On the chordae structure and dynamic behaviour of the mitral valve

Abstract We develop a fluid–structure interaction (FSI) model of the mitral valve (MV) that uses an anatomically and physiologically realistic description of the MV leaflets and chordae tendineae. Three different chordae models—complex, ‘pseudo-fibre’ and simplified chordae—are compared to determine how different chordae representations affect the dynamics of the MV. The leaflets and chordae are modelled as fibre-reinforced hyperelastic materials, and FSI is modelled using an immersed boundary–finite element method. The MV model is first verified under static boundary conditions against the commercial finite element software ABAQUS and then used to simulate MV dynamics under physiological pressure conditions. Interesting flow patterns and vortex formulation are observed in all three cases. To quantify the highly complex system behaviour resulting from FSI, an energy budget analysis of the coupled MV FSI model is performed. Results show that the complex and pseudo-fibre chordae models yield good valve closure during systole but that the simplified chordae model leads to poorer leaflet coaptation and an unrealistic bulge in the anterior leaflet belly. An energy budget analysis shows that the MV models with complex and pseudo-fibre chordae have similar energy distribution patterns but the MV model with the simplified chordae consumes more energy, especially during valve closing and opening. We find that the complex chordae and pseudo-fibre chordae have similar impact on the overall MV function but that the simplified chordae representation is less accurate. Because a pseudo-fibre chordal structure is easier to construct and less computationally intensive, it may be a good candidate for modelling MV dynamics or interaction between the MV and heart in patient-specific applications.

[1]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[2]  K S Kunzelman,et al.  Flexible versus rigid ring annuloplasty for mitral valve annular dilatation: a finite element model. , 1998, The Journal of heart valve disease.

[3]  Ajit P. Yoganathan,et al.  A High-Fidelity and Micro-anatomically Accurate 3D Finite Element Model for Simulations of Functional Mitral Valve , 2013, FIMH.

[4]  R. P. Cochran,et al.  Fluid–structure interaction models of the mitral valve: function in normal and pathological states , 2007, Philosophical Transactions of the Royal Society B: Biological Sciences.

[5]  T. David,et al.  Mitral valve replacement for mitral regurgitation with and without preservation of chordae tendineae. , 1984, The Journal of thoracic and cardiovascular surgery.

[6]  Boyce E. Griffith,et al.  Emerging Trends in Heart Valve Engineering: Part I. Solutions for Future , 2014, Annals of Biomedical Engineering.

[7]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[8]  Wei Sun,et al.  Computational modeling of cardiac valve function and intervention. , 2014, Annual review of biomedical engineering.

[9]  Boyce E. Griffith,et al.  Image-based fluid-structure interaction model of the human mitral valve , 2013 .

[10]  Xiaoyu Luo,et al.  Effect of ventricle motion on the dynamic behaviour of chorded mitral valves , 2008 .

[11]  Xiangmin Jiao,et al.  Fluid–structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future , 2010, International journal for numerical methods in engineering.

[12]  Boyce E. Griffith,et al.  Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies , 2015, Annals of Biomedical Engineering.

[13]  Boyce E. Griffith,et al.  A coupled mitral valve—left ventricle model with fluid–structure interaction , 2017, Medical engineering & physics.

[14]  R. Ogden,et al.  Hyperelastic modelling of arterial layers with distributed collagen fibre orientations , 2006, Journal of The Royal Society Interface.

[15]  Bjørn Skallerud,et al.  Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers , 2009 .

[16]  Q. Wang,et al.  Finite Element Modeling of Mitral Valve Dynamic Deformation Using Patient-Specific Multi-Slices Computed Tomography Scans , 2012, Annals of Biomedical Engineering.

[17]  A. Yoganathan,et al.  Energy loss for evaluating heart valve performance. , 2008, The Journal of thoracic and cardiovascular surgery.

[18]  B Skallerud,et al.  Modeling active muscle contraction in mitral valve leaflets during systole: a first approach , 2011, Biomechanics and modeling in mechanobiology.

[19]  R. P. Cochran,et al.  Stress/Strain Characteristics of Porcine Mitral Valve Tissue: Parallel Versus Perpendicular Collagen Orientation , 1992, Journal of cardiac surgery.

[20]  K S Kunzelman,et al.  The effect of chordal replacement suture length on function and stresses in repaired mitral valves: a finite element study. , 1996, The Journal of heart valve disease.

[21]  C. Liang,et al.  Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve , 2012, Biomechanics and modeling in mechanobiology.

[22]  W. S. Ring,et al.  Finite element analysis of the mitral valve. , 1993, The Journal of heart valve disease.

[23]  Boyce E. Griffith,et al.  A finite strain nonlinear human mitral valve model with fluid-structure interaction , 2014, International journal for numerical methods in biomedical engineering.

[24]  Boyce E. Griffith,et al.  Hybrid finite difference/finite element immersed boundary method , 2016, International journal for numerical methods in biomedical engineering.

[25]  Boyce E. Griffith,et al.  Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading , 2014, International journal for numerical methods in biomedical engineering.

[26]  Young Joon Choi,et al.  Computational Study of the Dynamics of a Bileaflet Mechanical Heart Valve in the Mitral Position , 2014, Annals of Biomedical Engineering.

[27]  D. Hukins,et al.  The role of Chordae tendineae in mitral valve competence. , 2005, The Journal of heart valve disease.

[28]  Alberto Redaelli,et al.  Mitral Valve Patient-Specific Finite Element Modeling from Cardiac MRI: Application to an Annuloplasty Procedure , 2011 .

[29]  Colin Berry,et al.  Modelling mitral valvular dynamics–current trend and future directions , 2017, International journal for numerical methods in biomedical engineering.

[30]  Charles S. Peskin,et al.  Dynamics of a Closed Rod with Twist and Bend in Fluid , 2008, SIAM J. Sci. Comput..

[31]  Alberto Redaelli,et al.  Mitral valve finite element modeling: implications of tissues' nonlinear response and annular motion. , 2009, Journal of biomechanical engineering.

[32]  K S Kunzelman,et al.  Effect of papillary muscle position on mitral valve function: relationship to homografts. , 1998, The Annals of thoracic surgery.

[33]  Richard P. Cochran,et al.  Fluid–Structure Interaction Analysis of Papillary Muscle Forces Using a Comprehensive Mitral Valve Model with 3D Chordal Structure , 2015, Annals of Biomedical Engineering.

[34]  X. Luob,et al.  Effect of ventricle motion on the dynamic behaviour of chorded mitral valves , 2008 .

[35]  Ajit P Yoganathan,et al.  On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve , 2015, Biomechanics and modeling in mechanobiology.

[36]  F. Yin,et al.  A constitutive law for mitral valve tissue. , 1998, Journal of biomechanical engineering.

[37]  Boyce E. Griffith,et al.  An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner , 2009, J. Comput. Phys..

[38]  Boyce E. Griffith,et al.  Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method , 2009 .

[39]  Boyce E. Griffith,et al.  Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method , 2012 .

[40]  K S Kunzelman,et al.  Annular dilatation increases stress in the mitral valve and delays coaptation: a finite element computer model. , 1997, Cardiovascular surgery.