Skip to main content
SpringerLink
Log in

Asymptotic Model of Fluid–Tissue Interaction for Mitral Valve Dynamics

  • Published:
Cardiovascular Engineering and Technology Aims and scope Submit manuscript

Abstract

The vortex formation process inside the left ventricle is intrinsically connected to the dynamics of the mitral leaflets while they interact with the flow crossing the valve during diastole. The description of the dynamics of a natural mitral valve still represents a challenging issue, especially because its material properties are not measurable in vivo. Medical imaging can provide some indications about the geometry of the valve, but not about its mechanical properties. In this work, we introduce a parametric model of the mitral valve geometry, whose motion is described in the asymptotic limit under the assumption that it moves with the flow, without any additional resistance other than that given by its shape, and without the need to specify its material properties. The mitral valve model is coupled with a simple description of the left ventricle geometry, and their dynamics is solved numerically together with the equations ruling the blood flow. The intra-ventricular flow is analyzed in its relationship with the valvular motion. It is found that the initial valve opening anticipates the peak velocity of the Early filling wave with little influence of the specific geometry; while subsequent closure and re-opening are more dependent on the intraventricular vortex dynamics and thus on the leaflets’ geometry itself. The limitations and potential applications of the proposed model are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  1. Baccani, B., F. Domenichini, and G. Pedrizzetti. Model and influence of mitral valve opening during the left ventricular filling. J. Biomech. 36(3):355–361, 2003.

    Article  Google Scholar 

  2. Borazjani, I., L. Ge, and F. Sotiropoulos. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227:7587–7620, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cheng, R., Y. G. Lai, and K. B. Chandran. Three-dimensional fluid–structure interaction simulation of bileaflet mechanical heart valve flow dynamics. Ann. Biomed. Eng. 32(11):1471–1483, 2004.

    Article  Google Scholar 

  4. Dabiri, J. O. Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41:17–33, 2009.

    Article  MathSciNet  Google Scholar 

  5. de Tullio, M. D., A. Cristallo, E. Balaras, and R. Verzicco. Direct numerical simulation of the pulsatile low trough an aortic bileaflet mechanical heart valve. J. Fluid Mech. 622:259–290, 2009.

    Article  MATH  Google Scholar 

  6. de Tullio, M. D., G. Pedrizzetti, and R. Verzicco. On the effect of aortic root geometry on the coronary entry-flow after a bileaflet mechanical heart valve implant: a numerical study. Acta Mech. 216:147–163, 2011.

    Article  MATH  Google Scholar 

  7. Domenichini, F. Three-dimensional impulsive vortex formation from slender orifices. J. Fluid Mech. 666:506–520, 2011.

    Article  MATH  Google Scholar 

  8. Domenichini, F., and G. Pedrizzetti. Intraventricular vortex flow changes in the infarcted left ventricle: numerical results in an idealised 3D shape. Comput. Methods Biomech. Biomed. Eng. 14:95–101, 2011.

    Article  Google Scholar 

  9. Domenichini, F., G. Pedrizzetti, and B. Baccani. Three-dimensional filling flow into a model left ventricle. J. Fluid Mech. 539:179–198, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  10. Domenichini, F., G. Querzoli, A. Cenedese, and G. Pedrizzetti. Combined experimental and numerical analysis of the flow structure into the left ventricle. J. Biomech. 40(9):1988–1994, 2007.

    Article  Google Scholar 

  11. Faludi, R., M. Szulik, J. D’hooge, P. Herijgers, F. Rademakers, G. Pedrizzetti, and J.-U. Voigt. Left ventricular flow patterns in healthy subjects and patients with prosthetic mitral valves: an in vivo study using echocardiographic particle image velocimetry. J. Thorac. Cardiovasc. Surg. 139:1501–1510, 2010.

    Article  Google Scholar 

  12. Gharib, M., E. Rambod, A. Kheradvar, D. J. Sahn, and J. O. Dabiri. Optimal vortex formation as an index of cardiac health. Proc. Natl. Acad. Sci. U.S.A. 109:6205–6308, 2006.

    Google Scholar 

  13. Griffith, B. E., X. Luo, D. M. mcQueen, and C. S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int. J. Appl. Mech. 1(1):137–177, 2009.

    Article  Google Scholar 

  14. Hong, G. R., G. Pedrizzetti, G. Tonti, P. Li, P. Wei, J. K. Kim, A. Bawela, S. Liu, N. Chung, H. Houle, J. Narula, and M. A. Vannan. Characterization and quantification of vortex flow in the human left ventricle by contrast echocardiography using vector particle image velocimetry. J. Am. Coll. Cardiol. Imaging 1:705–717, 2008.

    Article  Google Scholar 

  15. Jeong, J., and F. Hussain. On the identification of a vortex. J. Fluid Mech. 285:69–94, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  16. Kilner, P. J., G. Z. Yang, A. J. Wilkes, R. H. Mohiaddin, D. N. Firmin, and M. H. Yacoub. Asymmetric redirection of flow through the heart. Nature 404:759–761, 2000.

    Article  Google Scholar 

  17. Le, T. B., and F. Sotiropoulos. Fluid-structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle. J. Comput. Phys. 244:41–62, 2013.

