Biomechanics and Modeling in Mechanobiology

, Volume 14, Issue 6, pp 1281–1302 | Cite as

On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve

  • Chung-Hao Lee
  • Jean-Pierre Rabbah
  • Ajit P. Yoganathan
  • Robert C. Gorman
  • Joseph H. GormanIII
  • Michael S. SacksEmail author
Original Paper


Recent long-term studies showed an unsatisfactory recurrence rate of severe mitral regurgitation 3–5 years after surgical repair, suggesting that excessive tissue stresses and the resulting strain-induced tissue failure are potential etiological factors controlling the success of surgical repair for treating mitral valve (MV) diseases. We hypothesized that restoring normal MV tissue stresses in MV repair techniques would ultimately lead to improved repair durability through the restoration of MV normal homeostatic state. Therefore, we developed a micro- and macro- anatomically accurate MV finite element model by incorporating actual fiber microstructural architecture and a realistic structure-based constitutive model. We investigated MV closing behaviors, with extensive in vitro data used for validating the proposed model. Comparative and parametric studies were conducted to identify essential model fidelity and information for achieving desirable accuracy. More importantly, for the first time, the interrelationship between the local fiber ensemble behavior and the organ-level MV closing behavior was investigated using a computational simulation. These novel results indicated not only the appropriate parameter ranges, but also the importance of the microstructural tuning (i.e., straightening and re-orientation) of the collagen/elastin fiber networks at the macroscopic tissue level for facilitating the proper coaptation and natural functioning of the MV apparatus under physiological loading at the organ level. The proposed computational model would serve as a logical first step toward our long-term modeling goal—facilitating simulation-guided design of optimal surgical repair strategies for treating diseased MVs with significantly enhanced durability.


Mapped fiber microstructural architecture Image-based FE simulation Simplified structural constitutive model Affine fiber kinematics In vitro validations 



Support from the National Institutes of Health (NIH) Grants R01 HL119297, HL63954, HL103723, and HL73021 is greatly acknowledged. Dr. Chung-Hao Lee was supported in part by the American Heart Association (AHA) Postdoctoral Fellowship (14POST18160013) and a UT Austin ICES Postdoctoral Fellowship. The assistance from Ted Weber and Ronen G. Aniti for image segmentation and development of the MV finite element model is greatly appreciated.

Conflict of interest

None of the authors have a conflict of interests with the present work.


