Assumptions in modelling of large artery hemodynamics
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.
KeywordsShear Rate Pulse Wave Velocity Carotid Bifurcation Flow Waveform Womersley Number
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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 49.Antiga L., Steinman D.A.: Rethinking turbulence in blood. Biorheology 46(2), 77–81, 2009.Google Scholar