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 assu
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Assumptions in modelling of large artery hemodynamics David A. Steinman
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.
1.1 Overview The vascular system is a complex network of branching vessels spanning length scales from meters to microns. Key features of the normal arterial system include compliant artery walls, complex branching or tortuous artery lumens, and nonNewtonian blood rheology. As Fig. 1.1 illustrates, and as outlined below, the relative importance of these features depends upon the hemodynamic scales of interest.
David A. Steinman ( ) Biomedical Simulation Laboratory, Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada email: [email protected]
Ambrosi D., Quarteroni A., Rozza G. (Eds.): Modeling of Physiological Flows. DOI 10.1007/978-88-470-1935-5 1, © Springer-Verlag Italia 2012
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D.A. Steinman
Fig. 1.1. Representation of the relative importance of various factors in models of the different hemodynamic scales: ++ indicates primary importance; – indicates secondary or negligible importance; ?? indicates potential or unclear importance (taken from Creative Commons)
At the largest scales, it has been shown reasonable to model the vascular network analogously to an AC electrical circuit [1], where inductance and resistance (i.e., impedance) represent inertia and frictional (viscous) losses of the pulsating blood. Capacitance represents the compliance of the blood vessel walls, which act analogously via the alternating local storage and release of blood down the vessel. This latter feature largely determines the wave propagation phenomena – attenuation, dispersion, reflection, etc. – that can be used to infer the functional state of the vasculature from macroscopic pressure and flow measurements. For estimating vascular impedance, vessel diameters and
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