Inflow/outflow boundary conditions for particle-based blood flow simulations: Application to arterial bifurcations and trees

Lykov, Kirill; Li, Xuejin; Lei, Huan; Pivkin, Igor V.; Karniadakis, George Em; Feng, James

doi:10.1371/journal.pcbi.1004410

Title: Inflow/outflow boundary conditions for particle-based blood flow simulations: Application to arterial bifurcations and trees

Journal Article · Fri Aug 28 00:00:00 EDT 2015 · PLoS Computational Biology (Online)

DOI:https://doi.org/10.1371/journal.pcbi.1004410· OSTI ID:1229970

Lykov, Kirill ^[1]; Li, Xuejin ^[2]; Lei, Huan ^[3]; Pivkin, Igor V. ^[4]; Karniadakis, George Em ^[2]; Feng, James ^[5]

Univ. of Lugano, Lugano (Switzerland)
Brown Univ., Providence, RI (United States)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Univ. of Lugano, Lugano (Switzerland); Swiss Institute of Bioinformatics, Lausanne (Switzerland)
Univ. of British Columbia, Vancouver, BC (Canada)

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and R- BCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon valida- tion of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the \all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Lastly, we demonstrated the new methodology for simulating blood flow in ves- sels with multiple inlets and outlets, constructed using an angiogenesis model.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1229970

Report Number(s):: PNNL-SA-109087; KJ0401000

Journal Information:: PLoS Computational Biology (Online), Vol. 11, Issue 8; ISSN 1553-7358

Publisher:: Public Library of ScienceCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 41 works

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References (55)

