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The Impact of Fluid Inertia on In Vivo Estimation of Mitral Valve Leaflet Constitutive Properties and Mechanics

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Abstract

We examine the influence of the added mass effect (fluid inertia) on mitral valve leaflet stress during isovolumetric phases. To study this effect, oscillating flow is applied to a flexible membrane at various frequencies to control inertia. Resulting membrane strain is calculated through a three-dimensional reconstruction of markers from stereo images. To investigate the effect in vivo, the analysis is repeated on a published dataset for an ovine mitral valve (Journal of Biomechanics 42(16): 2697–2701). The membrane experiment demonstrates that the relationship between pressure and strain must be corrected with a fluid inertia term if the ratio of inertia to pressure differential approaches 1. In the mitral valve, this ratio reaches 0.7 during isovolumetric contraction for an acceleration of 6 m/s2. Acceleration is reduced by 72% during isovolumetric relaxation. Fluid acceleration also varies along the leaflet during isovolumetric phases, resulting in spatial variations in stress. These results demonstrate that fluid inertia may be the source of the temporally and spatially varying stiffness measurements previously seen through inverse finite element analysis of in vivo data during isovolumetric phases. This study demonstrates that there is a need to account for added mass effects when analyzing in vivo constitutive relationships of heart valves.

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References

  1. 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: Functional Imaging and Modeling of the Heart. Berlin: Springer, 2013, pp. 141–149.

  2. Askov, J. B., J. L. Honge, M. O. Jensen, H. Nygaard, J. M. Hasenkam, and S. L. Nielsen. Significance of force transfer in mitral valve–left ventricular interaction: in vivo assessment. J. Thorac. Cardiovasc. Surg. 145:1635–1641, e1631, 2013.

  3. Bhattacharya, S., and Z. He. Annulus tension of the prolapsed mitral valve corrected by edge-to-edge repair. J. Biomech. 45:562–568, 2012.

    Article  PubMed  Google Scholar 

  4. Chen, L., A. D. McCulloch, and K. May-Newman. Nonhomogeneous deformation in the anterior leaflet of the mitral valve. Ann. Biomed. Eng. 32:1599–1606, 2004.

    Article  PubMed  Google Scholar 

  5. Chong, M., M. Eng, and Y. Missirlis. Aortic valve mechanics part II: a stress analysis of the porcine aortic valve leaflets in diastole. Artif. Cells Blood Substit. Biotechnol. 6:225–244, 1978.

    CAS  Google Scholar 

  6. Clark, R. Stress–strain characteristics of fresh and frozen human aortic and mitral leaflets and chordae tendineae. Implications for clinical use. J. Thorac. Cardiovasc. Surg. 66:202, 1973.

    CAS  PubMed  Google Scholar 

  7. Einstein, D. R., F. Del Pin, X. Jiao, A. P. Kuprat, J. P. Carson, K. S. Kunzelman, R. P. Cochran, J. M. Guccione, and M. B. Ratcliffe. Fluid–structure interactions of the mitral valve and left heart: comprehensive strategies, past, present and future. Int. J. Numer. Methods Biomed. Eng. 26:348–380, 2010.

    Article  Google Scholar 

  8. Franz, T., D. Bezuidenhout, and P. Zilla. Flexible leaflet polymeric heart valves. In: Cardiovascular and Cardiac Therapeutic Devices. Berlin: Springer, 2014, pp. 93–129.

  9. Ghista, D. N., and A. P. Rao. Mitral-valve mechanics—stress/strain characteristics of excised leaflets, analysis of its functional mechanics and its medical application. Med. Biol. Eng. 11:691–702, 1973.

    Article  CAS  PubMed  Google Scholar 

  10. Gould, P. L., A. Cataloglu, G. Dhatt, A. Chattopadhyay, and R. E. Clark. Stress analysis of the human aortic valve. Comput. Struct. 3:377–384, 1973.

    Article  Google Scholar 

  11. Grego-Bessa, J., L. Luna-Zurita, G. del Monte, V. Bolós, P. Melgar, A. Arandilla, A. N. Garratt, H. Zang, Y.-S. Mukouyama, and H. Chen. Notch signaling is essential for ventricular chamber development. Dev. Cell 12:415–429, 2007.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. He, Z., and S. Bhattacharya. Papillary muscle and annulus size effect on anterior and posterior annulus tension of the mitral valve: an insight into annulus dilatation. J. Biomech. 41:2524–2532, 2008.

    Article  PubMed  Google Scholar 

  13. He, Z., J. Ritchie, J. S. Grashow, M. S. Sacks, and A. P. Yoganathan. In vitro dynamic strain behavior of the mitral valve posterior leaflet. J. Biomech. Eng. 127:504–511, 2005.

    Article  PubMed  Google Scholar 

  14. Heikali, D., and D. Di Carlo. A niche for microfluidics in portable hematology analyzers. J. Assoc. Lab. Autom. 15:319–328, 2010.

    Article  Google Scholar 

  15. Jamison, R. A., C. R. Samarage, R. J. Bryson-Richardson, and A. Fouras. In vivo wall shear measurements within the developing zebrafish heart. PLoS One 8:e75722, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Jimenez, J. H., D. D. Soerensen, Z. He, J. Ritchie, and A. P. Yoganathan. Mitral valve function and chordal force distribution using a flexible annulus model: an in vitro study. Ann. Biomed. Eng. 33:557–566, 2005.

    Article  PubMed  Google Scholar 

  17. Kendoush, A. K., M. Padela, D. Icenogle and A. P. Yoganathan. The inertia of the anterior leaflet of the heart’s mitral valve. In: ASME 2010 Summer Bioengineering Conference. Naples, FL, 2010, pp. 629–630.

