Image-based fluid-structure interaction model of the human mitral valve. (English) Zbl 1365.74070
Summary: The mitral valve (MV) is one of the four cardiac valves. It consists of two leaflets that are connected to the left ventricular papillary muscles via multiple fibrous chordae tendinae. The primary functions of the MV are to allow for the free flow of blood into the left ventricle (LV) of the heart from the left atrium (LA) during the diastolic and early systolic phases of the cardiac cycle, and to prevent regurgitant flow from the LV to the LA in deep systole. MV disorders such as mitral stenosis and regurgitation cause significant morbidity and mortality, and an improved understanding of MV biomechanics could lead to improved medical and surgical procedures to restore normal MV function in patients with such disorders. Computational models can realistically capture the anatomical and functional features of the MV and hence can provide detailed spatial and temporal data that may not be easily obtained clinically or experimentally. In this study, an anatomical model of a human MV is derived from in vivo magnetic resonance imaging (MRI) data. Using this clinical imaging-derived model, fluid-structure interaction (FSI) simulations are performed using the immersed boundary (IB) method under physiological, dynamic transvalvular pressure loads. Computational analyses show that the subject-specific MV geometry has a significant influence on the simulation results. An initial validation of the model is achieved by comparing the opening height and flow rates to clinical measurements.
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74L15 | Biomechanical solid mechanics |
| 76Z05 | Physiological flows |
Keywords:
human mitral valve; clinical imaging; magnetic resonance imaging; fluid-structure interaction; immersed boundary methodReferences:
| [1] | Muresian, H., The clinical anatomy of the mitral valve, Clin Anat, 22, 1, 85-98 (2009) |
| [2] | Gabriel, V.; Kamp, O.; Visser, C. A., Three-dimensional echocardiography in mitral valve disease, Euro J Echocardio, 6, 6, 443-454 (2005) |
| [3] | Lau, K. D.; Diaz, V.; Scambler, P.; Burriesci, G., Mitral valve dynamics in structural and fluid-structure interaction models, Med Eng Phys, 32, 9, 1057-1064 (2010) |
| [4] | Prot, V.; Skallerud, B., An improved transverse isotropic hyperelastic material model for simulation of mitral valve response, J Biomech, 39 (2006), S618 |
| [5] | Prot, V.; Haaverstad, R.; Skallerud, B., Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution, Biomech Model Mechanobiol, 8, 1, 43-55 (2009) |
| [6] | Prot, V.; Skallerud, B., Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers, Comput Mech, 43, 3, 353-368 (2009) · Zbl 1162.74474 |
| [7] | Prot, V.; Skallerud, B.; Sommer, G.; Holzapfel, G. A., On modelling and analysis of healthy and pathological human mitral valves: two case studies, J Mech Behav Biomed Mater, 3, 2, 167-177 (2010) |
| [8] | Skallerud, B.; Prot, V.; Nordrum, I. S., Modeling active muscle contraction in mitral valve leaflets during systole: a first approach, Biomech Model Mechanobiol, 10, 1, 1-16 (2011) |
| [9] | Votta, E.; Maisano, F.; Alfieri, O.; Montevecchi, F. M.; Redaelli, A., Finite element models of newly shaped prosthetic rings for the correction of functional mitral regurgitation, J Biomech, 39 (2006), S293-S293 |
