Lattice Boltzmann dynamic simulation of a mechanical heart valve device

A computational method for simulating blood flow through a heart mechanical valve in aortic position, based on lattice Boltzmann methods is presented in this work. Changes of fluid properties, affected by the valve opening and closing, were considered as well as time related changes of solid-liquid boundary conditions. The artificial devices opening and closing response is governed by the dynamic interaction of the mobile elements of the mechanic valve as the fluid passes through. Two-dimensional simulation results of two mechanical heart valve devices already existing in the market were conducted: St. Jude Medical's (bileaflet) valve model and Hall Kaster (HK) Medtronic Hall's (one-leaflet) valve model. Shear stresses and pressure distributions as well as velocity profiles were quantified at different times of the heart cycle. Results obtained compared very well with the experimental values published in the technical literature.

[1]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  Deane Keller,et al.  Leonardo da Vinci on the Human Body , 1952, The Yale Journal of Biology and Medicine.

[3]  van Aa Anton Steenhoven,et al.  Model studies of the closing behaviour of the aortic valve , 1979, Journal of Fluid Mechanics.

[4]  L. Munn,et al.  Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. , 2003, Biophysical Journal.

[5]  P. Lallemand,et al.  Momentum transfer of a Boltzmann-lattice fluid with boundaries , 2001 .

[6]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : notes added in 1951 , 1951 .

[7]  M Cerrolaza,et al.  Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice-Boltzmann methods. , 1998, Journal of biomechanics.

[8]  Hufnagel Ca,et al.  The surgical correction of aortic regurgitation preliminary report. , 1953 .

[9]  Michael Junk LBM - Discrete Dynamics and Finite Difference Method , 2001 .

[10]  M Grigioni,et al.  The influence of the leaflets' curvature on the flow field in two bileaflet prosthetic heart valves. , 2001, Journal of biomechanics.

[11]  A. Marty,et al.  Replacement Cardiac Valves , 1991 .

[12]  R. Cheng,et al.  Three-Dimensional Fluid-Structure Interaction Simulation of Bileaflet Mechanical Heart Valve Flow Dynamics , 2004, Annals of Biomedical Engineering.

[13]  James F. Doyle Static and Dynamic Analysis of Structures: with An Emphasis on Mechanics and Computer Matrix Methods , 1991 .

[14]  O. Filippova,et al.  Grid Refinement for Lattice-BGK Models , 1998 .

[15]  M. Thubrikar The Aortic Valve , 1990 .

[16]  I. Krukenkamp,et al.  Free emboli formation in the wake of bi-leaflet mechanical heart valves and the effects of implantation techniques. , 2002, Journal of biomechanics.

[17]  J. R. Carl,et al.  The Bjork-Shiley Aortic Prosthesis Flow Characteristics, Thrombus Formation and Tissue Overgrowth , 1978, Circulation.

[18]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[19]  H T Low,et al.  Steady flow dynamics of prosthetic aortic heart valves: a comparative evaluation with PIV techniques. , 1998, Journal of biomechanics.

[20]  Jie Zheng,et al.  Effect of Stenosis Asymmetry on Blood Flow and Artery Compression: A Three-Dimensional Fluid-Structure Interaction Model , 2003, Annals of Biomedical Engineering.

[21]  Xiaoyan Lu,et al.  Force evaluations in lattice Boltzmann simulations with moving boundaries in two dimensions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  D. Low,et al.  Atlas of Cardiothoracic Surgery , 1990 .

[23]  J. A. Cosgrove,et al.  Application of the lattice Boltzmann method to arterial flow simulation: Investigation of boundary conditions for complex arterial geometries , 2004, Australasian Physics & Engineering Sciences in Medicine.

[24]  Zhifang Lin,et al.  Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Pascal Frey,et al.  Fluid-structure interaction in blood flows on geometries based on medical imaging , 2005 .

[26]  H Reul,et al.  Model studies at mechanical aortic heart valve prostheses--Part I: Steady-state flow fields and pressure loss coefficients. , 1988, Journal of biomechanical engineering.

[27]  H. Grad On the kinetic theory of rarefied gases , 1949 .

[28]  P. Lallemand,et al.  Lattice Boltzmann method for moving boundaries , 2003 .

[29]  F P T Baaijens,et al.  A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. , 2003, Journal of biomechanics.

[30]  M Grigioni,et al.  19 mm Sized Bileaflet Valve Prostheses’ flow Field Investigated by Bidimensional Laser Doppler Anemometry (part I: Velocity Profiles) , 1997, The International journal of artificial organs.

[31]  Miguel Cerrolaza,et al.  ANALYSIS OF TRANSIENT BLOOD FLOW PASSING THROUGH MECHANICAL HEART VALVES BY LATTICE BOLTZMANN METHODS , 2004 .

[32]  A. M. Awruch,et al.  Numerical simulation of fluid–structure interaction using the finite element method , 2005 .

[33]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  Ernst Rank,et al.  Two-dimensional simulation of fluid–structure interaction using lattice-Boltzmann methods , 2001 .

[35]  H. Bijl,et al.  Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations , 2005 .

[36]  C. Pekeris,et al.  SOLUTION OF THE BOLTZMANN-HILBERT INTEGRAL EQUATION. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[37]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .