Transport of platelets induced by red blood cells based on mixture theory

Abstract The near-wall enrichment of platelets strongly influences thrombus formation in vivo and in vitro . This paper develops a multi-constituent continuum approach to study this phenomenon. A mixture theory model is used to describe the motion of plasma and red blood cells (RBCs) and the interactions between the two components. A transport model is developed to study the influence of the RBCs field on the platelets. The model is used to study blood flow in a rectangular micro-channel, a sudden expansion micro-channel, and a channel containing micro crevices (representing a practical problem encountered in most blood-wetted devices). The simulations show that in the rectangular channel the concentration of the platelets near the walls is about five times higher than the concentration near the channel centerline. It is also noticed that in the channel with crevices, a large number of platelets accumulate in the deep part of the crevices and this may serve as nidus for excessive thrombus formation occurring in medical devices.

[1]  A. Concha.  Theory of Mixtures , 2014 .

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

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

[4]  R. Silver,et al.  Examination of platelet function in whole blood under dynamic flow conditions with the cone and plate(let) analyzer: effect of erythrocytosis and thrombocytosis. , 2007, American journal of clinical pathology.

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

[6]  F. Weller.  Platelet deposition in non-parallel flow , 2008, Journal of mathematical biology.

[7]  Nader Moazami,et al.  An analysis of pump thrombus events in patients in the HeartWare ADVANCE bridge to transplant and continued access protocol trial. , 2014, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[8]  C M Care,et al.  A multi-component lattice Boltzmann scheme: towards the mesoscale simulation of blood flow. , 2006, Medical engineering & physics.

[9]  Mehrdad Massoudi,et al.  Modeling and numerical simulation of blood flow using the Theory of Interacting Continua. , 2012, International journal of non-linear mechanics.

[10]  J F Antaki,et al.  A mathematical model for shear-induced hemolysis. , 1995, Artificial organs.

[11]  S. Sutera,et al.  Platelet adhesion and aggregation in pulsatile shear flow: effects of red blood cells. , 1998, Thrombosis research.

[12]  K. Rajagopal,et al.  The flow of blood in tubes: theory and experiment , 1998 .

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

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

[15]  V. Fuster,et al.  Characterization of a tubular flow chamber for studying platelet interaction with biologic and prosthetic materials: deposition of indium 111-labeled platelets on collagen, subendothelium, and expanded polytetrafluoroethylene. , 1987, The Journal of laboratory and clinical medicine.

[16]  Drake D Pedersen,et al.  Visualization and analysis of biomaterial-centered thrombus formation within a defined crevice under flow. , 2016, Biomaterials.

[17]  H. Goldsmith,et al.  Aggregation of human platelets in an annular vortex distal to a tubular expansion. , 1979, Microvascular research.

[18]  David N. Ku,et al.  Determination of Critical Parameters in Platelet Margination , 2012, Annals of Biomedical Engineering.

[19]  A. Fogelson,et al.  Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. , 2001, Biophysical journal.

[20]  Arie Blitz,et al.  Pump thrombosis-A riddle wrapped in a mystery inside an enigma. , 2014, Annals of cardiothoracic surgery.

[21]  M. Anand,et al.  A SHEAR-THINNING VISCOELASTIC FLUID MODEL FOR DESCRIBING THE FLOW OF BLOOD , 2004 .

[22]  K. R. Rajagopal,et al.  A mathematical model to describe the change in the constitutive character of blood due to platelet activation , 2002 .

[23]  M. Acker,et al.  Pump thrombosis in the Thoratec HeartMate II device: An update analysis of the INTERMACS Registry. , 2015, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

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

[25]  J. Antaki,et al.  Flow of blood in micro-channels: recent results based on mixture theory , 2017 .

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

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

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

[29]  R. E. Craine,et al.  Continuum Theories of Mixtures: Applications , 1976 .

[30]  H. Weiss,et al.  Red blood cells: their dual role in thrombus formation. , 1980, Science.

[31]  A. M. Benis,et al.  Platelet Diffusion in Flowing Blood , 1972 .

[32]  V. Fuster,et al.  Synergistic action of severe wall injury and shear forces on thrombus formation in arterial stenosis: definition of a thrombotic shear rate threshold. , 1994, Journal of the American College of Cardiology.

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

[34]  J. Hirsh,et al.  Medical device‐induced thrombosis: what causes it and how can we prevent it? , 2015, Journal of thrombosis and haemostasis : JTH.

[35]  K. Rajagopal,et al.  A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot , 2006 .

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

[37]  J. Antaki,et al.  An extended convection diffusion model for red blood cell-enhanced transport of thrombocytes and leukocytes , 2009, Physics in medicine and biology.

[38]  Salvatore Cito,et al.  A review of macroscopic thrombus modeling methods. , 2013, Thrombosis research.

[39]  H. J. Sauer,et al.  Engineering thermodynamics, 2nd Ed , 1985 .

[40]  J. Bigby.  Harrison's Principles of Internal Medicine , 1988 .

