Effects of stenosis and RBC motion on mass transfer in the microvessels using immersed boundary-lattice Boltzmann method

Document Type : Article

Authors

1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 8415683111, Iran

2 Foolad Institute of Technology, Fooladshahr, Isfahan, 8491663763, Iran

3 Department of Physics, Imam Khomeini International University, Ghazvin, 3414896818, Iran

4 Department of Biomedical Engineering, AmirKabir University of Technology, Tehran, 1591634311, Iran

Abstract

In this work, for better understanding of microvessels disorders, mass transfer at a stenotic and the straight capillary wall in the presence of RBC motion is investigated. The immersed boundary- lattice Boltzmann method is used for this purpose. The erythrocyte is considered as an immersed biconcave shaped tissue around the capillary as a porous media. The gamma function for input concentration, which is close to the actual stenosis brain capillary, is used. The simulated results obtained for both stenosis and straight capillaries are compared. It is shown that while the RBC motion has negligibly small effects on wall mass transfer in straight capillaries, its effect is not negligible at stenosis capillaries.

Keywords

Main Subjects


References
1. Stergaard, L., Jespersen, S.N., Mouridsen, K., et al.
The role of the cerebral capillaries in acute ischemic
stroke: the extended penumbra model", Journal of
Cerebral Blood Flow & Metabolism, 33, pp. 635-648
(2013).
2. Wang, T. and Xing, Z.W. Erythrocyte hemodynamics
in stenotic microvessels: A numerical investigation",
Physical Review E, 88, pp. 1-9 (2013).
3. Dimakopoulos, Y., Kelesidis, G., Tsouka, S., Georgiou,
G.C., and Tsamopoulos, J. Hemodynamics in stenotic
vessels of small diameter under steady state conditions:
e ect of viscoelasticity and migration of red blood
cells", Biorheology, 52, pp. 183-210 (2015).
4. Vahidkhah, K., Balogh, P., and Bagchi, P. Flow of red
blood cells in stenosed microvessels", Scienti c Rep.,
6, pp. 1-15 (2016).
5. Jiang, X.M., Tong, W., and Zhongwen X. Simulation
study of hemodynamics of red blood cells in stenotic
microvessels", Advanced Materials Research, 647, pp.
321-324 (2013).
6. Xiao, L.L., Chen, S., Lin, C.S., and Liu, Y. Simulation
of a single red blood cell
owing through a microvessel
stenosis using dissipative particle dynamics",
Mol Cell Biomech., 11(1), pp. 67-85 (2014)
7. Yuan-Qing, X., Xiao-Ying, T., Fang-Bao, T., Yu-Hua,
P., Yong, X., and Yan-Jun, Z. IB-LBM simulation
of the haemocyte dynamics in a stenotic capillary",
Computer Methods in Biomechanics and Biomedical
Engineering, 17(9), pp. 978-985 (2014).
8. Yahaghi, E., et al., Estimation of contrast agent
concentration in intra-and extra-vascular spaces of
brain tissue", Mathematical Biosciences, 204, pp. 102-
118 (2006).
M. Alafzadeh et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2561{2569 2569
9. Johnson, J.A. and Wilson, T.A. A model for capillary
exchange", Am. J. Physiol., 210, pp. 1299-1303
(1966).
10. Ye, S.S., Ng, Y.C., Tan, J., Leo, H.L., and Kim, S.
Two-dimensional strain-hardening membrane model
for large deformation behavior of multiple red blood
cells in high shear conditions", Theoretical Biology and
Medical Modelling, 11, pp. 11-19 (2014).
11. Guyton Arthur, C. and Hall, J.E., Textbook of Medical
Physiology, Elsevier Saunders (2006).
12. Yang, N. and Vafai, K. Modeling of low-density
lipoprotein (LDL) transport in the artery-e ects of
hypertension", International Journal of Heat and Mass
Transfer, 49, pp. 850-867 (2006).
13. D'Humieres D., Generalized lattice Boltzmann
equations in rare ed gas dynamics: theory and simulations",
Prog. Aeronaut. Astronaut, 159, pp. 450-458
(1992).
14. Liu, Q., He, Y.L., Li, Q., and Tao, W.Q. A multiplerelaxation-
time lattice Boltzmann Model for convection
heat transfer in porous media", International
Journal of Heat and Mass Transfer, 73, pp. 761-775.
15. Inammuro, T., Yoshino, M., Inoue, H., Mizuno, R.,
and Ogino F. A lattice Boltzmann method for a
binary miscible
uid mixture and its application to
a heat-transfer problem", Journal of Computational
Physics, 179, pp. 201-215 (2002).
16. Vafai, K., Porous Media Application in Biological
Systems and Biotechnology, Taylor & Francis Group
(2011).
17. Evans, E.A. and Fung, Y.C. Improved measurements
of the erythrocyte geometry", Microvasc. Res., 4, pp.
335-347 (1972).
18. Vahidkhah, K. and Fatouraee, N. Numerical simulation
of red blood cell Behavior in a stenosed arteriole
using the immersed boundary- Lattice Boltzmann
method", Int. J. Numer. Meth. Biomed. Engng., 28,
pp. 239-256 (2011).
19. He, X. and Zou, Q. Analysis and boundary condition
of the lattice Boltzmann BGK model with two velocity
components", Journal of Statistical Physics, 87, pp.
115-136 (1995).
20. Guo, Zh., Zhang, Ch., and Shi, B. An extrapolation
method for boundary conditions in lattice Boltzmann
method", Physics of Fluids, 14(6), pp. 2007-2010
(2002).
21. Wang, J., Wang, M., and Li, Zh. A lattice Boltzmann
algorithm for
uid-solid conjugate heat Transfer",
International Journal of Thermal Sciences, 46, pp.
228-234 (2007).
22. Filippova, O. and Hanel, D. Grid re nement for
lattice- BGK models", J. Comput. Phys., 147, pp. 219-
228 (1998).
23. Xiong, W. and Zhang, J. Shear stress variation
induced by red blood cell Motion in microvessel",
Annals of Biomedical Engineering, 38(8), pp. 2649-
2659 (2010).