Quantification and simulation of layer-specific mitral valve interstitial cells deformation under physiological loading

Journal of Theoretical Biology

Volumn 373, Issue , 2015, Pages 26-39

  Lee, Chung Hao ^a   Carruthers, Christopher A ^b   Ayoub, Salma ^a   Gorman, Robert C ^c   Gorman, Joseph H ^c   Sacks, Michael S ^a  

^a The University of Texas at Austin   (United States)

^b Cardiac Rhythm Disease Management   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Finite element simulations; MPM imaging analysis; Multi level macro micro modeling; MVIC microenvironment; Simplified structural constitutive model

Indexed keywords

CONSTITUTIVE EQUATION; DEFORMATION; FINITE ELEMENT METHOD; IMAGE ANALYSIS; LOADING; MODELING; PHYSIOLOGY;

ANIMAL EXPERIMENT; ANIMAL MODEL; ANIMAL TISSUE; ARTICLE; BIOMECHANICS; CELL DAMAGE; CELL FUNCTION; CELL NUCLEUS; CONTROLLED STUDY; CYTOARCHITECTURE; EXTRACELLULAR MATRIX; FINITE ELEMENT ANALYSIS; IN VIVO STUDY; LEYDIG CELL; LIMIT OF QUANTITATION; MATHEMATICAL ANALYSIS; MECHANICAL STIMULATION; MICROENVIRONMENT; MITRAL VALVE; MITRAL VALVE DISEASE; MITRAL VALVE INTERSTITIAL CELL DEFORMATION; MULTIPHOTON MICROSCOPY; MUSCLE RIGIDITY; NONHUMAN; PATHOPHYSIOLOGY; PHENOTYPE; PRIORITY JOURNAL; SIMULATION; SINUS NODE; SPONGIOSA LAYER; TISSUE LOADING; ANIMAL; BIOLOGICAL MODEL; CELL SHAPE; CYTOLOGY; ELASTICITY; MECHANICAL STRESS; PHYSIOLOGY; SHEEP; WEIGHT BEARING;

ANIMALS; CELL SHAPE; ELASTICITY; EXTRACELLULAR MATRIX; FINITE ELEMENT ANALYSIS; MITRAL VALVE; MODELS, CARDIOVASCULAR; SHEEP; STRESS, MECHANICAL; WEIGHT-BEARING;

EID: 84925934817     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2015.03.004     Document Type: Article

References (95)