| [10] | Votta, E.; Maisano, F.; Bolling, S. F.; Alfieri, O.; Montevecchi, F. M.; Redaelli, A., The geoform disease-specific annuloplasty system: a finite element study, Ann Thor Surg, 84, 1, 92-101 (2007) |
| [11] | Lim, K. H.; Yeo, J. H.; Duran, C. M., Three-dimensional asymmetrical modeling of the mitral valve: a finite element study with dynamic boundaries, J Heart Valve Dis, 14, 3, 386-392 (2005) |
| [12] | Kunzelman, K. S.; Cochran, R. P.; Chuong, C.; Ring, W. S.; Verrier, E. D.; Eberhart, R. D., Finite element analysis of the mitral valve, J Heart Valve Dis, 2, 3, 326-340 (1993) |
| [13] | Einstein, D. R.; Reinhall, P.; Nicosia, M.; Cochran, R. P.; Kunzelman, K., Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes, Comput Meth Biomech Biomed Eng, 6, 1, 33-44 (2003) |
| [14] | Einstein, D. R.; Kunzelman, K. S.; Reinhall, P. G.; Nicosia, M. A.; Cochran, R. P., Non-linear fluid-coupled computational model of the mitral valve, J Heart Valve Dis, 14, 3, 376-385 (2005) |
| [15] | Kunzelman, K. S.; Reimink, M. S.; Cochran, R. P., Annular dilatation increases stress in the mitral valve and delays coaptation: a finite element computer model, Cardiovasc Surg, 5, 4, 427-434 (1997) |
| [16] | Kunzelman, K. S.; Reimink, M. S.; Cochran, R. P., Flexible versus rigid ring annuloplasty for mitral valve annular dilatation: a finite element model, J Heart Valve Dis, 7, 1, 108-116 (1998) |
| [17] | Reimink, M. S.; Kunzelman, K. S.; Cochran, R. P., The effect of chordal replacement suture length on function and stresses in repaired mitral valves: a finite element study, J Heart Valve Dis, 5, 4, 365-375 (1996) |
| [18] | Watton, P. N.; Luo, X. Y.; Wang, X.; Bernacca, G. M.; Molloy, P.; Wheatley, D. J., Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method, J Biomech, 40, 3, 613-626 (2007) |
| [19] | Watton, P. N.; Luo, X. Y.; Yin, M.; Bernacca, G. M.; Wheatley, D. J., Effect of ventricle motion on the dynamic behaviour of chorded mitral valves, J Fluids Struct, 24, 1, 58-74 (2008) |
| [21] | Yin, M.; Luo, X. Y.; Wang, T. J.; Watton, P. N., Effects of flow vortex on a chorded mitral valve in the left ventricle, Int J Numer Meth Biomed Eng, 26, 3-4, 381-404 (2010) · Zbl 1183.92024 |
| [22] | Luo, X. Y.; Griffith, B. E.; Ma, X. S.; Yin, M.; Wang, T. J.; Liang, C. L., Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve, Biomech Model Mechanobiol, 11, 6, 815-827 (2012) |
| [23] | Griffith, B. E., Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions, Int J Numer Meth Biomed Eng, 28, 3, 317-345 (2012) · Zbl 1243.92017 |
| [24] | Griffith, B. E., On the volume conservation of the immersed boundary method, Commun Comput Phys, 12, 401-432 (2012) · Zbl 1373.74098 |
| [25] | Griffith, B. E.; Lim, S., Simulating an elastic ring with bend and twist by an adaptive generalized immersed boundary method, Commun Comput Phys, 12, 433-461 (2012) · Zbl 1373.74038 |
| [26] | Lai, M. C.; Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J Comput Phys, 160, 2, 705-719 (2000) · Zbl 0954.76066 |
| [27] | Griffith, B. E.; Peskin, C. S., On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J Comput Phys, 208, 1, 75-105 (2005) · Zbl 1115.76386 |
| [28] | Clark, R. E.; Butterworth, G. A., Characterization of the mechanics of human ortic and mitral valve leaflets, Surg Forum, 22, 134-136 (1971) |
