Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T09:09:28.425Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Modelling of Cell Distribution in BloodFlow

Published online by Cambridge University Press:  31 July 2014

N. Bessonov ,
E. Babushkina ,
S. F. Golovashchenko ,
A. Tosenberger ,
F. Ataullakhanov ,
M. Panteleev ,
A. Tokarev  and
V. Volpert
N. Bessonov*
Affiliation:
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences 199178 Saint Petersburg, Russia
E. Babushkina
Affiliation:
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences 199178 Saint Petersburg, Russia
S. F. Golovashchenko
Affiliation:
Manufacturing Research Department, Ford Research Laboratory, 481214 Dearborn, USA
A. Tosenberger
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France INRIA Team Dracula, INRIA Antenne Lyon la Doua, 69603 Villeurbanne, France
F. Ataullakhanov
Affiliation:
National Research Center for Haematology, Ministry of Healthcare of Russian Federation, 125167 Moscow, Russia Federal Research and Clinical Centre of Paediatric Haematology, Oncology and Immunology Ministry of Healthcare of Russian Federation, 117198 Moscow, Russia Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia Center for Theoretical Problems of Physicochemical Pharmacology Russian Academy of Sciences, 119991 Moscow, Russia
M. Panteleev
Affiliation:
National Research Center for Haematology, Ministry of Healthcare of Russian Federation, 125167 Moscow, Russia Federal Research and Clinical Centre of Paediatric Haematology, Oncology and Immunology Ministry of Healthcare of Russian Federation, 117198 Moscow, Russia Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia Center for Theoretical Problems of Physicochemical Pharmacology Russian Academy of Sciences, 119991 Moscow, Russia
A. Tokarev
Affiliation:
National Research Center for Haematology, Ministry of Healthcare of Russian Federation, 125167 Moscow, Russia Federal Research and Clinical Centre of Paediatric Haematology, Oncology and Immunology Ministry of Healthcare of Russian Federation, 117198 Moscow, Russia
V. Volpert
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France INRIA Team Dracula, INRIA Antenne Lyon la Doua, 69603 Villeurbanne, France European Institute of Systems Biology and Medicine, 69007 Lyon, France Department of Mahematics, Mechanics and Computer Science Southern Federal University, Rostov-on-Don, Russia
*
⋆Corresponding author. E-mail: nickbessonov@yahoo.com
Get access

Abstract

Properties of blood cells and their interaction determine their distribution in flow. Itis observed experimentally that erythrocytes migrate to the flow axis, platelets to thevessel wall, and leucocytes roll along the vessel wall. In this work, a three-dimensionalmodel based on Dissipative Particle Dynamics method and a new hybrid (discrete-continuous)model for blood cells is used to study the interaction of erythrocytes with platelets andleucocytes in flow. Erythrocytes are modelled as elastic highly deformable membranes,while platelets and leucocytes as elastic membranes with their shape close to a sphere.Separation of erythrocytes and platelets in flow is shown for different values ofhematocrit. Erythrocyte and platelet distributions are in a good qualitative agreementwith the existing experimental results. Migration of leucocyte to the vessel wall and itsrolling along the wall is observed.