    Article  MathSciNet  Google Scholar 

  18. Lemmon, J. D., and A. P. Yoganathan. Three-Dimensional computational model of left heart diastolic function with fluid–structure interaction. J. Biomech. Eng. 122:109–117, 2000.

    Article  Google Scholar 

  19. Lemmon, J. D., and A. P. Yoganathan. Computational modeling of left heart diastolic function: examination of ventricular dysfunction. J. Biomech. Eng. 122:297–303, 2000.

    Article  Google Scholar 

  20. Ma, X., H. Gao, B. E. Griffith, C. Berry, and X. Luo. Image-based fluid–structure interaction model of the human mitral valve. Comput. Fluids 71:417–425, 2013.

    Article  MathSciNet  Google Scholar 

  21. Machler, H., M. Perthel, G. Reiter, U. Reiter, M. Zink, P. Bergmann, A. Waltensdorfer, and J. Laas. Influence of bileaflet prosthetic mitral valve orientation on left ventricular flow—an experimental in vivo magnetic resonance imaging study. Eur. J. Cardiothorac. Surg. 26:747–753, 2004.

    Article  Google Scholar 

  22. Mangual, J. O., A. De Luca, E. Kraigher-Krainer, L. Toncelli, A. Shah, S. Solomon, G. Galanti, F. Domenichini, and G. Pedrizzetti. Comparative numerical study on left ventricular fluid dynamics after dilated cardiomyopathy. J. Biomech. 46:1611–1617, 2013.

    Article  Google Scholar 

  23. Mangual, J. O., F. Domenichini, and G. Pedrizzetti. Describing the highly three dimensional right ventricle flow. Ann. Biomed. Eng. 40(8):1790–1801, 2012.

    Article  Google Scholar 

  24. Mangual, J. O., F. Domenichini, and G. Pedrizzetti. Three dimensional numerical assessment of the right ventricular flow using 4D echocardiography boundary data. Eur. J. Mech. B/Fluids 25:25–30, 2012.

    Article  Google Scholar 

  25. Narula, J., M. A. Vannan, and A. N. De Maria. Of that waltz in my heart. J. Am. Coll. Cardiol. 49:917–920, 2007.

    Article  Google Scholar 

  26. Pedrizzetti, G., and F. Domenichini. Nature optimizes the swirling flow in the human left ventricle. Phys. Rev. Lett. 95:108101, 2005.

    Article  Google Scholar 

  27. Pedrizzetti, G., and F. Domenichini. Asymmetric opening of a simple bi-leaflet valve. Phys. Rev. Lett. 98:214503, 2007.

    Article  Google Scholar 

  28. Pedrizzetti, G., F. Domenichini, and G. Tonti. On the left ventricular vortex reversal after mitral valve replacement. Ann. Biomed. Eng. 38(3):769–773, 2010.

    Article  Google Scholar 

  29. Peskin, C. S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:252–271, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  30. Quaini, A., S. Canic, G. Guidoboni, R. Glowinski, S. R. Igo, C. J. Hartley, W. A. Zoghbi, and S. H. Little. A three-dimensional computational fluid dynamics model of regurgitant mitral valve flow: validation against in vitro standards and 3D Color Doppler methods. Cardiovasc. Eng. Technol. 2(2):77–89, 2011.

    Article  Google Scholar 

  31. Querzoli, G., S. Fortini, and A. Cenedese. Effect of the prosthetic mitral valve on the vortex dynamics and turbulence of the left ventricular flow. Phys. Fluids 22(4):1–10, 2010.

    Article  Google Scholar 

  32. Seo, J. H., and R. Mittal. Effect of diastolic flow patterns on the function of the left ventricle. Phys. Fluids 25:110801, 2013.

    Article  Google Scholar 

  33. Su, B., L. Zhong, X.-K. Wang, J.-M. Zhang, R. S. Tan, J. C. Allen, S. K. Tan, S. Kim, and H. L. Leo. Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach. Comput. Methods Programs Biomed. 113:474–482, 2014.

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by MIUR (Italian Ministry of University and Research) under the Grant PRIN 2012HMR7CF.

Statement of Human Studies

Authors declare that human subjects were not involved in this study.

Statement of Animal Studies

Authors declare that animals were not involved in this study.

Conflict of Interest

Authors declare that there are no conflicts of interest to disclose.

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Civile e Ambientale, Università di Firenze, Via S. Marta 3, 50139, Florence, Italy

    Federico Domenichini

  2. Dipartimento di Ingegneria e Architettura, Università di Trieste, P. le Europa 1, 34127, Trieste, Italy

    Gianni Pedrizzetti

Authors
  1. Federico Domenichini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gianni Pedrizzetti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federico Domenichini.

Additional information

Associate Editor Ajit P. Yoganathan oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Domenichini, F., Pedrizzetti, G. Asymptotic Model of Fluid–Tissue Interaction for Mitral Valve Dynamics. Cardiovasc Eng Tech 6, 95–104 (2015). https://doi.org/10.1007/s13239-014-0201-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13239-014-0201-y

Keywords

Search

Navigation