Towards Patient-Specific Mitral Valve Surgical Simulations

  • Amir H. Khalighi
  • Bruno V. Rego
  • Andrew Drach
  • Robert C. Gorman
  • Joseph H. Gorman
  • Michael S. SacksEmail author


Ischemic mitral regurgitation (IMR) occurs when a mitral valve (MV) is rendered incompetent by left ventricular (LV) remodeling induced by a myocardial infarction (MI). Hemodynamically significant, IMR affects at least 300,000 Americans. This important clinical problem is expected to grow substantially during the next 20 years as the population ages. MV repair with undersized ring annuloplasty has been the preferred treatment for IMR. However, 1/3 of all patients treated this way develop significant recurrent IMR within 6 months. Using real-time 3D echocardiography (rt-3DE) image analysis software, it has been demonstrated that IMR in humans is etiologically heterogeneous. In one subset of patients the predominant cause of IMR is annular dilatation and flattening; in the remaining patients, leaflet tethering is the dominant pathology. It has been demonstrated that recurrent IMR after ring annuloplasty occurs most commonly when leaflet tethering is the primary cause of IMR. There is now agreement that adjunctive procedures are required to treat IMR caused by leaflet tethering. However, there is no consensus regarding the best procedure. Multicenter registries and randomized trials would be necessary to prove which procedure is superior. Given the number of proposed procedures and the complexity and duration of such studies, it is highly unlikely that IMR procedure optimization will be achieved by prospective clinical trials. Novel computational approaches directed towards optimized surgical repair procedures can substantially reduce the need for such trial-and-error approaches. We thus present a state-of-the-art means to produce patient-specific MV computational models, which can directly utilize rt-3DE imaging data that can be used develop quantitatively optimized devices and procedures for MV repair.


Mitral valve Ischemic mitral regurgitation Finite element modeling Image-based modeling Patient-specific model Chordae tendineae Surgical repair 



This work was supported by National Heart, Lung, and Blood Institute of the National Institutes of Health under grant no. R01-HL119297, the National Science Foundation grant no. DGE-1610403, and the American Heart Association grant no. 18PRE34030258.


  1. 1.
    Atluri P, Panlilio CM, Liao GP, Suarez EE, McCormick RC, Hiesinger W, Cohen JE, Smith MJ, Patel AB, Feng W, Woo YJ. Transmyocardial revascularization to enhance myocardial vasculogenesis and hemodynamic function. J Thorac Cardiovasc Surg. 2008;135(2):283–91, 291.e1; discussion 91. Epub 2008/02/05.CrossRefPubMedGoogle Scholar
  2. 2.
    Grigioni F, Enriquez-Sarano M, Zehr KJ, Bailey KR, Tajik AJ. Ischemic mitral regurgitation: long-term outcome and prognostic implications with quantitative Doppler assessment. Circulation. 2001;103(13):1759–64. Epub 2001/04/03.CrossRefGoogle Scholar
  3. 3.
    Lamas GA, Mitchell GF, Flaker GC, Smith SC Jr, Gersh BJ, Basta L, Moye L, Braunwald E, Pfeffer MA. Clinical significance of mitral regurgitation after acute myocardial infarction. Survival and Ventricular Enlargement Investigators. Circulation. 1997;96(3):827–33. Epub 1997/08/05.CrossRefGoogle Scholar
  4. 4.
    Trichon BH, Glower DD, Shaw LK, Cabell CH, Anstrom KJ, Felker GM, O’Connor CM. Survival after coronary revascularization, with and without mitral valve surgery, in patients with ischemic mitral regurgitation. Circulation. 2003;108(Suppl 1):II103–10. Epub 2003/09/13.CrossRefPubMedGoogle Scholar
  5. 5.
    Borger MA, Alam A, Murphy PM, Doenst T, David TE. Chronic ischemic mitral regurgitation: repair, replace or rethink? Ann Thorac Surg. 2006;81(3):1153–61. Epub 2006/02/21.CrossRefPubMedGoogle Scholar
  6. 6.
    Trichon BH, Felker GM, Shaw LK, Cabell CH, O’Connor CM. Relation of frequency and severity of mitral regurgitation to survival among patients with left ventricular systolic dysfunction and heart failure. Am J Cardiol. 2003;91(5):538–43. Epub 2003/03/05.CrossRefGoogle Scholar
  7. 7.
    Gillinov AM, Wierup PN, Blackstone EH, Bishay ES, Cosgrove DM, White J, Lytle BW, McCarthy PM. Is repair preferable to replacement for ischemic mitral regurgitation? J Thorac Cardiovasc Surg. 2001;122(6):1125–41.CrossRefGoogle Scholar
  8. 8.
    Grossi EA, Goldberg JD, LaPietra A, Ye X, Zakow P, Sussman M, Delianides J, Culliford AT, Esposito RA, Ribakove GH, Galloway AC, Colvin SB. Ischemic mitral valve reconstruction and replacement: comparison of long-term survival and complications. J Thorac Cardiovasc Surg. 2001;122(6):1107–24. Epub 2001/12/01.CrossRefPubMedGoogle Scholar
  9. 9.
    Nishimura RA, Otto CM, Bonow RO, Carabello BA, Erwin JP 3rd, Guyton RA, O’Gara PT, Ruiz CE, Skubas NJ, Sorajja P, Sundt TM 3rd, Thomas JD, American College of Cardiology/American Heart Association Task Force on Practice Guidelines. 2014 AHA/ACC guideline for the management of patients with valvular heart disease: executive summary: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines. J Am Coll Cardiol. 2014;63(22):2438–88. Epub 2014/03/08.CrossRefPubMedGoogle Scholar
  10. 10.
    McGee EC, Gillinov AM, Blackstone EH, Rajeswaran J, Cohen G, Najam F, Shiota T, Sabik JF, Lytle BW, McCarthy PM, Cosgrove DM. Recurrent mitral regurgitation after annuloplasty for functional ischemic mitral regurgitation. J Thorac Cardiovasc Surg. 2004;128(6):916–24. Scholar
  11. 11.
    Hung J, Papakostas L, Tahta SA, Hardy BG, Bollen BA, Duran CM, Levine RA. Mechanism of recurrent ischemic mitral regurgitation after annuloplasty: continued LV remodeling as a moving target. Circulation. 2004;110(11 Suppl 1):II85–90. Epub 2004/09/15.CrossRefPubMedGoogle Scholar
  12. 12.
    Acker MA, Parides MK, Perrault LP, Moskowitz AJ, Gelijns AC, Voisine P, Smith PK, Hung JW, Blackstone EH, Puskas JD. Mitral-valve repair versus replacement for severe ischemic mitral regurgitation. N Engl J Med. 2014;370(1):23–32.CrossRefGoogle Scholar
  13. 13.
    Mihaljevic T, Lam BK, Rajeswaran J, Takagaki M, Lauer MS, Gillinov AM, Blackstone EH, Lytle BW. Impact of mitral valve annuloplasty combined with revascularization in patients with functional ischemic mitral regurgitation. J Am Coll Cardiol. 2007;49(22):2191–201. Epub 2007/06/05.CrossRefPubMedGoogle Scholar
  14. 14.
    Kron IL, Hung J, Overbey JR, Bouchard D, Gelijns AC, Moskowitz AJ, Voisine P, O’Gara PT, Argenziano M, Michler RE, Gillinov M, Puskas JD, Gammie JS, Mack MJ, Smith PK, Sai-Sudhakar C, Gardner TJ, Ailawadi G, Zeng X, O’Sullivan K, Parides MK, Swayze R, Thourani V, Rose EA, Perrault LP, Acker MA, CTSN Investigators. Predicting recurrent mitral regurgitation after mitral valve repair for severe ischemic mitral regurgitation. J Thorac Cardiovasc Surg. 2015;149(3):752–61.e1. Epub 2014/12/17.CrossRefPubMedGoogle Scholar
  15. 15.
    Bouma W, Lai EK, Levack MM, Shang EK, Pouch AM, Eperjesi TJ, Plappert TJ, Yushkevich PA, Mariani MA, Khabbaz KR, Gleason TG, Mahmood F, Acker MA, Woo YJ, Cheung AT, Jackson BM, Gorman JH 3rd, Gorman RC. Preoperative three-dimensional valve analysis predicts recurrent ischemic mitral regurgitation after mitral annuloplasty. Ann Thorac Surg. 2016;101(2):567–75. Scholar
  16. 16.
