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Annals of Biomedical Engineering

, Volume 44, Issue 4, pp 942–953 | Cite as

Fluid–Structure Interaction Analysis of Papillary Muscle Forces Using a Comprehensive Mitral Valve Model with 3D Chordal Structure

  • Milan Toma
  • Morten Ø. Jensen
  • Daniel R. Einstein
  • Ajit P. Yoganathan
  • Richard P. Cochran
  • Karyn S. Kunzelman
Article

Abstract

Numerical models of native heart valves are being used to study valve biomechanics to aid design and development of repair procedures and replacement devices. These models have evolved from simple two-dimensional approximations to complex three-dimensional, fully coupled fluid–structure interaction (FSI) systems. Such simulations are useful for predicting the mechanical and hemodynamic loading on implanted valve devices. A current challenge for improving the accuracy of these predictions is choosing and implementing modeling boundary conditions. In order to address this challenge, we are utilizing an advanced in vitro system to validate FSI conditions for the mitral valve system. Explanted ovine mitral valves were mounted in an in vitro setup, and structural data for the mitral valve was acquired with \(\mu\)CT. Experimental data from the in vitro ovine mitral valve system were used to validate the computational model. As the valve closes, the hemodynamic data, high speed leaflet dynamics, and force vectors from the in vitro system were compared to the results of the FSI simulation computational model. The total force of 2.6 N per papillary muscle is matched by the computational model. In vitro and in vivo force measurements enable validating and adjusting material parameters to improve the accuracy of computational models. The simulations can then be used to answer questions that are otherwise not possible to investigate experimentally. This work is important to maximize the validity of computational models of not just the mitral valve, but any biomechanical aspect using computational simulation in designing medical devices.

Keywords

Fluid–structure interaction Mitral valve Forces Comprehensive computational model Papillary muscle Chordal structure 

Notes

Acknowledgments

This study was supported by a grant from the National Heart Lung and Blood Institute (R01-HL092926).

Conflict of interest

No benefits in any form have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript.