Keywords

modellingerythrocytesblood flowdissipative particle dynamicsplatelet distributionleucocyte rolling
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 6: Blood flows , 2014 , pp. 69 - 84
Copyright
© EDP Sciences, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alizadehrad, D., Imai, Y., Nakaaki, K., Ishikawa, T., Yamaguchi, T.. Parallel simulation of cellular flow in microvessels using a particle method. Journal of Biomechanical Science and Engineering, 7 (2012), no. 1, 57-71. CrossRefGoogle Scholar
M.P. Allen, D.J. Tidesley. Computer Simulation of Liquids. Clarendon, Oxford, 1987.
AlMomani, T., Udaykumar, H.S., Marshall, J.S., Chandran, K.B.. Micro-scale dynamic simulation of erythrocyte-platelet interaction in blood flow. Annals of Biomedical Engineering, Vol. 36 (2008), no. 6, 905-920. CrossRefGoogle Scholar
Bessonov, N. M., Golovashchenko, S.F., Volpert, V.A.. Numerical Modelling of Contact Elastic-Plastic Flows. Math. Model. Nat. Phenom., Vol. 4 (2009), no. 1, 44-87. CrossRefGoogle Scholar
Bodnar, T., Rajagopal, K., Sequeira, A.. Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model. Mathematical Modelling of Natural Phenomena, vol. 6 (2011), no. 5, 1-24. CrossRefGoogle Scholar
Bui, C., Lleras, V., Pantz, O.. Dynamics of red blood cells in 2d. ESAIM: Proc., Vol. 28 (2009), 182-194. CrossRefGoogle Scholar
Crowl, L.M., Fogelson, A.L.. Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Int j numer method biomed eng., 26 (2010), no. 3-4, 471-487. CrossRefGoogle ScholarPubMed
M.M. Dupin, I. Halliday, C.M. Care, L. Alboul, L.L. Munn. Modeling the flow of dense suspensions of deformable particles in three dimensions. Physical Review E 75, 066707, 2007.
W. Dzwinel, K. Boryczko, D.A. Yuen. Modeling Mesoscopic Fluids with Discrete-Particles Methods. Algorithms and Results., In: Spasic AM, Hsu JP (eds) Finely Dispersed Particles: Micro-, Nano-, and Atto-Engineering. Taylor & Francis, CRC Press, 715-778.
D. Fedosov, B. Caswell, G.E. Karniadakis. General coarse-grained red blood cell models: I. Mechanics. (2009), arXiv:0905.0042 [q-bio.CB].
Fedosov, D., Caswell, B., Karniadakis, G.E.. A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics. Biophysical Journal, Volume 98 (2010), 2215-2225. CrossRefGoogle ScholarPubMed
D.A. Fedosov. Multiscale Modeling of Blood Flow and Soft Matter. PhD dissertation at Brown University, (2010).
Fedosov, D.A., Lei, H., Caswell, B., Suresh, S., Karniadakis, G.E.. Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria. PLoS Computational Biology, Vol. 7 (2011), no. 12, e1002270. CrossRefGoogle ScholarPubMed
Fedosov, D.A., Pivkin, I.V., Karniadakis, G.E.. Velocity limit in DPD simulations of wall-bounded flows. J. Comp. Phys., 227 (2008), 2540-2559. CrossRefGoogle Scholar
Goldsmith, H.L., Turitto, V.T.. Rheological aspects of thrombosis and haemostasis: basic principles and applications. Thrombosis and Haemostasis, 55 (1986), no. 3, 415-435. Google ScholarPubMed
Groot, R.D., Warren, P.B.. Dissipative particle dynamics: Bridging the Gap Between Atomistic and Mesoscopic Simulation. J. Chem. Phys., 107 (1997), no. 11, 4423–4435. CrossRefGoogle Scholar
Hosseini, S.M., Feng, J.J.. A particle-based model for the transport of erythrocytes in capillaries. Chem. Eng. Sci. 64, (2009) 4488-4497. CrossRefGoogle Scholar
Imai, Y., Kondo, H., Ishikawa, T., Lim, C.T., Yamaguchi, T.. Modeling of hemodynamics arising from malaria infection. Journal of Biomechanics, (2010), no. 43, 1386-1393. CrossRefGoogle Scholar
Imai, Y., Nakaaki, K., Kondo, H., Ishikawa, T., Lim, C.T., Yamaguchi, T.. Margination of red blood cells infected by Plasmodium falciparum in a microvessel. Journal of Biomechanics, (2011), no. 44, 1553-1558. CrossRefGoogle Scholar
M. Karttunen, I. Vattulainen, A. Lukkarinen. A novel methods in soft matter simulations. Springer, Berlin, 2004.
Koleski, J.F., Eckstein, E.C.. Near wall concentration profiles of 1.0 and 2.5 um beads during flow of blood suspensions. Trans. Ann. Soc. Intern. Organs, 37 (1991), 9-12. CrossRefGoogle Scholar
Kuchel, P.W., Fackerell, E.D.. Parametric-Equation Representation of Biconcave Erythrocytes. Bulletin of Mathematical Biology, 61 (1999), 209-220. CrossRefGoogle ScholarPubMed
Lawrence, M. B., Springer, T. A.. Leukocytes roll on a selectin at physiological flow rates: distinction from and prerequisite for adhesion through integrins. Cell, 65 (1991), 859-873. CrossRefGoogle Scholar
Leif, R.C., Vinograd, J.. The Distribution of Buoyant Density of Human Erythrocytes in Bovine Albumin Solutions. Proc Natl Acad Sci U S A., 51 (1964), no. 3, 520-528. CrossRefGoogle ScholarPubMed
