Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-09T07:58:31.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational Modeling of Membrane Viscosity of Red Blood Cells

Published online by Cambridge University Press:  30 April 2015

John Gounley  and
Yan Peng
John Gounley
Affiliation:
Deparment of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23507, USA
Yan Peng*
Affiliation:
Deparment of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23507, USA
*
*Corresponding author. Email addresses: [email protected] (J. Gounley), [email protected] (Y. Peng)
Get access

Abstract

Despite its demonstrated importance in the deformation and dynamics of red blood cells, membrane viscosity has not received the same attention in computational models as elasticity and bending stiffness. Recent experiments on red blood cells indicated a power law response due to membrane viscosity. This is potentially much different from the solid viscoelastic models, such as Kelvin-Voigt and standard linear solid (SLS), currently used in computation to describe this aspect of the membrane. Within the context of a framework based on lattice Boltzmann and immersed boundary methods, we introduce SLS and power law models for membrane viscosity. We compare how the Kelvin-Voigt (as approximated by SLS) and power law models alter the deformation and dynamics of a spherical capsule in shear flows.

Keywords

74F10Capsulemembrane viscosityviscoelastic modelspower law models
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 4 , April 2015 , pp. 1073 - 1087
Copyright
Copyright © Global-Science Press 2015 

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

[1]Amin, M. S., Park, Y., Lue, N., Dasari, R. R., Badizadegan, K., Feld, M. S., and Popescu, G., Microrheology of red blood cell membranes using dynamic scattering microscopy, Opt. Express, 15 (2007), pp. 17001–17009.Google Scholar
[2]Athanasiou, K. and Natoli, R., Introduction to Continuum Biomechanics, Synthesis Lectures on Biomedical Engineering, Morgan & Claypool Publishers, 2008.Google Scholar
[3]Bagchi, P., Multiscale modeling in large-scale simulation of blood flow in microcirculation, in Multiscale Modeling of Particle Interactions: Applications in Biology and Nanotechnology, King, M. and Gee, D., eds., Wiley, New York, NY, 2010.Google Scholar
[4]Barthes-Biesel, D., Diaz, A., and Dhenin, E., Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation, J. Fluid Mech., 460 (2002), pp. 211–222.Google Scholar
[5]Barthes-Biesel, D. and Sgaier, H., Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow, J. Fluid Mech., 160 (1985), pp. 119–135.Google Scholar
[6]Charrier, J., Shrivastava, S., and Wu, R., Free and constrained inflation of elastic membranes in relation to thermoforming – non-axisymmetric problems, J. Strain Anal. Eng. Des., 24 (1989), pp. 55–74.Google Scholar
[7]Christensen, R., A nonlinear theory of viscoelasticity for application to elastomers, J. Appl. Mech., 47 (1980), pp. 762–768.Google Scholar
[8]Clausen, J. R. and Aidun, C. K., Capsule dynamics and rheology in shear flow: Particle pressure and normal stress, Phys. Fluids, 22 (2010), p. 123302.Google Scholar
[9]Dao, M., Lim, C., and Suresh, S., Mechanics of the human red blood cell deformed by optical tweezers, J. Mech. Phys. Solids, 51 (2003), pp. 2259–2280.CrossRefGoogle Scholar
[10]Deville, M. O. and Gatski, T. B., Mathematical Modeling for Complex Fluids and Flows, Springer, New York, NY, 2012.Google Scholar
[11]D’Humières, D., Generalized lattice Boltzmann equations, Prog. Astronaut. Aeronaut., 159 (1992), pp. 450–458.Google Scholar
[12]D’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L.-S., Multiple–relaxation–time lattice Boltzmann models in three dimensions, Phil. Trans. R. Soc. A, 360 (2002), pp. 437–451.Google Scholar
[13]Eggleton, C. D. and Popel, A. S., Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10 (1998), pp. 1834–1845.Google Scholar
[14]Evans, E. and Hochmuth, R., Membrane viscoelasticity, Biophys. J., 16 (1976), pp. 1–11.Google Scholar
[15]Fedosov, D. A., Caswell, B., and Karniadakis, G. E., A multiscale red blood cell model with accurate mechanics, rheology, and dynamics, Biophys. J., 98 (2010), pp. 2215–2225.Google Scholar
