Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization

Abstract

Ischemic mitral regurgitation (IMR) is a currently prevalent disease in the US that is projected to become increasingly common as the aging population grows. In recent years, image-based simulations of mitral valve (MV) function have improved significantly, providing new tools to refine IMR treatment. However, clinical implementation of MV simulations has long been hindered as the in vivo MV chordae tendineae (MVCT) geometry cannot be captured with sufficient fidelity for computational modeling. In the current study, we addressed this challenge by developing a method to produce functionally equivalent MVCT models that can be built from the image-based MV leaflet geometry alone. We began our analysis using extant micron-resolution 3D imaging datasets to first build anatomically accurate MV models. We then systematically simplified the native MVCT structure to generate a series of synthetic models by consecutively removing key anatomic features, such as the thickness variations, branching patterns, and chordal origin distributions. In addition, through topology optimization, we identified the minimal structural complexity required to capture the native MVCT behavior. To assess the performance and predictive power of each synthetic model, we analyzed their performance by comparing the mismatch in simulated MV closed shape, as well as the strain and stress tensors, to ground-truth MV models. Interestingly, our results revealed a substantial redundancy in the anatomic structure of native chordal anatomy. We showed that the closing behavior of complete MV apparatus under normal, diseased, and surgically repaired scenarios can be faithfully replicated by a functionally equivalent MVCT model comprised of two representative papillary muscle heads, single strand chords, and a uniform insertion distribution with a density of 15 insertions/cm2. Hence, even though the complete sub-valvular structure is mostly missing in in vivo MV images, we believe our approach will allow for the development of patient-specific complete MV models for surgical repair planning.

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References

  1. 1.

    Acker, M. A., M. K. Parides, L. P. Perrault, A. J. Moskowitz, A. C. Gelijns, P. Voisine, P. K. Smith, J. W. Hung, E. H. Blackstone, J. D. Puskas et al. Mitral-valve repair versus replacement for severe ischemic mitral regurgitation. New England Journal of Medicine 370:23–32, 2014.

    Article  CAS  PubMed  Google Scholar 

  2. 2.

    Aggarwal, A., V. S. Aguilar, C.-H. Lee, G. Ferrari, J. H. Gorman, R. C. Gorman, and M. S. Sacks. Patient-specific modeling of heart valves: from image to simulation. In: International Conference on Functional Imaging and Modeling of the Heart, pp. 141–149, Springer 2013.

  3. 3.

    Ayoub, S., G. Ferrari, R. C. Gorman, J. H. Gorman, F. J. Schoen, and M. S. Sacks. Heart valve biomechanics and underlying mechanobiology. Comprehensive Physiology 6:1743–1780, 2016.

    Article  PubMed Central  PubMed  Google Scholar 

  4. 4.

    Ayoub, S., K. C. Tsai, A. H. Khalighi, and M. S. Sacks. The three-dimensional microenvironment of the mitral valve: insights into the effects of physiological loads. Cellular and Molecular Bioengineering 11(4):291–306, 2018.

    Article  Google Scholar 

  5. 5.

    Ayoub, S., C.-H. Lee, K. H. Driesbaugh, W. Anselmo, C. T. Hughes, G. Ferrari, R. C. Gorman, J. H. Gorman, and M. S. Sacks. Regulation of valve interstitial cell homeostasis by mechanical deformation: implications for heart valve disease and surgical repair. Journal of The Royal Society Interface 14:20170580, 2017.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  6. 6.

    Benjamin, E. J., M. J. Blaha, S. E. Chiuve, M. Cushman, S. R. Das, R. Deo, J. Floyd, M. Fornage, C. Gillespie, C. Isasi et al. Heart disease and stroke statistics-2017 update: a report from the american heart association. Circulation 135:e146–e603, 2017.

    Article  PubMed Central  PubMed  Google Scholar 

  7. 7.

    Bloodworth, C. H., E. L. Pierce, T. F. Easley, A. Drach, A. H. Khalighi, M. Toma, M. O. Jensen, M. S. Sacks, and A. P. Yoganathan. Ex vivo methods for informing computational models of the mitral valve. Annals of biomedical engineering 45:496–507, 2017.

    Article  Google Scholar 

  8. 8.

    Bouma, W., E. K. Lai, M. M. Levack, E. K. Shang, A. M. Pouch, T. J. Eperjesi, T. J. Plappert, P. A. Yushkevich, M. A. Mariani, K. R. Khabbaz et al. Preoperative three-dimensional valve analysis predicts recurrent ischemic mitral regurgitation after mitral annuloplasty. The Annals of thoracic surgery 101:567–575, 2016.