  1. Adams DH, Rosenhek R, Falk V (2010) Degenerative mitral valve regurgitation: best practice revolution. Eur Heart J 31:1958–1966CrossRefGoogle Scholar
  2. Aggarwal A, Aguilar VS, Lee C-H, Ferrari G, Gorman JH, Gorman RC, Sacks MS (2013) Patient-specific modeling of heart valves: from image to simulation. In: Qurselin S, Rueckert D, Smith N (eds) Functional imaging and modeling of the heart. Springer, Berlin, pp 141–149Google Scholar
  3. Aggarwal A, Ferrari G, Joyce E, Daniels MJ, Sainger R, Gorman JH 3rd, Gorman R, Sacks MS (2014) Architectural trends in the human normal and bicuspid aortic valve leaflet and its relevance to valve disease. Ann Biomed Eng 42:986–998CrossRefGoogle Scholar
  4. Amini R, Eckert CE, Koomalsingh K, McGarvey J, Minakawa M, Gorman JH, Gorman RC, Sacks MS (2012) On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann Biomed Eng 40:1455–1467CrossRefGoogle Scholar
  5. Bouxsein ML, Boyd SK, Christiansen BA, Guldberg RE, Jepsen KJ, Müller R (2010) Guidelines for assessment of bone microstructure in rodents using micro-computed tomography. J Bone Miner Res 25:1468–1486CrossRefGoogle Scholar
  6. Braunberger E, Deloche A, Berrebi A, Abdallah F, Celestin JA, Meimoun P, Chatellier G, Chauvaud S, Fabiani JN, Carpentier A (2001) Very long-term results (more than 20 years) of valve repair with carpentier’s techniques in nonrheumatic mitral valve insufficiency. Circulation 104:I8–11CrossRefGoogle Scholar
  7. Carpentier A (1983) Cardiac valve surgery-the “French correction”. J Thorac Cardiovasc Surg 86:323–337Google Scholar
  8. Carpentier A, Relland J, Deloche A, Fabiani J-N, D’Allaines C, Blondeau P, Piwnica A, Chauvaud S, Dubost C (1978) Conservative management of the prolapsed mitral valve. Ann Thorac Surg 26:294–302CrossRefGoogle Scholar
  9. Choi A, Rim Y, Mun JS, Kim H (2014) A novel finite element-based patient-specific mitral valve repair: virtual ring annuloplasty. Biomed Mater Eng 24:341–347Google Scholar
  10. Dal-Bianco JP, Aikawa E, Bischoff J, Guerrero JL, Handschumacher MD, Sullivan S, Johnson B, Titus JS, Iwamoto Y, Wylie-Sears J, Levine RA, Carpentier A (2009) Active adaptation of the tethered mitral valve: insights into a compensatory mechanism for functional mitral regurgitation. Circulation 120:334–342CrossRefGoogle Scholar
  11. David TE, Ivanov J, Armstrong S, Christie D, Rakowski H (2005) A comparison of outcomes of mitral valve repair for degenerative disease with posterior, anterior, and bileaflet prolapse. J Thorac Cardiovasc Surg 130:1242–1249CrossRefGoogle Scholar
  12. David TE, Omran A, Armstrong S, Sun Z, Ivanov J (1998) Long-term results of mitral valve repair for myxomatous disease with and without chordal replacement with expanded polytetrafluoroethylene sutures. J Thorac Cardiovasc Surg 115:1279–1286CrossRefGoogle Scholar
  13. Eckert CE, Zubiate B, Vergnat M, Gorman JH 3rd, Gorman RC, Sacks MS (2009) In vivo dynamic deformation of the mitral valve annulus. Ann Biomed Eng 37:1757–1771CrossRefGoogle Scholar
  14. Einstein DR, Kunzelman KS, Reinhall PG, Cochran RP, Nicosia MA (2004) Haemodynamic determinants of the mitral valve closure sound: a finite element study. Med Biol Eng Comput 42:832–846CrossRefGoogle Scholar
  15. Einstein DR, Kunzelman KS, Reinhall PG, Nicosia MA, Cochran RP (2005) The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound. J Biomech Eng 127:134–147CrossRefGoogle Scholar
  16. Fan R, Sacks MS (2014) Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J Biomech 47:2043–2054CrossRefGoogle Scholar
  17. Flameng W, Herijgers P, Bogaerts K (2003) Recurrence of mitral valve regurgitation after mitral valve repair in degenerative valve disease. Circulation 107:1609–1613CrossRefGoogle Scholar