1. Aikawa E., Whittaker P., Farber M., Mendelson K., Padera R.F., Aikawa M., Schoen F.J. Human semilunar cardiac valve remodeling by activated cells from fetus to adult: implications for postnatal adaptation, pathology, and tissue engineering. Circulation 2006, 113:1344-1352.
2. Bairati A., DeBiasi S. Presence of a smooth muscle system in aortic valve leaflets. Anat. Embryol. 1981, 161:329-340.
3. Balachandran K., Sucosky P., Jo H., Yoganathan A.P. Elevated cyclic stretch alters matrix remodeling in aortic valve cusps: implications for degenerative aortic valve disease. Am. J. Physiol. Heart Circ. Physiol. 2009, 296:H756-H764. 10.1152/ajpheart.00900.2008.
4. Balachandran K., Sucosky P., Jo H., Yoganathan A.P. Elevated cyclic stretch alters matrix remodeling in aortic valve cusps: implications for degenerative aortic valve disease. Am. J. Physiol.-Heart Circ. Physiol. 2009, 296:H756-H764.
5. Balachandran K., Konduri S., Sucosky P., Jo H., Yoganathan A. An ex vivo study of the biological properties of porcine aortic valves in response to circumferential cyclic stretch. Ann. Biomed. Eng. 2006, 34:1655-1665.
6. Balachandran K., Konduri S., Sucosky P., Jo H., Yoganathan A.P. An ex vivo study of the biological properties of porcine aortic valves in response to circumferential cyclic stretch. Ann. Biomed. Eng. 2006, 34:1655-1665.
7. Buchanan R.M., Sacks M.S. Interlayer micromechanics of the aortic heart valve leaflet. Biomech. Model Mechanobiol. 2013, 13:813-826. doi:10.1007/s10237-013-0536-6, In Press. 10.1007/s10237-013-0536-6.
8. Carruthers C.A., Alfieri C.M., Joyce E.M., Watkins S.C., Yutzey K.E., Sacks M.S. Gene expression and collagen fiber micromechanical interactions of the semilunar heart valve interstitial cell. Cell. Mol. Bioeng. 2012, 5:254-265. 10.1007/s12195-012-0230-2.
9. Carruthers, C.A., Good, B., D'Amore, A., Liao, J., Amini, R., Watkins, S.C., Sacks, M.S., 2012b. Alterations in the microstructure of the anterior mitral valve leaflet under physiological stress. In: ASME 2012 Summer Bioengineering Conference. American Society of Mechanical Engineers, pp. 227-228.
10. Chen J.H., Simmons C.A. Cell-matrix interactions in the pathobiology of calcific aortic valve disease: critical roles for matricellular, matricrine, and matrix mechanics cues. Circ. Res. 2011, 108:1510-1524. 10.1161/CIRCRESAHA.110.234237.
11. Chuong C.J., Fung Y.C. On residual stresses in arteries. J. Biomech. Eng. 1986, 108:189-192.
12. D'Amore, A., Stella, J.A., Schmidt, D.E., Wagner, W.R., Sacks, M.S., 2009. Micro-meso scale model of electrospun poly (ester urethane) urea scaffolds. In: Proceedings of the ASME 2009 Summer Bioengineering Conference, Lake Tahoe, CA.
13. Dal-Bianco J.P., Aikawa E., Bischoff J., Guerrero J.L., Handschumacher M.D., Sullivan S., Johnson B., Titus J.S., Iwamoto Y., Wylie-Sears J., Levine R.A., Carpentier A. Active adaptation of the tethered mitral valve: insights into a compensatory mechanism for functional mitral regurgitation. Circulation 2009, 120:334-342. 10.1161/CIRCULATIONAHA.108.846782.
14. Dunkman A.A., Buckley M.R., Mienaltowski M.J., Adams S.M., Thomas S.J., Kumar A., Beason D.P., Iozzo R.V., Birk D.E., Soslowsky L.J. The injury response of aged tendons in the absence of biglycan and decorin. Matrix Biol. 2014, 35:232-238. In Press. 10.1016/j.matbio.2013.10.008.
15. Dunkman A.A., Buckley M.R., Mienaltowski M.J., Adams S.M., Thomas S.J., Satchell L., Kumar A., Pathmanathan L., Beason D.P., Iozzo R.V. Decorin expression is important for age-related changes in tendon structure and mechanical properties. Matrix Biol. 2013, 32:3-13.
16. Einstein D.R., Kunzelman K.S., Reinhall P.G., Cochran R.P., Nicosia M.A. Haemodynamic determinants of the mitral valve closure sound: a finite element study. Med. Biol. Eng. Comput. 2004, 42:832-846.
