Numerical Methods in Modelling of Red Blood Cellflow Behaviour Through a Specific Stacking Pattern

Abstract: The dynamics of red blood cells (RBCs) is one of the major aspects of the cardiovascular system that has been studied intensively in the past few decades. Using computational fluid dynamics, complex nonlinear fluid flows have been modeled. The dynamics of biconcave RBCs are thought to have major influences in cardiovascular diseases and other problems associated with cardiovascular flow behaviour, and the determination of blood rheology and properties. Most reported computational models have been confined to the behaviour of a single RBC in 2-dimensional domains, under physiological flow conditions. This work investigates a particular stacking pattern in analyzing the RBC flow behavior under physiological flow conditions, using the D2Q9 lattice Boltzmann numerical method created using Matlab. Prior to the analysis the Matlab script was benchmarked using the Poiseuille flow and the flow around the cross-section of a cylinder, after which the accuracy of the method used was determined. The benchmarks showed that the lattice Boltzmann code had minimal error. The accuracy was determined using the data obtained from Matlab and a created excel program. It also showed that the lattice Boltzmann method was of the first order, which corresponds with results existing in literatures. The analysis of the stacking pattern showed how RBC flows through the chosen stacking pattern, and the results are shown.

Mathematics and Biology (Biomathematics)

1. Chung, T. J. (2010). Computational Fluid Dynamics. In T. J. Chung, Computational Fluid Dynamics. Cambridge: Cambridge University Press. [Google Scholar] [Crossref]

2. Chen, S., & Doolen, G. D. (1998). Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30(1), 329-364. [Google Scholar] [Crossref]

3. Dadvand A, Baghalnezhad M, Mirzaee I, Khoo B. C, and Ghoreishi S. (2014). “An immersed boundary-lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows,” Journal of Computational Science, vol. 5, no. 5, pp. 709–718. [Google Scholar] [Crossref]

4. Hardy, J., & de Pazzis, Y. (1976). Models of lattice gas automata for simulating fluid dynamics. Journal of Statistical Physics, 15(6), 129-148. [Google Scholar] [Crossref]

5. Hardy, J., and de Pazzis, O. (1976). Molecular dynamics of a classical lattice gas. In J. Hardy, & O. de Pazzis, Molecular dynamics of a classical lattice gas. [Google Scholar] [Crossref]

6. Hess, J. L. (1967). Calculation of Potential Flow About Arbitrary Bodies. In J. L. Hess, Calculation of Potential Flow About Arbitrary Bodies. [Google Scholar] [Crossref]

7. Hess, J., & Smith, A. M. O. (1967). Calculation of potential flow about arbitrary bodies. Journal of Ship Research, 9(2), 22-44. [Google Scholar] [Crossref]

8. Kundu, P. K., Cohen, I. M., & Dowling, D. R. (2015). Fluid Mechanics (6th ed.). Academic Press. [Google Scholar] [Crossref]

9. Mohamad, A. A. (2011). Lattice Boltzmann method: Fundamentals and engineering applications with computer codes. Springer. [Google Scholar] [Crossref]

10. Niclas Berg (2018) Blood flow and cell transport in arteries and medical assist devices. ISBN: 978-91-7873-037-7 [Google Scholar] [Crossref]

11. Rohde, M. (2004). Extending the lattice Boltzmann method. Delft. [Google Scholar] [Crossref]

12. Rohde, C. (2009). Lattice-Boltzmann and finite-difference lattice-Boltzmann methods for fluid dynamics. Elsevier. [Google Scholar] [Crossref]

13. Rohde, M. (2009). Cellular Automata. In M. Rohde, Cellular Automata. Delft. walls at the same scale,” Acta Physica Sinica, vol. 63, article 174701, no. 17, 2014 (Chinese). [Google Scholar] [Crossref]

14. Skalak, R., Tozeren, A., Zarda, R. P., & Chien, S. (1973). Biophysical strain energy function of red blood cell membranes. Biophysical Journal, 13(9), 245-264. [Google Scholar] [Crossref]

15. Versteeg, H. K., & Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd ed.). Pearson Education. [Google Scholar] [Crossref]

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