Modelling of erythrocyte behaviour in blood capillaries by structural model combined with Lattice-Boltzmann approach

• Autorzy: Przekop R. , Majewski I. , Moskal A.

Identyfikatory

DOI

10.24425/122960

• Języki publikacji: EN

Abstrakty

EN

A microstructural model of Red Blood Cell (RBC) behaviour was proposed. The erythrocyte is treated as a viscoelastic object, which is denoted by a network of virtual particles connected by elastic springs and dampers (Kelvin-Voigt model). The RBC is submerged in plasma modelled by lattice Boltzmann fluid. Fluid – structure interactions are taken into account. The simulations of RBC behaviour during flow in a microchannel and wall impact were performed. The results of RBC deformation during the flow are in good agreement with experimental data. The calculations of erythrocyte disaggregation from the capillary surface show the impact of RBC structure stiffness on the process.

Słowa kluczowe

EN

Red Blood Cells; Kelvin-Voigt model; lattice Boltzmann

PL

czerwone krwinki; Model Kelvina-Voigta; krata Boltzmanna

• Wydawca: Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk
• Czasopismo: Chemical and Process Engineering
• Rocznik: 2018
• Tom: Vol. 39, nr 4
• Strony: 411–--426
• Opis fizyczny: Bibliogr. 46 poz.

Twórcy

autor

Przekop R.

• Faculty of Chemical and Process Engineering, Warsaw University of Technology, ul. Waryńskiego 1, 00-645 Warszawa, Poland

autor

Majewski I.

• Faculty of Chemical and Process Engineering, Warsaw University of Technology, ul. Waryńskiego 1, 00-645 Warszawa, Poland

autor

Moskal A.

• Faculty of Chemical and Process Engineering, Warsaw University of Technology, ul. Waryńskiego 1, 00-645 Warszawa, Poland

