Advertisement

Assumptions in modelling of large artery hemodynamics

  • David A. Steinman
Part of the MS&A — Modeling, Simulation and Applications book series (MS&A, volume 5)

Abstract

The last decade has seen tremendous growth in the use of computational methods for simulating large artery hemodynamics. As computational models become more sophisticated and their applications more varied, it is worth (re)considering the simplifying assumptions that are traditionally, and often implicitly, made. This chapter reviews some of the common assumptions about the constitutive properties of the arteries and the blood within, and their potential impact on the computed hemodynamics. It will be seen, for example, that the assumption of rigid walls, while reasonable and expedient, may be questionable for extensive domains and/or heterogeneities in the arterial wall structure and properties, and that this has implications for the way in which prevailing flow conditions are imposed. Simplifying assumptions about the properties of blood are undoubtedly necessary, but the Newtonian/non-Newtonian dichotomy may prove too simplistic, especially as simulations move from laminar flows to unstable and turbulent flows. Rather than dwelling upon the potential limitations arising from these assumptions, this chapter attempts to highlight some of the potentially interesting research opportunities that may arise in investigating and overcoming them.

Keywords

Shear Rate Pulse Wave Velocity Carotid Bifurcation Flow Waveform Womersley Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author thanks the many students, fellows, colleagues and study participants, without whom these adventures would not have been possible. Numerous funding agencies have supported this research, none more so than Heart and Stroke Foundation of Canada, whose early and ongoing support for the author’s image-based CFD investigations has allowed him to ask questions that are sometime uncomfortable but ultimately rewarding.