    Article  PubMed  Google Scholar 

  9. 9.

    Braunberger, E., A. Deloche, A. Berrebi, A. Fayssoil, J. Celestin, P. Meimoun, G. Chatellier, S. Chauvaud, J. Fabiani, and A. Carpentier. Very long-term results (more than 20 years) of valve repair with Carpentier’s techniques in nonrheumatic mitral valve insufficiency. Circulation 104: I–8, 2001.

    Article  Google Scholar 

  10. 10.

    Bursi, F., M. Enriquez-Sarano, V. T. Nkomo, S. J. Jacobsen, S. A. Weston, R. A. Meverden, and V. L. Roger. Heart failure and death after myocardial infarction in the community: the emerging role of mitral regurgitation. Circulation 111:295–301, 2005.

    Article  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Chen, L., F. C. Yin, and K. May-Newman. The structure and mechanical properties of the mitral valve leaflet-strut chordae transition zone. Journal of biomechanical engineering 126:244–251, 2004.

    Article  PubMed  Google Scholar 

  12. 12.

    Dal-Bianco, J. P., J. Beaudoin, M. D. Handschumacher, and R. A. Levine. Basic mechanisms of mitral regurgitation. Canadian Journal of Cardiology 30:971–981, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  13. 13.

    Dal-Bianco, J. P. and R. A. Levine. Anatomy of the mitral valve apparatus: role of 2d and 3d echocardiography. Cardiology clinics 31:151–164, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Drach, A., A. H. Khalighi, and M. S. Sacks. A comprehensive pipeline for multi-resolution modeling of the mitral valve: Validation, computational efficiency, and predictive capability. International journal for numerical methods in biomedical engineering 34:e2921, 2018.

    Article  Google Scholar 

  15. 15.

    Drach, A., A. H. Khalighi, F. M. ter Huurne, C.-H. Lee, C. Bloodworth, E. L. Pierce, M. O. Jensen, A. P. Yoganathan, and M. S. Sacks. Population-averaged geometric model of mitral valve from patient-specific imaging data. Journal of Medical Devices 9:030952, 2015.

    Article  Google Scholar 

  16. 16.

    Enriquez-Sarano, M., H. V. Schaff, T. A. Orszulak, A. J. Tajik, K. R. Bailey, and R. L. Frye. Valve repair improves the outcome of surgery for mitral regurgitation: a multivariate analysis. Circulation 91:1022–1028, 1995.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. 17.

    Eschenauer, H. A. and N. Olhoff. Topology optimization of continuum structures: a review. Applied Mechanics Reviews 54:331–390, 2001.

    Article  Google Scholar 

  18. 18.

    Fan, R. and M. S. Sacks. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. Journal of biomechanics 47:2043–2054, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  19. 19.

    Fung, Y.-C. Biomechanics: mechanical properties of living tissues, Springer Science & Business Media, 2013.

  20. 20.

    Gao, H., L. Feng, N. Qi, C. Berry, B. E. Griffith, and X. Luo. A coupled mitral valve-left ventricle model with fluid-structure interaction. Medical Engineering and Physics 47:128–136, 2017.

    Article  PubMed  Google Scholar 

  21. 21.

    Goldstein, D., A. J. Moskowitz, A. C. Gelijns, G. Ailawadi, M. K. Parides, L. P. Perrault, J. W. Hung, P. Voisine, F. Dagenais, A. M. Gillinov et al. Two-year outcomes of surgical treatment of severe ischemic mitral regurgitation. New England Journal of Medicine 374:344–353, 2016.

    Article  CAS  PubMed  Google Scholar 

  22. 22.

    Harb, S. C. and B. P. Griffin. Mitral valve disease: a comprehensive review. Current cardiology reports 19:73, 2017.

    Article  PubMed  Google Scholar 

  23. 23.

    Holda, J., K. Tyrak, M. Holda, A. Krawczyk-Ozog, and W. Klimek-Piotrowska. Mitral subvalvular apparatus. Journal of the American College of Cardiology 71:A1088, 2018.

    Article  Google Scholar 

  24. 24.

    Jassar, A. S., C. J. Brinster, M. Vergnat, J. D. Robb, T. J. Eperjesi, A. M. Pouch, A. T. Cheung, S. J. Weiss, M. A. Acker, J. H. Gorman et al. Quantitative mitral valve modeling using real-time three-dimensional echocardiography: technique and repeatability. The Annals of thoracic surgery 91:165–171, 2011.

