Fluid-structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future

International Journal for Numerical Methods in Biomedical Engineering

Volumn 26, Issue 3-4, 2010, Pages 348-380

  Einstein, Daniel R ^a   Del Pin, Facundo ^b   Jiao, Xiangmin ^c   Kuprat, Andrew P ^a   Carson, James P ^a   Kunzelman, Karyn S ^d   Cochran, Richard P ^e   Guccione, Julius M ^f   Ratcliffe, Mark B ^f  

^a PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

^b LIVERMORE SOFTWARE TECHNOLOGY CORPORATION   (United States)

^c Stony Brook University   (United States)

^d UNIVERSITY OF MAINE   (United States)

^e Central Maine Heart and Vascular Institute   (United States)

^f VETERANS AFFAIRS MEDICAL CENTER   (United States)

Author keywords

Biofluid structure interactions; Imaging based finite element models; Ischemic mitral regurgitation

Indexed keywords

ABNORMAL TISSUES; CARDIAC STRESS; COMPUTATIONAL MODELING; COUPLED SOLVER; DATA COLLECTION; FINITE ELEMENT MODELS; GENERATION ALGORITHM; IN-VIVO; INVERSE ANALYSIS; LAGRANGIAN; MITRAL ANNULUS; MITRAL REGURGITATION; MITRAL VALVE FUNCTION; MITRAL VALVES; MYOCARDIAL INFARCTION; PAPILLARY MUSCLE; SPATIAL ORGANIZATION; STRUCTURE INTERACTIONS; TISSUE MICROSTRUCTURES; WALL STRESS;

DIMENSIONAL STABILITY; FLUID STRUCTURE INTERACTION; GEOMETRY; HEART; IMAGE ANALYSIS; MESH GENERATION;

FINITE ELEMENT METHOD;

EID: 77953087905     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1280     Document Type: Article

References (121)