References

  1. 1.
    Westerhof N., Bosman F., De Vries C.J., Noordergraaf A.: Analog studies of the human systemic arterial tree. J. Biomech. 2(2): 121–143, 1969.CrossRefGoogle Scholar
  2. 2.
    Pries A.R., Secomb T.W., Gaehtgens P.: Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res. 32(4): 654–667, 1996.Google Scholar
  3. 3.
    O’Rourke M.F., Staessen J.A., Vlachopoulos C., Duprez D., Plante G.E.: Clinical applications of arterial stiffness; definitions and reference values. Am. J. Hypertens. 15(5): 426–444, 2002.CrossRefGoogle Scholar
  4. 4.
    Davies J.I., Struthers A.D.: Pulse wave analysis and pulse wave velocity: a critical review of their strengths and weaknesses. J. Hypertens. 21(3): 463–472, 2003.CrossRefGoogle Scholar
  5. 5.
    O’Rourke M.F.: Pressure and flow waves in systemic arteries and the anatomical design of the arterial system. J. Appl. Physiol. 23(2), 139–149, 1967.Google Scholar
  6. 6.
    Steinman D.A., Ethier C.R.: The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. J. Biomech. Eng. 116(3): 294–301 , 1994.CrossRefGoogle Scholar
  7. 7.
    Perktold K., Rappitsch G.: Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech. 28(7): 845–856, 1995.CrossRefGoogle Scholar
  8. 8.
    Zhao S.Z., Xu X.Y., Hughes A.D., Thom S.A., Stanton A.V., Ariff B., Lon, Q.: Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation. J. Biomech. 33(8): 975–984, 2000.CrossRefGoogle Scholar
  9. 9.
    Jin S., Oshinski J., Giddens D.P.: Effects of wall motion and compliance on flow patterns in the ascending aorta. J. Biomech. Eng. 125(3), 347–354, 2003.CrossRefGoogle Scholar
  10. 10.
    Torii R., Keegan J., Wood N.B., Dowsey A.W., Hughes A.D., Yang G.Z., Firmin D.N., Thom S.A., Xu X.Y.: MR image-based geometric and hemodynamic investigation of the right coronary artery with dynamic vessel motion. Ann. Biomed. Eng. 38(8), 2606–2620, 2010.CrossRefGoogle Scholar
  11. 11.
    Steinman D.A., Thomas J.B., Ladak H.M., Milner J.S., Rutt B.K., Spence J.D.: Reconstruction of carotid bifurcation hemodynamics and wall thickness using computational fluid dynamics and MRI. Magn. Reson. Med. 47(1), 149–159, 2002.CrossRefGoogle Scholar
  12. 12.
    Antiga L., Wasserman B.A., Steinman D.A.: On the overestimation of early wall thickening at the carotid bulb by black blood MRI, with implications for coronary and vulnerable plaque imaging. Magn. Reson. Med. 60(5), 1020–1028, 2008.CrossRefGoogle Scholar
  13. 13.
    Steinman D.A., Antiga L., Wasserman B.A.: Overestimation of cerebral aneurysm wall thickness by black blood MRI? J. Magn. Reson. Imaging 31(3), 766, 2010.CrossRefGoogle Scholar
  14. 14.
    Kips J., Vanmolkot F., Mahieu D., Vermeersch S., Fabry I., de Hoon J., Van Bortel L., Segers P.: The use of diameter distension waveforms as an alternative for tonometric pressure to assess carotid blood pressure. Physiol. Meas. 31(4), 543–553, 2010.CrossRefGoogle Scholar
  15. 15.
    Thomas J.B., Milner J.S., Rutt B.K., Steinman D.A.: Reproducibility of image-based computational fluid dynamics models of the human carotid bifurcation. Ann. Biomed. Eng. 31(2), 132–141, 2003.CrossRefGoogle Scholar
  16. 16.
    Cebral J.R., Putman C.M., Pergolesi R., Burgess J., Yim P.: Multi-modality image-based models of carotid artery hemodynamics. Proc. SPIE Medical Imaging 5369, 529–538, 2004.Google Scholar
  17. 17.
    Qiu Y., Tarbell J.M.: Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery. J. Biomech. Eng. 122(1), 77–85, 2000.CrossRefGoogle Scholar
  18. 18.
    Ford M.D., Xie J., Wasserman B.A., Steinman D.A.: Is flow in the common carotid artery fully developed? Physiol. Meas. 29(11), 1335–1349, 2008.CrossRefGoogle Scholar
  19. 19.
    Hoi Y., Wasserman B.A., Lakatta E.G., Steinman D.A.: Effect of common carotid artery inlet length on normal carotid bifurcation hemodynamics. J. Biomech. Eng. 132(12), 121008, 2010.CrossRefGoogle Scholar
  20. 20.
    Ford M.D., Nikolov H.N., Milner J.S., Lownie S.P., Demont E.M., Kalata W., Loth, F., Holdsworth, D.W., Steinman, D.A.: PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models. J. Biomech. Eng. 130(2), 021015, 2008.CrossRefGoogle Scholar
  21. 21.
    Hoi Y., Zhou Y.Q., Zhang X., Henkelman R.M., Steinman D.A.: Correlation between local hemodynamics and lesion distribution in a novel aortic regurgitation murine model of atherosclerosis. Ann. Biomed. Eng. 39(5), 1414–1422, 2011.CrossRefGoogle Scholar
  22. 22.
    Zhou Y.Q., Zhu S.N., Foster F.S., Cybulsky M.I., Henkelman R.M.: Aortic regurgitation dramatically alters the distribution of atherosclerotic lesions and enhances atherogenesis in mice. Arterioscler. Thromb. Vasc. Biol. 30(6), 1181–1188, 2010.CrossRefGoogle Scholar
  23. 23.
    Hoi Y., Wasserman B.A., Xie Y.J., Najjar S.S., Ferruci L., Lakatta E.G., Gerstenblith G., Steinman D.A.: Characterization of volumetric flow rate waveforms at the carotid bifurcations of older adults. Physiol. Meas. 31(3), 291–302, 2010.CrossRefGoogle Scholar
  24. 24.
    Marshall I., Papathanasopoulou P., Wartolowska K.: Carotid flow rates and flow division at the bifurcation in healthy volunteers. Physiol. Meas. 25(3), 691–697, 2004.CrossRefGoogle Scholar
  25. 25.
    Milner J.S., Moore J.A., Rutt B.K., Steinman D.A.: Hemodynamics of human carotid artery bifurcations: computational studies with models reconstructed from magnetic resonance imaging of normal subjects. J. Vasc. Surg. 28(1), 143–156, 1998.CrossRefGoogle Scholar
  26. 26.
    Cebral J.R., Yim P.J., Lohner R., Soto O., Choyke P.L.: Blood flow modeling in carotid arteries with computational fluid dynamics and MR imaging. Acad. Radiol. 9(11), 1286–1299, 2002.CrossRefGoogle Scholar
  27. 27.