17. El-Hamamsy I., Balachandran K., Yacoub M.H., Stevens L.M., Sarathchandra P., Taylor P.M., Yoganathan A.P., Chester A.H. Endothelium-dependent regulation of the mechanical properties of aortic valve cusps. J. Am. Coll. Cardiol. 2009, 53:1448-1455.
18. Fan R., Sacks M.S. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J. Biomech. 2014, 53:2045-2054. In Press. 10.1016/j.jbiomech.2014.03.014.
19. Fata B., Carruthers C.A., Gibson G., Watkins S.C., Gottlieb D., Mayer J.E., Sacks M.S. Regional structural and biomechanical alterations of the ovine main pulmonary artery during postnatal growth. J. Biomech. Eng. 2013, 135:021022. 10.1115/1.4023389.
20. Filip D.A., Radu A., Simionescu M. Interstitial cells of the heart valve possess characteristics similar to smooth muscle cells. Circ. Res. 1986, 59:310-320.
21. Flanagan T.C., Black A., O'Brien M., Smith T.J., Pandit A.S. Reference models for mitral valve tissue engineering based on valve cell phenotype and extracellular matrix analysis. Cells Tissues Organs 2006, 183:12-23.
22. Fung Y.C. What are the residual stresses doing in our blood vessels?. Ann. Biomed. Eng. 1991, 19:237-249.
23. Fung Y.C. Biomechanics: Mechanical Properties of Living Tissues 1993, Springer Verlag, New York.
24. Fung Y.C., Liu S.Q. Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J. Appl. Physiol. 1991, 70:2455-2470.
25. Gillinov A.M., Wierup P.N., Blackstone E.H., Bishay E.S., Cosgrove D.M., White J., Lytle B.W., McCarthy P.M. Is repair preferable to replacement for ischemic mitral regurgitation?. J. Thorac. Cardiovasc. Surg. 2001, 122:1125-1141.
26. Grande-Allen K., Liao J. The heterogeneous biomechanics and mechanobiology of the mitral valve: implications for tissue engineering. Curr. Cardiol. Rep. 2011, 13:113-120. 10.1007/s11886-010-0161-2.
27. Grande-Allen K.J., Griffin B.P., Ratliff N.B., Cosgrove D.M., Vesely I. Glycosaminoglycan profiles of myxomatous mitral leaflets and chordae parallel the severity of mechanical alterations. J. Am. Coll. Cardiol. 2003, 42:271-277.
28. Gupta V., Grande-Allen K.J. Effects of static and cyclic loading in regulating extracellular matrix synthesis by cardiovascular cells. Cardiovasc. Res. 2006, 72:375-383.
29. Gupta V., Werdenberg J.A., Mendez J.S., Grande-Allen K.J. Influence of strain on proteoglycan synthesis by valvular interstitial cells in 3D culture. Acta Biomater. 2007, 4:88-96.
30. Gupta V., Tseng H., Lawrence B.D., Jane Grande-Allen K. Effect of cyclic mechanical strain on glycosaminoglycan and proteoglycan synthesis by heart valve cells. Acta Biomater. 2009, 5:531-540.
31. Huang H.Y., Liao J., Sacks M.S. In-situ deformation of the aortic valve interstitial cell nucleus under diastolic loading. J. Biomech. Eng. 2007, 129:880-889. 10.1115/1.2801670.
32. Konduri S., Xing Y., Warnock J.N., He Z., Yoganathan A.P. Normal physiological conditions maintain the biological characteristics of porcine aortic heart valves: an ex vivo organ culture study. Ann. Biomed. Eng. 2005, 33:1158-1166.
33. Kunzelman K.S., Einstein D.R., Cochran R.P. Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philos. Trans. R. Soc. London B Biol. Sci. 2007, 362:1393-1406.
34. Kunzelman K.S., Cochran R.P., Murphree S.S., Ring W.S., Verrier E.D., Eberhart R.C. Differential collagen distribution in the mitral valve and its influence on biomechanical behaviour. J. Heart Valve Dis. 1993, 2:236-244.
35. Lacerda C.M., Kisiday J., Johnson B., Orton E.C. Local serotonin mediates cyclic strain-induced phenotype transformation, matrix degradation, and glycosaminoglycan synthesis in cultured sheep mitral valves. Am. J. Physiol. Heart Circ. Physiol. 2012, 302:H1983-H1990.