[16]Lallemand, P. and Luo, L.-S., Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Phys. Rev. E, 68 (2003), p. 036706.Google Scholar
[17]Lallemand, P., Luo, L.-S., and Peng, Y., A lattice Boltzmann front-tracking method for interface dynamics with surface tension in two dimensions, J. Comput. Phys, 226 (2007), pp. 1367–1384.Google Scholar
[18]Li, X. and Sarkar, K., Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane, J. Comput. Phys, 227 (2008), pp. 4998–5018.CrossRefGoogle Scholar
[19]Mxseyers, M. and Chawla, K., Mechanical Behavior of Materials, Cambridge, 1999.Google Scholar
[20]Mittal, R. and Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37 (2005), pp. 239–261.Google Scholar
[21]Noguchi, H., Dynamic modes of red blood cells in oscillatory shear flow, Phys. Rev. E, 81 (2010), p. 061920.Google Scholar
[22]Noguchi, H. and Gompper, G., Dynamics of fluid vesicles in shear flow: Effect of membrane viscosity and thermal fluctuations, Phys. Rev. E, 72 (2005), p. 011901.Google Scholar
[23]Omori, T., Ishikawa, T., Barthès-Biesel, D., Salsac, A.-V., Imai, Y., and Yamaguchi, T., Tension of red blood cell membrane in simple shear flow, Phys. Rev. E, 86 (2012), p. 056321.Google Scholar
[24]Peng, Y. and Luo, L.-S., A comparative study of immersed-boundary and interpolated bounce-back methods in LBE, Progr. Comput. Fluid Dynam. Int. J., 8 (2008), pp. 156–167.Google Scholar
[25]Peskin, C. S., Numercial analysis of blood flow in the heart, Phys. Fluids, 13 (1997), pp. 3452–3459.Google Scholar
[26]Peskin, C. S., The immersed boundary method, Acta Numer., 11 (2002), pp. 479–517.Google Scholar
[27]Pozrikidis, C., Effect of membrane bending stiffness on the deformation of capsules in simple shear flow, J. Fluid Mech., 440 (2001), pp. 269–291.CrossRefGoogle Scholar
[28]Pozrikidis, C., Numerical simulation of the flow-induced deformation of red blood cells, Ann. Biomed. Eng., 31 (2003), pp. 1194–1205.CrossRefGoogle ScholarPubMed
[29]Puig-de Morales-Marinkovic, M., Turner, K. T., Butler, J. P., Fredberg, J. J., and Suresh, S., Viscoelasticity of the human red blood cell, Am. J. Physiol. Cell Physiol., 293 (2007), pp. C597–C605.Google Scholar
[30]Ramanujan, S. and Pozrikidis, C., Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, J. Fluid Mech., 361 (1998), pp. 117–143.Google Scholar
[31]Reuter, M., Biasotti, S., Giorgi, D., Patanè, G., and Spagnuolo, M., Discrete laplace–beltrami operators for shape analysis and segmentation, Comput. Gr., 33 (2009), pp. 381–390.Google Scholar
[32]Shrivastava, S. and Tang, J., Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming, J. Strain Anal. Eng. Des., 28 (1993), pp. 31–51.Google Scholar
[33]Sui, Y., Low, H., Chew, Y., and Roy, P., A front-tracking lattice Boltzmann method to study flow-induced deformation of three-dimensional capsules, Comput. Fluids, 39 (2010), pp. 499–511.Google Scholar
[34]Wang, R., Ding, H., Mir, M., Tangella, K., and Popescu, G., Effective 3D viscoelasticity of red blood cells measured by diffraction phase microscopy, Biomed. Opt. Express, 2 (2011), p. 485.Google Scholar
[35]Yazdani, A. and Bagchi, P., Influence of membrane viscosity on capsule dynamics in shear flow, J. Fluid Mech., 718 (2013), pp. 569–595.Google Scholar
[36]Yazdani, A. Z. and Bagchi, P., Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow, Phys. Rev. E, 84 (2011), p. 026314.Google Scholar
[37]Yoon, Y. Z., Kotar, J., Brown, A. T., and Cicuta, P., Red blood cell dynamics: from spontaneous fluctuations to non-linear response, Soft Matter, 7 (2011), pp. 2042–2051.Google Scholar
[38]Yoon, Y.-Z., Kotar, J., Yoon, G., and Cicuta, P., The nonlinear mechanical response of the red blood cell, Phys. Biol., 5 (2008), p. 036007.Google Scholar
[39]Zhang, J., Effect of suspending viscosity on red blood cell dynamics and blood flows in microvessels, Microcirculation, 18 (2011), pp. 562–573.Google Scholar
[40]Zhang, J., Johnson, P. C., and Popel, A. S., Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method, J. Biomech., 41 (2008), pp. 47–55.Google Scholar