Study on the packed volume and the void ratio of idealized human red blood cells using a ?nite-discrete element method
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摘要
Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.
Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.
Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.
引文
[1]BASKURT,O.K.Handbook of Hemorheology and Hemodynamics,IOS Press,Inc.,Virginia(2007)
[2]XU,D.,KALIVIOTIS,E.,MUNJIZA,A.,AVITAL,E.,JI,C.N.,and WILLIAMS,J.Large scale simulation of red blood cell aggregation in shear flows.Journal of Biomechanics,46,1810-1817(2013)
[3]AHMED,F.,MEHRABADI,M.,LIU,Z.X.,BARABINO,G.A.,and AIDUN,C.K.Internal viscosity-dependent margination of red blood cells in microfluidic channels.Journal of Biomechanical Engineering,140,061013(2018)
[4]CHANG,H.Y.,LI,X.J.,and KARNIADAKIS,G.E.Modeling of biomechanics and biorheology of red blood cells in type 2 diabetes mellitus.Biophysical Journal,113,481-490(2017)
[5]KABACAOGLU,G.,QUAIFE,B.,and BIROS,G.Low-resolution simulations of vesicle suspensions in 2D.Journal of Computational Physics,357,43-77(2018)
[6]BALOGH,P.and BAGCHI,P.Direct numerical simulation of cellular-scale blood flow in 3Dmicrovascular networks.Biophysical Journal,113,2815-2826(2017)
[7]FEDOSOV,D.A.,NOGUCHI,H.,and GOMPPER,G.Multiscale modeling of blood flow:from single cells to blood rheology.Biomechanics and Modeling in Mechanobiology,13,239-258(2014)
[8]FREUND,J.B.Numerical simulation of flowing blood cells.Annual Review of Fluid Mechanics,46,67-95(2014)
[9]OMORI,T.,HOSAKA,H.,IMAI,Y.,YAMAGUCHI,T.,and ISHIKAWA,T.Numerical analysis of a red blood cell flowing through a thin micropore.Physical Review E,89,013008(2014)
[10]YE,T.,NHAN,P.T.,KHOO,B.C.,and LIM,C.T.A file of red blood cells in tube flow:a three-dimensional numerical study.Journal of Applied Physics,116,124703(2014)
[11]FEDOSOV,D.A.,CASWELL,B.,and KARNIADAKIS,G.E.A multiscale red blood cell model with accurate mechanics,rheology,and dynamics.Biophysical Journal,98,2215-2225(2010)
[12]FEDOSOV,D.A.,PAN,W.X.,CASWELL,B.,GOMPPER,G.,and KARNIADAKIS,G.E.Predicting human blood viscosity in silico.Proceedings of the National Academy of Sciences of the United States of America,108,11772-11777(2011)
[13]CHESNUTT,J.K.W.and MARSHALL,J.S.Blood cell transport and aggregation using discrete ellipsoidal particles.Computers and Fluids,38,1782-1794(2009)
[14]XU,D.,JI,C.,AVITAL,E.,KALIVIOTIS,E.,MUNJIZA,A.,and WILLIAMS,J.An investigation on the aggregation and rheodynamics of human red blood cells using high performance computations.Scientifica,2017,6524156(2017)
[15]YAZDANI,A.and KARNIADAKIS,G.E.Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction.Soft Matter,12,4339-4351(2016)
[16]LI,H.,CHANG,H.Y.,YANG,J.,LU,L.,TANG,Y.H.,and LYKOTRAFITIS,G.Modeling biomembranes and red blood cells by coarse-grained particle methods.Applied Mathematics and Mechanics(English Edition),39(1),3-20(2018)https://doi.org/10.1007/s10483-018-2252-6
[17]YE,H.L.,SHEN,Z.Q.,and LI,Y.Computational modeling of magnetic particle margination within blood flow through LAMMPS.Computational Mechanics,62,457-476(2018)
[18]SPANN,A.,CAMPBELL,J.E.,FITZGIBBON,S.R.,and RODRIGUEZ,A.The effect of hematocrit on platelet adhesion:experiments and simulations.Biophysical Journal,111,577-588(2016)