    Gorman RC, McCaughan JS, Ratcliffe MB, Gupta KB, Streicher JT, Ferrari VA, St John-Sutton MG, Bogen DK, Edmunds LH Jr. Pathogenesis of acute ischemic mitral regurgitation in three dimensions. J Thorac Cardiovasc Surg. 1995;109(4):684–93.CrossRefGoogle Scholar
  17. 17.
    Gorman JH 3rd, Gorman RC, Jackson BM, Enomoto Y, St John-Sutton MG, Edmunds LH Jr. Annuloplasty ring selection for chronic ischemic mitral regurgitation: lessons from the ovine model. Ann Thorac Surg. 2003;76(5):1556–63. pii: S0003497503008919. Epub 2003/11/07.CrossRefPubMedGoogle Scholar
  18. 18.
    Tibayan FA, Rodriguez F, Langer F, Zasio MK, Bailey L, Liang D, Daughters GT, Ingels NB Jr, Miller DC. Annular remodeling in chronic ischemic mitral regurgitation: ring selection implications. Ann Thorac Surg. 2003;76(5):1549–54; discussion 54–5. pii: S0003497503008804. Epub 2003/11/07.CrossRefPubMedGoogle Scholar
  19. 19.
    Minakawa M, Robb JD, Morital M, Koomalsinghl KJ, Vergnat M, Gillespie MJ, Gorman JH 3rd, Gorman RC. A model of ischemic mitral regurgitation in pigs with three-dimensional echocardiographic assessment. J Heart Valve Dis. 2014;23(6):713–20. Epub 2015/03/21.PubMedGoogle Scholar
  20. 20.
    Jassar AS, Vergnat M, Jackson BM, McGarvey JR, Cheung AT, Ferrari G, Woo YJ, Acker MA, Gorman RC, Gorman JH. Regional annular geometry in patients with mitral regurgitation: implications for annuloplasty ring selection. Ann Thorac Surg. 2014;97(1):64–70.CrossRefGoogle Scholar
  21. 21.
    Otsuji Y, Handschumacher MD, Schwammenthal E, Jiang L, Song JK, Guerrero JL, Vlahakes GJ, Levine RA. Insights from three-dimensional echocardiography into the mechanism of functional mitral regurgitation: direct in vivo demonstration of altered leaflet tethering geometry. Circulation. 1997;96(6):1999–2008.CrossRefGoogle Scholar
  22. 22.
    Srichai MB, Grimm RA, Stillman AE, Gillinov AM, Rodriguez LL, Lieber ML, Lara A, Weaver JA, McCarthy PM, White RD. Ischemic mitral regurgitation: impact of the left ventricle and mitral valve in patients with left ventricular systolic dysfunction. Ann Thorac Surg. 2005;80(1):170–8. Epub 2005/06/25.CrossRefPubMedGoogle Scholar
  23. 23.
    Gorman JH 3rd, Jackson BM, Enomoto Y, Gorman RC. The effect of regional ischemia on mitral valve annular saddle shape. Ann Thorac Surg. 2004;77(2):544–8.CrossRefGoogle Scholar
  24. 24.
    Ryan LP, Jackson BM, Parish LM, Plappert TJ, St John-Sutton MG, Gorman JH 3rd, Gorman RC. Regional and global patterns of annular remodeling in ischemic mitral regurgitation. Ann Thorac Surg. 2007;84(2):553–9. Epub 2007/07/24.CrossRefPubMedGoogle Scholar
  25. 25.
    Vergnat M, Jassar AS, Jackson BM, Ryan LP, Eperjesi TJ, Pouch AM, Weiss SJ, Cheung AT, Acker MA, Gorman JH 3rd, Gorman RC. Ischemic mitral regurgitation: a quantitative three-dimensional echocardiographic analysis. Ann Thorac Surg. 2011;91(1):157–64. Epub 2010/12/22.CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Kuwahara E, Otsuji Y, Iguro Y, Ueno T, Zhu F, Mizukami N, Kubota K, Nakashiki K, Yuasa T, Yu B, Uemura T, Takasaki K, Miyata M, Hamasaki S, Kisanuki A, Levine RA, Sakata R, Tei C. Mechanism of recurrent/persistent ischemic/functional mitral regurgitation in the chronic phase after surgical annuloplasty: importance of augmented posterior leaflet tethering. Circulation. 2006;114(1 Suppl):I529–34. Epub 2006/07/06.CrossRefPubMedGoogle Scholar
  27. 27.