  18. Flameng W, Meuris B, Herijgers P, Herregods M-C (2008) Durability of mitral valve repair in Barlow disease versus fibroelastic deficiency. J Thorac Cardiovasc Surg 135:274–282CrossRefGoogle Scholar
  19. Flugge W (1972) Tensor analysis and continuum mechanics. Springer, New YorkCrossRefGoogle Scholar
  20. Frater R, Vetter H, Zussa C, Dahm M (1990) Chordal replacement in mitral valve repair. Circulation 82:IV125–IV130Google Scholar
  21. Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  22. Gillinov AM, Blackstone EH, Nowicki ER, Slisatkorn W, Al-Dossari G, Johnston DR, George KM, Houghtaling PL, Griffin B, Sabik JF III (2008) Valve repair versus valve replacement for degenerative mitral valve disease. J Thorac Cardiovas Surg 135:885–893 e882CrossRefGoogle Scholar
  23. Gorman JH 3rd, Gupta KB, Streicher JT, Gorman RC, Jackson BM, Ratcliffe MB, Bogen DK, Edmunds LH Jr (1996) Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization. J Thorac Cardiovasc Surg 112:712–726CrossRefGoogle Scholar
  24. Gorman RC, Gorman JH 3rd (2006) Why should we repair ischemic mitral regurgitation? Ann Thorac Surg 81:785 (author reply 785–786)Google Scholar
  25. Grande-Allen KJ, Borowski AG, Troughton RW, Houghtaling PL, Dipaola NR, Moravec CS, Vesely I, Griffin BP (2005) Apparently normal mitral valves in patients with heart failure demonstrate biochemical and structural derangements: an extracellular matrix and echocardiographic study. J Am Coll Cardiol 45:54–61CrossRefGoogle Scholar
  26. Grashow JS, Yoganathan AP, Sacks MS (2006) Biaxial stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Ann Biomed Eng 34:315–325CrossRefGoogle Scholar
  27. He Z, Ritchie J, Grashow JS, Sacks MS, Yoganathan AP (2005) In vitro dynamic strain behavior of the mitral valve posterior leaflet. J Biomech Eng 127:504–511CrossRefGoogle Scholar
  28. Jassar AS, Minakawa M, Shuto T, Robb JD, Koomalsingh KJ, Levack MM, Vergnat M, Eperjesi TJ, Jackson BM, Gorman JH III (2012) Posterior leaflet augmentation in ischemic mitral regurgitation increases leaflet coaptation and mobility. Ann Thorac Surg 94:1438–1445CrossRefGoogle Scholar
  29. Jensen MO, Jensen H, Levine RA, Yoganathan AP, Andersen NT, Nygaard H, Hasenkam JM, Nielsen SL (2011) Saddle-shaped mitral valve annuloplasty rings improve leaflet coaptation geometry. J Thorac Cardiovasc Surg 142:697–703CrossRefGoogle Scholar
  30. Jimenez JH, Soerensen DD, He Z, He S, Yoganathan AP (2003) Effects of a saddle shaped annulus on mitral valve function and chordal force distribution: an in vitro study. Ann Biomed Eng 31:1171–1181CrossRefGoogle Scholar
  31. Kincaid EH, Riley RD, Hines MH, Hammon JW, Kon ND (2004) Anterior leaflet augmentation for ischemic mitral regurgitation. Ann Thorac Surg 78:564–568 discussion 568CrossRefGoogle Scholar
  32. Komeda M, Glasson JR, Bolger AF, Daughters GT 2nd, MacIsaac A, Oesterle SN, Ingels NB Jr, Miller DC (1997) Geometric determinants of ischemic mitral regurgitation. Circulation 96(II):128–133Google Scholar
  33. Krishnamurthy G, Ennis DB, Itoh A, Bothe W, Swanson JC, Karlsson M, Kuhl E, Miller DC, Ingels NB Jr (2008) Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis. Am J Physiol Heart Circ Physiol 295:H1141–H1149CrossRefGoogle Scholar
  34. Kunzelman KS, Cochran RP, Chuong C, Ring WS, Verrier ED, Eberhart RD (1993a) Finite element analysis of the mitral valve. J Heart Valve Dis 2:326–340Google Scholar
  35. Kunzelman KS, Cochran RP, Murphree SS, Ring WS, Verrier ED, Eberhart RC (1993b) Differential collagen distribution in the mitral valve and its influence on biomechanical behaviour. J Heart Valve Dis 2:236–244Google Scholar
