Simulation of blood flow in a sudden expansion channel and a coronary artery

Abstract In this paper, we numerically simulate the flow of blood in two benchmark problems: the flow in a sudden expansion channel and the flow through an idealized curved coronary artery with pulsatile inlet velocity. Blood is modeled as a suspension (a non-linear complex fluid) and the movement of the red blood cell (RBCs) is modeled by using a concentration flux equation. The viscosity of blood is obtained from experimental data. In the sudden expansion flow, the predicted velocity profiles for two different Reynolds numbers (based on the inlet velocity) agree well with the available experiments; furthermore, the numerical results also show that after the sudden expansion there exists a RBCs depletion region. For the second problem, the idealized curved coronary artery, it is found that the RBCs move towards and concentrate near the inner surface where the viscosity is higher and the shear stress is lower; this phenomenon may be related to the atherosclerotic plaque formation which usually occurs on the inside surface of the arteries.

[1]  J. Antaki,et al.  Study of blood flow in several benchmark micro-channels using a two-fluid approach. , 2015, International journal of engineering science.

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

[3]  Shu Chien,et al.  Shear Dependence of Effective Cell Volume as a Determinant of Blood Viscosity , 1970, Science.

[4]  A. Bertozzi,et al.  Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows , 2014 .

[5]  M. Dupin,et al.  Modeling the flow of dense suspensions of deformable particles in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  S. Lehoux,et al.  Shear stress, arterial identity and atherosclerosis , 2015, Thrombosis and Haemostasis.

[7]  Toshio Kobayashi,et al.  Finite element simulation of blood flow in the cerebral artery , 2001 .

[8]  Aaron L Fogelson,et al.  Platelet motion near a vessel wall or thrombus surface in two-dimensional whole blood simulations. , 2013, Biophysical journal.

[9]  G. Thurston,et al.  Frequency and shear rate dependence of viscoelasticity of human blood. , 1973, Biorheology.

[10]  Shigeo Wada,et al.  Particle method for computer simulation of red blood cell motion in blood flow , 2006, Comput. Methods Programs Biomed..

[11]  H Kiesewetter,et al.  Basic phenomena of red blood cell rouleaux formation. , 1999, Biorheology.

[12]  John C. Slattery,et al.  Advanced transport phenomena , 1999 .

[13]  Jean-Philippe Ponthot,et al.  An improved constitutive model for the numerical simulation of semi-solid thixoforming , 2010, J. Comput. Appl. Math..

[14]  Nadine Aubry,et al.  Multi-Constituent Simulation of Thrombus Deposition , 2016, Scientific Reports.

[15]  Nadine Aubry,et al.  High fidelity computational simulation of thrombus formation in Thoratec HeartMate II continuous flow ventricular assist device , 2016, Scientific Reports.

[16]  Tian-Jian Hsu,et al.  On modeling boundary layer and gravity‐driven fluid mud transport , 2007 .

[17]  Nadine Aubry,et al.  Transport of platelets induced by red blood cells based on mixture theory , 2017, 1703.00611.

[18]  Yuliya Gorb,et al.  Finite element simulation of three-dimensional particulate flows using mixture models , 2014, J. Comput. Appl. Math..

[19]  Samuel R. Subia,et al.  Modelling of concentrated suspensions using a continuum constitutive equation , 1998, Journal of Fluid Mechanics.

[20]  Pierre-Yves Schobbens,et al.  Model checking lots of systems: efficient verification of temporal properties in software product lines , 2010, 2010 ACM/IEEE 32nd International Conference on Software Engineering.

[21]  Nadine Aubry,et al.  Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms , 2017 .

[22]  D. A. Drew.  Production and Dissipation of Energy in the Turbulent Flow of a Particle-Fluid Mixture, With Some Results on Drag Reduction , 1976 .

[23]  Aleksander S Popel,et al.  Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. , 2008, Journal of biomechanics.

[24]  James F. Antaki,et al.  An Anisotropic Constitutive Equation for the Stress Tensor of Blood Based on Mixture Theory , 2008 .

[25]  James F. Antaki,et al.  Micro-Flow Visualization of Red Blood Cell-Enhanced Platelet Concentration at Sudden Expansion , 2008, Annals of Biomedical Engineering.

[26]  Kyehan Rhee,et al.  CFD modeling of blood flow following coil embolization of aneurysms. , 2004, Medical engineering & physics.