[19]GEKLE,S.Strongly accelerated margination of active particles in blood flow.Biophysical Journal,110,514-520(2016)
[20]GROEMER,H.Some basic properties of packing and covering constants.Discrete and Computational Geometry,1,183-193(1986)
[21]DESMOND,K.W.and WEEKS,E.R.Random close packing of disks and spheres in confined geometries.Physical Review E,80,051305(2009)
[22]DESMOND,K.W.and WEEKS,E.R.Influence of particle size distribution on random close packing of spheres.Physical Review E,90,022204(2014)
[23]CAMENEN,J.F.,DESCANTES,Y.,and RICHARD,P.Effect of confinement on dense packings of rigid frictionless spheres and polyhedra.Physical Review E,86,061317(2012)
[24]NAJAFI,J.,STOOP,N.,WITTEL,F.,and HABIBI,M.Ordered packing of elastic wires in a sphere.Physical Review E,85,061108(2012)
[25]HIHINASHVILI,R.and BLUMENFELD,R.Statistical-mechanical characteristics of dense planar granular systems.Granular Matter,14,277-282(2012)
[26]KURITA,R.and WEEKS,E.R.Experimental study of random-close-packed colloidal particles.Physical Review E,82,030401(2010)
[27]WANG,X.Z.Mean-field cage theory for the random close packed state of a metastable hardsphere glass.Physica A:Statistical Mechanics and Its Applications,391,3566-3573(2012)
[28]RITVANEN,J.and JALALI,P.On near-wall effects in hard disk packing between two concentric cylinders.Physica A:Statistical Mechanics and Its Applications,387,5381-5386(2008)
[29]KURITA,R.and WEEKS,E.R.Incompressibility of polydisperse random-close-packed colloidal particles.Physical Review E,84,030401(2011)
[30]MUNJIZA,A.The Combined Finite-Discrete Element Method,John Wiley&Sons,Ltd.,New York(2004)
[31]MUNJIZA,A.A.,KNIGHT,E.E.,and ROUGIER,E.Computational Mechanics of Discontinua,John Wiley&Sons,Ltd.,New York(2011)
[32]JI,C.,MUNJIZA,A.,AVITAL,E.,MA,J.,and WILLIAMS,J.J.R.Direct numerical simulation of sediment entrainment in turbulent channel flow.Physics of Fluids,25,056601(2013)
[33]JI,C.N.,ANTE,M.,ELDAD,A.,XU,D.,and JOHN,W.Numerical investigation of particle saltation in the bed-load regime.Science China-Technological Sciences,57,1500-1511(2014)
[34]JI,C.N.,MUNJIZA,A.,AVITAL,E.,XU,D.,and WILLIAMS,J.Saltation of particles in turbulent channel flow.Physical Review E,89,052202(2014)
[35]DAO,M.,LIM,C.T.,and SURESH,S.Mechanics of the human red blood cell deformed by optical tweezers.Journal of the Mechanics and Physics of Solids,51,2259-2280(2003)
[36]EVANS,E.and FUNG,Y.C.Improved measurements of the erythrocyte geometry.Microvascular Research,4,335-347(1972)
[37]LIU,Y.L.and LIU,W.K.Rheology of red blood cell aggregation by computer simulation.Journal of Computational Physics,220,139-154(2006)
[38]SUI,Y.,CHEW,Y.T.,and LOW,H.T.A lattice Boltzmann study on the large deformation of red blood cells in shear flow.International Journal of Modern Physics C,18,993-1011(2007)
[39]SUI,Y.,CHEW,Y.T.,ROY,P.,CHENG,Y.P.,and LOW,H.T.Dynamic motion of red blood cells in simple shear flow.Physics of Fluids,20,112106(2008)
[40]TANG,Y.H.and KARNIADAKIS,G.E.Accelerating dissipative particle dynamics simulations on GPUs:Algorithms,numerics and applications.Computer Physics Communications,185,2809-2822(2014)