Bibliografia

• 1. Betz T., Lenz M., Joanny J.F., Sykes C., 2009. ATP-dependent mechanics of red blood cells. PNAS, 106, 15312–15317. DOI: 10.1073/pnas.0904614106.
• 2. Boltzmann L., 1995. Lectures on Gas Theory. Dover Publishing, New York, USA.
• 3. Bouzidi, M., Firdaouss, P., Lallemand, P., 2002. Momentum transfer of lattice-Boltzmann fluid with boundaries. Phys. Fluids, 13, 3452–3459. DOI: 10.1063/1.1399290.
• 4. Chee C.Y., Lee H.P., Lu C., 2008. Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte. Phys. Lett. A, 372, 1357–1363. DOI: 10.1016/j.physleta.2007.09.067.
• 5. Ciana A., Achilli C., Bakluini C., Minetti G., 2011. On the association of lipid rafts to the spectrin skeleton in human erythrocytes. Biochim. Biophys. Acta, 1808, 183–190. DOI: 10.1016/j.bbamem.2010.08.019.
• 6. Cordasco D., Bagchi. P., 2014. Intermittency and synchronized motion of red blood cells dynamics in shear flow. J. Fluid Mech., 759, 472–488. DOI: 10.1017/jfm.2014.587.
• 7. Dao M., Lim C.T., Suresh S., 2003. Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids, 51, 2259–2280. DOI: 10.1016/j.jmps.2003.09.019.
• 8. Deuling H.J., Helfrich W., 1976. The curvature elasticity of fluid membranes: A catalogue of vesicle shapes. J. Phys., 37, 1335–1345. DOI: 10.1051/jphys:0197600370110133500.
• 9. Evans E.A., 1973. New membrane concept applied to the analysis of fluid-shear and micropipette-deformed red blood cells. Biophys. J., 13, 941–954. DOI: 10.1016/S0006-3495(73)86036-9.
• 10. Evans E.A., 1983. Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipette aspiration tests. Biophys. J., 43, 27–30. DOI: 10.1016/S0006-3495(83)84319-7.
• 11. Evans E.A., Hochmuth R.M., 1976. Membrane viscoelasticity. Biophys. J., 16, 1–11. DOI: 10.1016/S0006-3495(76)85658-5.
• 12. Evans E.A., La Celle P.L., 1975. Intrinsic material properties of the erythrocyte membrane indicated by mechanical analysis of deformation. Blood, 45, 29–43.
• 13. Fedosov D.A., Caswell B., Karniadakis G.E., 2010. Systematic coarse-graining of spectrin-level red blood cells models. Comput. Metods. Appl. Mech. Eng., 199, 1937–1948. DOI: 10.1016/j.cma.2010.02.001.
• 14. Funaki H., 1955. Contributions on the shapes of red blood corpuscles. Jpn. J. Physiol., 5, 81–92. DOI: 10.2170/jjphysiol.5.81.
• 15. Fung Y.C., Evans E., 1972. Improved measurements of the erythrocyte geometry. Microvasc. Res., 4, 335–347.DOI: 10.1016/0026-2862(72)90069-6.
• 16. Gingold R.A., Monaghan J.J., 1977. Smoothed particle hydrodynamics: theory and application to non-sphericalstars. Mon. Not. R. Astron. Soc., 181, 375–389. DOI: 10.1093/mnras/181.3.375.
• 17. Gov N., Zilman A.G., Safran S., 2003. Cytoskeleton confinement and tension of red blood cells membranes. Phys.Rev. Lett., 90, 228101. DOI: 10.1103/PhysRevLett.90.228101.
• 18. Hoogerbrugge P.J., Koleman J.M.V.A., 1992. Simulating microscopic hydrodynamic phenomena with dissipativeparticle dynamics. Europhys. Lett., 19, 155–160. DOI: 10.1209/0295-5075/19/3/001.
• 19. Hosseini S.M., Feng J.J., 2009. A particle-based model for the transport of erythrocytes in capillaries. Chem. Eng.Sci., 64, 4488–4497. DOI: 10.1016/j.ces.2008.11.028.
• 20. Lallemand P., Luo L.S., 2003. Lattice Boltzmann method for moving boundaries. J. Comput. Phys., 184, 406–421.DOI: 10.1016/S0021-9991(02)00022-0.
• 21. Li J., Dao M., Lim C.T., Suresh S., 2005. Spectrin-level modelling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys. J., 88, 3707–3719. DOI: 10.1529/biophysj.104.047332.
• 22. Liu Y., Liu W.K., 2006. Rheology of red blood cells aggregation by computer simulation. J. Comput. Phys., 220, 139–154. DOI: 10.1016/j.jcp.2006.05.010.
• 23. Lucy L.B., 1977. A numerical approach to the testing of fission hypothesis. Astron. J., 82, 1013–1024. DOI:10.1086/112164.
• 24. Lux S.E., 2016. Anatomy of the red cell membrane skeleton: unanswered questions. Blood, 127, 527–536. DOI: 10.1182/blood-2014-12-512772.
• 25. Mills J., Qie L., Dao M., Lim C., Shuresh S., 2004. Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mol. Cell. Biomech., 1, 169–180. DOI: 10.3970/mcb.2004.001.169.