    Khang A, Buchanan RM, Ayoub S, Rego BV, Lee CH, Ferrari G, Anseth KS, Sacks MS. Mechanobiology of the heart valve interstitial cell: Simulation, experiment, and discovery. In: Verbruggen SW, editor. Mechanobiology in health and disease, vol. 2018. London: Elsevier; 2018. p. 249–83.CrossRefGoogle Scholar
  28. 28.
    Sacks MS, Khalighi A, Rego B, Ayoub S, Drach A. On the need for multi-scale geometric modelling of the mitral heart valve. Healthc Technol Lett. 2017;4(5):150.CrossRefGoogle Scholar
  29. 29.
    Rego BV, Ayoub S, Khalighi AH, Drach A, Gorman JH, Gorman RC, Sacks MS. Alterations in mechanical properties and in vivo geometry of the mitral valve following myocardial infarction. Summer biomechanics, bioengineering and biotransport conference, Tucson, AZ, USA; 2017.Google Scholar
  30. 30.
    Khalighi AH, Drach A, Sacks MS. Patient-specific mitral valve annuloplasty repair: The optimal ring design for treating ischemic mitral regurgitation. Summer biomechanics, bioengineering and biotransport conference, Tucson, AZ, USA; 2017.Google Scholar
  31. 31.
    Carpentier A. [Reconstructive valvuloplasty. A new technique of mitral valvuloplasty]. La Presse medicale. 1969;77(7):251–3.Google Scholar
  32. 32.
    Carpentier A, Deloche A, Dauptain J, Soyer R, Blondeau P, Piwnica A, Dubost C, McGoon DC. A new reconstructive operation for correction of mitral and tricuspid insufficiency. J Thorac Cardiovasc Surg. 1971;61(1):1–13.PubMedGoogle Scholar
  33. 33.
    Carpentier A. Cardiac valve surgery—the “French correction”. J Thorac Cardiovasc Surg. 1983;86(3):323–37.PubMedGoogle Scholar
  34. 34.
    Ryan LP, Jackson BM, Eperjesi TJ, Plappert TJ, St John-Sutton M, Gorman RC, Gorman JH 3rd. A methodology for assessing human mitral leaflet curvature using real-time 3-dimensional echocardiography. J Thorac Cardiovasc Surg. 2008;136(3):726–34. Epub 2008/09/23.CrossRefPubMedGoogle Scholar
  35. 35.
    Ryan LP, Jackson BM, Hamamoto H, Eperjesi TJ, Plappert TJ, St John-Sutton M, Gorman RC, Gorman JH 3rd. The influence of annuloplasty ring geometry on mitral leaflet curvature. Ann Thorac Surg. 2008;86(3):749–60; discussion 60. pii: S0003-4975(08)00726-1. Epub 2008/08/30.CrossRefPubMedGoogle Scholar
  36. 36.
    Robb JD, Minakawa M, Koomalsingh KJ, Shuto T, Jassar AS, Ratcliffe SJ, Gorman RC, Gorman JH 3rd. Posterior leaflet augmentation improves leaflet tethering in repair of ischemic mitral regurgitation. Eur J Cardiothorac Surg. 2011;40:1501–7. Epub 2011/05/07.CrossRefPubMedPubMedCentralGoogle Scholar
  37. 37.
    Jassar AS, Minakawa M, Shuto T, Robb JD, Koomalsingh KJ, Levack MM, Vergnat M, Eperjesi TJ, Jackson BM, Gorman JH III. Posterior leaflet augmentation in ischemic mitral regurgitation increases leaflet coaptation and mobility. Ann Thorac Surg. 2012;94(5):1438–45.CrossRefGoogle Scholar
  38. 38.
    Onorati F, Rubino AS, Marturano D, Pasceri E, Santarpino G, Zinzi S, Mascaro G, Renzulli A. Midterm clinical and echocardiographic results and predictors of mitral regurgitation recurrence following restrictive annuloplasty for ischemic cardiomyopathy. J Thorac Cardiovasc Surg. 2009;138(3):654–62. Epub 2009/08/25.CrossRefPubMedGoogle Scholar
  39. 39.
    Kron IL, Green GR, Cope JT. Surgical relocation of the posterior papillary muscle in chronic ischemic mitral regurgitation. Ann Thorac Surg. 2002;74(2):600–1. Epub 2002/08/14.CrossRefGoogle Scholar
  40. 40.