1. Peskin CS. Flow patterns around heart valves: a numerical method. Journal of Computational Physics 1972; 10:252-271.
2. Cheng Y, Oertel H, Schenkel T. Fluid-structure coupled CFD simulation of the left ventricular flow during filling phase. Annals of Biomedical Engineering 2005; 33(5):567-576.
3. Lemmon JD, Yoganathan AP. Three-dimensional computational model of left heart diastolic function with fluid-structure interaction. Journal of Biomechanical Engineering 2000; 122(2):109-117.
4. Redaelli A, Montevecchi FM. Computational evaluation of intraventricular pressure gradients based on a fluid-structure approach. Journal of Biomechanical Engineering 1996; 118(4):529-537.
5. Watanabe H, Sugiura S, Kafuku H, Hisada T. Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophysical Journal 2004; 87(3):2074-2085.
6. Redaelli A, Maisano F, Schreuder JJ, Montevecchi FM. Ventricular motion during the ejection phase: a computational analysis. Journal of Applied Physiology 2000; 89(1):314-322.
7. Carmody CJ, Burriesci G, Howard IC, Patterson EA. An approach to the simulation of fluid-structure interaction in the aortic valve. Journal of Biomechanics 2006; 39(1):158-169.
8. Tang D, Yang C, Geva T, del Nido PJ. Two-layer passive/active anisotropic FSI models with fiber orientation: MRI-based patient-specific modeling of right ventricular response to pulmonary valve insertion surgery. Molecular and Cellular Biomechanics 2007; 4(3):159-176.
9. Tang D, Yang C, Geva T, Del Nido PJ. Patient-specific MRI-based 3D FSI RV/LV/patch models for pulmonary valve replacement surgery and patch optimization. Journal of Biomechanical Engineering 2008; 130(4):041010.
10. Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Hsu EW, Saloner DA, Guccione JM. Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. Journal of Thoracic and Cardiovascular Surgery 2008; 135(5):1094-1102.e2.
11. Wall ST, Walker JC, Healy KE, Ratcliffe MB, Guccione JM. Theoretical impact of the injection of material into the myocardium: a finite element model simulation. Circulation 2006; 114(24):2627-2635.
12. Nickerson D, Niederer S, Stevens C, Nash M, Hunter P. A computational model of cardiac electromechanics. Conference Proceedings-IEEE Engineering in Medicine and Biology Society, New York City, NY, U.S.A. vol. 1, 2006; 5311-5314.
13. Kerckhoffs RC, Neal ML, Gu Q, Bassingthwaighte JB, Omens JH, McCulloch AD. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Annals of Biomedical Engineering 2007; 35(1):1-18.
14. De Hart J, Peters GW, Schreurs PJ, Baaijens FP. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. Journal of Biomechanics 2003; 36(1):103-112.
15. Dumont K, Stijnen JM, Vierendeels J, van de Vosse FN, Verdonck PR. Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in fluent. Computer Methods in Biomechanics and Biomedical Engineering 2004; 7(3):139-146.
16. Guivier C, Deplano V, Pibarot P. New insights into the assessment of the prosthetic valve performance in the presence of subaortic stenosis through a fluid-structure interaction model. Journal of Biomechanics 2007; 40(10):2283-2290.
17. Kaminsky R, Dumont K, Weber H, Schroll M, Verdonck P. PIV validation of blood-heart valve leaflet interaction modelling. International Journal of Artificial Organs 2007; 30(7):640-648.
18. Makhijani VB, Yang HQ, Dionne PJ, Thubrikar MJ. Three-dimensional coupled fluid-structure simulation of pericardial bioprosthetic aortic valve function. ASAIO Journal 1997; 43:M387-M392.
19. Morsi YS, Yang WW, Wong CS, Das S. Transient fluid-structure coupling for simulation of a trileaflet heart valve using weak coupling. Journal of Artificial Organs 2007; 10(2):96-103.
20. Nicosia MA, Cochran RP, Einstein DR, Rutland CJ, Kunzelman KS. A coupled fluid-structure finite element model of the aortic valve and root. Journal of Heart Valve Disease 2003; 12(6):781-789.
21. Weinberg EJ, Kaazempur Mofrad MR. Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovascular Engineering 2007; 7(4):140-155.