36. Lanir Y. Mechanisms of residual stress in soft tissues. J. Biomech. Eng. 2009, 131:044506. 10.1115/1.3049863.
37. Lee C.H., Amini R., Gorman R.C., Gorman J.H., Sacks M.S. An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment. J. Biomech. 2014, 47:2055-2063. 10.1016/j.jbiomech.2013.10.058.
38. Li C., Xu Q. Mechanical stress-initiated signal transductions in vascular smooth muscle cells. Cell. Signall. 2000, 12:435-445.
39. Liu S.Q., Fung Y.C. Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 1989, 111:325-335.
40. Lopez-Pamies O., Castañeda P.P. Second-order homogenization estimates incorporating field fluctuations in finite elasticity. Math. Mech. Solids 2004, 9:243-270.
41. Mansi T., Voigt I., Georgescu B., Zheng X., Mengue E.A., Hackl M., Ionasec R.I., Noack T., Seeburger J., Comaniciu D. An integrated framework for finite-element modeling of mitral valve biomechanics from medical images: application to MitralClip intervention planning. Med. Image Anal. 2012, 16:1330-1346.
42. May-Newman K., Yin F.C. A constitutive law for mitral valve tissue. J. Biomech. Eng. 1998, 120:38-47.
43. Merryman, W.D., Youn, I., Guilak, F., Sacks, M.S., 2004. Contractile Abilities of the Aortic Valve Leaflet Interstitial Cell. Biomedical Engineering Society (BMES) Annual Fall Meeting, Philadelphia, PA.
44. Merryman W.D., Huang H.Y.S., Schoen F.J., Sacks M.S. The effects of cellular contraction on aortic valve leaflet flexural stiffness. J. Biomech. 2006, 39:88-96.
45. Merryman W.D., Bieniek P.D., Guilak F., Sacks M.S. Viscoelastic properties of the aortic valve interstitial cell. J. Biomech. Eng. 2009, 131:041005. 10.1115/1.3049821.
46. Merryman W.D., Liao J., Parekh A., Candiello J.E., Lin H., Sacks M.S. Differences in tissue-remodeling potential of aortic and pulmonary heart valve interstitial cells. Tissue Eng. 2007, 13:2281-2289.
47. Merryman W.D., Youn I., Lukoff H.D., Krueger P.M., Guilak F., Hopkins R.A., Sacks M.S. Correlation between heart valve interstitial cell stiffness and transvalvular pressure: implications for collagen biosynthesis. Am. J. Physiol. Heart Circ. Physiol. 2006, 59:H224-H231.
48. Merryman W.D., Youn I., Lukoff H.D., Krueger P.M., Guilak F., Hopkins R.A., Sacks M.S. Correlation between heart valve interstitial cell stiffness and transvalvular pressure: implications for collagen biosynthesis. Am. J. Physiol. Heart Circ. Physiol. 2006, 290:H224-H231.
49. Messier R.H., Bass B.L., Aly H.M., Jones J.L., Domkowski P.W., Wallace R.B., Hopkins R.A. Dual structural and functional phenotypes of the porcine aortic valve interstitial population: characteristics of the leaflet myofibroblast. J. Surg. Res. 1994, 57:1-21.
50. Mulholland D.L., Gotlieb A.I. Cell biology of valvular interstitial cells. Can. J. Cardiol. 1996, 12:231-236.
51. Mura T. Micromechanics of Defects in Solids 1987, Springer.
52. Ogden R. Nonlinear elasticity, anisotropy, material stability, and residual stresses in soft tissue. Biomechanics of Soft Tissue in Cardiovascular System 2003, Springer, New York. R. Ogden (Ed.).
53. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I-theory. J. Mech. Phys. Solids 2002, 50:737-757.
54. Prot V., Skallerud B. Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers. Comput. Mech. 2009, 43:353-368. 10.1007/s00466-008-0310-2.
55. Prot V., Skallerud B., Holzapfel G. Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation. Int. J. Numer. Methods Eng. 2007, 71:987-1008. 10.1002/nme.1983.
56. Quick D.W., Kunzelman K.S., Kneebone J.M., Cochran R.P. Collagen synthesis is upregulated in mitral valves subjected to altered stress. Asaio J. 1997, 43:181-186.
