Lattice Boltzmann simulation of blood flow properties and vessel geometry in open and closed vessels: A numerical study

Document Type : Article


1 Department of Mechanical Engineering, Urmia University, Urmia, Postal Code: 5756151818, Iran

2 Department of Mechanical Engineering, Urmia University, Urmia, Postal Code: 5756151818, Iran.


In the present article, Lattice Boltzmann method is utilized to simulate two-dimensional incompressible viscous flow in an open and closed microchannel (vessel). The main focus of the present research is to study physical parameters of blood flow in a vessel. To find the effect of oscillatory flow inside the vessel, we take account of the Reynolds number from 0.05 to 1.5 for numerical computation in the present manuscript in an open straight vessel. In addition, the accuracy of Poiseuille Law is investigated for blood flow in open vessel too. For this purpose, the effect of the vessel diameter and blood viscosity on the blood flow is studied numerically. As extra results, the effect of blood injection to a coronary bifurcation with two closed ends are studied. The blood pressure drop is high at the beginning of the vessel (pressure variation is high between the adjacent points along the vessel), but after the path along the vessel, the speed of dropping pressure decreases and the pressure difference between the adjoining points decreases along the vessel. Finally, the present results have been compared with the available experimental and numerical results that show good agreements.


Main Subjects

1. DiVito, K.A., Daniele, M.A., Roberts, S.A., Ligler, F.S., and Adams, A.A. "Microfabricated blood vessels undergo neoangiogenesis", Data in Brief, 14, pp. 156- 162 (2017).
2. Moccia, S., De Momi, E., El Hadji, S., and Mattos, L.S. "Blood vessel segmentation algorithms-review of methods, datasets and evaluation metrics", Comp. Meth. and Prog. in Biomed., 158, pp. 71-91 (2018).
3. Fedosov, D.A., Caswell, B., Suresh, S., and Karniadakis, G.E. "Quantifying the biophysical characteristics of Plasmodium-falciparum-parasitized red blood cells in microcirculation", Proc. Nat. Acad. Sci., 108(1), pp. 35-39 (2011).
4. Wu, J., Hu, Q., and Ma, X. "Comparative study of surface modeling methods for vascular structures", Comp. Med. Imaging Graph., 37(1), pp. 4-14 (2013).
5. Campochiaro, P.A. "Molecular pathogenesis of retinal and choroidal vascular diseases", Prog. Retin. Eye Res., 49, pp. 67-81 (2015).
6. De Momi, E., Caborni, C., Cardinale, F., Casaceli, G., Castana, L., Cossu, M., Mai, R., Gozzo, F., Francione, S., and Tassi, L. "Multi-trajectories automatic planner for Stereo Electro Encephalo Graphy (SEEG)", Int. J. Comput. Assist. Radiol. Surg., 9(6), pp. 1087-1097 (2014).
7. Essert, C., Fernandez-Vidal, S., Capobianco, A., Haegelen, C., Karachi, C., Bardinet, E., Marchal, M., and Jannin, P. "Statistical study of parameters for deep brain stimulation automatic preoperative planning of electrodes trajectories", Int. J. Comput. Assist. Radiol. Surg., 10(12), pp. 1973-1983 (2015).
8. Navidbakhsh, M. and Rezazadeh, M. "An immersed boundary-lattice Boltzmann model for simulation of malaria-infected red blood cell in micro-channel", Scientia Iranica, 19(5), pp. 1329-1336 (2012).
9. Faria, C., Sadowsky, O., Bicho, E., Ferrigno, G., Joskowicz, L., Shoham, M., Vivanti, R., and De Momi, E. "Validation of a stereo camera system to quantify brain deformation due to breathing and pulsatility", Med. Phys., 41(11), p. 113502 (2014).