22. van de Vosse FN, van Loon R, Anderson PD. A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. Journal of Computational Physics 2006; 217(2):806-823.
23. van Loon R, Anderson PD, de Hart J, Baaijens FPT. A combined fictitious domain/adaptive meshing method for fluid-structure interaction in heart valves. International Journal for Numerical Methods in Fluids 2004; 46(5):533-544.
24. Watton PN, Luo XY, Wang X, Bernacca GM, Molloy P, Wheatley DJ. Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method. Journal of Biomechanics 2007; 40(3):613-626.
25. Einstein DR, Kunzelman KS, Reinhall PG, Nicosia MA, Cochran RP. Non-linear fluid-coupled computational model of the mitral valve. Journal of Heart Valve Disease 2005; 14(3):376-385.
26. Watton P, Luo XY, Yin M, Bernacca GM, Wheatley DJ. Effect of ventricle motion on the dynamic behaviour of chorded mitral valves. Journal of Fluids and Structures 2008; 24:58-74.
27. Thubrikar M, Piepgrass WC, Shaner TW, Nolan SP. The design of the normal aortic valve. American Journal of Physiology 1981; 241(6):H795-H801.
28. Grande-Allen KJ, Cochran RP, Reinhall PG, Kunzelman KS. Re-creation of sinuses is important for sparing the aortic valve: a finite element study. Journal of Thoracic and Cardiovascular Surgery 2000; 119(4 Pt 1):753-763.
29. Kunzelman KS, Cochran RP, Chuong C, Ring WS, Verrier ED, Eberhart RD. Finite element analysis of the mitral valve. Journal of Heart Valve Disease 1993; 2(3):326-340.
30. Votta E, Caiani E, Veronesi F, Soncini M, Montevecchi FM, Redaelli A. Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios. Philosophical Transactions of the Royal Society 2008; 366:3411-3434.
31. Pierard LA, Lancellotti P. The role of ischemic mitral regurgitation in the pathogenesis of acute pulmonary edema. New England Journal of Medicine 2004; 351(16):1627-1634.
32. White HD, Norris RM, Brown MA, Brandt PW, Whitlock RM, Wild CJ. Left ventricular end-systolic volume as the major determinant of survival after recovery from myocardial infarction. Circulation 1987; 76(1):44-51.
33. Kunzelman KS, Einstein DR, Cochran RP. Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences 2007; 362(1484):1393-1406.
34. Einstein DR, Kunzelman KS, Reinhall PG, Nicosia MA, Cochran RP. The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound. Journal of Biomechanical Engineering 2005; 127(1):134-147.
35. Einstein DR, Kunzelman KS, Reinhall PG, Cochran RP, Nicosia MA. Haemodynamic determinants of the mitral valve closure sound: a finite element study. Medical and Biological Engineering and Computing 2004; 42(6):832-846.
36. Cochran RP, Kunzelman KS, Chuong CJ, Sacks MS, Eberhart RC. Nondestructive analysis of mitral valve collagen fiber orientation. ASAIO Transactions 1991; 37(3):M447-M448.
37. May-Newman K, Yin FC. Biaxial mechanical behavior of excised porcine mitral valve leaflets. American Journal of Physiology 1995; 269(4 Pt 2):H1319-H1327.
38. May-Newman K, Yin FC. A constitutive law for mitral valve tissue. Journal of Biomechanical Engineering 1998; 120(1):38-47.
39. Kunzelman KS, Cochran RP, Verrier ED, Eberhardt RC. Anatomic basis for mitral valve modeling. Journal of Heart Valve Disease 1994; 3:491-496.
40. Salisbury PF, Cross CE, Rieben PA. Chorda tendinae tension. American Journal of Physiology 1962; 205(2): 385-392.
41. Komeda M, Glasson JR, Bolger AF, Daughters GT, Niczyporuk MA, Ingels NB, Miller DC. Three-dimensional dynamic geometry of the normal canine mitral annulus and papillary muscles. Circulation 1996; 94(9 Supplement):159-163.
42. Dagum P, Timek TA, Green GR, Lai D, Daughters GT, Liang DH, Hayase M, Ingels NB, Miller DC. Coordinatefree analysis of mitral valve dynamics in normal and iscemic hearts. Circulation 2000; 102(Suppl-III):62-69.
43. Komeda M, Glasson JR, Bolger AF, Daughters GT, Ingels NB, Miller DC. Papillary muscle-left ventricular wall 'complex'. Journal of Thoracic and Cardiovascular Surgery 1997; 113(2):292-301.
44. Reimink MS, Kunzelman KS, Verrier ED, Cochran RP. The effect of anterior chordal replacement on mitral valve function and stresses. A finite element study. ASAIO Journal 1995; 41(3):M754-M762.