[41]DEULING,H.J.and HELFRICH,W.Red blood-cell shapes as explained on basis of curvature elasticity.Biophysical Journal,16,861-868(1976)
[42]LEI,H.and KARNIADAKIS,G.E.Quantifying the rheological and hemodynamic characteristics of sickle cell anemia.Biophysical Journal,102,185-194(2012)
[43]PARK,Y.,BEST,C.A.,BADIZADEGAN,K.,DASARI,R.R.,FELD,M.S.,KURIABOVA,T.,HENLE,M.L.,LEVINE,A.J.,and POPESCU,G.Measurement of red blood cell mechanics during morphological changes.Proceedings of the National Academy of Sciences of the United States of America,107,6731-6736(2010)
[44]TRIPETTE,J.,ALEXY,T.,HARDY-DESSOURCES,M.D.,MOUGENEL,D.,BELTAN,E.,CHALABI,T.,CHOUT,R.,ETIENNE-JULAN,M.,HUE,O.,MEISELMAN,H.J.,and CONNES,P.Red blood cell aggregation,aggregate strength and oxygen transport potential of blood are abnormal in both homozygous sickle cell anemia and sickle-hemoglobin C disease.Haematologica-the Hematology Journal,94,1060-1065(2009)
[45]DIEZ-SILVA,M.,DAO,M.,HAN,J.Y.,LIM,C.T.,and SURESH,S.,Shape and biomechanical characteristics of human red blood cells in health and disease.Mrs Bulletin,35,382-388(2010)
[46]MEHRABADI,M.,KU,D.N.,and AIDUN,C.K.Effects of shear rate,confinement,and particle parameters on margination in blood flow.Physical Review E,93,023109(2016)
[47]LINDERKAMP,O.,WU,P.Y.K.,and MEISELMAN,H.J.Geometry of neonatal and adult red blood cells.Pediatric Research,17,250-253(1983)
[48]TOMAIUOLO,G.Biomechanical properties of red blood cells in health and disease towards microfluidics.Biomicrofluidics,8,051501(2014)
[49]HARIPRASAD,D.S.and SECOMB,T.W.Motion of red blood cells near microvessel walls:effects of a porous wall layer.Journal of Fluid Mechanics,705,195-212(2012)
[50]GUCKENBERGER,A.,SCHRAML,M.P.,CHEN,P.G.,LEONETTI,M.,and GEKLE,S.On the bending algorithms for soft objects in flows.Computer Physics Communications,207,1-23(2016)
[2]XU,D.,KALIVIOTIS,E.,MUNJIZA,A.,AVITAL,E.,JI,C.N.,and WILLIAMS,J.Large scale simulation of red blood cell aggregation in shear flows.Journal of Biomechanics,46,1810-1817(2013)
[3]AHMED,F.,MEHRABADI,M.,LIU,Z.X.,BARABINO,G.A.,and AIDUN,C.K.Internal viscosity-dependent margination of red blood cells in microfluidic channels.Journal of Biomechanical Engineering,140,061013(2018)
[4]CHANG,H.Y.,LI,X.J.,and KARNIADAKIS,G.E.Modeling of biomechanics and biorheology of red blood cells in type 2 diabetes mellitus.Biophysical Journal,113,481-490(2017)
[5]KABACAOGLU,G.,QUAIFE,B.,and BIROS,G.Low-resolution simulations of vesicle suspensions in 2D.Journal of Computational Physics,357,43-77(2018)
[6]BALOGH,P.and BAGCHI,P.Direct numerical simulation of cellular-scale blood flow in 3Dmicrovascular networks.Biophysical Journal,113,2815-2826(2017)
[7]FEDOSOV,D.A.,NOGUCHI,H.,and GOMPPER,G.Multiscale modeling of blood flow:from single cells to blood rheology.Biomechanics and Modeling in Mechanobiology,13,239-258(2014)
[8]FREUND,J.B.Numerical simulation of flowing blood cells.Annual Review of Fluid Mechanics,46,67-95(2014)
[9]OMORI,T.,HOSAKA,H.,IMAI,Y.,YAMAGUCHI,T.,and ISHIKAWA,T.Numerical analysis of a red blood cell flowing through a thin micropore.Physical Review E,89,013008(2014)
[10]YE,T.,NHAN,P.T.,KHOO,B.C.,and LIM,C.T.A file of red blood cells in tube flow:a three-dimensional numerical study.Journal of Applied Physics,116,124703(2014)