    Article  Google Scholar 

  25. 25.

    Kaji, S., M. Nasu, A. Yamamuro, K. Tanabe, K. Nagai, T. Tani, K. Tamita, K. Shiratori, M. Kinoshita, M. Senda et al. Annular geometry in patients with chronic ischemic mitral regurgitation. Circulation 112: I–409, 2005.

    Article  Google Scholar 

  26. 26.

    Khalighi, A. H. The mitral valve computational anatomy and geometry analysis. The University of Texas at Austin, Austin, 2015.

    Google Scholar 

  27. 27.

    Khalighi, A. H., A. Drach, C. H. Bloodworth, E. L. Pierce, A. P. Yoganathan, R. C. Gorman, J. H. Gorman, and M. S. Sacks. Mitral valve chordae tendineae: topological and geometrical characterization. Annals of biomedical engineering 45:378–393, 2017.

    Article  PubMed  Google Scholar 

  28. 28.

    Khalighi, A. H., A. Drach, R. C. Gorman, J. H. Gorman, and M. S. Sacks. Multi-resolution geometric modeling of the mitral heart valve leaflets. Biomechanics and modeling in mechanobiology 17:351-366, 2018.

    Article  PubMed  Google Scholar 

  29. 29.

    Khalighi, A. H., A. Drach, F. M. ter Huurne, C.-H. Lee, C. Bloodworth, E. L. Pierce, M. O. Jensen, A. P. Yoganathan, and M. S. Sacks. A comprehensive framework for the characterization of the complete mitral valve geometry for the development of a population-averaged model. In: International Conference on Functional Imaging and Modeling of the Heart, pp. 164–171, Springer 2015.

  30. 30.

    Khang, A., R. M. Buchanan, S. Ayoub, B. V. Rego, C. H. Lee, G. Ferrari, K. S. Anseth, and M. S. Sacks. Mechanobiology of the heart valve interstitial cell: simulation, experiment, and discovery. In: Mechanobiology in Health and Disease, pp. 249–283, Academic Press 2018.

  31. 31.

    Lee, C.-H., J.-P. Rabbah, A. P. Yoganathan, R. C. Gorman, J. H. Gorman, and M. S. Sacks. On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve. Biomechanics and modeling in mechanobiology 14:1281–1302, 2015.

    Article  PubMed Central  PubMed  Google Scholar 

  32. 32.

    Mansi, T., I. Voigt, B. Georgescu, X. Zheng, E. A. Mengue, M. Hackl, R. I. Ionasec, T. Noack, J. Seeburger, and D. Comaniciu. An integrated framework for finite-element modeling of mitral valve biomechanics from medical images: application to mitralclip intervention planning. Medical image analysis 16:1330–1346, 2012.

    Article  PubMed  Google Scholar 

  33. 33.

    McCarthy, K. P., L. Ring, and B. S. Rana. Anatomy of the mitral valve: understanding the mitral valve complex in mitral regurgitation. European Journal of echocardiography 11:i3–i9, 2010.

    Article  PubMed  Google Scholar 

  34. 34.

    Mick, S. L., S. Keshavamurthy, and A. M. Gillinov. Mitral valve repair versus replacement. Annals of cardiothoracic surgery 4:230, 2015.

    Google Scholar 

  35. 35.

    Morgan, A. E., J. L. Pantoja, J. Weinsaft, E. Grossi, J. M. Guccione, L. Ge, and M. Ratcliffe. Finite element modeling of mitral valve repair. Journal of biomechanical engineering 138:021009, 2016.

    Article  PubMed  Google Scholar 

  36. 36.

    Mozaffarian, D., E. J. Benjamin, A. S. Go, D. K. Arnett, M. J. Blaha, M. Cushman, S. R. Das, S. de Ferranti, J.-P. Després, H. J. Fullerton et al. Heart disease and stroke statistics2016 update: a report from the american heart association. Circulation 133:e38–e360, 2016.

    Google Scholar 

  37. 37.

    Obadia, J. F., C. Casali, J. F. Chassignolle, and M. Janier. Mitral subvalvular apparatus: different functions of primary and secondary chordae. Circulation 96:3124–3128, 1997.

    Article  CAS  PubMed  Google Scholar 

  38. 38.

    Pham, T., F. Kong, C. Martin, Q. Wang, C. Primiano, R. McKay, J. Elefteriades, and W. Sun. Finite element analysis of patient-specific mitral valve with mitral regurgitation. Cardiovascular engineering and technology 8:3–16, 2017.

