CFD Simulation of Steady Blood Flow through Left Subclavian Stenosed Artery, Turbulence Modeling and Critical Narrowing
In this work, we first propose a precise geometry for any arterial stenosis. Then we use the CFX-ICEM-ANSYS 15.0 code to perform a computational simulation of blood flow in the aortic arch, both in the healthy case and in the case of presence of stenosis in the left sub-clavian artery with various stenosis degrees. Then, we discuss our results obtained for the main hemodynamic parameters (velocity, pressure, wall shear stress) and compare them with those obtained from medical imaging and numerical studies. We also study the turbulent effects, via a modeling of the Reynolds number in function of stenosis degree, the length of recirculation zone and the critical narrowing.
2. Ahmed S.A. and Giddens D.P. (1984), Pulsatile poststenotic flow studies with laser Doppler anemometry, J. Biomech. Vol.17, p695-705.
3. Akbar N.S. and Nadeem S (2014), Carreau fluid model for blood flow through a tapered artery with a stenosis, Ain Shems Engineering Journal 5, p1307–1316.
4. Berger S.A. and Jou L-D. (2000), Flows in stenotic vessels, in Annual Review of Fluid Mechanics, Annual Reviews, Palo Alto.
5. Blanco P.J. and al (2016), Computational modeling of blood flow steal phenomena caused by subclavian stenoses, J. Biomech. 49 (9), p1593–1600.
6. Bluestein D. and al (1997), Fluid Mechanics of Arterial Stenosis: Relationship to the Development of Mural Thrombus, Ann. Biomed. Eng. 25, p344–356.
7. Bluestein D and al (1999), Vortex Shedding in Steady Flow Through a Model of an Arterial Stenosis and Its Relevance to Mural Platelet Deposition, Ann. Biomed. Eng. 27, p763–773.
8. Deshpande Mohan D. (1977), Steady Laminar and turbulent flow through vascular stenosis models, PhD Thesis, Georgia Institute of Technology.
9. Donnelly R. and London Nick J.M. (2009), Eds of ABC of Arterial and venous disease, 2nd Edition, Wiley- Blackwell, BMJ Books.
10. Effat M.A. and al (2016), Clinical outcomes of combined flow-pressure drop measurements using newly developed diagnostic endpoint: Pressure drop coefficient in patients with coronary artery dysfunction, World J. Cardiol. 8(3), p283–292.
11. Gao F. and al (2011), Numerical Simulation in Aortic Arch Aneurysm , DOI: 10.5772/18566, In book, chap. 12: Etiology, Pathogenesis and Pathophysiology of Aortic Aneurysms and Aneurysm Rupture, edited by Reinhart Grundmann.
12. Gaur M. and Gupta M. K. (2014), Steady slip blood flow through a stenosed porous artery, Advances in Applied Science Research 5(5), p249-259.
13. Gerhard-Herman M. and al (2006), Guidelines for Noninvasive Vascular Laboratory Testing: A Report from the American Society of Echocardiography and the Society of Vascular Medicine and Biology, J. Am. Soc. Echocardiogr. 19, p955-972.
14. Glass C.K. and Witztum J.L. (2001): Atherosclerosis: The road ahead, Cell 104, p503-516.
15. Griffith M.D. (2007), The stability and behaviour of flows in stenotic geometries, Doctorate Thesis, University of Provence Aix-Marseille I, (2007), HAL Id: tel-00437443.
16. Griffith M.D. and al (2008), Steady Inlet Flow in Stenotic Geometries: Convective and Absolute Instabilities, Journal of Fluid Mechanics 616, p111-133.
17. Grigioni M. and al (2002), The role of wall shear stress in unsteady vascular dynamics, Progress in Biomedical Research Vol7, p204-212.
18. Haidekker M.A. (2013), Medical Imaging Technology, Springer.
19. Hazarika G. C. and Sarmah A. (2014), Blood Flow through a Stenosed Artery with the Effect of Transverse Magnetic Field using a Non-Newtonian Model, International Journal of Computer Applications Vol.101– No.1, p5-8.
