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Numerical simulations of the motion and deformation of three RBCs during Poiseuille flow through a constricted vessel using IB-LBM. (English) Zbl 1411.92074

Summary: The immersed boundary-lattice Boltzmann method (IB-LBM) was used to examine the motion and deformation of three elastic red blood cells (RBCs) during Poiseuille flow through constricted microchannels. The objective was to determine the effects of the degree of constriction and the Reynolds (Re) number of the flow on the physical characteristics of the RBCs. It was found that, with decreasing constriction ratio, the RBCs experienced greater forced deformation as they squeezed through the constriction area compared to at other parts of the microchannel. It was also observed that a longer time was required for the RBCs to squeeze through a narrower constriction. The RBCs subsequently regained a stable shape and gradually migrated toward the centerline of the flow beyond the constriction area. However, a sick RBC was observed to be incapable of passing through a constricted vessel with a constriction ratio \(\leq 1/3\) for Re numbers below 0.40.

MSC:

92C35 Physiological flow
92C17 Cell movement (chemotaxis, etc.)
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[1] Zhang, J.; Johnson, P. C.; Popel, A. S., An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows, Physical Biology, 4, 4, 285-295 (2007) · doi:10.1088/1478-3975/4/4/005
[2] Vahidkhah, K.; Fatouraee, N., Numerical simulation of red blood cell behavior in a stenosed arteriole using the immersed boundary-lattice Boltzmann method, International Journal for Numerical Methods in Biomedical Engineering, 28, 2, 239-256 (2012) · Zbl 1243.92036 · doi:10.1002/cnm.1463
[3] Xu, Y.-Q.; Tian, F.-B.; Deng, Y.-L., An efficient red blood cell model in the frame of IB-LBM and its application, International Journal of Biomathematics, 6, 1, 1-22 (2013) · Zbl 1297.92027 · doi:10.1142/s1793524512500611
[4] Zhang, J. F.; Johnson, P. C.; Popel, A. S., Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method, Journal of Biomechanics, 41, 1, 47-55 (2008) · doi:10.1016/j.jbiomech.2007.07.020
[5] Tsubota, K.-I.; Wada, S., Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane’s natural state, International Journal of Mechanical Sciences, 52, 2, 356-364 (2010) · doi:10.1016/j.ijmecsci.2009.10.007
[6] Xiong, W.; Zhang, J., Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: Cell deformability and suspending viscosity effects, Biomechanics and Modeling in Mechanobiology, 11, 3-4, 575-583 (2012) · doi:10.1007/s10237-011-0334-y
[7] Ghafouri, A.; Hassanzadeh, A., Numerical study of red blood cell motion and deformation through a michrochannel using lattice Boltzmann-immersed boundary method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 6, 1873-1882 (2017) · doi:10.1007/s40430-016-0604-9
[8] Wu, Z. L.; Chen, Y.; Wang, M., Continuous inertial microparticle and blood cell separation in straight channels with local microstructures, Lab on a Chip, 16, 532-542 (2016)
[9] Dadvand, A.; Baghalnezhad, M.; Mirzaee, I.; Khoo, B. C.; Ghoreishi, S., An immersed boundary-lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows, Journal of Computational Science, 5, 5, 709-718 (2014) · doi:10.1016/j.jocs.2014.06.006
[10] Hu, H. H.; Patankar, N. A.; Zhu, M. Y., Direct Numerical Simulations of Fluid-Solid Systems Using the Arbitrary Lagrangian-Eulerian Technique, Journal of Computational Physics, 169, 2, 427-462 (2001) · Zbl 1047.76571 · doi:10.1006/jcph.2000.6592
[11] Xu, S.; Wang, Z. J., An immersed interface method for simulating the interaction of a fluid with moving boundaries, Journal of Computational Physics, 216, 2, 454-493 (2006) · Zbl 1220.76058 · doi:10.1016/j.jcp.2005.12.016
[12] Liu, W. K.; Kim, D. W.; Tang, S., Mathematical foundations of the immersed finite element method, Computational Mechanics, 39, 3, 211-222 (2007) · Zbl 1178.74170 · doi:10.1007/s00466-005-0018-5
[13] Tian, F.-B.; Dai, H.; Luo, H.; Doyle, J. F.; Rousseau, B., Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems, Journal of Computational Physics, 258, 451-469 (2014) · Zbl 1349.76274 · doi:10.1016/j.jcp.2013.10.047
[14] Tian, F.-B., Deformation of a capsule in a power-law shear flow, Computational and Mathematical Methods in Medicine, 2016 (2016) · Zbl 1367.76041 · doi:10.1155/2016/7981386
[15] Wei, Q.; Xu, Y. Q.; Tian, F. B., IB-LBM simulation on blood cell sorting with a micro-fence structure, Bio-Medical Materials and Engineering, 24, 475-481 (2014)