[41]  R. E. Craine,et al.  CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT , 1976 .

[42]  S. Russell,et al.  Advanced heart failure treated with continuous-flow left ventricular assist device. , 2009, The New England journal of medicine.

[43]  R. M. Bowen.  Part I – Theory of Mixtures , 1976 .

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

[45]  H. Goldsmith,et al.  Rheological Aspects of Thrombosis and Haemostasis: Basic Principles and Applications , 1986, Thrombosis and Haemostasis.

[46]  K R Rajagopal,et al.  A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. , 2008, Journal of theoretical biology.

[47]  V. Fuster,et al.  Platelet/vessel wall interactions, rheologic factors and thrombogenic substrate in acute coronary syndromes: preventive strategies. , 1987, The American journal of cardiology.

[48]  B. Furie,et al.  Mechanisms of thrombus formation. , 2008, The New England journal of medicine.

[49]  P. S. Ramalho.  Microcirculation and hemorheology. , 1983, Acta medica portuguesa.

[50]  S. Diamond,et al.  Multiscale Systems Biology and Physics of Thrombosis Under Flow , 2012, Annals of Biomedical Engineering.

[51]  D. Ku,et al.  Fluid mechanics of vascular systems, diseases, and thrombosis. , 1999, Annual review of biomedical engineering.

[52]  Ahmed Hassanein,et al.  Three-phase CFD analytical modeling of blood flow. , 2008, Medical engineering & physics.

[53]  K. Rajagopal,et al.  A Model for the Formation and Lysis of Blood Clots , 2006, Pathophysiology of Haemostasis and Thrombosis.

[54]  Satish Karra,et al.  On modeling the response of the synovial fluid: Unsteady flow of a shear-thinning, chemically-reacting fluid mixture , 2010, Comput. Math. Appl..

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

[56]  J. Antaki,et al.  Drag-reducing polymers diminish near-wall concentration of platelets in microchannel blood flow. , 2010, Biorheology.

[57]  V. Fuster,et al.  Thrombosis: Studies under Flow Conditions , 1987, Annals of the New York Academy of Sciences.

[58]  J. S. Guseh,et al.  Advanced Heart Failure Treated with Continuous-Flow Left Ventricular Assist Device , 2018 .

[59]  A. Fogelson,et al.  Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells , 2010, International journal for numerical methods in biomedical engineering.

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

[61]  Mehrdad Massoudi,et al.  Constitutive relations for the interaction force in multicomponent particulate flows , 2003 .

[62]  Willi Jäger,et al.  Mathematical modeling and simulation of the evolution of plaques in blood vessels , 2016, Journal of mathematical biology.

[63]  James B. Young,et al.  What is the truth behind pump thrombosis in the HeartMate II device? A National Heart, Lung, and Blood Institute perspective based on data from the Interagency Registry for Mechanically Assisted Circulatory Support. , 2015, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[64]  Mehrdad Massoudi,et al.  Chemically-reacting fluids with variable transport properties , 2012, Appl. Math. Comput..

[65]  Scott L Diamond,et al.  Platelet dynamics in three-dimensional simulation of whole blood. , 2014, Biophysical journal.

[66]  Kumbakonam R. Rajagopal,et al.  Mechanics of Mixtures , 1995 .

[67]  M. D. Rourke,et al.  A METHOD FOR CORRECTING THE ERYTHROCYTE SEDIMENTATION RATE FOR VARIATIONS IN THE CELL VOLUME PERCENTAGE OF BLOOD. , 1930, The Journal of clinical investigation.

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

[69]  S. Middleman,et al.  Transport phenomena in the cardiovascular system , 1972 .

[70]  W. van Oeveren,et al.  Stirred, shaken, or stagnant: What goes on at the blood-biomaterial interface. , 2017, Blood reviews.

[71]  Alfredo Alexander-Katz,et al.  Elongational flow induces the unfolding of von Willebrand factor at physiological flow rates. , 2010, Biophysical journal.

[72]  H S Borovetz,et al.  Red blood cell aging and risk of cardiovascular diseases. , 1998, Clinical hemorheology and microcirculation.

[73]  Robert L Kormos,et al.  The Fourth INTERMACS Annual Report: 4,000 implants and counting. , 2012, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[74]  M. Massoudi,et al.  On the coefficients of the interaction forces in a two-phase flow of a fluid infused with particles , 2014 .

[75]  J. Antaki,et al.  Investigation of platelet margination phenomena at elevated shear stress. , 2007, Biorheology.

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

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

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

[79]  Mehrdad Massoudi,et al.  Flow of a fluid—solid mixture between flat plates , 1991 .

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

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

[82]  S. Hanson,et al.  Effects of red blood cell concentration on hemostasis and thrombus formation in a primate model. , 1990, Blood.

[83]  Kenneth A. Solen,et al.  Computational Model of Device-Induced Thrombosis and Thromboembolism , 2005, Annals of Biomedical Engineering.