45. Reimink MS, Kunzelman KS, Cochran RP. The effect of chordal replacement suture length on function and stresses in repaired mitral valves: a finite element study. Journal of Heart Valve Disease 1996; 5(4):365-375.
46. Cochran RP, Kunzelman KS. Effect of papillary muscle position on mitral valve function: relationship to homografts. Annals of Thoracic Surgery 1998; 66(6 Supplement):S155-S161.
47. Benson DJ. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering 1992; 99:235-394.
48. Benson DJ. Momentum advection on a staggered mesh. Journal of Computational Physics 1992; 100:143-162.
49. Souli M. An Eulerian and fluid-structure coupling algorithm in LS-DYNA. Emerging Technologies in Fluids, Structures and Fluid/Structure Interactions, vol. 396. ASME: New York, 1999.
50. Jensen KT, Fontaine A, Yoganathan AP. Improved in vitro quantification of the force exerted by the papillary muscle on the left ventricular wall: three-dimensional force vector measurement system. Annals of Biomedical Engineering 2001; 29(5):406-413.
51. Blick EF, Sabbah HN, Stein PD. One-dimensional model of diastolic semilunar valve vibrations productive of heart sounds. Journal of Biomechanics 1979; 12:223-227.
52. Genest J, Durand LG. Relationship of the left ventricular and apical first sounds to the left ventricular derivative. Medical and Biological Engineering and Computing 1985; 23:95-98.
53. Harvey WP. Cardiac pearls. Disease-A-Month 1994; 40(2):41-113.
54. Perloff JK. Cardiac auscultation. Disease-A-Month 1980; 26(9):1-47.
55. Sakamoto T. So-called 'apical' systolic murmur of mitral regurgitation is not 'apical'. Journal of Cardiology 1995; 25(6):329-334.
56. Hashim SR, Fontaine A, Shengqui H, Levine RA, Yoganathan AJ. A three-component force vector cell for in vitro quantification of force exerted by the papillary muscle on the left ventricular wall. Journal of Biomechanics 1997; 30(10):1071-1075.
57. Nielsen RA, Nygaard H, Fontaine A. Chordal force distribution determines systolic mitral leaflet configuration and severity of functional mitral regurgitation. Journal of the American College of Cardiology 1999; 33:843-853.
58. Moussou P. A kinematic method for the computation of the natural modes of fluid-structure interaction systems. Journal of Fluids and Structures 2005; 20(10):643-658.
59. Lorensen WE, Cline HE. Marching cubes: a high resolution 3d surface construction algorithm. Computer Graphics 1987; 21:163-169.
60. Walker JC, Guccione JM, Jiang Y, Zhang P,Wallace AW, Hsu EW, Ratcliffe MB. Helical myofiber orientation after myocardial infarction and left ventricular surgical restoration in sheep. Journal of Thoracic and Cardiovascular Surgery 2005; 129(2):382-390.
61. Kuprat AP, Mosso SJ. Efficient algorithms for mapping cell quantities between overlapped 3-d unstructured meshes. Technical Report LA-UR-05-5084, Los Alamos National Laboratory, 2005.
62. Jiang Y, Guccione JM, Ratcliffe MB, Hsu EW. Transmural heterogeneity of diffusion anisotropy in the sheep myocardium characterized by mr diffusion tensor imaging. American Journal of Physiology: Heart and Circulatory Physiology 2007; 293(4):H2377-H2384.
63. Anderson RH, Sanchez-Quintana D, Niederer P. Structural-functional correlates of the 3-dimensional arrangement of myocytes making up the ventricular walls. Journal of Thoracic and Cardiovascular Surgery 2008; 136(1): 10-18.
64. Einstein DR, Freed AD, Stander N, Fata B, Vesely I. Inverse parameter fitting of biological tissues: a response surface approach. Annals of Biomedical Engineering 2005; 33(12):1819-1830.
65. Chen K, Fata B, Einstein DR. Characterization of the highly nonlinear and anisotropic vascular tissues from experimental inflation data: a validation study toward the use of clinical data for in-vivo modeling and analysis. Annals of Biomedical Engineering 2008; 36(10):1668-1680.
66. Roux WJ, Stander N, Haftka RT. Response surface approximations for structural optimization. International Journal for Numerical Methods in Engineering 1998; 42:517-534.