[11]FEDOSOV,D.A.,CASWELL,B.,and KARNIADAKIS,G.E.A multiscale red blood cell model with accurate mechanics,rheology,and dynamics.Biophysical Journal,98,2215-2225(2010)
[12]FEDOSOV,D.A.,PAN,W.X.,CASWELL,B.,GOMPPER,G.,and KARNIADAKIS,G.E.Predicting human blood viscosity in silico.Proceedings of the National Academy of Sciences of the United States of America,108,11772-11777(2011)
[13]CHESNUTT,J.K.W.and MARSHALL,J.S.Blood cell transport and aggregation using discrete ellipsoidal particles.Computers and Fluids,38,1782-1794(2009)
[14]XU,D.,JI,C.,AVITAL,E.,KALIVIOTIS,E.,MUNJIZA,A.,and WILLIAMS,J.An investigation on the aggregation and rheodynamics of human red blood cells using high performance computations.Scientifica,2017,6524156(2017)
[15]YAZDANI,A.and KARNIADAKIS,G.E.Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction.Soft Matter,12,4339-4351(2016)
[16]LI,H.,CHANG,H.Y.,YANG,J.,LU,L.,TANG,Y.H.,and LYKOTRAFITIS,G.Modeling biomembranes and red blood cells by coarse-grained particle methods.Applied Mathematics and Mechanics(English Edition),39(1),3-20(2018)https://doi.org/10.1007/s10483-018-2252-6
[17]YE,H.L.,SHEN,Z.Q.,and LI,Y.Computational modeling of magnetic particle margination within blood flow through LAMMPS.Computational Mechanics,62,457-476(2018)
[18]SPANN,A.,CAMPBELL,J.E.,FITZGIBBON,S.R.,and RODRIGUEZ,A.The effect of hematocrit on platelet adhesion:experiments and simulations.Biophysical Journal,111,577-588(2016)
[19]GEKLE,S.Strongly accelerated margination of active particles in blood flow.Biophysical Journal,110,514-520(2016)
[20]GROEMER,H.Some basic properties of packing and covering constants.Discrete and Computational Geometry,1,183-193(1986)
[21]DESMOND,K.W.and WEEKS,E.R.Random close packing of disks and spheres in confined geometries.Physical Review E,80,051305(2009)
[22]DESMOND,K.W.and WEEKS,E.R.Influence of particle size distribution on random close packing of spheres.Physical Review E,90,022204(2014)
[23]CAMENEN,J.F.,DESCANTES,Y.,and RICHARD,P.Effect of confinement on dense packings of rigid frictionless spheres and polyhedra.Physical Review E,86,061317(2012)
[24]NAJAFI,J.,STOOP,N.,WITTEL,F.,and HABIBI,M.Ordered packing of elastic wires in a sphere.Physical Review E,85,061108(2012)
[25]HIHINASHVILI,R.and BLUMENFELD,R.Statistical-mechanical characteristics of dense planar granular systems.Granular Matter,14,277-282(2012)
[26]KURITA,R.and WEEKS,E.R.Experimental study of random-close-packed colloidal particles.Physical Review E,82,030401(2010)
[27]WANG,X.Z.Mean-field cage theory for the random close packed state of a metastable hardsphere glass.Physica A:Statistical Mechanics and Its Applications,391,3566-3573(2012)
[28]RITVANEN,J.and JALALI,P.On near-wall effects in hard disk packing between two concentric cylinders.Physica A:Statistical Mechanics and Its Applications,387,5381-5386(2008)
[29]KURITA,R.and WEEKS,E.R.Incompressibility of polydisperse random-close-packed colloidal particles.Physical Review E,84,030401(2011)
[30]MUNJIZA,A.The Combined Finite-Discrete Element Method,John Wiley&Sons,Ltd.,New York(2004)
[31]MUNJIZA,A.A.,KNIGHT,E.E.,and ROUGIER,E.Computational Mechanics of Discontinua,John Wiley&Sons,Ltd.,New York(2011)
