Coupling the lattice‐Boltzmann and spectrin‐link methods for the direct numerical simulation of cellular blood flow

The implementation of a spectrin-link (SL) red blood cell (RBC) membrane method coupled with a lattice-Boltzmann (LB) fluid solver is discussed. Details of the methodology are included along with subtleties associated with its integration into a massively parallel hybrid LB finite element (FE) suspension flow solver. A comparison of the computational performance of the coupled LB–SL method with that of the previously implemented LB–FE is given for an isolated RBC and for a dense suspension in Hagen–Poiseuille flow. Validating results for RBCs isolated in shear and parachuting in microvessel flow are also presented. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[2]  Cyrus K. Aidun,et al.  Lattice Boltzmann simulation of solid particles suspended in fluid , 1995 .

[3]  S. Suresh,et al.  Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. , 2005, Biophysical journal.

[4]  C. Aidun,et al.  Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation , 1998, Journal of Fluid Mechanics.

[5]  George Em Karniadakis,et al.  A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. , 2010, Biophysical journal.

[6]  G. Karniadakis,et al.  Coarse-grained red blood cell model with accurate mechanical properties, rheology and dynamics , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[7]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[8]  Robert MacMeccan,et al.  Mechanistic Effects of Erythrocytes on Platelet Deposition in Coronary Thrombosis , 2007 .

[9]  K. F. Chen,et al.  Observation of the Decay B0J , 2007 .

[10]  David R. Noble,et al.  A consistent hydrodynamic boundary condition for the lattice Boltzmann method , 1995 .

[11]  H Minamitani,et al.  Direct measurement of erythrocyte deformability in diabetes mellitus with a transparent microchannel capillary model and high-speed video camera system. , 2001, Microvascular research.

[12]  T W Secomb,et al.  Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. , 2007, Physical review letters.

[13]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[14]  P. Adler,et al.  Boundary flow condition analysis for the three-dimensional lattice Boltzmann model , 1994 .

[15]  S. Suresh,et al.  Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. , 2004, Mechanics & chemistry of biosystems : MCB.

[16]  J. Clausen,et al.  Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method , 2009, Journal of Fluid Mechanics.

[17]  S. Chien,et al.  Low viscosity Ektacytometry and its validation tested by flow chamber. , 2001, Journal of biomechanics.

[18]  C. Bustamante,et al.  Ten years of tension: single-molecule DNA mechanics , 2003, Nature.

[19]  Donald Ziegler,et al.  Boundary conditions for lattice Boltzmann simulations , 1993 .

[20]  Cyrus K. Aidun,et al.  Capsule dynamics and rheology in shear flow: Particle pressure and normal stress , 2010 .

[21]  C. Lim,et al.  Mechanics of the human red blood cell deformed by optical tweezers , 2003 .

[22]  G. Karniadakis,et al.  Systematic coarse-graining of spectrin-level red blood cell models. , 2010, Computer Methods in Applied Mechanics and Engineering.

[23]  Cyrus K. Aidun,et al.  Parallel performance of a lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture , 2010, Comput. Phys. Commun..

[24]  Magalie Faivre,et al.  Swinging of red blood cells under shear flow. , 2007, Physical review letters.

[25]  Subra Suresh,et al.  Molecularly based analysis of deformation of spectrin network and human erythrocyte , 2006 .

[26]  Iliya V. Karlin,et al.  Perfect entropy functions of the Lattice Boltzmann method , 1999 .

[27]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[28]  George Em Karniadakis,et al.  Accurate coarse-grained modeling of red blood cells. , 2008, Physical review letters.

[29]  Derek B. Ingham,et al.  Laminar boundary layer on an impulsively started rotating sphere , 1979 .

[30]  Cyrus K. Aidun,et al.  Extension of the Lattice-Boltzmann Method for Direct Simulation of Suspended Particles Near Contact , 2003 .

[31]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .