Computational model of simulation for mechanics of biofluids using the generalized lattice boltzman method

O. Pelliccioni


A 3D model for the numerical simulation of artificial aortic prostheses is presented, considering fluid-structure interaction.  The method is based in the General Lattice Boltzmann equation under a multi-relaxation scheme.  Stream lines, velocities and shear stresses inside the biological fluid are reported and discussed. Technical details of the algorithm are also described.  As well, an algorithm for the LB mesh generation is presented and evaluated. Numerical results of artificial heart valves in aortic position are reported here, showing the versatility of the proposed approach.

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Beddo V., (2002) Applications of Parallel Programming in Statistics, University of California, Los Angeles, USA.

Boyd J., Buick J.M., Cosgrove J.A. y Stansell P., (2004) Application of the lattice boltzmann method to arterial flow simulation: investigation of boundary conditions for complex arterial geometries, Australas Phys. Eng. Sci. Med. 27 4, pp. 207−12.

Chapman S. y Cowling T.G., (1970) The Mathematical Theory of Non Uniform Gases, Cambridge Univ. Press, Cambridge.

Chatterjee S. y Prins J., (2002) Parallel and Distributed Computing PRAM Algorithms, COMP 203, pp. 13.

Clark R. y Finke E., (1974) Scanning and light microscopy of human aortic leaflets in stressed and relaxed states, J. of Thoracic and Cardiovascular Surgery, 67 5, pp. 792−804.

Correia D., Palacio C., (2005) Optimización de simulaciones de mecánica de fluidos bajo el método de lattice Boltzmann a través de técnicas de paralelismo. Caso de estudio: simulación de válvulas cardíacas del CeBio, Tesis de licenciatura en Computación, Universidad Central de Venezuela.

Fang H., Wang Z., Lin Z. y Liu M., (2002) Lattice boltzmann method for simulating the viscous flow in large distensible blood vessels, Phys. Rev. E Stat. Nonlin. Soft. Matter. Phys. 65 5, pp. 051925(11).

Foster I., (1995) Designing and Building Parallel Programs, Addison-Wesley, N14.

Foster I., (1995a) Designing and Building Parallel Programs, Addison-Wesley, N15.

dHumières D., Ginzburg I., Krafczyk M., Lallemand P. y Luo L. −S., (2002) Multiple-relaxation-time lattice boltzmann models in three dimensions, The Royal Society, Phil. Trans. R. Soc. Lond. A 360, pp. 437−451.

dHumières D., (1992) Generalized lattice Boltzmann equations, Rarefied Gas Dynamics: Theory and Simulations, Progress in Astronautics and Aeronautics, AIAA 159, pp. 12.

Grad H., (1949) On the kinetic theory of rarefied gases, Commun. Pure Appl. Math. 2, pp. 331.

Grigioni M., Daniele C., DAvenio G. y Barbaro V., (2001) The influence of the leaflets curvature on the flow field in two bileaflet prosthetic heart valves, Journal of Biomechanics 34, pp. 613 – 621.

He X. y Luo L. –S., (1997) Lattice Boltzmann model for the incompressible Navier-Stokes equation, Journal of Statistical Physics 88, pp. 927–945.

He X., Luo L-S. y Dembo M., (1996) Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids, Journal of Computational Physics 129 2, pp. 357−363.

Hernández H., (1999) Simulación numérica del flujo sanguíneo en bifurcación de la arteria carótica y comparación con mediciones In Vivo, Tesis de Ingeniería Mecánica, Universidad Central de Venezuela, Caracas.

Hize J.O., (1987) Turbulence, McGraw-Hill, New York.

Hufnagel C. y Harvey W., (1953) Surgical correction of aortic insufficiency: Preliminary report, Bull, Georgetown Univ. Med. Ctr. 6.

Krafczyk M., Cerrolaza M., Schulz M. y Rank E., (1998) Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice-Boltzmann methods, Journal of Biomechanics 31 5, pp. 453−462.

Lallemand P., Luo L. –S., (2003) Lattice Boltzmann method for moving boundaries, J. of Comp. Phys. 184, pp. 406−421.

Pelliccioni O., Cerrolaza M. y Herrera M., (2005) A three-dimensional fluid-structure interaction analysis of a bileaflet mechanical heart valve using the general lattice Boltzmann equation, enviado al Journal Applied Numerical Mathematics, Elsevier B.V.

Pekeris C.L., (1955) Solution of the Boltzmann-Hilbert integral equation, Proc. Nat. Acad. Soc. 41, pp. 661.

Sauren A., (1981) The Mechanical Behaviour of the Aortic Valve, Tesis Ph.D., Eindhoven University of Technology, Eindhoven.

Sitio web oficial de la empresa © 2003 Microsoft Corporation (

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Sitio web oficial de la empresa © TECPLOT (

Sun C., Migliorini C. y Munn LL., (2003) Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis, Biophys. J. 85 1, pp. 208−22.

Swanson, W. y Clark, R., (1974) Dimensions and geometric relationships of the human aortic valve as function of pressure, Circulation Research 35 6, pp. 871−882.

Willis A.G., Parallel and distributed processing with glish and AIPS++, (2000) National Research Council of Canada.

Yoganathan A., He -Z. y Casey -S., (2004) Fluid mechanics of heart valves, Annu. Rev. Biomed. Eng. 6, pp. 331−362

Zee C., (2004) Overview of the MPI standard and Implementations, Universität Stuttgart, Alemania.


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