, N. , Moore, J. E., Jr. , and Meister, J. J. , 1997, “ Residual Strain Effects on the Stress Field in a Thick Wall Finite Element Model of the Human Carotid Bifurcation,” J. Biomech., 30(8), pp. 777–786. [CrossRef] [PubMed]
Ohayon, J. , Dubreuil, O. , Tracqui, P. , Le Floc'h, S. , Rioufol, G. , Chalabreysse, L. , Thivolet, F. , Pettigrew, R. I. , and Finet, G. , 2007, “ Influence of Residual Stress/Strain on the Biomechanical Stability of Vulnerable Coronary Plaques: Potential Impact for Evaluating the Risk of Plaque Rupture,” Am. J. Physiol., 293(3), pp. H1987–H1996.
Huang, X. , Yang, C. , Yuan, C. , Liu, F. , Canton, G. , Zheng, J. , Woodard, P. K. , Sicard, G. A. , and Tang, D. , 2009, “ Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on In Vivo MRI Data,” Mol. Cell. Biomech., 6(2), pp. 121–134. [PubMed]
Speelman, L. , Bosboom, E. M. , Schurink, G. W. , Buth, J. , Breeuwer, M. , Jacobs, M. J. , and van de Vosse, F. N. , 2009, “ Initial Stress and Nonlinear Material Behavior in Patient-Specific AAA Wall Stress Analysis,” J. Biomech., 42(11), pp. 1713–1719. [CrossRef] [PubMed]
Holzapel, G. A. , Sommer, G. , Auer, M. , Regitnig, P. , and Ogden, R. W. , 2007, “ Layer-Specific 3D Residual Deformations of Human Aortas With Non-Atherosclerotic Intimal Thickening,” Ann. Biomed. Eng., 35(4), pp. 530–545. [CrossRef] [PubMed]
Pierce, D. M. , Fastl, T. E. , Rodriguez-Vila, B. , Verbrugghe, P. , Fourneau, I. , Maleux, G. , Herijgers, P. , Gomez, E. J. , and Holzapfel, G. A. , 2015, “ A Method for Incorporating Three-Dimensional Residual Stretches/Stresses Into Patient-Specific Finite Element Simulation of Arteries,” J. Mech. Behav. Biomed. Mater., 47, pp. 147–164. [CrossRef] [PubMed]
Gee, M. W. , Förster, C. H. , and Wall, W. A. , 2010, “ A Computational Strategy for Prestressing Patient-Specific Biomechanical Problems Under Finite Deformation,” Int. J. Numer. Methods Biomed. Eng., 26(1), pp. 52–72. [CrossRef]
Mintz, G. S. , Nissen, S. E. , Anderson, W. D. , Bailey, S. R. , Erbel, R. , Fitzgerald, P. J. , Pinto, F. J. , Rosenfield, K. , Siegel, R. J. , Tuzcu, E. M. , and Yock, P. G. , 2001, “ American College of Cardiology Clinical Expert Consensus Document on Standards for Acquisition, Measurement and Reporting of Intravascular Ultrasound Studies (IVUS): A Report of the American College of Cardiology Task Force on Clinical Expert Consensus Documents,” J. Am. Coll. Cardiol., 37(5), pp. 1478–1492. [CrossRef] [PubMed]
Nair, A. , Kuban, B. D. , Tuzcu, E. M. , Schoenhagen, P. , Nissen, S. E. , and Vince, D. G. , 2002, “ Coronary Plaque Classification With Intravascular Ultrasound Radiofrequency Data Analysis,” Circulation, 106(17), pp. 2200–2206. [CrossRef] [PubMed]
Liu, H. , Cai, M. , Yang, C. , Zheng, J. , Bach, R. , Kural, M. H. , Billiar, K. L. , Muccigrosso, D. , Lu, D. , and Tang, D. , 2012, “ IVUS-Based Computational Modeling and Planar Biaxial Artery Material Properties for Human Coronary Plaque Vulnerability Assessment,” Mol. Cell. Biomech., 9(1), pp. 77–93. [CrossRef] [PubMed]
Bathe, K. J. , ed., 2002, Theory and Modeling Guide, Vol I: ADINA, ADINA R & D, Watertown, MA.
Bathe, K. J. , ed., 2002, Theory and Modeling Guide, Vol II: ADINA-F, ADINA R & D, Watertown, MA.
Yang, C. , Bach, R. G. , Zheng, J. , Naqa, I. E. , Woodard, P. K. , Teng, Z. , Billiar, K. L. , and Tang, D. , 2009, “ In Vivo IVUS-Based 3D Fluid Structure Interaction Models With Cyclic Bending and Anisotropic Vessel Properties for Human Atherosclerotic Coronary Plaque Mechanical Analysis,” IEEE Trans. Biomed. Eng., 56(10), pp. 2420–2428. [CrossRef] [PubMed]
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. Elasticity, 61(1), pp. 1–48. [CrossRef]
Liu, H. , Canton, G. , Yuan, C. , Yang, C. , Billiar, K. L. , Teng, Z. , Hoffman, A. H. , and Tang, D. , 2012, “ Using In Vivo Cine and 3D Multi-Contrast MRI to Determine Human Atherosclerotic Carotid Artery Material Properties and Circumferential Shrinkage Rate and Their Impact on Stress/Strain Predictions,” ASME J. Biomech. Eng., 134(1), p. 011008. [CrossRef]
Kural, M. H. , Cai, M. , Tang, D. , Gwyther, T. , Zheng, J. , and Billiar, K. L. , 2012, “ Planar Biaxial Characterization of Diseased Human Coronary and Carotid Arteries for Computational Modeling,” J. Biomech., 45(5), pp. 790–798. [CrossRef] [PubMed]

Figures

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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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