20. He X. and Ku D. N. (1996): Pulsatile flow in the human left coronary artery bifurcation: average conditions, J. Biomech. Eng. 118, p74.
21. Hiratzka L.F. and al (2010), Guidelines for the Diagnosis and Management of Patients With Thoracic Aortic Disease, Circulation 121, e266-e369, (see Figure 12).
22. Huda W. and Slone R. (2003), Review of Radiologic Physics, 2nd edition. Lippincott Williams & Wilkins, Chapter 11 – Ultrasound pp. 173-191.
23. Incropera F.P. and al (2007): Fundamentals of Heat and Mass Transfer, John Wiley and sons, sixth edition.
24. Javadzadegan A. and al (2013), Flow recirculation zone length and shear rate are differentially affected by stenosis severity in human coronary arteries, Am. .J Physiol. Heart Circ. Physiol. 304, H559–H566.
25. Jianjun Wu and al (2016), Endovascular treatment of subclavian artery stenosis complicated with subclavian artery aneurysms: a case report, Int. J. Clin. Exp. Med. 9(10), (p20401-20405.
26. Kartik J. (2016), Direct numerical simulation of transitional pulsatile stenotic flow using Lattice Boltzmann Method, Peer PrePrints, https://doi. org/10.7287/peerj.preprints.1548v3, CC-BY 4.0 Open Access.
27. Kliewer M.A. and al (2000), Vertebral artery Doppler waveform changes indicating subclavian steal physiology, American Journal of Roentgenology 174, p815-819. Erratum in Am. J. Roentgenology 174(5), p1464. 28. Ku, D.N. and al (1985), Pulsatile flow and artherosclerosis in the human carotid bifurcation, Artherosclerosis 5, p293-302.
29. Ku, D.N. (1997), Blood flow in arteries, Ann. Rev. Fluid Mech. 29, p399-434.
30. Libby, P. (2003), Vascular biology of atherosclerosis: overview and state of the art, Am. J. Cardiol. 91, p3-6.
31. Loree H.M. and al (1991), Turbulent pressure fluctuations on surface of model vascular stenoses, American Journal of Physiology – Heart and Circulatory Physiology Vol. 261 no.3, H644-650.
32. Lusis, A.J. (2000), Atherosclerosis, Nature 407,p233- 241, http://dx.doi.org/10.1038/35025203.
33. Mittal R. and al (2003), Numerical study of pulsatile flow in a constricted channel. J. Fluid Mech. vol 485, p337-378.
34. Moumen F. (2010), Etudes des effets turbulents de l’écoulement sanguin dans la crosse aortique. Théorie et simulation, Magister thesis, Univ. of Oran Es-sénia.
35. Moumen F. and Djemaï A.E.F. (2016), Computational Fluid Dynamics Analysis of the Aortic Coarctation, Natural Science 8, p271-283.
36. Mrdjen S. (2013), Basic Principles of Doppler ultrasonography, European Congress of Radiology, DOI: 10.1594/ecr2013/C-0363.
37. Ochoa V.M. and Yeghiazarians Y. (2010), Subclavian artery stenosis: A review for the vascular medicine practitioner, Vascular Medicine 16(1), p29–34.
38. Päivänsalo M. and al (1998), Duplex ultrasound in the subclavian steal syndrome, Acta Radiol. 39, p183–188. 39. Pandit S. and Lierbermann G. (2013, October): To Catch a Thief: Imaging of Subclavian Steal, Beth Israel Deaconess Medical center, http://eradiology.bidmc. harvard.edu/LearningLab/cardio/Pandit.pdf.
40. Perktold K. and al (1991a), Pulsatile non-Newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles, J. Biomech. Eng. 13(6).
41. Perktold K. and al (1991b), Pulsatile non-newtonian flow characteristics in a three-dimensional human carotid bifurcation model, Transactions of the ASME 113, p464–475.