    Article  PubMed Central  PubMed  Google Scholar 

  39. 39.

    Pouch, A. M., C. Xu, P. A. Yushkevich, A. S. Jassar, M. Vergnat, J. H. Gorman, R. C. Gorman, C. M. Sehgal, and B. M. Jackson. Semi-automated mitral valve morphometry and computational stress analysis using 3d ultrasound. Journal of biomechanics 45:903–907, 2012.

    Article  PubMed Central  PubMed  Google Scholar 

  40. 40.

    Prot, V., R. Haaverstad, and B. Skallerud. Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution. Biomechanics and modeling in mechanobiology 8:43–55, 2009.

    Article  CAS  PubMed  Google Scholar 

  41. 41.

    Prot, V., B. Skallerud, G. Sommer, and G. A. Holzapfel. On modelling and analysis of healthy and pathological human mitral valves: two case studies. Journal of the mechanical behavior of biomedical materials 3:167–177, 2010.

    Article  CAS  PubMed  Google Scholar 

  42. 42.

    Rausch, M. K., N. Famaey, T. O. Shultz, W. Bothe, D. C. Miller, and E. Kuhl. Mechanics of the mitral valve. Biomechanics and modeling in mechanobiology 12:1053–1071, 2013.

    Article  PubMed  Google Scholar 

  43. 43.

    Redaelli, A. A model of health: Mathematical modeling tools play an important role in optimizing new treatment options for heart disease. IEEE pulse 6:27–32, 2015.

    Article  PubMed  Google Scholar 

  44. 44.

    Rego, B. V., S. Ayoub, A. H. Khalighi, A. Drach, R. C. Gorman, J. H. Gorman, and M. S. Sacks. Alterations in mechanical properties and in vivo geometry of the mitral valve following myocardial infarction. In: Proceedings of the 2017 Summer Biomechanics, Bioengineering and Biotransport Conference, SB3C2017-1. 2017.

  45. 45.

    Rego, B. V., A. H. Khalighi, A. Drach, E. K. Lai, A. M. Pouch, R. C. Gorman, J. H. Gorman, and M. S. Sacks. A noninvasive method for the determination of in vivo mitral valve leaflet strains. International Journal for Numerical Methods in Biomedical Engineering, 2018. https://doi.org/10.1002/cnm.3142.

    Article  Google Scholar 

  46. 46.

    Rego, B. V. and M. S. Sacks. A functionally graded material model for the transmural stress distribution of the aortic valve leaflet. Journal of biomechanics 54:88–95, 2017.

    Article  PubMed Central  PubMed  Google Scholar 

  47. 47.

    Rego, B. V., S. M. Wells, C.-H. Lee, and M. S. Sacks. Mitral valve leaflet remodelling during pregnancy: insights into cell-mediated recovery of tissue homeostasis. Journal of The Royal Society Interface 13:20160709, 2016.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  48. 48.

    Rim, Y., D. D. McPherson, K. B. Chandran, and H. Kim. The effect of patient-specific annular motion on dynamic simulation of mitral valve function. Journal of biomechanics 46:1104–1112, 2013.

    Article  PubMed Central  PubMed  Google Scholar 

  49. 49.

    Ritchie, J., J. Jimenez, Z. He, M. S. Sacks, and A. P. Yoganathan. The material properties of the native porcine mitral valve chordae tendineae: an in vitro investigation. Journal of biomechanics 39:1129–1135, 2006.

    Article  PubMed  Google Scholar 

  50. 50.

    Rozenberg, G. and A. Salomaa. The mathematical theory of L systems, volume 90, Academic press, 1980.

  51. 51.

    Sacks, M. S., A. Khalighi, B. Rego, S. Ayoub, and A. Drach. On the need for multi-scale geometric modelling of the mitral heart valve. Healthcare Technology Letters 4:150, 2017.

    Article  PubMed Central  PubMed  Google Scholar 

  52. 52.

    Sacks, M. S., D. B. Smith, and E. D. Hiester. A small angle light scattering device for planar connective tissue microstructural analysis. Annals of biomedical engineering 25:678–689, 1997.

    Article  CAS  PubMed  Google Scholar 

  53. 53.

    Sand, M., D. Naftel, E. Blackstone, J. Kirklin, and R. Karp. A comparison of repair and replacement for mitral valve incompetence. The Journal of thoracic and cardiovascular surgery 94:208–219, 1987.

    CAS  PubMed  Google Scholar 

  54. 54.