[27]  J. Marshall,et al.  Micro-scale Dynamic Simulation of Erythrocyte–Platelet Interaction in Blood Flow , 2008, Annals of Biomedical Engineering.

[28]  Damien Garcia,et al.  A Particle Dynamic Model of Red Blood Cell Aggregation Kinetics , 2009, Annals of Biomedical Engineering.

[29]  Gonçalo Pena,et al.  High-order fluid-structure interaction in 2D and 3D application to blood flow in arteries , 2013, J. Comput. Appl. Math..

[30]  Rui Zhao.  Experimental and theoretical investigation of blood flow dynamics associated with blood contacting devices , 2008 .

[31]  Prosenjit Bagchi,et al.  Mesoscale simulation of blood flow in small vessels. , 2007, Biophysical journal.

[32]  James F. Antaki,et al.  Computational study of blood flow in microchannels , 2016, J. Comput. Appl. Math..

[33]  H. Goldsmith,et al.  Flow behaviour of blood cells and rigid spheres in an annular vortex. , 1977, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[34]  Nadine Aubry,et al.  A numerical study of blood flow using mixture theory. , 2014, International journal of engineering science.

[35]  S Chien,et al.  Comparative hemorheology--hematological implications of species differences in blood viscosity. , 1971, Biorheology.

[36]  Aleksander S Popel,et al.  Microcirculation and Hemorheology. , 2005, Annual review of fluid mechanics.

[37]  G. Thurston,et al.  Viscoelasticity of human blood. , 1972, Biophysical journal.

[38]  S Chien,et al.  Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. , 1966, Journal of applied physiology.

[39]  J. Antaki,et al.  A non-linear fluid suspension model for blood flow. , 2018, International journal of non-linear mechanics.

[40]  Maryam Abedi,et al.  Interfacial instabilities in sediment suspension flows , 2014, Journal of Fluid Mechanics.

[41]  R. Bouzerar,et al.  Blood flow patterns in an anatomically realistic coronary vessel: influence of three different reconstruction methods. , 2002, Journal of biomechanics.

[42]  O. Ubbink.  Numerical prediction of two fluid systems with sharp interfaces , 1997 .

[43]  W. Nichols,et al.  McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles , 1998 .

[44]  J. Antaki,et al.  Design of microfluidic channels for magnetic separation of malaria-infected red blood cells , 2016, Microfluidics and nanofluidics.

[45]  G. Karniadakis,et al.  Blood–plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study , 2012, Physical biology.

[46]  Mehrdad Massoudi,et al.  Heat Transfer and Dissipation Effects in the Flow of a Drilling Fluid , 2016 .

[47]  Nadine Aubry,et al.  Heat transfer and flow of a dense suspension between two cylinders , 2017 .

[48]  Andreas Acrivos,et al.  Shear-induced resuspension in a couette device , 1993 .

[49]  J. W. Goodwin,et al.  Interactions among erythrocytes under shear. , 1970, Journal of applied physiology.

[50]  Junfeng Zhang,et al.  Multiple red blood cell flows through microvascular bifurcations: cell free layer, cell trajectory, and hematocrit separation. , 2013, Microvascular research.

[51]  H. Goldsmith,et al.  Adhesion of human platelets to collagen on the walls distal to a tubular expansion. , 1979, Microvascular research.

[52]  Ahmed Hassanein,et al.  Multiphase hemodynamic simulation of pulsatile flow in a coronary artery. , 2006, Journal of biomechanics.

[53]  J. F. Richardson,et al.  The sedimentation of a suspension of uniform spheres under conditions of viscous flow , 1954 .

[54]  Arthur T. Andrews,et al.  Multiscale modeling of gas-fluidized beds , 2006 .

[55]  J. R. Abbott,et al.  A constitutive equation for concentrated suspensions that accounts for shear‐induced particle migration , 1992 .

[56]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[57]  Miltiadis Papalexandris,et al.  A two-phase model for compressible granular flows based on the theory of irreversible processes , 2004, Journal of Fluid Mechanics.

[58]  H. Rusche.  Computational fluid dynamics of dispersed two-phase flows at high phase fractions , 2003 .

[59]  Adélia Sequeira,et al.  A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries , 2010, J. Comput. Appl. Math..