Stochastic flow in capillary blood vessels Fung, Yuan-Cheng Microvascular Research, Vol. 5, Issue 1 https://doi.org/10.1016/S0026-2862(73)80005-6	journal	January 1973
Margination of leukocytes in blood flow through small tubes Goldsmith, Harry L.; Spain, Samira Microvascular Research, Vol. 27, Issue 2 https://doi.org/10.1016/0026-2862(84)90054-2	journal	March 1984
A Numerical Study of Plasma Skimming in Small Vascular Bifurcations Enden, G.; Popel, A. S. Journal of Biomechanical Engineering, Vol. 116, Issue 1 https://doi.org/10.1115/1.2895708	journal	February 1994
Red cell distribution at microvascular bifurcations Pries, A. R.; Ley, K.; Claassen, M. Microvascular Research, Vol. 38, Issue 1 https://doi.org/10.1016/0026-2862(89)90018-6	journal	July 1989
A Numerical Study of the Shape of the Surface Separating Flow Into Branches in Microvascular Bifurcations Enden, G.; Popel, A. S. Journal of Biomechanical Engineering, Vol. 114, Issue 3 https://doi.org/10.1115/1.2891401	journal	August 1992
Hematocrit, viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel Sherwood, Joseph M.; Kaliviotis, Efstathios; Dusting, Jonathan Biomechanics and Modeling in Mechanobiology, Vol. 13, Issue 2 https://doi.org/10.1007/s10237-012-0449-9	journal	November 2012
Nonuniform red cell distribution in 20 to 100 μm bifurcations Fenton, Bruce M.; Carr, Russell T.; Cokelet, Giles R. Microvascular Research, Vol. 29, Issue 1 https://doi.org/10.1016/0026-2862(85)90010-X	journal	January 1985
Microvascular blood viscosity in vivo and the endothelial surface layer Pries, A. R.; Secomb, T. W. American Journal of Physiology-Heart and Circulatory Physiology, Vol. 289, Issue 6 https://doi.org/10.1152/ajpheart.00297.2005	journal	December 2005
A microfluidic device for continuous, real time blood plasma separation Yang, Sung; Ündar, Akif; Zahn, Jeffrey D. Lab Chip, Vol. 6, Issue 7 https://doi.org/10.1039/B516401J	journal	January 2006
Numerical Simulation of Flowing Blood Cells Freund, Jonathan B. Annual Review of Fluid Mechanics, Vol. 46, Issue 1 https://doi.org/10.1146/annurev-fluid-010313-141349	journal	January 2014
Shape transitions of fluid vesicles and red blood cells in capillary flows Noguchi, H.; Gompper, G. Proceedings of the National Academy of Sciences, Vol. 102, Issue 40 https://doi.org/10.1073/pnas.0504243102	journal	September 2005
Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries McWhirter, J. L.; Noguchi, H.; Gompper, G. Proceedings of the National Academy of Sciences, Vol. 106, Issue 15 https://doi.org/10.1073/pnas.0811484106	journal	April 2009
Deformation and clustering of red blood cells in microcapillary flows McWhirter, J. Liam; Noguchi, Hiroshi; Gompper, Gerhard Soft Matter, Vol. 7, Issue 22 https://doi.org/10.1039/c1sm05794d	journal	January 2011
Combined Simulation and Experimental Study of Large Deformation of Red Blood Cells in Microfluidic Systems Quinn, David J.; Pivkin, Igor; Wong, Sophie Y. Annals of Biomedical Engineering, Vol. 39, Issue 3 https://doi.org/10.1007/s10439-010-0232-y	journal	December 2010
Margination of White Blood Cells in Microcapillary Flow Fedosov, Dmitry A.; Fornleitner, Julia; Gompper, Gerhard Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.028104	journal	January 2012
Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model Li, Xuejin; Peng, Zhangli; Lei, Huan Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2021 https://doi.org/10.1098/rsta.2013.0389	journal	August 2014
Predicting human blood viscosity in silico Fedosov, D. A.; Pan, W.; Caswell, B. Proceedings of the National Academy of Sciences, Vol. 108, Issue 29 https://doi.org/10.1073/pnas.1101210108	journal	July 2011
Quantifying the biophysical characteristics of Plasmodium-falciparum -parasitized red blood cells in microcirculation Fedosov, D. A.; Caswell, B.; Suresh, S. Proceedings of the National Academy of Sciences, Vol. 108, Issue 1 https://doi.org/10.1073/pnas.1009492108	journal	December 2010
How Malaria Parasites Reduce the Deformability of Infected Red Blood Cells Hosseini, S. Majid; Feng, James J. Biophysical Journal, Vol. 103, Issue 1 https://doi.org/10.1016/j.bpj.2012.05.026	journal	July 2012
Lipid bilayer and cytoskeletal interactions in a red blood cell Peng, Z.; Li, X.; Pivkin, I. V. Proceedings of the National Academy of Sciences, Vol. 110, Issue 33 https://doi.org/10.1073/pnas.1311827110	journal	July 2013
Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations Lei, H.; Karniadakis, G. E. Proceedings of the National Academy of Sciences, Vol. 110, Issue 28 https://doi.org/10.1073/pnas.1221297110	journal	June 2013
Modeling of hemodynamics arising from malaria infection Imai, Yohsuke; Kondo, Hitoshi; Ishikawa, Takuji Journal of Biomechanics, Vol. 43, Issue 7 https://doi.org/10.1016/j.jbiomech.2010.01.011	journal	May 2010
A microfabricated deformability-based flow cytometer with application to malaria Bow, Hansen; Pivkin, Igor V.; Diez-Silva, Monica Lab on a Chip, Vol. 11, Issue 6 https://doi.org/10.1039/c0lc00472c	journal	January 2011
Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria Fedosov, Dmitry A.; Lei, Huan; Caswell, Bruce PLoS Computational Biology, Vol. 7, Issue 12 https://doi.org/10.1371/journal.pcbi.1002270	journal	December 2011
Margination of red blood cells infected by Plasmodium falciparum in a microvessel Imai, Yohsuke; Nakaaki, Keita; Kondo, Hitoshi Journal of Biomechanics, Vol. 44, Issue 8 https://doi.org/10.1016/j.jbiomech.2011.02.084	journal	May 2011
Simulation of malaria-infected red blood cells in microfluidic channels: Passage and blockage Wu, Tenghu; Feng, James J. Biomicrofluidics, Vol. 7, Issue 4 https://doi.org/10.1063/1.4817959	journal	July 2013
Dynamical clustering of red blood cells in capillary vessels Boryczko, Krzysztof; Dzwinel, Witold; A. Yuen, David Journal of Molecular Modeling, Vol. 9, Issue 1 https://doi.org/10.1007/s00894-002-0105-x	journal	January 2003
Modeling Heterogeneous Mesoscopic Fluids in Irregular Geometries using Shared Memory Systems Boryczko, Krzysztof; Dzwinel, Witold; Yuen, David A. Molecular Simulation, Vol. 31, Issue 1 https://doi.org/10.1080/08927020412331299341	journal	January 2005
Simplified particulate model for coarse-grained hemodynamics simulations Janoschek, F.; Toschi, F.; Harting, J. Physical Review E, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevE.82.056710	journal	November 2010
Blood–plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study Li, Xuejin; Popel, Aleksander S.; Karniadakis, George Em Physical Biology, Vol. 9, Issue 2 https://doi.org/10.1088/1478-3975/9/2/026010	journal	April 2012
Flux boundary conditions in particle simulations Flekkøy, Eirik G.; Delgado-Buscalioni, Rafael; Coveney, Peter V. Physical Review E, Vol. 72, Issue 2 https://doi.org/10.1103/PhysRevE.72.026703	journal	August 2005
Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics Lei, Huan; Fedosov, Dmitry A.; Karniadakis, George Em Journal of Computational Physics, Vol. 230, Issue 10 https://doi.org/10.1016/j.jcp.2011.02.003	journal	May 2011
Accurate Coarse-Grained Modeling of Red Blood Cells Pivkin, Igor V.; Karniadakis, George Em Physical Review Letters, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevLett.101.118105	journal	September 2008
Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhysics Letters (EPL), Vol. 19, Issue 3 https://doi.org/10.1209/0295-5075/19/3/001	journal	June 1992
Shape Transformations of Membrane Vesicles from Amphiphilic Triblock Copolymers: A Dissipative Particle Dynamics Simulation Study Li, Xuejin; Pivkin, Igor V.; Liang, Haojun Macromolecules, Vol. 42, Issue 8 https://doi.org/10.1021/ma9000918	journal	April 2009
Construction of dissipative particle dynamics models for complex fluids via the Mori–Zwanzig formulation Li, Zhen; Bian, Xin; Caswell, Bruce Soft Matter, Vol. 10, Issue 43 https://doi.org/10.1039/C4SM01387E	journal	January 2014
A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics Fedosov, Dmitry A.; Caswell, Bruce; Karniadakis, George Em Biophysical Journal, Vol. 98, Issue 10 https://doi.org/10.1016/j.bpj.2010.02.002	journal	May 2010
Blood Flow and Cell-Free Layer in Microvessels: Blood Flow and Cell-Free Layer in Microvessels Fedosov, Dmitry A.; Caswell, Bruce; Popel, Aleksander S. Microcirculation, Vol. 17, Issue 8 https://doi.org/10.1111/j.1549-8719.2010.00056.x	journal	November 2010
Blood flow in small tubes: quantifying the transition to the non-continuum regime Lei, Huan; Fedosov, Dmitry A.; Caswell, Bruce Journal of Fluid Mechanics, Vol. 722 https://doi.org/10.1017/jfm.2013.91	journal	March 2013
Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator Li, Ju; Liao, Dongyi; Yip, Sidney Physical Review E, Vol. 57, Issue 6 https://doi.org/10.1103/PhysRevE.57.7259	journal	June 1998
A new method to impose no-slip boundary conditions in dissipative particle dynamics Pivkin, Igor V.; Karniadakis, George Em Journal of Computational Physics, Vol. 207, Issue 1 https://doi.org/10.1016/j.jcp.2005.01.006	journal	July 2005
Simulating flow of DNA suspension using dissipative particle dynamics Fan, Xijun; Phan-Thien, Nhan; Chen, Shuo Physics of Fluids, Vol. 18, Issue 6 https://doi.org/10.1063/1.2206595	journal	January 2006
Hydrodynamic interactions for single dissipative-particle-dynamics particles and their clusters and filaments Pan, Wenxiao; Fedosov, Dmitry A.; Karniadakis, George Em Physical Review E, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevE.78.046706	journal	October 2008
Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles Perktold, K.; Peter, R. O.; Resch, M. Journal of Biomedical Engineering, Vol. 13, Issue 6 https://doi.org/10.1016/0141-5425(91)90100-L	journal	November 1991
Spatial Distributions of Red Blood Cells Significantly Alter Local Haemodynamics Sherwood, Joseph M.; Holmes, David; Kaliviotis, Efstathios PLoS ONE, Vol. 9, Issue 6 https://doi.org/10.1371/journal.pone.0100473	journal	June 2014
A Hybrid Model for Three-Dimensional Simulations of Sprouting Angiogenesis Milde, Florian; Bergdorf, Michael; Koumoutsakos, Petros Biophysical Journal, Vol. 95, Issue 7 https://doi.org/10.1529/biophysj.107.124511	journal	October 2008
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Multiscale modeling of red blood cell mechanics and blood flow in malaria. Fedosov, Dmitry A.; Lei, Huan; Caswell, Bruce Carnegie Mellon University https://doi.org/10.1184/r1/6096554	text	January 2011
A hybrid model for three-dimensional simulations of sprouting angiogenesis. Milde, F.; Bergdorf, M.; Koumoutsakos, P. Biophysical Society https://doi.org/10.5167/uzh-39538	text	January 2008
Multiscale modeling of red blood cell mechanics and blood flow in malaria. Fedosov, Dmitry A.; Lei, Huan; Caswell, Bruce Carnegie Mellon University https://doi.org/10.1184/r1/6096554.v1	text	January 2011
A simplified particulate model for coarse-grained hemodynamics simulations Janoschek, Florian; Toschi, Federico; Harting, Jens arXiv https://doi.org/10.48550/arxiv.1005.2594	text	January 2010
Geometry effect in multi-step crossflow microfluidic devices for red blood cells separation and deformability assessment Faustino, Vera; Pinho, Diana; Catarino, Susana O. Biomedical Microdevices, Vol. 24, Issue 2 https://doi.org/10.1007/s10544-022-00616-0	journal	June 2022
Strain-induced room-temperature ferroelectricity in SrTiO3 membranes Xu, Ruijuan; Huang, Jiawei; Barnard, Edward S. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-16912-3	journal	June 2020
Controlling Density Fluctuations in Wall-Bounded Dissipative Particle Dynamics Systems Pivkin, Igor V.; Karniadakis, George Em Physical Review Letters, Vol. 96, Issue 20 https://doi.org/10.1103/physrevlett.96.206001	journal	May 2006
Effects of erythrocyte aggregation and venous network geometry on red blood cell axial migration Bishop, Jeffrey J.; Popel, Aleksander S.; Intaglietta, Marcos American Journal of Physiology-Heart and Circulatory Physiology, Vol. 281, Issue 2 https://doi.org/10.1152/ajpheart.2001.281.2.h939	journal	August 2001

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Red blood cell distribution in a microvascular network with successive bifurcations Ye, Ting; Peng, Lina; Li, Guansheng Biomechanics and Modeling in Mechanobiology, Vol. 18, Issue 6 https://doi.org/10.1007/s10237-019-01179-5	journal	June 2019
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Going beyond 20 μ m-sized channels for studying red blood cell phase separation in microfluidic bifurcations Roman, Sophie; Merlo, Adlan; Duru, Paul Biomicrofluidics, Vol. 10, Issue 3 https://doi.org/10.1063/1.4948955	journal	May 2016
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Theory and algorithms to compute Helfrich bending forces: a review Guckenberger, Achim; Gekle, Stephan Journal of Physics: Condensed Matter, Vol. 29, Issue 20 https://doi.org/10.1088/1361-648x/aa6313	journal	April 2017
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