    Masuyama S, Marui A, Shimamoto T, Nonaka M, Tsukiji M, Watanabe N, Ikeda T, Yoshida K, Komeda M. Chordal translocation for ischemic mitral regurgitation may ameliorate tethering of the posterior and anterior mitral leaflets. J Thorac Cardiovasc Surg. 2008;136(4):868–75. Epub 2008/10/29.CrossRefPubMedGoogle Scholar
  41. 41.
    Arai H, Itoh F, Someya T, Oi K, Tamura K, Tanaka H. New surgical procedure for ischemic/functional mitral regurgitation: mitral complex remodeling. Ann Thorac Surg. 2008;85(5):1820–2. Epub 2008/04/30.CrossRefPubMedGoogle Scholar
  42. 42.
    Fayad G, Marechaux S, Modine T, Azzaoui R, Larrue B, Ennezat PV, Bekhti H, Decoene C, Deklunder G, Le Tourneau T, Warembourg H. Chordal cutting VIA aortotomy in ischemic mitral regurgitation: surgical and echocardiographic study. J Card Surg. 2008;23(1):52–7. Epub 2008/02/23.CrossRefPubMedGoogle Scholar
  43. 43.
    Kincaid EH, Riley RD, Hines MH, Hammon JW, Kon ND. Anterior leaflet augmentation for ischemic mitral regurgitation. Ann Thorac Surg. 2004;78(2):564–8; discussion 8. Epub 2004/07/28.CrossRefPubMedGoogle Scholar
  44. 44.
    de Varennes B, Chaturvedi R, Sidhu S, Cote AV, Shan WL, Goyer C, Hatzakorzian R, Buithieu J, Sniderman A. Initial results of posterior leaflet extension for severe type IIIb ischemic mitral regurgitation. Circulation. 2009;119(21):2837–43. Epub 2009/05/20.CrossRefPubMedGoogle Scholar
  45. 45.
    Dobre M, Koul B, Rojer A. Anatomic and physiologic correction of the restricted posterior mitral leaflet motion in chronic ischemic mitral regurgitation. J Thorac Cardiovasc Surg. 2000;120(2):409–11. Epub 2000/08/05.CrossRefPubMedGoogle Scholar
  46. 46.
    Rendon F, Aramendi JI, Rodrigo D, Baraldi C, Martinez P. Patch enlargement of the posterior mitral leaflet in ischemic regurgitation. Asian Cardiovasc Thorac Ann. 2002;10(3):248–50. Epub 2002/09/06.CrossRefPubMedGoogle Scholar
  47. 47.
    Rabbah J-P, Saikrishnan N, Yoganathan AP. A novel left heart simulator for the multi-modality characterization of native mitral valve geometry and fluid mechanics. Ann Biomed Eng. 2013;41(2):305–15. Scholar
  48. 48.
    Fan R, Sacks MS. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J Biomech. 2014;47:2043–54.CrossRefGoogle Scholar
  49. 49.
    Drach A, Khalighi AH, Sacks MS. A comprehensive pipeline for multi-resolution modeling of the mitral valve: validation, computational efficiency, and predictive capability. Int J Numer Methods Biomed Eng. 2017;34:e2921. Epub 2017/08/05.CrossRefGoogle Scholar
  50. 50.
    Pouch AM, Jackson BM, Yushkevich PA, Gorman JH 3rd, Gorman RC. 4D-transesophageal echocardiography and emerging imaging modalities for guiding mitral valve repair. Ann Cardiothorac Surg. 2015;4(5):461–2. Scholar
  51. 51.
    Jassar AS, Brinster CJ, Vergnat M, Robb JD, Eperjesi TJ, Pouch AM, Cheung AT, Weiss SJ, Acker MA, Gorman JH 3rd, Gorman RC, Jackson BM. Quantitative mitral valve modeling using real-time three-dimensional echocardiography: technique and repeatability. Ann Thorac Surg. 2011;91(1):165–71. Epub 2010/12/22.CrossRefPubMedPubMedCentralGoogle Scholar
  52. 52.
    Rego BV, Khalighi AH, Drach A, Lai EK, Pouch AM, Gorman RC, Gorman JH 3rd, Sacks MS. A non-invasive method for the determination of in vivo mitral valve leaflet strains. Int J Numer Meth Biomed Eng.; e3142.CrossRefGoogle Scholar
  53. 53.
