Formation of the three-dimensional geometry of the red blood cell membrane

Polwaththe Gallage, Hasitha Nayanajith ; Saha, Suvash C. ; Gu, YuanTong

ANZIAM Journal, Tome 55 (2014), / Harvested from Australian Mathematical Society

Résumé

Red blood cells (RBCs) are nonnucleated liquid capsules, enclosed in deformable viscoelastic membranes with complex three dimensional geometrical structures. Generally, RBC membranes are highly incompressible and resistant to areal changes. However, RBC membranes show a planar shear deformation and out of plane bending deformation. The behaviour of RBCs in blood vessels is investigated using numerical models. All the characteristics of RBC membranes should be addressed to develop a more accurate and stable model. This article presents an effective methodology to model the three dimensional geometry of the RBC membrane with the aid of commercial software COMSOL Multiphysics 4.2a and Fortran programming. Initially, a mesh is generated for a sphere using the COMSOL Multiphysics software to represent the RBC membrane. The elastic energy of the membrane is considered to determine a stable membrane shape. Then, the actual biconcave shape of the membrane is obtained based on the principle of virtual work, when the total energy is minimised. The geometry of the RBC membrane could be used with meshfree particle methods to simulate motion and deformation of RBCs in micro-capillaries. References J. B. Freund and H. Zhao. A High-Resolution Fast Boundary-Integral Method for Multiple Interacting Blood Cells. In Computational Hydrodynamics of Capsules and Biological Cells, page 71. Chapman and Hall, 2010. C. Pozrikidis. Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Eng., 31(10):1194–1205, 2003. doi:10.1114/1.1617985 D. A. Fedosov, B. Caswell, and G. E. Karniadakis. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys. J., 98(10):2215–2225, 2010. doi:10.1016/j.bpj.2010.02.002 H. N. P. Gallage, Y. T. Gu, S. C. Saha, W. Senadeera, and A. Oloyede. Numerical simulation of red blood cells' motion : a review. In Y. T. Gu and S. C. Saha, editors, 4th International Conference on Computational Methods (ICCM 2012), Crowne Plaza, Gold Coast, QLD, November 2012. T. W. Pan and T. Wang. Dynamical simulation of red blood cell rheology in microvessels. Int. J. Numer. Anal. Mod., 6:455–473, 2009. K. I. Tsubota, S. Wada, H. Kamada, Y. Kitagawa, R. Lima, and T. Yamaguchi. A particle method for blood flow simulation: application to flowing red blood cells and platelets. Journal of the Earth Simulator, 5:2–7, 2006. http://www.jamstec.go.jp/esc/publication/journal/jes_vol.5/index.html H. N. P. Gallage, Y. T. Gu, S. C. Saha, W. Senadeera, and A. Oloyede. Numerical simulation of red blood cells' deformation using sph method. In Y. T. Gu and S. C. Saha, editors, 4th International Conference on Computational Methods (ICCM 2012), Crowne Plaza, Gold Coast, QLD, November 2012. T. W. Secomb, B. Styp-Rekowska, and A. R. Pries. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann. Biomed. Eng., 35(5):755–765, 2007. doi:10.1007/s10439-007-9275-0 K. I. Tsubota and S. Wada. Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane's natural state. Int. J. Mech. Sci., 52(2):356–364, 2010. doi:10.1016/j.ijmecsci.2009.10.007 M. Bessis. Red Cell Shapes. An Illustrated Classification and its Rationale. In M. Bessis, R. I. Weed, P. F. Leblond, Eds., Red Cell Shape, pages 1–25. Springer Berlin Heidelberg, 1973. doi:10.1007/978-3-642-88062-9_1 K. Tsukada, E. Sekizuka, C. Oshio, and H. Minamitani. Direct measurement of erythrocyte deformability in diabetes mellitus with a transparent microchannel capillary model and high-speed video camera system. Microvasc. Res., 61(3):231–239, 2001. doi:10.1006/mvre.2001.2307

Détail

Publié le : 2014-01-01
DOI : https://doi.org/10.21914/anziamj.v55i0.7820