[16] Krüger, T.; Varnik, F.; Raabe, D., Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Computers & Mathematics with Applications, 61, 12, 3485-3505 (2011) · Zbl 1225.76231 · doi:10.1016/j.camwa.2010.03.057
[17] Alizadeh, A.; Dadvand, A., Simulation of the motion of two elastic membranes in Poiseuille shear flow via a combined immersed boundary-lattice Boltzmann method, Journal of Computational Science, 12, 51-61 (2016) · doi:10.1016/j.jocs.2015.11.008
[18] Hassanzadeh, A.; Pourmahmoud, N.; Dadvand, A., Numerical simulation of motion and deformation of healthy and sick red blood cell through a constricted vessel using hybrid lattice Boltzmann-immersed boundary method, Computer Methods in Biomechanics and Biomedical Engineering, 20, 7, 1-13 (2017) · doi:10.1080/10255842.2017.1298746
[19] Shi, L.; Pan, T.-W.; Glowinski, R., Numerical simulation of lateral migration of red blood cells in Poiseuille flows, International Journal for Numerical Methods in Fluids, 68, 11, 1393-1408 (2012) · Zbl 1302.92021 · doi:10.1002/fld.2455
[20] Peskin, C. S., Numerical analysis of blood flow in the heart, Journal of Computational Physics, 25, 3, 220-252 (1977) · Zbl 0403.76100 · doi:10.1016/0021-9991(77)90100-0
[21] Krüger, T.; Gross, M.; Raabe, D.; Varnik, F., Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells, Soft Matter, 9, 37, 9008-9015 (2013) · doi:10.1039/C3SM51645H
[22] Navidbakhsh, M.; Rezazadeh, M., An immersed boundary-lattice Boltzmann model for simulation of malaria-infected red blood cell in micro-channel, Scientia Iranica, 19, 5, 1329-1336 (2012) · doi:10.1016/j.scient.2012.08.001
[23] Navidbakhsh, M.; Rezazadeh, M., A computational study of a capsule lateral migration in microchannel flow, Acta Mechanica Sinica, 29, 4, 513-525 (2013) · Zbl 1346.76028 · doi:10.1007/s10409-013-0034-1
[24] Sui, Y.; Chew, Y. T.; Roy, P.; Low, H. T., A hybrid method to study flow-induced deformation of three-dimensional capsules, Journal of Computational Physics, 227, 12, 6351-6371 (2008) · Zbl 1160.76028 · doi:10.1016/j.jcp.2008.03.017
[25] Sui, Y.; Chew, Y. T.; Roy, P.; Low, H. T., Inertia effect on the transient deformation of elastic capsules in simple shear flow, Computers & Fluids, 38, 1, 49-59 (2009) · Zbl 1237.76143 · doi:10.1016/j.compfluid.2007.11.006
[26] Low, H.-T.; Ju, M.; Sui, Y.; Nazir, T.; Namgung, B.; Kim, S., Numerical simulations of deformation and aggregation of red blood cells in shear flow, Critical Reviews in Biomedical Engineering, 41, 4-5, 425-434 (2013) · doi:10.1615/CritRevBiomedEng.2014010689
[27] Ma, X.; Huang, B.; Wang, G.; Fu, X.; Qiu, S., Numerical simulation of the red blood cell aggregation and deformation behaviors in ultrasonic field, Ultrasonics Sonochemistry, 38, 604-613 (2017) · doi:10.1016/j.ultsonch.2016.08.021
[28] Ju, M.; Leo, H. L.; Kim, S., Numerical investigation on red blood cell dynamics in microflow: Effect of cell deformability, Clinical Hemorheology and Microcirculation, 65, 2, 105-117 (2017) · doi:10.3233/CH-16128
[29] Xu, Y. Q.; Tang, X. Y.; Tian, F. B.; Peng, Y. H.; Xu, Y.; Zeng, Y. J., IB-LBM simulation of the haemocyte dynamics in a stenotic capillary, Computer Methods in Biomechanics and Biomedical Engineering, 17, 9, 978-985 (2014) · doi:10.1080/10255842.2012.729581
[30] Shen, Z.-Y.; He, Y., A lattice Boltzmann method for simulating the separation of red blood cells at microvascular bifurcations, Chinese Physics Letters, 29, 2 (2012) · doi:10.1088/0256-307X/29/2/024703
[31] Yin, X.; Thomas, T.; Zhang, J., Multiple red blood cell flows through microvascular bifurcations: Cell free layer, cell trajectory, and hematocrit separation, Microvascular Research, 89, 47-56 (2013) · doi:10.1016/j.mvr.2013.05.002
[32] Stamou, A. C.; Buick, J. M., An LBM based model for initial stenosis development in the carotid artery, Journal of Physics A: Mathematical and Theoretical, 49, 19 (2016) · Zbl 1342.92064 · doi:10.1088/1751-8113/49/19/195602
[33] Wang, T.; Tao, Y.; Rongin, U.; Xing, Z., A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels, BioMed Research International, 2016 (2016) · doi:10.1155/2016/1801403
[34] Franke, T.; Schmid, H., Tank-trading motion of red blood cell membranes in viscometric flow: behavior of intracellular and extracellular markers, Blood Cells, 3, 351-365 (1997)
[35] Franke, T.; Hoppe, R. H. W.; Linsenmann, C.; Schmid, L.; Willbold, C.; Wixforth, A., Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows, Computing and Visualization in Science, 14, 4, 167-180 (2011) · Zbl 1402.92066 · doi:10.1007/s00791-012-0172-1
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