67. Stander N. On the robustness of a simple domain reduction scheme for simulation-based optimization. Engineering Computations 2002; 19(4):431-450.
68. Myers RH. Response Surface Methodology: Process and Product Optimization using Designed Experiments. Wiley: New York, 2002.
69. Guccione JM, Waldman LK, McCulloch AD. Mechanics of active contraction in cardiac muscle: part II-cylindrical models of the systolic left ventricle. Journal of Biomechanical Engineering 1993; 115(1):82-90.
70. An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data
71. Variational generation of prismatic boundarylayer meshes
72. Jiao X. Face offsetting: a unified approach for explicit moving interfaces. Journal of Computational Physics 2007; 220:612-625.
73. Lorensen WE, Cline HE. Marching cubes: a high resolution 3-d surface construction algorithm. Computer Graphics 1987; 21(4):163-170.
74. Newman TS, Yi H. A survey of the marching cubes algorithm. Computers and Graphics 2006; 30:854-879.
75. Amenta N, Bern M. Surface reconstruction by Voronoi filtering. Discrete and Computational Geometry 1999; 22:481-504.
76. Khamayseh A, Hansen G. Use of the spatial kD-tree in computational physics applications. Communications in Computational Physics 2007; 2:545-576.
77. Zhang Y, Bajaj C, Sohn BS. 3d finite element meshing from imaging data. Computer Methods in Applied Mechanics and Engineering 2005; 194:5083-5106.
78. Zarins CK, Taylor CA, Hughes TJR. Finite element modeling of blood flow in arteries. Computer Methods in Applied Mechanics and Engineering 1998; 158:155-196.
79. Longest WP. Comparison of blood particle deposition models for non-parallel flow domains. Journal of Biomechanics 2003; 36(3):421-430.
80. Chiou MC. Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder. Acta Mechanica 1998; 129:1619-6937.
81. Kroger C, Drossinos Y. Particle deposition in a turbulent boundary layer over a large particle size spectrum. Journal of Aerosol Science 1997; 28:631-632.
82. Adaptive tetrahedral mesh generation by constrained Delaunay refinement
83. Cattaruzza M, Guzik TJ, Slodowski W, Pelvan A, Becker J, Halle M, Buchwald AB, Channon KM, Hecker M. Shear stress insensitivity of endothelial nitric oxide synthase expression as a genetic risk factor for coronary heart disease. Circulation Research 2004; 95(8):841-847.
84. Chen LC, Nadziejko C. Effects of subchronic exposures to concentrated ambient particles (CAPs) in mice. V. CAPs exacerbate aortic plaque development in hyperlipidemic mice. Inhalation Toxicology 2005; 17(4-5): 217-224.
85. Chien S, Li S, Shiu YT, Li YS. Molecular basis of mechanical modulation of endothelial cell migration. Frontiers in Bioscience 2005; 10:1985-2000.
86. Cummins PM, Cotter EJ, Cahill PA. Hemodynamic regulation of metallopeptidases within the vasculature. Protein and Peptide Letters 2004; 11(5):433-442.
87. Dardik A, Yamashita A, Aziz F, Asada H, Sumpio BE. Shear stress-stimulated endothelial cells induce smooth muscle cell chemotaxis via platelet-derived growth factor-BB and interleukin-1alpha. Journal of Vascular Surgery 2005; 41(2):321-331.
88. Ganguli A, Persson L, Palmer IR, Evans I, Yang L, Smallwood R, Black R, Qwarnstrom EE. Distinct NF-kappaB regulation by shear stress through ras-dependent IkappaBalpha oscillations: real-time analysis of flow-mediated activation in live cells. Circulation Research 2005; 96(6):626-634.
89. Butcher JT, Markwald RR. Valvulogenesis: the moving target. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences 2007; 362(1484):1489-1503.
90. Butcher JT, Nerem RM. Valvular endothelial cells and the mechanoregulation of valvular pathology. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences 2007; 362(1484):1445-1457.
91. Butcher JT, Tressel S, Johnson T, Turner D, Sorescu G, Jo H, Nerem RM. Transcriptional profiles of valvular and vascular endothelial cells reveal phenotypic differences: influence of shear stress. Arteriosclerosis, Thrombosis, and Vascular Biology 2006; 26(1):69-77.
92. Idelsohn SR, O{ogonek}nate E, Calvo N, Del Pin F. The meshless finite element method. International Journal for Numerical Methods in Engineering 2003; 58:893-912.