[32]JI,C.,MUNJIZA,A.,AVITAL,E.,MA,J.,and WILLIAMS,J.J.R.Direct numerical simulation of sediment entrainment in turbulent channel flow.Physics of Fluids,25,056601(2013)
[33]JI,C.N.,ANTE,M.,ELDAD,A.,XU,D.,and JOHN,W.Numerical investigation of particle saltation in the bed-load regime.Science China-Technological Sciences,57,1500-1511(2014)
[34]JI,C.N.,MUNJIZA,A.,AVITAL,E.,XU,D.,and WILLIAMS,J.Saltation of particles in turbulent channel flow.Physical Review E,89,052202(2014)
[35]DAO,M.,LIM,C.T.,and SURESH,S.Mechanics of the human red blood cell deformed by optical tweezers.Journal of the Mechanics and Physics of Solids,51,2259-2280(2003)
[36]EVANS,E.and FUNG,Y.C.Improved measurements of the erythrocyte geometry.Microvascular Research,4,335-347(1972)
[37]LIU,Y.L.and LIU,W.K.Rheology of red blood cell aggregation by computer simulation.Journal of Computational Physics,220,139-154(2006)
[38]SUI,Y.,CHEW,Y.T.,and LOW,H.T.A lattice Boltzmann study on the large deformation of red blood cells in shear flow.International Journal of Modern Physics C,18,993-1011(2007)
[39]SUI,Y.,CHEW,Y.T.,ROY,P.,CHENG,Y.P.,and LOW,H.T.Dynamic motion of red blood cells in simple shear flow.Physics of Fluids,20,112106(2008)
[40]TANG,Y.H.and KARNIADAKIS,G.E.Accelerating dissipative particle dynamics simulations on GPUs:Algorithms,numerics and applications.Computer Physics Communications,185,2809-2822(2014)
[41]DEULING,H.J.and HELFRICH,W.Red blood-cell shapes as explained on basis of curvature elasticity.Biophysical Journal,16,861-868(1976)
[42]LEI,H.and KARNIADAKIS,G.E.Quantifying the rheological and hemodynamic characteristics of sickle cell anemia.Biophysical Journal,102,185-194(2012)
[43]PARK,Y.,BEST,C.A.,BADIZADEGAN,K.,DASARI,R.R.,FELD,M.S.,KURIABOVA,T.,HENLE,M.L.,LEVINE,A.J.,and POPESCU,G.Measurement of red blood cell mechanics during morphological changes.Proceedings of the National Academy of Sciences of the United States of America,107,6731-6736(2010)
[44]TRIPETTE,J.,ALEXY,T.,HARDY-DESSOURCES,M.D.,MOUGENEL,D.,BELTAN,E.,CHALABI,T.,CHOUT,R.,ETIENNE-JULAN,M.,HUE,O.,MEISELMAN,H.J.,and CONNES,P.Red blood cell aggregation,aggregate strength and oxygen transport potential of blood are abnormal in both homozygous sickle cell anemia and sickle-hemoglobin C disease.Haematologica-the Hematology Journal,94,1060-1065(2009)
[45]DIEZ-SILVA,M.,DAO,M.,HAN,J.Y.,LIM,C.T.,and SURESH,S.,Shape and biomechanical characteristics of human red blood cells in health and disease.Mrs Bulletin,35,382-388(2010)
[46]MEHRABADI,M.,KU,D.N.,and AIDUN,C.K.Effects of shear rate,confinement,and particle parameters on margination in blood flow.Physical Review E,93,023109(2016)
[47]LINDERKAMP,O.,WU,P.Y.K.,and MEISELMAN,H.J.Geometry of neonatal and adult red blood cells.Pediatric Research,17,250-253(1983)
[48]TOMAIUOLO,G.Biomechanical properties of red blood cells in health and disease towards microfluidics.Biomicrofluidics,8,051501(2014)
[49]HARIPRASAD,D.S.and SECOMB,T.W.Motion of red blood cells near microvessel walls:effects of a porous wall layer.Journal of Fluid Mechanics,705,195-212(2012)
[50]GUCKENBERGER,A.,SCHRAML,M.P.,CHEN,P.G.,LEONETTI,M.,and GEKLE,S.On the bending algorithms for soft objects in flows.Computer Physics Communications,207,1-23(2016)