    Smith, P. K., J. D. Puskas, D. D. Ascheim, P. Voisine, A. C. Gelijns, A. J. Moskowitz, J. W. Hung, M. K. Parides, G. Ailawadi, L. P. Perrault et al. Surgical treatment of moderate ischemic mitral regurgitation. New England Journal of Medicine 371:2178–2188, 2014.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  55. 55.

    Stevanella, M., F. Maffessanti, C. A. Conti, E. Votta, A. Arnoldi, M. Lombardi, O. Parodi, E. G. Caiani, and A. Redaelli. Mitral valve patient-specific finite element modeling from cardiac mri: application to an annuloplasty procedure. Cardiovascular Engineering and Technology 2:66–76, 2011.

    Article  Google Scholar 

  56. 56.

    Sturla, F., F. Onorati, E. Votta, K. Pechlivanidis, M. Stevanella, A. D. Milano, G. Puppini, A. Mazzucco, A. Redaelli, and G. Faggian. Is it possible to assess the best mitral valve repair in the individual patient? preliminary results of a finite element study from magnetic resonance imaging data. The Journal of thoracic and cardiovascular surgery 148:1025–1034, 2014.

    Article  PubMed  Google Scholar 

  57. 57.

    Sun, W., C. Martin, and T. Pham. Computational modeling of cardiac valve function and intervention. Annual review of biomedical engineering 16:53–76, 2014.

    Article  CAS  Google Scholar 

  58. 58.

    Trichon, B. H., G. M. Felker, L. K. Shaw, C. H. Cabell, and C. M. OConnor. Relation of frequency and severity of mitral regurgitation to survival among patients with left ventricular systolic dysfunction and heart failure. American Journal of Cardiology 91:538–543, 2003.

    Article  PubMed  Google Scholar 

  59. 59.

    Wenk, J. F., Z. Zhang, G. Cheng, D. Malhotra, G. Acevedo-Bolton, M. Burger, T. Suzuki, D. A. Saloner, A. W. Wallace, J. M. Guccione et al. First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. The Annals of thoracic surgery 89:1546–1553, 2010.

    Article  PubMed Central  PubMed  Google Scholar 

  60. 60.

    Yun, K. and D. Miller. Mitral valve repair versus replacement. Cardiology clinics 9:315–327, 1991.

    Article  CAS  PubMed  Google Scholar 

  61. 61.

    Zhang, F., J. Kanik, T. Mansi, I. Voigt, P. Sharma, R. I. Ionasec, L. Subrahmanyan, B. A. Lin, L. Sugeng, D. Yuh et al et al. Towards patient-specific modeling of mitral valve repair: 3d transesophageal echocardiography-derived parameter estimation. Medical image analysis 35:599–609, 2017.

    Article  PubMed  Google Scholar 

  62. 62.

    Zhang, W., S. Ayoub, J. Liao, and M. S. Sacks. A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets. Acta biomaterialia 32:238–255, 2016.

    Article  PubMed  Google Scholar 

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Acknowledgments

Research reported in this publication was supported by National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Number R01-HL119297, National Science Foundation Grant No. DGE-1610403 to BVR, and the American Heart Association Grant No. 18PRE34030258 to BVR.

Conflict of interest

The authors declare no conflict of interest.

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Correspondence to Michael S. Sacks.

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Associate Editor Elena S. Di Martino oversaw the review of this article.

Appendix

Appendix

We performed our analysis presented in this work on 3 valves that were randomly selected from our extant dataset of micro-CT based MV models (Fig. 10). The optimal models developed for all valves faithfully reproduced the effect of native chordal anatomy in terms of organ-level simulations of the MV closure under normal, dilated, and repaired conditions (Figs. 11 and 12). This consistency further indicates that functionally equivalent MVCT models allow performing predictive simulations of the MV apparatus to simulate clinically important conditions of the MV.

Figure 10
figure10

The study was performed on 3 specimens to reproduce the results of functionally equivalent models of the MVCT on multiple valves.

Figure 11
figure11

Closure simulations of MV2 are shown for a functionally equivalent MVCT and the ground truth models.

Figure 12
figure12

Closure simulations of MV3 are shown for a functionally equivalent MVCT and the ground truth models.

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Khalighi, A.H., Rego, B.V., Drach, A. et al. Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization. Ann Biomed Eng 47, 60–74 (2019). https://doi.org/10.1007/s10439-018-02122-y

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Keywords

  • Mitral valve
  • Chordae tendineae
  • Topology optimization
  • Finite element analysis
  • Sub-valvular apparatus