93. Idelsohn SR, O{ogonek}nate E, Del Pin F. A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Computers and Structures 2003; 82:655-671.
94. Idelsohn SR, O{ogonek}nate E, Del Pin F. The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves. International Journal for Numerical Methods in Engineering 2004; 61:964-984.
95. Aubry R, Idelsohn SR, O{ogonek}nate E. Particle finite element method in fluid mechanics including thermal convection-diffusion. Computers and Structures 2004; 83:1459-1475.
96. Del Pin F, Idelsohn SR, O{ogonek}nate E, Aubry R. The ALE/lagrangian particle finite element method: a new approach to computation of free-surface flows and fluid-object interactions. Computers and Fluids 2007; 36:27-38.
97. Freed AD, Einstein DR, Vesely I. Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay. Biomechanics and Modeling in Mechanobiology 2005; 4(2-3):100-117.
98. Badia S, Codina R. Pressure segregation methods based on a discrete pressure poisson equation. An algebraic approach. International Journal for Numerical Methods in Fluids 2007; 56:351-382.
99. Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite elements methods. Computer Methods in Applied Mechanics and Engineering 2000; 190:1579-1599.
100. Codina R. Pressure stability in fractional step finite element methods for incompressible flows. Journal of Computational Physics 2001; 170:112-140.
101. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
102. Watson SF. Computing the Delaunay tesselation with application to voronoi polytopes. The Computer Journal 1981; 24:167-172.
103. Stijnen JMA, de Hart J, Bovendeerd PHM, van de Vosse FN. Evaluation of a ficticious domain method for predicting the dynamic response of mechanical heart valves. Journal of Fluids and Structures 2004; 19:835-850.
104. van Loon R, Anderson PD, van de Vosse FN, Sherwin SJ. Comparison of various fluid-structure interaction methods for deformable bodies. Computers and Structures 2007; 85(11-14):833-843.
105. Dumont K, Vierendeels JA, Segers P, Van Nooten GJ, Verdonck PR. Predicting ats open pivot heart valve performance with computational fluid dynamics. Journal of Heart Valve Disease 2005; 14(3):393-399.
106. De Hart J, Baaijens FP, Peters GW, Schreurs PJ. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. Journal of Biomechanics 2003; 36(5):699-712.
107. Carson JP, Ju T, Lu HC, Thaller C, Xu M, Pallas SL, Crair MC, Warren J, Chiu W, Eichele G. A digital atlas to characterize the mouse brain transcriptome. PLoS Computational Biology 2005; 1(4):e41.
108. Bello M, Ju T, Carson J, Warren J, Chiu W, Kakadiaris IA. Learning-based segmentation framework for tissue images containing gene expression data. IEEE Transactions on Medical Imaging 2007; 26(5):728-744.
109. Ju T, Warren J, Carson J, Bello M, Kakadiaris I, Chiu W, Thaller C, Eichele G. 3d volume reconstruction of a mouse brain from histological sections using warp filtering. Journal of Neuroscience Methods 2006; 156(1-2):84-100.
110. Ju T, Warren J, Carson J, Eichele G, Chiu W, Bello M, Kakadiaris I. Building 3d surface networks from 2d curve networks with application to anatomical modeling. The Visual Computer 2005; 21(8-10):764-773.
111. Glocker B, Komodakis N, Paragios N, Tziritas G, Navab N. Inter and intra-modal deformable registration: continuous deformations meet efficient optimal linear programming. Information Processing in Medical Imaging, Kerkrade, Netherlands, July 2007.
112. Guccione JM, Walker JC, Beitler JR, Moonly SM, Zhang P, Guttman MA, Ozturk C, McVeigh ER, Wallace AW, Saloner DA, Ratcliffe MB. The effect of anteroapical aneurysm plication on end-systolic three-dimensional strain in the sheep: a magnetic resonance imaging tagging study. Journal of Thoracic and Cardiovascular Surgery 2006; 131(3):579-586e3.
113. Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Fata B, Hsu EW, Saloner D, Guccione JM. MRI-based finite-element analysis of left ventricular aneurysm. American Journal of Physiology: Heart and Circulatory Physiology 2005; 289(2):H692-H700.