    Younis H.F., Kaazempur-Mofrad M.R., Chan R.C., Isasi A.G., Hinton D.P., Chau A.H., Kim L.A., Kamm R.D.: Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation. Biomech. Model. Mechanobiol. 3(1), 17–32, 2004.CrossRefGoogle Scholar
  28. 28.
    Ethier C.R., Simmons C.A.: Introductory Biomechanics: From Cells to Organisms. Cambridge University Press, Cambridge, 2007.CrossRefGoogle Scholar
  29. 29.
    Yilmaz F., Gundogdu M.Y.: A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions. Korea Australia Rheol. J. 20(4), 197–211, 2008.Google Scholar
  30. 30.
    Lee S.W., Steinman D.A.: On the relative importance of rheology for image-based CFD models of the carotid bifurcation. J. Biomech. Eng. 129(2), 273–278, 2007.CrossRefGoogle Scholar
  31. 31.
    Ballyk P.D., Steinman D.A., Ethier C.R.: Simulation of non-Newtonian blood flow in an endto-side anastomosis. Biorheology 31(5), 565–586, 1994.Google Scholar
  32. 32.
    Johnston B.M., Johnston P.R., Corney S., Kilpatrick D.: Non-Newtonian blood flow in human right coronary arteries: steady state simulations. J. Biomech. 37(5), 709–720, 2004.CrossRefGoogle Scholar
  33. 33.
    Johnston, B.M., Johnston, P.R., Corney, S., Kilpatrick, D.: Non-Newtonian blood flow in human right coronary arteries: transient simulations. J Biomech 39(6), 1116–1128 (2006).CrossRefGoogle Scholar
  34. 34.
    Gijsen F.J., Allanic E., van de Vosse F.N., Janssen J.D.: The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube. J. Biomech. 32(7), 705–713, 1999.CrossRefGoogle Scholar
  35. 35.
    Box F.M., van der Geest R.J., Rutten M.C., Reiber J.H.: The influence of flow, vessel diameter, and non-newtonian blood viscosity on the wall shear stress in a carotid bifurcation model for unsteady flow. Invest. Radiol. 40(5), 277–294, 2005.CrossRefGoogle Scholar
  36. 36.
    Steinman D.A., Milner J.S., Norley C.J., Lownie S.P., Holdsworth D.W.: Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR Am. J. Neuroradiol. 24(4), 559–566, 2003.Google Scholar
  37. 37.
    Rayz V.L., Boussel L., Lawton M.T., Acevedo-Bolton G., Ge L., Young W.L., Higashida R.T., Saloner D.: Numerical modeling of the flow in intracranial aneurysms: prediction of regions prone to thrombus formation. Ann. Biomed. Eng. 36(11), 1793–1804, 2008.CrossRefGoogle Scholar
  38. 38.
    Paeng D.G., Nam K.H., Shung K.K.: Cyclic and radial variation of the echogenicity of blood in human carotid arteries observed by harmonic imaging. Ultrasound. Med. Biol. 36(7), 1118–1124, 2010.CrossRefGoogle Scholar
  39. 39.
    Nerem R.M., Seed W.A.: An in vivo study of aortic flow disturbances. Cardiovasc. Res. 6(1), 1–14, 1972.CrossRefGoogle Scholar
  40. 40.
    Ferguson G.G.: Turbulence in human intracranial saccular aneurysms. J. Neurosurg. 33(5), 485–497, 1970.CrossRefGoogle Scholar
  41. 41.
    Lee S.E., Lee S.W., Fischer P.F., Bassiouny H.S., Loth F.: Direct numerical simulation of transitional flow in a stenosed carotid bifurcation. J. Biomech. 41(11), 2551–2561, 2008.CrossRefGoogle Scholar
  42. 42.
    Ahmed S.A., Giddens D.P.: Pulsatile poststenotic flow studies with laser Doppler anemometry. J. Biomech. 17(9), 695–705, 1984.CrossRefGoogle Scholar
  43. 43.
    Ryval J., Straatman A.G., Steinman D.A.: Two-equation turbulence modeling of pulsatile flow in a stenosed tube. J. Biomech. Eng. 126(5), 625–635, 2004.CrossRefGoogle Scholar
  44. 44.
    Varghese S., Frankel S., Fischer P.: Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow. Journal of Fluid Mechanics 582, 281, 2007.MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Baek H., Jayaraman M.V., Richardson P.D., Karniadakis G.E.: Flow instability and wall shear stress variation in intracranial aneurysms. J. R. Soc. Interface 7(47), 967–988, 2009.CrossRefGoogle Scholar
  46. 46.
    Les A.S., Shadden S.C., Figueroa C.A., Park J.M., Tedesco M.M., Herfkens R.J., Dalman R.L., Taylor C.A.: Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38(4), 1288–1313.Google Scholar
  47. 47.
    Wang C., Pekkan K., de Zelicourt D., Horner M., Parihar A., Kulkarni A., Yoganathan A.P.: Progress in the CFD modeling of flow instabilities in anatomical total cavopulmonary connections. Ann. Biomed. Eng. 35(11), 1840–1856, 2007.CrossRefGoogle Scholar
  48. 48.
    Liu J.S., Lu P.C., Chu S.H.: Turbulence characteristics downstream of bileaflet aortic valve prostheses. J. Biomech. Eng. 122(2), 118–124 (2000).CrossRefGoogle Scholar
  49. 49.
    Antiga L., Steinman D.A.: Rethinking turbulence in blood. Biorheology 46(2), 77–81, 2009.Google Scholar
  50. 50.
    Ge L., Dasi L.P., Sotiropoulos F., Yoganathan A.P.: Characterization of hemodynamic forces induced by mechanical heart valves: Reynolds vs. viscous stresses. Ann. Biomed. Eng. 36(2), 276–297 (2008).CrossRefGoogle Scholar
  51. 51.
    Quinlan N.J., Dooley P.N.: Models of flow-induced loading on blood cells in laminar and turbulent flow, with application to cardiovascular device flow. Ann. Biomed. Eng. 35(8), 1347–1356, 2007.CrossRefGoogle Scholar
  52. 52.
    Cristini V., Kassab G.S.: Computer modeling of red blood cell rheology in the microcirculation: a brief overview. Ann. Biomed. Eng. 33(12), 1724–1727, 2005.CrossRefGoogle Scholar
  53. 53.
    Roache P.J.: Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid Mech. 29, 123–160, 1997.MathSciNetCrossRefGoogle Scholar
  54. 54.
    Taylor C.A., Steinman D.A.: Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions: Sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28–30, 2008 Pasadena, California. Ann Biomed Eng 38(3), 1188–1203, 2010.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Biomedical Simulation Laboratory, Department of Mechanical & Industrial EngineeringUniversity of TorontoTorontoCanada

Personalised recommendations