57. Rabkin-Aikawa E., Farber M., Aikawa M., Schoen F.J. Dynamic and reversible changes of interstitial cell phenotype during remodeling of cardiac valves. J. Heart Valve Dis. 2004, 13:841-847.
58. Rabkin E., Hoerstrup S.P., Aikawa M., Mayer J.E., Schoen F.J. Evolution of cell phenotype and extracellular matrix in tissue-engineered heart valves during in-vitro maturation and in-vivo remodeling. J. Heart Valve Dis. 2002, 11:308-314. discussion 314.
59. Rabkin E., Aikawa M., Stone J.R., Fukumoto Y., Libby P., Schoen F.J. Activated interstitial myofibroblasts express catabolic enzymes and mediate matrix remodeling in myxomatous heart valves. Circulation 2001, 104:2525-2532.
60. Raghupathy R., Barocas V.H. A closed-form structural model of planar fibrous tissue mechanics. J. Biomech. 2009, 42:1424-1428. S0021-9290(09)00202-4 [pii]. 10.1016/j.jbiomech.2009.04.005.
61. Rausch M.K., Famaey N., Shultz T.O., Bothe W., Miller D.C., Kuhl E. Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain. Biomech. Model. Mechanobiol. 2012, 12:1053-1071. 10.1007/s10237-012-0462-z.
62. Robinson P.S., Derwin K.A., Iozzo R.V., Soslowsky L.J., Lin T.W., Reynolds P.R. Strain-rate sensitive mechanical properties of tendon fascicles from mice with genetically engineered alterations in collagen and decorin. J. Biomech. Eng. 2004, 126:252-257.
63. Robinson P.S., Huang T.-F., Kazam E., Iozzo R.V., Soslowsky L.J., Birk D.E. Influence of decorin and biglycan on mechanical properties of multiple tendons in knockout mice. J. Biomech. Eng. 2005, 127:181-185.
64. Ruifrok, A.C., Johnston, D.A., 2001. Quantification of Histochemical Staining by Color Deconvolution. Analytical and Quantitative Cytology and Histology/the International Academy of Cytology [and] American Society of Cytology 23, 291-299.
65. Sacks M. Biaxial mechanical evaluation of planar biological materials. J. Elast. 2000, 61:199-246.
66. Sacks M.S., Yoganathan A.P. Heart valve function: a biomechanical perspective. Philos. Trans. R. Soc. London B Biol. Sci. 2008, 363:1369-1391. doi:814417U817GQHL00 [pii] 10.1098/rstb.2008.0062.
67. Sacks M.S., Smith D.B., Hiester E.D. A small angle light scattering device for planar connective tissue microstructural analysis. Ann. Biomed. Eng. 1997, 25:678-689.
68. Sacks M.S., Merryman W.D., Schmidt D.E. On the biomechanics of heart valve function. J. Biomech. 2009, 42:1804-1824. doi:S0021-9290(09)00265-6 [pii] 10.1016/j.jbiomech.2009.05.015.
69. Sacks M.S., Enomoto Y., Graybill J.R., Merryman W.D., Zeeshan A., Yoganathan A.P., Levy R.J., Gorman R.C., Gorman J.H. In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann. Thorac. Surg. 2006, 82:1369-1377.
70. Sadoshima J., Izumo S. The cellular and molecular response of cardiac myocytes to mechanical stress. Ann. Rev. Physiol. 1997, 59:551-571.
71. Schmidt C., Pommerenke H., Dürr F., Nebe B., Rychly J. Mechanical stressing of integrin receptors induces enhanced tyrosine phosphorylation of cytoskeletally anchored proteins. J. Biol. Chem. 1998, 273:5081-5085.
72. Simo J.C., Hughes T.J.R. Computational Inelasticity 1998, Springer, New York.
73. Skallerud B., Prot V., Nordrum I.S. Modeling active muscle contraction in mitral valve leaflets during systole: a first approach. Biomech. Model Mechanobiol. 2011, 10:11-26. 10.1007/s10237-010-0215-9.
74. Smith S., Taylor P.M., Chester A.H., Allen S.P., Dreger S.A., Eastwood M., Yacoub M.H. Force generation of different human cardiac valve interstitial cells: relevance to individual valve function and tissue engineering. J. Heart Valve Dis. 2007, 16:440.
75. Stella J.A., Sacks M.S. On the biaxial mechanical properties of the layers of the aortic valve leaflet. J. Biomech. Eng. 2007, 129:757-766. 10.1115/1.2768111.
