Mathematical modelling of the non-Newtonian blood flow in the aortic arc

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List of references:

  1. Ataullakhanov F. I., R. I. Volkova, G. T. Guriia, V. I. Sarbash. Spatial aspects of blood coagulation dynamics. III. Growth of clots in vitro // Biophysics. 1995. — V. 40, no. 6. — P. 1320–1328.
  2. O. K. Baskurt, H. J. Meiselman. Blood rheology and haemodynamics // Seminars in thrombosis and hemostasis. 2003. — V. 29, no. 5. — P. 435–450. — DOI: 10.1055/s-2003-44551.
  3. N. Bessonov, A. Sequeira, S. Simakov, Yu. Vassilevski, V. Volpert. Methods of blood flow modelling // Mathematical modelling of natural phenomena. 2016. — V. 11, no. 1. — P. 1–25. — DOI: 10.1051/mmnp/201611101. — MathSciNet: MR3452632.
  4. J. Chen, X.-Y. Lu. Numerical investigation of the Non-Newtonian blood flow in a bifurcation model with non-planar branch // Journal of Biomechanics. 2004. — V. 37, no. 12. — P. 1899– 1911. — DOI: 10.1016/j.jbiomech.2004.02.030.
  5. Y. I. Cho, K. R. Kensey. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady Flows // Biorheology. 1991. — V. 28. — P. 241–262.
  6. F. J. H. Gijsen, E. Allanic, F. N. Van De Vosse, J. D. Janssen. The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 900 curved tube // Journal of Biomechanics. 1999. — V. 32. — P. 705–713. — DOI: 10.1016/S0021-9290(99)00014-7.
  7. G. Th . Guria, M. A. Herrero, K. E. Zlobina. A mathematical model of blood coagulation induced by activation sourcesv // Discrete and Continuous Dynamical Systems. 2009. — V. 25, no. 1. — P. 175–194. — DOI: 10.3934/dcds.2009.25.175. — MathSciNet: MR2525174. — zbMATH: Zbl 1170.92015.
  8. Y. C. Fung. Biomechanics circulation. — New York: Springer, 1997. — P. 108–200. — 2nd ed.
  9. H. W. Hoogstraten, J. G. Kootstra, B. Hillen, J. K. B. Krijger, P. J. W. Wensing. Numerical simulation of blood flow in an artery with two successive bends // Journal of Biomechanics. 1996. — V. 29, no. 8. — P. 1075–1083. — DOI: 10.1016/0021-9290(95)00174-3.
  10. Johnson, B. M. , P. R. Johnson, S. Corney, D. Kilpatrick. Non-Newtonian blood flow in human right coronary arteries: Steady State Simulations // Journal of Biomech. 2004. — V. 37. — P. 709.
  11. H. Liu, K. Fukasaku, H. Iwase, N. Mutsunaga, Y. He, K. Yokoi, R. Himeno. Influences of nonplanarity, bifurcations, dynamics inflow and outflows of blood flow patterns in aortic arch: a multi-scale computational study / Book of abstracts of 2003 Summer Bioengineering Conf. — P. 511–512. — Florida, 2003. — zbMATH: Zbl 1339.05238.
  12. S. Numata, K. Itatani, K. Kanda, K. Doi, S. Yamazaki, K. Morimoto, K. Manabe, K. Ikemoto, H. Yaku. Blood flow analysis of the aortic arch using computational fluid dynamics. European // Journal of Cardio-Thoracic Surgery. 2016. — V. 49, no. 6. — P. P. 1–8.
  13. M. S. Olufsen, C. S. Peskin, W. Y. Kim, E. M. Pedersen, A. Nadim, J. Larsen. Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions // Annals of Biomedical Engineering. 2000. — V. 28. — P. 1281–1299. — DOI: 10.1114/1.1326031. — MathSciNet: MR2443016.
  14. Y. Papaharilaou, D. J. Doorly, S. J. Sherwin. The influence of out-in-plane geometry on pulsative flow within a distal end-to-side anastomosis // Journal of Biomechanics. 2002. — V. 35, no. 9. — P. 1225–1239. — DOI: 10.1016/S0021-9290(02)00072-6.
  15. V. P. Tregubov. Mathematical modelling of biological fluid flows / Selected papers of the Int. Conf. on Computer Technologies in Phys. and Eng. Applications. — Saint-Petersburg, 2014. — P. 97–100.
  16. J. Ravensbergen, J. K. B. Krijger, B. Hillen, H. W. Hoogstraten. The influence of the angle of confluence on the flow in a vertebro-basilar junction model // Journal of Biomechanics. 1996. — V. 29, no. 3. — P. 281–299. — DOI: 10.1016/0021-9290(95)00064-X.
  17. M. C. Roco. Particulate two-phase flow. Series in chemical engineering. — Butterwors-Heinemann publ, 1993.
  18. D. A. Siginer, D. De Kee, R. P. Chhabra. Advances in the flow and reology of Non-Newtonian fluids. — Elsevier, 1999. — 1515 p.
  19. R. A. Sultanov, D. Guster, B. Engelbrekt, R. Blankenbecler. 3D Computer simulations of pulsatile human blood flows in vessels and in the aortic arch: Investigation of Non-Newtonian characteristics of human blood. 2008. —
  20. Y. Tokuda, M. H. Song, Y. Ueda, A. Usui, T. Akita, S. Yoneyama, S. Maruyama. Three-dimensional numerical simulation of blood flow in the aortic arch during cardiopulmonary bypass // European Journal of Cardio-thoracic Surgery. 2008. — V. 33. — P. 164–167. — DOI: 10.1016/j.ejcts.2007.11.021.
  21. F. J. Walburn, D. J. Schneck. A constitutive equation for whole human blood / Biorheology. 1976. — V. 13. — P. 201–210.

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