  18. Krishnamurthy, G., D. B. Ennis, A. Itoh, W. Bothe, J. C. Swanson, M. Karlsson, E. Kuhl, D. C. Miller, and N. B. Ingels, Jr. Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis. Am. J. Physiol. Heart Circ. Physiol. 295:H1141–H1149, 2008.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Kunzelman, K. S., and R. Cochran. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J. Card. Surg. 7:71–78, 1992.

    Article  CAS  PubMed  Google Scholar 

  20. Kunzelman, K., D. R. Einstein, and R. Cochran. Fluid–structure interaction models of the mitral valve: function in normal and pathological states. Philos. Trans. R. Soc. B Biol. Sci. 362:1393–1406, 2007.

    Article  CAS  Google Scholar 

  21. Lauboeck, H. The conditions of mitral valve closure. J. Biomed. Eng. 2:93–96, 1980.

    Article  CAS  PubMed  Google Scholar 

  22. Lee, J. Y., H. S. Ji, and S. J. Lee. Micro-PIV measurements of blood flow in extraembryonic blood vessels of chicken embryos. Physiol. Meas. 28:1149, 2007.

    Article  PubMed  Google Scholar 

  23. Lee, J., M. E. Moghadam, E. Kung, H. Cao, T. Beebe, Y. Miller, B. L. Roman, C.-L. Lien, N. C. Chi, and A. L. Marsden. Moving domain computational fluid dynamics to interface with an embryonic model of cardiac morphogenesis. PLoS One 8:e72924, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Leslie, D. C., A. Waterhouse, J. B. Berthet, T. M. Valentin, A. L. Watters, A. Jain, P. Kim, B. D. Hatton, A. Nedder, and K. Donovan. A bioinspired omniphobic surface coating on medical devices prevents thrombosis and biofouling. Nat. Biotechnol. 32:1134–1140, 2014.

    Article  CAS  PubMed  Google Scholar 

  25. May-Newman, K., and F. C. Yin. Biaxial mechanical behavior of excised porcine mitral valve leaflets. Am. J. Physiol. Heart Circ. Physiol. 38:H1319, 1995.

    Google Scholar 

  26. Oberdisse, J. Structure and rheological properties of latex-silica nanocomposite films: stress–strain isotherms. Macromolecules 35:9441–9450, 2002.

    Article  CAS  Google Scholar 

  27. Peshkovsky, C., R. Totong, and D. Yelon. Dependence of cardiac trabeculation on neuregulin signaling and blood flow in zebrafish. Dev. Dyn. 240:446–456, 2011.

    Article  PubMed  Google Scholar 

  28. Prot, V., B. Skallerud, G. Sommer, and G. A. Holzapfel. On modelling and analysis of healthy and pathological human mitral valves: two case studies. J. Mech. Behav. Biomed. Mater. 3:167–177, 2010.

    Article  CAS  PubMed  Google Scholar 

  29. Reser, D., B. Seifert, M. Klein, T. Dreizler, P. Hasenclever, V. Falk, and C. Starck. Retrospective analysis of outcome data with regards to the use of Phisio(R)-, Bioline(R)- or Softline(R)-coated cardiopulmonary bypass circuits in cardiac surgery. Perfusion 27:530–534, 2012.

    Article  CAS  PubMed  Google Scholar 

  30. Sacks, M. S., Y. Enomoto, J. R. Graybill, W. D. Merryman, A. Zeeshan, A. P. Yoganathan, R. J. Levy, R. C. Gorman, and J. H. Gorman, III. In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann. Thorac. Surg. 82:1369–1377, 2006.

    Article  PubMed  Google Scholar 

  31. Sacks, M., Z. He, L. Baijens, S. Wanant, P. Shah, H. Sugimoto, and A. Yoganathan. Surface strains in the anterior leaflet of the functioning mitral valve. Ann. Biomed. Eng. 30:1281–1290, 2002.

    Article  CAS  PubMed  Google Scholar 

  32. Tse, H. T. K., D. R. Gossett, Y. S. Moon, M. Masaeli, M. Sohsman, Y. Ying, K. Mislick, R. P. Adams, J. Rao, and D. Di Carlo. Quantitative diagnosis of malignant pleural effusions by single-cell mechanophenotyping. Sci. Transl. Med. 5:212ra163, 2013.

    Article  PubMed  Google Scholar 

  33. Weston, M. W., D. V. LaBorde, and A. P. Yoganathan. Estimation of the shear stress on the surface of an aortic valve leaflet. Ann. Biomed. Eng. 27:572–579, 1999.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

We would like to thank Dr. Neil Ingels and Dr. Julia Swanson of Stanford University for providing in vivo data. The authors gratefully acknowledge funding from National Institutes of Health (NIH) under Award Number R01HL119824. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

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Authors and Affiliations

  1. School of Mechanical Engineering, Colorado State University, Fort Collins, CO, 80523, USA

    David L. Bark Jr.

  2. Department of Biomedical Engineering, Dorothy Davis Heart and Lung Research Institute, 473 W 12th Avenue, Columbus, OH, 43210, USA

    Lakshmi P. Dasi

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  1. David L. Bark Jr.
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Correspondence to Lakshmi P. Dasi.

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Associate Editor Umberto Morbiducci oversaw the review of this article.

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Bark, D.L., Dasi, L.P. The Impact of Fluid Inertia on In Vivo Estimation of Mitral Valve Leaflet Constitutive Properties and Mechanics. Ann Biomed Eng 44, 1425–1435 (2016). https://doi.org/10.1007/s10439-015-1463-8

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  • DOI: https://doi.org/10.1007/s10439-015-1463-8

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