10. Cardinale, F., Pero, G., Quilici, L., Piano, M., Colombo, P., Moscato, A., Castana, L., Casaceli, G., Fuschillo, D., and Gennari, L. "Cerebral angiography for multimodal surgical planning in epilepsy surgery: description of a new three-dimensional technique and literature review", World Neurosurg, 84(2), pp. 358- 367 (2015).
11. Alishahi, M., Alishahi, M.M., and Emdad, H. "Numerical simulation of blood  flow in a flexible stenosed abdominal real aorta", Scientia Iranica, 18(6), pp. 1297-1305 (2011).
12. Hernandez-Perez, M., Puig, J., Blasco, G., de la Ossa, N.P., Dorado, L., Davalos, A., and Munuera, J. "Dynamic magnetic resonance angiography provides collateral circulation and hemodynamic information in acute ischemic stroke", Stroke, 47(2), pp. 531-534 (2016).
13. Rochitte, C.E., George, R.T., Chen, M.Y., Arbab-Zadeh, A., Dewey, M., Miller, J.M., Niinuma, H., Yoshioka, K., Kitagawa, K., and Nakamori, S. "Computed tomography angiography and perfusion to assess coronary artery stenosis causing perfusion defects by single photon emission computed tomography: the CORE320 study", Eur. Heart J., 35(17), pp. 1120-1130 (2014).
14. Pamme, N. "Continuous flow separations in micro fluidic devices", Lab on a Chip, 7, pp. 1644-1659 (2007).
15. McNamara, G. and Zanetti, G. "Use of the Boltzmann equation to simulate lattice gas automata", Physics of Review Letters, 61(5), pp. 23-32 (1998).
16. Chen, S. and Doolen, G.D. "Lattice Boltzmann method for  fluid flows", Ann. Rev. of Fluid Mech., 30(1), pp. 329-364 (1998).
17. Succi, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press: Oxford (2001).
18. Wang, H., Cater, J., Liu, H., Ding, X., and Huang, W. "A lattice Boltzmann model for solute transport in open channel  flow", J. of Hydrology, 556, pp. 419-426 (2018).
19. Cheng, Y. and Zhang, H. "Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow", Comp. and Fluids, 39(5), pp. 871-881 (2010).
20. Lecrivain, G., Rayan, R., Hurtado, A., and Hampel, U. "Using quasi-DNS to investigate the deposition of elongated aerosol particles in a wavy channel flow", Comp. and Fluids, 124, pp. 78-85 (2016).
21. Vi, A., Pouransari, H., Zamansky, R., and Mani, A. "Particle-laden flows forced by the disperse phase: Comparison between lagrangian and eulerian simulations", Int. J. of Multiphase Flow, 79, pp. 144-158 (2016).
22. Henn, T., Thater, G., Dorer, W., Nirschl, H., and Krause, M.J. "Parallel dilute particulate flow simulations in the human nasal cavity", Comp. and Fluids, 124, pp. 197-207 (2016).
23. Wu, J. and Shu, C. "An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows", J. of Comput. Phys., 229, pp. 5022-5042 (2010).
24. Carreau, P.J. "Rhology equations from molecular network theories", J. of Rheo., 16(1), p. 127 (1972).
25. Wang, C.H. and Ho, J.R. "A lattice Boltzmann approach for the non- newtonian effect in the blood flow", Comput. Math. Appl., 62, pp. 75-86 (2011).
26. Khodayari Bavil, A. and Razavi, S.E. "On the thermo flow behavior in a rectangular channel with skewed circular ribs", Mech. & Ind., 18(2), p. 225 (2017).
27. Bagchi, P. "Mesoscale simulation of blood flow in small vessels", Biophys. J., 92, pp. 858-1877 (2007).
28. De Hart, J., Baaijens, F.P.T., Peters, G.W.M., and Schreurs P.J.G. "A computational  fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve", J. of Biomech., 36, pp. 699-712 (2003).
29. Arokiaraj, M.C., De Santis, G., De Beule, M., and Palacios, I.F. "A novel tram stent method in the treatment of coronary bifurcation lesions - finite element study", PLoS ONE, 11, e0149838 (2016).