  36. Kunzelman KS, Einstein DR, Cochran RP (2007) Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philos Trans R Soc Lond B Biol Sci 362:1393–1406CrossRefGoogle Scholar
  37. Kunzelman KS, Reimink MS, Cochran RP (1998) Flexible versus rigid ring annuloplasty for mitral valve annular dilatation: a finite element model. J Heart Valve Dis 7:108–116Google Scholar
  38. Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16:1–12CrossRefGoogle Scholar
  39. Lee C-H, Amini R, Sakamoto Y, Carruthers CA, Aggarwal A, Gorman RC, Gorman JH III, Sacks MS (2015a) Mitral valves: a computational framework. In: De S, Hwang W, Kuhl E (eds) Multiscale modeling in biomechanics and mechanobiology. Springer, London, pp 223–255Google Scholar
  40. Lee CH, Amini R, Gorman RC, Gorman JH 3rd, Sacks MS (2014) An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment. J Biomech 47:2055–2063CrossRefGoogle Scholar
  41. Lee CH, Carruthers CA, Ayoub S, Gorman RC, Gorman JH, Sacks MS (2015b) Quantification and simulation of layer-specific mitral valve interstitial cell deformation under physiological loading. J Theor Biol 373:26–39CrossRefGoogle Scholar
  42. Lee CH, Zhang W, Liao J, Carruthers CA, Sacks J, Sacks MS (2015c) On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet under simulated physiological loading. Biophys J 108:1–14CrossRefGoogle Scholar
  43. Mahmood F, Gorman JH 3rd, Subramaniam B, Gorman RC, Panzica PJ, Hagberg RC, Lerner AB, Hess PE, Maslow A, Khabbaz KR (2010) Changes in mitral valve annular geometry after repair: saddle-shaped versus flat annuloplasty rings. Ann Thorac Surg 90:1212–1220CrossRefGoogle Scholar
  44. Mansi T, Voigt I, Georgescu B, Zheng X, Mengue EA, Hackl M, Ionasec RI, Noack T, Seeburger J, Comaniciu D (2012) An integrated framework for finite-element modeling of mitral valve biomechanics from medical images: application to MitralClip intervention planning. Med Image Anal 16:1330–1346CrossRefGoogle Scholar
  45. May-Newman K, Yin FC (1998) A constitutive law for mitral valve tissue. J Biomech Eng 120:38–47CrossRefGoogle Scholar
  46. Pouch AM, Wang H, Takabe M, Jackson BM, Gorman J, Gorman RC, Yushkevich PA, Sehgal CM (2014) Fully automatic segmentation of the mitral leaflets in 3D transesophageal echocardiographic images using multi-atlas joint label fusion and deformable medial modeling. Med Image Anal 18:118–129CrossRefGoogle Scholar
  47. Prot V, Haaverstad R, Skallerud B (2009) Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution. Biomech Model Mechanobiol 8:43–55CrossRefGoogle Scholar
  48. Prot V, Skallerud B (2009) Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers. Comput Mech 43:353–368zbMATHCrossRefGoogle Scholar
  49. Prot V, Skallerud B, Holzapfel G (2007) Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation. Int J Numer Methods Eng 71:987–1008zbMATHMathSciNetCrossRefGoogle Scholar
  50. Rabbah J-P, Saikrishnan N, Yoganathan AP (2013) A novel left heart simulator for the multi-modality characterization of native mitral valve geometry and fluid mechanics. Ann Biomed Eng 41:305–315CrossRefGoogle Scholar
  51. Rabkin-Aikawa E, Farber M, Aikawa M, Schoen FJ (2004) Dynamic and reversible changes of interstitial cell phenotype during remodeling of cardiac valves. J Heart Valve Dis 13:841–847Google Scholar
  52. Reimink MS, Kunzelman KS, Verrier ED, Cochran RP (1995) The effect of anterior chordal replacement on mitral valve function and stresses. A finite element study. Asaio J 41:M754–762CrossRefGoogle Scholar
  53. Ritchie J, Jimenez J, He Z, Sacks MS, Yoganathan AP (2006) The material properties of the native porcine mitral valve chordae tendineae: an in vitro investigation. J Biomech 39:1129–1135CrossRefGoogle Scholar
