Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve

We investigate the behaviour of a dynamic fluid–structure interaction model of a chorded polyurethane mitral valve prosthesis, focusing on the effects on valve dynamics of including descriptions of the bending stiffnesses of the valve leaflets and artificial chordae tendineae. Each of the chordae is attached at one end to the valve annulus and at the other to one of two chordal attachment points. These attachment points correspond to the positions where the chords of the real prosthesis would attach to the left-ventricular wall, although in the present study, these attachment points are kept fixed in space to facilitate comparison between our simulations and earlier results obtained from an experimental test rig. In our simulations, a time-dependent pressure difference derived from experimental measurements drives flow through the model valve during diastole and provides a realistic pressure load during systole. In previous modelling studies of this valve prosthesis, the valve presents an unrealistically large orifice at beginning of diastole and does not close completely at the end of diastole. We show that including a description of the chordal bending stiffness enables the model valve to close properly at the end of the diastolic phase of the cardiac cycle. Valve over-opening is eliminated only by incorporating a description of the bending stiffnesses of the valve leaflets into the model. Thus, bending stiffness plays a significant role in the dynamic behaviour of the polyurethane mitral valve prosthesis.

[1]  R GORLIN,et al.  Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. I. , 1951, American heart journal.

[2]  E. Rapaport.  Calculation of valve areas. , 1985, European heart journal.

[3]  Calculation of valve areas. , 1985, European heart journal.

[4]  J Fisher,et al.  Design of a function test apparatus for prosthetic heart valves. Initial results in the mitral position. , 1986, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[5]  Richard P. Cochran,et al.  Finite element analysis of mitral valve pathology , 1993 .

[6]  William Gropp,et al.  Modern Software Tools in Scientific Computing , 1994 .

[7]  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.

[8]  Richard A. Lange,et al.  Prosthetic heart valves. , 1996, The New England journal of medicine.

[9]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

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

[11]  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.

[12]  K S Kunzelman,et al.  Altered collagen concentration in mitral valve leaflets: biochemical and finite element analysis. , 1998, The Annals of thoracic surgery.

[13]  M. Lai,et al.  An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity 1 , 2000 .

[14]  M. Lai,et al.  An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity , 2000 .

[15]  Robert D. Falgout,et al.  hypre: A Library of High Performance Preconditioners , 2002, International Conference on Computational Science.

[16]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[17]  Scott R. Kohn,et al.  Managing application complexity in the SAMRAI object‐oriented framework , 2002, Concurr. Comput. Pract. Exp..

[18]  C. Peskin.  Acta Numerica 2002: The immersed boundary method , 2002 .

[19]  R. P. Cochran,et al.  Dynamic Finite Element Implementation of Nonlinear, Anisotropic Hyperelastic Biological Membranes , 2003, Computer methods in biomechanics and biomedical engineering.

[20]  X. Luob,et al.  A fluid – beam model for flow in a collapsible channel , 2003 .

[21]  John W. Clark,et al.  The myogenic response in isolated rat cerebrovascular arteries: vessel model. , 2003, Medical engineering & physics.

[22]  Ajit P Yoganathan,et al.  Fluid mechanics of heart valves. , 2004, Annual review of biomedical engineering.

[23]  Lucy T. Zhang,et al.  Immersed finite element method , 2004 .

[24]  Alberto Redaelli,et al.  An annular prosthesis for the treatment of functional mitral regurgitation: finite element model analysis of a dog bone-shaped ring prosthesis. , 2005, The Annals of thoracic surgery.

[25]  Fotis Sotiropoulos,et al.  Flow in Prosthetic Heart Valves: State-of-the-Art and Future Directions , 2005, Annals of Biomedical Engineering.

[26]  E. Weinberg.  Dynamic simulation of heart mitral valve with transversely isotropic material model , 2005 .

[27]  Joon Hock Yeo,et al.  Three-dimensional asymmetrical modeling of the mitral valve: a finite element study with dynamic boundaries. , 2005, The Journal of heart valve disease.

[28]  G Donzella,et al.  Structural effects of an innovative surgical technique to repair heart valve defects. , 2005, Journal of biomechanics.

[29]  Boyce E. Griffith,et al.  Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method , 2005 .

[30]  Boyce E. Griffith,et al.  On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems , 2005 .

[31]  Karyn S Kunzelman,et al.  Non-linear fluid-coupled computational model of the mitral valve. , 2005, The Journal of heart valve disease.

[32]  Scott R. Kohn,et al.  Managing complex data and geometry in parallel structured AMR applications , 2006, Engineering with Computers.

[33]  Jia Lu,et al.  An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations , 2006, Annals of Biomedical Engineering.

[34]  G. Holzapfel,et al.  Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation , 2007 .

[35]  Jia Lu,et al.  Dynamic Simulation of Bioprosthetic Heart Valves Using a Stress Resultant Shell Model , 2008, Annals of Biomedical Engineering.

[36]  Robert Michael Kirby,et al.  Unconditionally stable discretizations of the immersed boundary equations , 2007, J. Comput. Phys..

[37]  William J. Rider,et al.  Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations , 2007, J. Comput. Phys..

[38]  Boyce E. Griffith,et al.  An adaptive, formally second order accurate version of the immersed boundary method , 2007, J. Comput. Phys..

[39]  Alberto Redaelli,et al.  The Geoform disease-specific annuloplasty system: a finite element study. , 2007, The Annals of thoracic surgery.

[40]  Eli J Weinberg,et al.  A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3D constitutive material model. , 2007, Journal of biomechanics.

[41]  D J Wheatley,et al.  Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method. , 2007, Journal of biomechanics.

[42]  Enrico G. Caiani,et al.  Mitral Valve Models Reconstructor: a Python based GUI software in a HPC environment for patient-specific FEM structural analysis , 2008, SCSS.

[43]  L. Heltai,et al.  On the hyper-elastic formulation of the immersed boundary method , 2008 .

[44]  Timothy J. Pedley,et al.  The cascade structure of linear instability in collapsible channel flows , 2008, Journal of Fluid Mechanics.

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

[46]  Alberto Redaelli,et al.  Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[47]  Victorien Emile Prot,et al.  Modelling and numerical analysis of the porcine and human mitral apparatus , 2008 .

[48]  David E. Schmidt,et al.  On the biomechanics of heart valve function. , 2009, Journal of biomechanics.

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

[50]  Matts Karlsson,et al.  Stress-strain behavior of mitral valve leaflets in the beating ovine heart. , 2009, Journal of biomechanics.

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

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

[53]  R Haaverstad,et al.  Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution , 2009, Biomechanics and modeling in mechanobiology.

[54]  Timothy J. Pedley,et al.  Sensitivity of unsteady collapsible channel flows to modelling assumptions , 2009 .

[55]  S. Urankar.  MODELING SURGICAL INTERVENTIONS IN THE MITRAL VALVE WITH THE FINITE ELEMENT METHOD , 2009 .

[56]  Hee Sun Kim,et al.  Nonlinear multi-scale anisotropic material and structural models for prosthetic and native aortic heart valves , 2009 .

[57]  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..

[58]  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.

[59]  Gabriel Acevedo-Bolton,et al.  First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. , 2010, The Annals of thoracic surgery.

[60]  B Skallerud,et al.  On modelling and analysis of healthy and pathological human mitral valves: two case studies. , 2010, Journal of the mechanical behavior of biomedical materials.

[61]  Boyce E. Griffith,et al.  Immersed boundary method with finite element elasticity , 2010 .

[62]  M. Yin,et al.  Effects of flow vortex on a chorded mitral valve in the left ventricle , 2010 .

[63]  Eli J Weinberg,et al.  On the multiscale modeling of heart valve biomechanics in health and disease , 2010, Biomechanics and modeling in mechanobiology.

[64]  D. Hartmann.  A multiscale model for red blood cell mechanics , 2010, Biomechanics and modeling in mechanobiology.

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

[66]  Farshid Guilak,et al.  Three-dimensional finite element modeling of pericellular matrix and cell mechanics in the nucleus pulposus of the intervertebral disk based on in situ morphology , 2011, Biomechanics and modeling in mechanobiology.

[67]  Xiaoyu Luo,et al.  Stability and energy budget of pressure-driven collapsible channel flows , 2011, Journal of Fluid Mechanics.

[68]  Boyce E. Griffith,et al.  On the Volume Conservation of the Immersed Boundary Method , 2012 .

[69]  Boyce E. Griffith,et al.  Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions , 2012, International journal for numerical methods in biomedical engineering.