    Khalighi AH, Rego BV, Drach A, Gorman RC, Gorman JH 3rd, Sacks MS. Development of a functionally equivalent model of the mitral valve chordae tendineae through topology optimization. Ann Biomed Eng. Scholar
  54. 54.
    Aggarwal A, Aguilar VS, Lee C-H, Ferrari G, Gorman JH, Gorman RC, Sacks MS. Patient-specific modeling of heart valves: from image to simulation. In: Ourselin S, Rueckert D, Smith N, editors. Functional imaging and modeling of the heart. London: Springer; 2013. p. 141–9.CrossRefGoogle Scholar
  55. 55.
    Lee C-H, Oomen PA, Rabbah J, Yoganathan A, Gorman R, Gorman J III, Amini R, Sacks M. A high-fidelity and micro-anatomically accurate 3D finite element model for simulations of functional mitral valve. In: Ourselin S, Rueckert D, Smith N, editors. Functional imaging and modeling of the heart. Berlin: Springer; 2013. p. 416–24.CrossRefGoogle Scholar
  56. 56.
    Lee CH, Amini R, Gorman RC, Gorman JH 3rd, Sacks MS. An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment. J Biomech. 2014;47(9):2055–63. Scholar
  57. 57.
    Lee C-H, Amini R, Sakamoto Y, Carruthers CA, Aggarwal A, Gorman RC, Gorman JH III, Sacks MS. Mitral valves: a computational framework. In: Multiscale modeling in biomechanics and mechanobiology. London: Springer; 2015. p. 223–55.Google Scholar
  58. 58.
    Rego BV, Wells SM, Lee CH, Sacks MS. Mitral valve leaflet remodelling during pregnancy: insights into cell-mediated recovery of tissue homeostasis. J R Soc Interface. 2016;13(125):20160709. Scholar
  59. 59.
    Lee CH, Zhang W, Feaver K, Gorman RC, Gorman JH 3rd, Sacks MS. On the in vivo function of the mitral heart valve leaflet: insights into tissue-interstitial cell biomechanical coupling. Biomech Model Mechanobiol. 2017;16:1613–32. Scholar
  60. 60.
    Lee CH, Rabbah JP, Yoganathan AP, Gorman RC, Gorman JH 3rd, Sacks MS. On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve. Biomech Model Mechanobiol. 2015;14(6):1281–302. Scholar
  61. 61.
    Khalighi AH, Drach A, ter Huurne FM, Lee C-H, Bloodworth C, Pierce EL, Jensen MO, Yoganathan AP, Sacks MS. A comprehensive framework for the characterization of the complete mitral valve geometry for the development of a population-averaged model. In: Functional imaging and modeling of the heart. Cham: Springer; 2015. p. 164–71.CrossRefGoogle Scholar
  62. 62.
    Lee CH, Zhang W, Liao J, Carruthers CA, Sacks JI, Sacks MS. On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet. Biophys J. 2015;108(8):2074–87. Scholar
  63. 63.
    Khalighi AH, Drach A, Bloodworth CH 4th, Pierce EL, Yoganathan AP, Gorman RC, Gorman JH 3rd, Sacks MS. Mitral valve chordae tendineae: topological and geometrical characterization. Ann Biomed Eng. 2016;45:378–93. Scholar
  64. 64.
    Bloodworth CH 4th, Pierce EL, Easley TF, Drach A, Khalighi AH, Toma M, Jensen MO, Sacks MS, Yoganathan AP. Ex vivo methods for informing computational models of the mitral valve. Ann Biomed Eng. 2016;45:496–507. Scholar
  65. 65.
    Khalighi AH, Drach A, Gorman RC, Gorman JH 3rd, Sacks MS. Multi-resolution geometric modeling of the mitral heart valve leaflets. Biomech Model Mechanobiol. 2018;17:351–66. Epub 2017/10/07.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Amir H. Khalighi
    • 1
  • Bruno V. Rego
    • 1
  • Andrew Drach
    • 1
  • Robert C. Gorman
    • 2
  • Joseph H. Gorman
    • 2
  • Michael S. Sacks
    • 3
    Email author
  1. 1.James T. Willerson Center for Cardiovascular Modeling and SimulationInstitute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at AustinAustinUSA
  2. 2.Gorman Cardiovascular Research Group, Smilow Center for Translational Research, Perelman School of MedicineUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.The Oden Institute and the Department of Biomedical EngineeringThe University of Texas at AustinAustinUSA

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