References

  1. 1.
    Carson, J. P., A. P. Kuprat, X. Jiao, F. del Pin, and D. R. Einstein. An anisotropic fluid-solid model of the mouse heart. Comput. Cardiol. 36:377–380, 2009.Google Scholar
  2. 2.
    Chandran, K. B. and H. Kim. Computational mitral valve evaluation and potential clinical applications. Annal. Biomed. Eng. 43(6):1348–1362, 2015.CrossRefPubMedGoogle Scholar
  3. 3.
    Cochran, R. P. and K. S. Kunzelman. Effect of papillary muscle position on mitral valve function: relationship to mitral homografts. Annal. Thorac. Surg., 66(Suppl):S155–S161, 1998.CrossRefPubMedGoogle Scholar
  4. 4.
    Couprie, C., L. Grady, L. Najman, and H. Talbot. Power watersheds: a new image segmentation framework extending graph cuts, random walker and optimal spanning forest. in International Conference on Computer Vision, 2009.Google Scholar
  5. 5.
    Couprie, C., L. Grady, L. Najman, and H. Talbot. Power watersheds: a unifying graph-based optimization framework. IEEE Trans. Pattern Anal. Mach. Intell. 33(7):1384–1399, 2010.CrossRefPubMedGoogle Scholar
  6. 6.
    Einstein, D. R., F. DelPin, X. Jiao, A. P. Kuprat, J. P. Carson, K. S. Kunzelman, R. P. Cochran, J. M. Guccione, and M. B. Ratclifee. Fluid-structure interactions of the mitral valve and left heart: comprehensive strategies, past, present, and future. Int. J. Numer. Methods Biomed. Eng. 26(3–4):348–380, 2010.CrossRefGoogle Scholar
  7. 7.
    Einstein, D., X. Jiao, and A. Kuprat. BioGeom: an integrated environment for geometric computations in biomedicine. URL: https://simtk.org/home/biogeom.CrossRefGoogle Scholar
  8. 8.
    Einstein, D. R., K. S. Kunzelman, P. G. Reinhall, M. A. Nicosia, and R. P. Cochran. The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound. Trans. ASME 127:134–147, 2005.Google Scholar
  9. 9.
    Einstein, D. R., P. G. Reinhall, K. S. Kunzelman, and R. P. Cochran. Nonlinear finite element analysis of the mitral valve. J. Heart Valve Dis. 3:376–385, 2005.Google Scholar
  10. 10.
    Freed, A. D., D. R. Einstein, and I. Vesely. Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay. Biomech. Model Mechanobiol. 4:100–117, 2005.CrossRefPubMedGoogle Scholar
  11. 11.
    He, S., J. D. Lemmon, M. W. Weston, M. O. Jensen, R. A. Levine, and A. P. Yoganathan. Mitral valve compensation for annular dilatation: in vitro study into the mechanisms of functional mitral regurgitation with an adjustable annulus model. J. Heart Valve Dis.8:294–302, 1999.PubMedGoogle Scholar
  12. 12.
    Ingels, Jr. N. B., and M. Karlsson. Mitral valve mechanics. Dropbox https://www.dropbox.com/sh/lbd9l7pl9cj8s1o/AADp8vFqWboXXsn0P4wTKgjNa Chapter 22, 2014.
  13. 13.
    Jensen, M. O., A. A. Fontaine, and A. P. Yoganathan. Improved in vitro quantification of the force exerted by the papillary muscle on the left ventricular wall: three-dimensional force vector measurement system. Annal. Biomed. Eng., 29: 406–412, 2001.CrossRefPubMedGoogle Scholar
  14. 14.
    Jensen, H., M. O. Jensen, and M. H. Smerup. Three-dimensional assessment of papillary muscle displacement in a porcine model of ischemic mitral regurgitation. J. Thorac. Cardiovasc. Surg. 140:1312–1318, 2010.Google Scholar
  15. 15.
    Kunzelman, K. S. and R. P. Cochran. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J. Cardiac Surg. 7(1):71–78, 1992.CrossRefGoogle Scholar
  16. 16.
    Kunzelman, K. S., R. P. Cochran, C. J. Chuong, W. S. Ring, E. D. Verier, and R. C. Eberhart. Finite element analysis of the mitral valve. J. Heart Valve Dis. 2:326–340, 1993.PubMedGoogle Scholar
  17. 17.
    Kunzelman, K. S., R. P. Cochran, C. J. Chuong, W. S. Ring, E. D. Verier, and R. C. Eberhart. Finite element analysis of mitral valve pathology. J. Long Term Eff. Med. Implant 3:161–179, 1993.Google Scholar
  18. 18.
    Kunzelman, K. S., D. R. Einstein, and R. P. Cochran. Fluid–structure interaction models of the mitral valve: function in normal and pathological states. Philos. Trans. R. Soc. B, 362:1393–1406, 2007.CrossRefGoogle Scholar
  19. 19.
    Kunzelman, K.S., M. S. Reimink, and R. P. Cochran. Annular dilatation increases stress in the mitral valve and delays coaptation: a finite element computer model. Cardiovasc. Surg. 5:427–434, 1997.CrossRefPubMedGoogle Scholar
  20. 20.
    Kunzelman, K.S., M. S. Reimink, and R. P. Cochran. Flexible versus rigid ring annuloplasty for mitral valve annular dilation: a finite element model. J. Heart Valve Dis., 7:108–116, 1998.PubMedGoogle Scholar
  21. 21.
    Kunzelman, K.S., M. S. Reimink, E. D. Verier, and R. P. Cochran. Replacement of mitral valve posterior chordae tendineae with expanded polytetrafluoroethylene suture: a finite element study. J. Card. Surg. 11:136–145, 1996.CrossRefPubMedGoogle Scholar
  22. 22.
    Kuprat, A. P. and D. R. Einstein. An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data. J. Comput. Phys. 228:619–640, 2009.CrossRefPubMedPubMedCentralGoogle Scholar
  23. 23.
    Kuprat, A., A. Khamayseh, D. George, and L. Larkey. Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines. J. Comput. Phys. 172: 99–118, 2001.CrossRefGoogle Scholar
  24. 24.