42. Pollard H. and al (1998), Subclavian Steal Syndrome. A Review, Australasian chiropractic and osteopathy (ACO) Vol. 7(1), p20-28.
43. Potter B.J. and Pinto D.S. (2014), Subclavian Steal Syndrome, Circulation 129, p2320-2323.
44. Reyna J. and al (2014), Subclavian Artery Stenosis: A Case Series and Review of the Literature, Rev. Cardiovasc. Med. 15(2), p189-195.
45. Sadeghi M.R. and al (2011), The effects of stenosis severity on the hemodynamic parameters-assessment of the correlation between stress phase angle and wall shear stress, Journal of Biomechanics Vol.44, p2614-2626. 46. Sakima H. and al (2011), Correlation between the Degree of Left Subclavian Artery Stenosis and the Left Vertebral Artery Waveform by Pulse Doppler Ultrasonography, Cerebrovascular Diseases 31(1), p64-67.
47. Salman R. and al (2016), Treatment of subclavian artery stenosis: A case series, International Journal of Surgery Case Reports 19, p69–74.
48. Schächinger V. and Zeiher A.M. (2002), Atherogenesisrecent insights into basic mechanisms and their clinical impact, Nephrol Dial Transplant 17, p2055–2064.
49. Schillinger M. and al (2002), Outcome of conservative versus interventional treatment of subclavian artery stenosis. J. Endovasc. Ther. 9, p139–146.
50. Shadman R. and al (2004), Subclavian Artery Stenosis: Prevalence, Risk Factors, and Association With Cardiovascular Diseases, Journal of the American College of Cardiology 44 (3), p618–623.
51. Sherwin S.J. and Blackburn H.M. (2005), Threedimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows, Journal of Fluid Mechanics 533, p297-327.
52. Sloop G.D. and al (2015), The Interplay of Aging, Aortic Stiffness and Blood Viscosity in Atherogenesis, Journal of Cardiology and Therapy 2(4), p350-354.
53. Sultanov R.A. and al (2008), 3D Computer Simulations of Pulsatile Human Blood Flows in Vessels and in the Aortic Arch: Investigation of Non-Newtonian Characteristics of Human Blood, arXiv:0802.2362v1.
54. Sultanov R.A. and Guster D. (2008), Computer Simulations of Pulsatile Human Blood Flow Through 3D-Models of the Human Aortic Arch, Vessels of Simple Geometry and a Bifurcated Artery: Investigation of Blood Viscosity and Turbulent Effects, arXiv:0811.1363v1.
55. Tascanov M.B. and al (2016), Cardiac Arrest in a Patient with Critical Left Subclavian Artery Stenosis, Clinics in Surgery - Cardiovascular Surgery Vol.1, Article 1165, p1.
56. Varghese S.S. and al (2007a), Direct numerical simulation of stenotic flows. Part1. Steady flow, Journal of Fluid Mechanics Vol.582, p253-280.
57. Varghese S.S. and al (2007b), Direct numerical simulation of stenotic flows. Part2. Pulsatile flow, Journal of Fluid Mechanics Vol.582, p281-318.
58. Viduetsky A. (2011), Subclavian Steal Syndrome: Diagnostic Imaging Correlations and Review of Literature, Journal of Diagnostic Medical Sonography Vol.14.
59. Wittek A. and al (2013), Ed. Computational Biomechanics for Medicine: Models, Algorithms and Implementation, Springer.
60. World Health Organization, (2014), The top 10 causes of death, (Accessed March 26, 2015), http://www.who. int/mediacentre/factsheets/fs310/en/
61. Wu J. and al (2016), Endovascular treatment of subclavian artery stenosis complicated with subclavian artery aneurysms: a case report, Int. J. Clin. Exp. Med. 9(10), p20401-20405.
62. Young, D.F. (1979), Fluid mechanics of arterial stenosis, J Biomech. Eng. 101, p157-173.