  54. Robb JD, Minakawa M, Koomalsingh KJ, Shuto T, Jassar AS, Ratcliffe SJ, Gorman RC, Gorman JH, 3rd (2011) Posterior leaflet augmentation improves leaflet tethering in repair of ischemic mitral regurgitation. Eur J Cardiothorac Surg 40(6):1501–1507Google Scholar
  55. Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125:280–287CrossRefGoogle Scholar
  56. Sacks MS, Chuong CJ, Templeton GH, Peshock R (1993) In vivo 3-D reconstruction and geometric characterization of the right ventricular free wall. Ann Biomed Eng 21:263–275CrossRefGoogle Scholar
  57. Sacks MS, He Z, Baijens L, Wanant S, Shah P, Sugimoto H, Yoganathan AP (2002) Surface strains in the anterior leaflet of the functioning mitral valve. Ann Biomed Eng 30:1281–1290CrossRefGoogle Scholar
  58. Sacks MS, Smith DB, Hiester ED (1997) A small angle light scattering device for planar connective tissue microstructural analysis. Ann Biomed Eng 25:678–689CrossRefGoogle Scholar
  59. Sacks MS, Yoganathan AP (2008) Heart valve function: a biomechanical perspective. Philos Trans R Soc Lond B Biol Sci 363:2481CrossRefGoogle Scholar
  60. Schoen FJ, Levy RJ (2005) Calcification of tissue heart valve substitutes: progress toward understanding and prevention. Ann Thorac Surg 79:1072–1080CrossRefGoogle Scholar
  61. Shuhaiber J, Anderson RJ (2007) Meta-analysis of clinical outcomes following surgical mitral valve repair or replacement. Eur J Cardiothorac Surg 31:267–275CrossRefGoogle Scholar
  62. Skallerud B, Prot V, Nordrum IS (2011) Modeling active muscle contraction in mitral valve leaflets during systole: a first approach. Biomech Model Mechanobiol 10:11–26CrossRefGoogle Scholar
  63. Smith DB, Sacks MS, Vorp DA, Thornton M (2000) Surface geometric analysis of anatomic structures using biquintic finite element interpolation. Ann Biomed Eng 28:598–611CrossRefGoogle Scholar
  64. Stevanella M, Maffessanti F, Conti CA, Votta E, Arnoldi A, Lombardi M, Parodi O, Caiani EG, Redaelli A (2011) Mitral valve patient-specific finite element modeling from cardiac MRI: application to an annuloplasty procedure. Cardiovas Eng Technol 2:66–76CrossRefGoogle Scholar
  65. Stevanella M, Votta E, Redaelli A (2009) Mitral valve finite element modeling: implications of tissues’ nonlinear response and annular motion. J Biomech Eng 131:121010CrossRefGoogle Scholar
  66. Vassileva CM, Boley T, Markwell S, Hazelrigg S (2011) Meta-analysis of short-term and long-term survival following repair versus replacement for ischemic mitral regurgitation. Eur J Cardiothorac Surg 39:295–303CrossRefGoogle Scholar
  67. Votta E, Le TB, Stevanella M, Fusini L, Caiani EG, Redaelli A, Sotiropoulos F (2013) Toward patient-specific simulations of cardiac valves: state-of-the-art and future directions. J Biomech 46:217–228CrossRefGoogle Scholar
  68. Wang Q, Sun W (2013) Finite element modeling of mitral valve dynamic deformation using patient-specific multi-slices computed tomography scans. Ann Biomed Eng 41:142–153CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Chung-Hao Lee
    • 1
  • Jean-Pierre Rabbah
    • 2
  • Ajit P. Yoganathan
    • 2
  • Robert C. Gorman
    • 3
  • Joseph H. GormanIII
    • 3
  • Michael S. Sacks
    • 4
    Email author
  1. 1.Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES)The University of Texas at AustinAustinUSA
  2. 2.Cardiovascular Fluid Mechanics Laboratory, Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Gorman Cardiovascular Research GroupUniversity of PennsylvaniaPhiladelphiaUSA
  4. 4.W. A. “Tex” Moncrief, Jr. Simulation-Based Engineering Science Chair I, Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES)The University of Texas at AustinAustinUSA

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