    Lau, K. D., V. Diaz, P. Scambler, and G. Burriesci. Mitral valve dynamics in structural and fluid–structure interaction models. Med. Eng. Phys. 32:1057–1064, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Lee, C. -H., J.- P. Rabbah, A. P. Yoganathan, R. C. Gorman III, J. H. Gorman, and M. S. Sacks. On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve. Biomech. Model Mechanobiol. 2015. doi: 10.1007/s10237-015-0674-0.
  26. 26.
    Magne, J., M. Senechal, J. G. Dumesnil, and P. Pibarot. Ischemic mitral regurgitation: a complex multifaceted disease. Cardiology 112:244–259, 2009.CrossRefPubMedGoogle Scholar
  27. 27.
    Maisano, F., A. Redaelli, M. Soncini, E. Votta, L. Arcobasso, and O. Alfieri. An annular prosthesis for the treatment of functional mitral regurgitation: finite element model analysis of a dog bone–shaped ring prosthesis. Ann. Thorac. Surg. 79:1268–1275, 2005.CrossRefPubMedGoogle Scholar
  28. 28.
    Mansi, T., I. Voigt, B. Georgescu, X. Zheng, E. A. Mengue, M. Hackl, R. 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. Med. Image Anal. 16:1330–1346, 2012.CrossRefPubMedGoogle Scholar
  29. 29.
    Mansi, T.,  I. Voigt, E. A. Mengue, R. Ionasec, B. Georgescu, T. Noack, J. Seeburger, and D. Comaniciu, Medical Image Computing and Computer-Assisted Intervention, chapter Towards Patient-Specific Finite-Element Simulation of MitralClip Procedure, Springer Berlin, Heidelberg, 2011.Google Scholar
  30. 30.
    Pouch, A. M., P. A. Yushkevich, B. M. Jackson, A. S. Jassaar, M. Vergnat, J. H. Gorman, R. C. Gorman, and C. M. Sehgal. Development of a semi-automated method for mitral valve modeling with medial axis representation using 3d ultrasound. Med. Phys. 39(2):933–950, 2012.CrossRefPubMedGoogle Scholar
  31. 31.
    Prot, V., R. Haaverstad, and B. Skallerud. Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution. Biomech. Model. Mechanobiol. 8(1):43–55, 2009.CrossRefPubMedGoogle Scholar
  32. 32.
    Rabbah, J.-P., N. Saikrishnan, and A. P. Yoganathan. A novel left heart simulator for the multi-modality characterization of native mitral valve geometry and fluid mechanics. Ann. Biomed. Eng. 41(2):305–315, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  33. 33.
    Rahmani, A., A. Q. Rasmussen, J. L. Honge, B. Ostli, R. A. Levine, A. Hagege, H. Nygaard, S. L. Nielsen, and M. O. Jensen. Mitral valve mechanics following posterior leaflet patch augmentation. J. Heart Valve Dis. 22(1):28–35, 2013.PubMedPubMedCentralGoogle Scholar
  34. 34.
    Reimink, M. S., K. S. Kunzelman, and R. P. Cochran. The effect of chordal replacement suture length on function and stresses in repaired mitral valves: a finite element study. J. Heart Valve Dis. 5:365–375, 1996.PubMedGoogle Scholar
  35. 35.
    Reimink, M. S., K. S. Kunzelman, E. D. Verier, and R. P. Cochran. The effect of anterior chordal replacement on mitral valve function and stresses. ASAIO Trans. 41:M754–M762, 1995.CrossRefGoogle Scholar
  36. 36.
    Rim, Y., S. T. Laing, D. D. McPherson, and H. Kim. Mitral valve repair using eptfe sutures for ruptured mitral chordae tendineae: a computational simulation study. Ann. Biomed. Eng. 42(1): 139–148, 2013.CrossRefPubMedGoogle Scholar
  37. 37.
    M. S. Sacks. Incorporation of experimentally-derived fiber orientation into a structual constitutive model for planar collagenous tissues. J. Biomech. Eng. 125(2):280–287, 2003.CrossRefPubMedGoogle Scholar
  38. 38.
    Schievano, S., K. S. Kunzelman, M. A. Nicosia, R. P. Cochran, D. R. Einstein, S. Khambadkone, and P. Bonhoeffer. Percutaneous mitral valve dilatation: single balloon versus double balloon. A finite element study. J. Heart Valve Dis., 18:28–34, 2009.PubMedGoogle Scholar
  39. 39.
    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. Cardiovasc. Eng. Technol. 2(2):66–76, 2011.CrossRefGoogle Scholar
  40. 40.
    van Rijk-Zwikker, G. L., B. J. Delemarre, and H. A. Huysmans. Mitral valve anatomy and morphology: relevance to mitral valve replacement and valve reconstruction. J. Card. Surg. 9(2 Suppl):255–261, 1994.CrossRefPubMedGoogle Scholar
  41. 41.
    Votta, E., E. G. Caiani, F. Veronesi, M. Soncini, F. M. Motevecchi, and A. Redaelli. Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios. Philos. Trans. Ser. A 366(1879):3411–3434, 2008.CrossRefGoogle Scholar
  42. 42.
    Votta, E., T. B. Le, M. Stevanella, L. Fusini, E. G. Caiani, A. Redaelli, and F. Sotiropoulos. Toward patient-specific simulations of cardiac valves: state-of-the-art and future directions. J. Biomech. 46(2):217–228, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  43. 43.
    Wenk, J. F., Z. Zhang, G. Cheng, D. Malhotra, G. A.-Bolton, M. Burger, T. Suzuki, D. A. Saloner, A. W. Wallace, J. M. Guccione, and M. B. Ratclifee. First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann. Thorac. Surg. 89:1546–1554, 2010.CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  • Milan Toma
    • 1
  • Morten Ø. Jensen
    • 1
  • Daniel R. Einstein
    • 2
  • Ajit P. Yoganathan
    • 1
  • Richard P. Cochran
    • 3
  • Karyn S. Kunzelman
    • 3
  1. 1.Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Computational Biology & BioinformaticsPacific Northwest National LaboratoryRichlandUSA
  3. 3.Department of Mechanical EngineeringUniversity of MaineOronoUSA

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