Leibler, S., Maggs, A.C.. Simulation of shape changes and adhesion phenomena in an elastic model of erythrocytes. Proc. Natl. Acad. Sci. USA, vol. 87 (1990), 6433-6435. CrossRefGoogle Scholar
Lopez, L., Duck, I.M., Hunt, W.A.. On the shape of the erythrocyte. Biophys J., 8 (1968), no. 11, 1228-1235. CrossRefGoogle ScholarPubMed
McWhirter, J.L., Noguchi, H., Gompper, G.. Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. PNAS, vol. 106 (2009), no. 15, 6039-6043. CrossRefGoogle ScholarPubMed
Mohandas, N., Gallagher, P.G.. Red cell membrane: past, present, and future. Blood, 112 (2008), 3939-48. CrossRefGoogle ScholarPubMed
Munn, L.L., Dupin, M.M., Blood Cell Interactions and Segregation in Flow. Annals of Biomedical Engineering, Vol. 36 (2008), no. 4, 534-544. CrossRefGoogle ScholarPubMed
S. Muñoz San Martín, J.L. Sebastián, M. Sancho1, G. Álvarez. Modeling Human Erythrocyte Shape and Size Abnormalities, arXiv:q-bio/0507024 [q-bio.QM], 14 Jul 2005.
Noguchi, H., Gompper, G.. Shape transitions of fluid vesicles and red blood cells in capillary flows. PNAS, vol. 102 (2005), no. 40, 14159-14164. CrossRefGoogle ScholarPubMed
D. Obrist, B. Weber, A. Buck, P. Jenny. Red blood cell distribution in simplified capillary networks. Phil. Trans. R. Soc. A 2010 368, doi: 10.1098/rsta.2010.0045, 2010.
D. Pinho, A. Pereira, R. Lima, T. Ishikawa, Y. Imai, T. Yamaguchi. Red blood cell dispersion in 100 μ m glass capillaries: the temperature effect. C.T. Lim and J.C.H. Goh (Eds.), WCB 2010, IFMBE Proceedings, 31 (2010), 1067–1070.
E. Pinto, B. Taboada, R. Rodrigues, V. Faustino, A. Pereira, R. Lima. Cell-free layer (CFL) analysis in a polydimethysiloxane (PDMS) microchannel: a global approach. WebmedCentral Biomedical Engineering, 4 (2013), no.8, WMC004374.
I.V. Pivkin, G.E. Karniadakis. Accurate Coarse-Grained Modeling of Red Blood Cells. Physical review letters, PRL 101 (2008) 118105.
C. Pozrikidis. Modeling and Simulation of Capsules and Biological Cells. by Chapman & Hall/CRC, ISBN (2003) 1-58488-359-6.
U.D. Schiller. Dissipative Particle Dynamics. A Study of the Methodological Background. Diploma thesis at Faculty of Physics University of Bielefeld, 2005.
Tokarev, A.A., Butylin, A.A., Ermakova, E.A., Shnol, E.E., Panasenko, G.P., Ataullakhanov, F.I.. Finite Platelet Size Could Be Responsible for Platelet Margination Effect. Biophysical Journal, Vol. 101 (2011), 1835-1843. CrossRefGoogle ScholarPubMed
Tosenberger, A., Salnikov, V., Bessonov, N., Babushkina, E., Volpert, V.. Particle Dynamics Methods of Blood Flow Simulations. Math. Model. Nat. Phenom., 6 (2011), no. 5, 320–332. CrossRefGoogle Scholar
Tsubota, K., Wada, S.. Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membraneâ’s natural state. International Journal of Mechanical Sciences, 52 (2010), 356-364. CrossRefGoogle Scholar
Tsubota, K., Wada, S., Kamada, H., Kitagawa, Y., Lima, R., Yamaguchi, T.. A Particle Method for Blood Flow Simulation, Application to Flowing Red Blood Cells and Platelets. Journal of the Earth Simulator, vol. 5 (2006), 2-7. Google Scholar
Yeh, C., Calvez, A.C., Eckstein, E.C.. An estimated shape function for drift in a platelet-transport model. Biophysical journal, vol. 67 (1994), 1252-1259. CrossRefGoogle Scholar
Yeh, C., Eckstein, E.C.. Transient Lateral Transport of Platelet-Sized Particles in Flowing Blood Suspensions. Biophysical journal, vol. 66 (1994), 1706-1716. CrossRefGoogle ScholarPubMed
Zhang, J., Johnson, P.C., Popel, A.S.. Effects of Erythrocyte Deformability and Aggregation on the Cell Free Layer and Apparent Viscosity of Microscopic Blood Flows. Microvasc Res., 77 (2009), no. 3, 265-272. CrossRefGoogle ScholarPubMed
Bagchi, P.. Mesoscale simulation of blood flow in small vessels. Biophysical Journal, 92 (2007), no. 6, 1858-1877 [PubMed: 17208982]. CrossRefGoogle Scholar
Skalak, R., Tozeren, A., Zarda, R., Chein, S.. Strain energy function of red blood cell membranes. Biophysical Journal 13 (1973), no. 3, 245-264 [PubMed: 4697236]. CrossRefGoogle ScholarPubMed
Tokarev, A.A., Butylin, A.A., Ataullakhanov, F.I.. Platelet Adhesion from Shear Blood Flow Is Controlled by Near-Wall Rebounding Collisions with Erythrocytes. Biophys. J., 100 (2011), no. 4, 799-808. CrossRefGoogle ScholarPubMed
Tokarev, A.A., Butylin, A.A., Ataullakhanov, F.I.. Platelet transport and adhesion in shear blood flow: the role of erythrocytes. Computer Research and Modeling, 4 (2012), no. 1, 185-200 [article in Russian]. Google Scholar
Suresh, S., Spatz, J., Mills, J. P., Micoulet, A., Dao, M., Lim, C. T., Beil, M., Seufferlein, T.. Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomaterialia, 1 (2005), 15-30. CrossRefGoogle ScholarPubMed