Biomedical Engineering Reference
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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 be-
come more sophisticated and their applications more varied, it is worth (re)con-
sidering the simplifying assumptions that are traditionally, and often implicitly,
made. This chapter reviews some of the common assumptions about the constitu-
tive 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 do-
mains 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 non-
Newtonian 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, Univer-
sity of Toronto, Toronto, ON, Canada
email: steinman@mie.utoronto.ca
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