• 26. Nash G., Meiselman H.J., 1985. Alteration of red cell membrane viscoelasticity by heat treatment: effect on cell deformability and suspension viscosity. Biorheology, 22, 73–84. DOI: 10.3233/BIR-1985-22106.
• 27. Park Y., Best C.A., Kuriabova T., Henle M.L., Feld M.S., Levine A.J., Popescu G., 2011. Measurement of the nonlinear elasticity of red blood cell membranes. Phys. Rev. E, 83, 051925. DOI: 10.1103/PhysRevE.83.051925.
• 28. Peng Z.L., Asaro R.J., Zhu Q., 2011. Multiscale simulation of erythrocyte membrane. Phys. Rev. E, 81, 031904. DOI: 10.1103/PhysRevE.81. 031904.
• 29. Peshkov I., Romenski E., 2016. A hyperbolic model for viscous Newtonian fluids. Continuum Mech. Thermodyn., 28, 85–104. DOI: 10.1007/s00161-014-0401-6. Philips K.G., Jacques S.L., McCarthy O.J.T., 2012. Measurement of the single cell refractive index, dry mass, volume and density using a transillumination microscope. Phys. Rev. Lett., 109, 118105. DOI: 1103/PhysRevLett. 109.118105.
• 30. Pozrikidis C., 2001. Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech., 440, 269–291. DOI: 10.1017/S0022112001004657.
• 31. Pozrikidis C., 2003. Numerical simulation of the flow-inducted deformation of red blood cells. Ann. Biomed. Eng., 31, 1194–1205. DOI: 19.1114/1.1617985.
• 32. Qian Y.H., d’Humieres D., Lallemand P., 1992. Lattice BGK model for Navier-Stokes equation. Europhys. Lett., 17, 479–484. DOI: 10.1209/0295-5075/17/6/001.
• 33. Rawicz W., Olbrich K.C., McIntosh T., Needham D., Evans E.A., 2000. Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J., 79, 328–339. DOI: 10.1016/S0006-3495(00)76295-3.
• 34. Romenski E., Resnyansky A.D., Toro E.F., 2007. Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures. Quart. App. Math., 45, 259–279. DOI: 10.1090/qam/1409.
• 35. Saffman P., Delbruck M., 1975. Brownian motion in biological membranes. Proc. Natl. Acad. Sci. USA, 72, 3111– 3113. DOI: 10.1073/pnas.72.8.3111.
• 36. Singer S.J., Nicolson G.L., 1972. The fluid mosaic model of the structure of cell membranes. Science, 175, 720– 731. DOI: 10.1126/science.1975.4023.720.
• 37. Suresh S., 2006. Mechanical response of human red blood cells in health and disease: Some structure-propertyfunction relationships. J. Mater. Res., 21, 1871–1877. DOI: 10.1557/jmr.2006.0260.
• 38. Tan Y., Sun D., HuangW., 2010. Mechanical modelling of red blood cells during stretching. J. Biomech. Eng., 132, 4001042. DOI: 10.1115/1.4001042.
• 39. Tsukada K., Sekizuka E., Oshio C., Minamitani H., 2001. Direct measurement of erythrocyte deformability in diabetes mellitus with a transparent microchannel capillary model and high-speed video camera system. Microvasc. Res., 61, 231–239. DOI: 10.1006/mvre.2001.2307.
• 40. Violeau D., 2012. Fluid mechanics and the SPH method: Theory and applications. Oxford University Press, Oxford, UK.
• 41. Waugh R., Evans E.A., 1979. Thermoelasticity of red blood cell membrane. Biophys. J., 26, 115–131. DOI: 10.1016/S0006-3495(79)85239-X.
• 42. Ye T., Phan-Thien N., Khoo B.C., Lim C.T., 2014. Numerical modelling of a healthy/malaria infected erythrocyte in shear flow using dissipative particle dynamics method. J. Appl. Phys., 115, 224710. DOI: 10.1063/1.4879418.
• 43. Yoon D., You D., 2016. Continuum modelling of deformation and aggregation of red blood cells. J. Biomech., 49, 2267–2279. DOI: 10.1016/j.biomech.2015.11.027.
• 44. Zeidan D., 2011. Numerical resolution for a compressible two-phase flow model based on the theory of thermodynamically compatible systems. Appl. Math. Comp., 217, 5023–5040. DOI: 10.1016/j.amc.2010.07.053.
• 45. Zeidan D., 2016. Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods. Appl. Math. Comp., 272, 707–719. DOI: 10.1016/j.amc.2015.09.038.
• 46. Zeidan D., Romenski E., Slaouti A., Toro F., 2007. Numerical study of wave propagation in compressible twophase flow. Int. J. Numer. Meth. Fluids, 54, 393–417. DOI: 10.1002/fld.1404.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).