76. Stephens E., Durst C., Swanson J., Grande-Allen K., Ingels N., Miller D. Functional coupling of valvular interstitial cells and collagen via α2β1 integrins in the mitral leaflet. Cell. Mol. Bioeng 2010, 3:428-437. 10.1007/s12195-010-0139-6.
77. Stephens E.H., Durst C.A., West J.L., Grande-Allen K.J. Mitral valvular interstitial cell responses to substrate stiffness depend on age and anatomic region. Acta Biomater. 2011, 7:75-82. 10.1016/j.actbio.2010.07.001.
78. Stephens E.H., de Jonge N., McNeill M.P., Durst C.A., Grande-Allen K.J. Age-related changes in material behavior of porcine mitral and aortic valves and correlation to matrix composition. Tissue Eng. Part A 2010, 16:867-878. 10.1089/ten.tea.2009.0288.
79. Stephens E.H., Nguyen T.C., Itoh A., Ingels N.B., Miller D.C., Grande-Allen K.J. The effects of mitral regurgitation alone are sufficient for leaflet remodeling. Circulation 2008, 118:S243-S249. 10.1161/circulationaha.107.757526.
80. Stephens E.H., Timek T.A., Daughters G.T., Kuo J.J., Patton A.M., Baggett L.S., Ingels N.B., Miller D.C., Grande-Allen K.J. Significant changes in mitral valve leaflet matrix composition and turnover with tachycardia-induced cardiomyopathy. Circulation 2009, 120:S112-S119. 10.1161/CIRCULATIONAHA.108.844159.
81. Stevanella M., Maffessanti F., Conti C.A., Votta E., Arnoldi A., Lombardi M., Parodi O., Caiani E.G., Redaelli A. Mitral valve patient-specific finite element modeling from cardiac MRI: application to an annuloplasty procedure. Cardiovasc. Eng. Tech. 2011, 2:66-76.
82. Sun W., Sacks M.S. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech. Model Mechanobiol. 2005.
83. Taber L.A., Humphrey J.D. Stress-modulated growth, residual stress, and vascular heterogeneity. J. Biomech. Eng. 2001, 123:528-535.
84. Taylor P.M., Batten P., Brand N.J., Thomas P.S., Yacoub M.H. The cardiac valve interstitial cell. Int. J. Biochem. Cell. Biol. 2003, 35:113-118.
85. Upton M.L., Chen J., Guilak F., Setton L.A. Differential effects of static and dynamic compression on meniscal cell gene expression. J. Orthop. Res. 2003, 21:963-969.
86. Votta E., Caiani E., Veronesi F., Soncini M., Montevecchi F.M., Redaelli A. Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios. Philos. Transact. A Math. Phys. Eng. Sci. 2008, 366:3411-3434. 10.1098/rsta.2008.0095.
87. Wang Q., Sun W. Finite element modeling of mitral valve dynamic deformation using patient-specific multi-slices computed tomography scans. Ann. Biomed. Eng. 2013, 41:142-153. 10.1007/s10439-012-0620-6.
88. Watkins S. Immunohistochemistry. Current Protocols in Cytometry 2001, John Wiley & Sons, Inc.
89. Weinberg E.J., Kaazempur-Mofrad M.R. A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics. J. Biomech. 2006, 39:1557-1561.
90. Weinberg E.J., Mofrad M.R.K. Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovasc. Eng. 2007, 7:140-155.
91. Weinberg E.J., Kaazempur Mofrad M.R. A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3D constitutive material model. J. Biomech. 2007, 40:705-711. 10.1016/j.jbiomech.2006.01.003.
92. Weinberg E.J., Kaazempur Mofrad M.R. A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis. J. Biomech. 2008, 41:3482-3487.
93. Weinberg E.J., Shahmirzadi D., Mofrad M.R.K. On the multiscale modeling of heart valve biomechanics in health and disease. Biomech. Model. Mechanobiol. 2010, 9:373-387.
94. Wenk J.F., Zhang Z., Cheng G., Malhotra D., Acevedo-Bolton G., Burger M., Suzuki T., Saloner D.A., Wallace A.W., Guccione J.M., Ratcliffe M.B. First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann. Thorac. Surg. 2010, 89:1546-1553. 10.1016/j.athoracsur.2010.02.036.
95. Wyss K., Yip C.Y., Mirzaei Z., Jin X., Chen J.-H., Simmons C.A. The elastic properties of valve interstitial cells undergoing pathological differentiation. J. Biomech. 2012, 45:882-887.