| [29] | Ghista, D. N.; Rao, A. P., Structural mechanics of the mitral valve: stresses sustained by the valve; non-traumatic determination of the stiffness of the in vivo valve, J Biomech, 5, 3, 295-296 (1972) |
| [30] | Clark, R. E., Stress-strain characteristics of fresh and frozen human aortic and mitral leaflets and chordae tendineae. implications for clinical use, J Thoracic Cardiovasc Surg, 66, 2, 202-208 (1973) |
| [31] | McDonald, P. C.; Wilson, J. E.; McNeill, S.; Gao, M.; Spinelli, J. J.; Rosenberg, F., The challenge of defining normality for human mitral and aortic valves: geometrical and compositional analysis, Cardiovasc Pathol, 11, 4, 193-209 (2002) |
| [32] | Levick, J. R., An introduction to cardiovascular physiology 5E (2012), Hodder Education |
| [33] | Peskin, C. S., The immersed boundary method, Acta Numer, 11, 479-517 (2002) · Zbl 1123.74309 |
| [34] | Lim, S.; Ferent, A.; Wang, X. S.; Peskin, C. S., Dynamics of a closed rod with twist and bend in fluid, SIAM J Scient Comput, 31, 273-302 (2008) · Zbl 1404.92138 |
| [35] | Lim, S., Dynamics of an open elastic rod with intrinsic curvature and twist in a viscous fluid, Phys Fluids, 22, 2, 024104 (2010), p. 11 · Zbl 1183.76313 |
| [36] | Griffith, B. E., An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner, J Comput Phys, 228, 20, 7565-7595 (2009) · Zbl 1391.76474 |
| [37] | Colella, P.; Woodward, P. R., The piecewise parabolic method (ppm) for gas-dynamical simulations, J Comput Phys, 54, 1, 174-201 (1984) · Zbl 0531.76082 |
| [38] | Rider, W. J.; Greenough, J. A.; Kamm, J. R., Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations, J Comput Phys, 225, 2, 1827-1848 (2007) · Zbl 1343.76036 |
| [39] | Miller, G. E.; Hunter, J. F.; Lively, W. M., A note on mitral valve mechanics: a pre-stressed leaflet concept, J Biomech, 14, 5, 373-375 (1981) |
| [40] | Sakai, T.; Okita, Y.; Ueda, Y.; Tahata, T.; Ogino, H.; Matsuyama, K., Distance between mitral anulus and papillary muscles: anatomic study in normal human hearts, J Thoracic Cardiovasc Surg, 118, 4, 636-641 (1999) |
| [42] | Votta, E.; Caiani, E.; Veronesi, F.; Soncini, M.; Montevecchi, F. M.; Redaelli, A., Philos Trans R Soc A: Mathe Phys Eng Sci, 366, 1879, 3411-3434 (2008) |
| [43] | Stevanella, M.; Maffessanti, F.; Conti, C. A.; Votta, E.; Arnoldi, A.; Lombardi, M., Mitral valve patient-specific finite element modeling from cardiac mri: application to an annuloplasty procedure, Cardiovasc Eng Technol, 2, 2, 66-76 (2011) |
| [44] | Kvitting, J. P.E.; Bothe, W.; Göktepe, S.; Rausch, M. K.; Swanson, J. C.; Kuhl, E., Anterior mitral leaflet curvature during the cardiac cycle in the normal ovine heart, Circulation, 122, 17, 1683-1689 (2010) |
| [45] | Karlsson, M. O.; Glasson, J. R.; Bolger, A. F.; Daughters, G. T.; Komeda, M.; Foppiano, L. E., Mitral valve opening in the ovine heart, Am J Physiol-Heart Circul Physiol, 274, 2, H552-H563 (1998) |
| [46] | Ryan, R.; Abbara, S.; Colen, R. R.; Arnous, S.; Quinn, M.; Cury, R. C., Cardiac valve disease: spectrum of findings on cardiac 64-mdct, Am J Roentgenol, 190, 5, W294-W303 (2008) |
| [47] | Gorlin, R.; Gorlin, S. G., Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts, Am Heart J, 41, 1, 1-29 (1951) |
| [48] | May-Newman, K.; Yin, F. C., Biaxial mechanical behavior of excised porcine mitral valve leaflets, Am J Physiol-Heart Circul Physiol, 269, 4, H1319-H1327 (1995) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
