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Erschienen in:
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2012 | OriginalPaper | Buchkapitel

1. Assumptions in modelling of large artery hemodynamics

verfasst von : David A. Steinman

Erschienen in: Modeling of Physiological Flows

Verlag: Springer Milan

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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.

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Nächstes Kapitel Simplified blood flow model with discontinuous vessel properties: Analysis and exact solutions
Fußnoten
1
1Even then, reflections arising from the microcirculation tend to dominate over the effects of such local impedance mismatches
 
2
2Re is defined as VD/v , where V is the lumen-averaged velocity, D is the lumen diameter, and v is the blood viscosity, usually assumed to be 0.03–0.04 cm2/s.
 
3
3Wo is defined as R(ω/v)1/2, where R is the lumen radius and ω is the frequency of the heart beat in rad/s. For a typically blood viscosity of 0.035 cm2/s and a heart rate of 60 bpm, large artery Womersley numbers range from around 2 (coronaries) to 20 (aorta).
 
4
4The questions this author is most often asked after presentations are: “How can you assume the wall is rigid?” and “How can you assume blood is a Newtonian fluid”. The former tends to be asked by clinicians, the latter by engineers; I’ll not hazard a guess why.
 
5
5These descriptive terms, as well as “stiffness” are often used interchangeably, but have specific meanings for quantifying arterial wall properties [3].
 
6
6In fact, PWV is often measured in vivo by measuring this shift at two or more locations spaced a known distance apart [4].
 
7
7The italics are mine, and I will return to this point in the next section, as it has implications for the measurement and prescription of prevailing flow conditions, and for the validation of so-called “patient-specific” CFD models against in vivo measurements.
 
8
8This was the principle used by Womersley to derive his famous analytic solution for flow in compliant tubes. It was later exploited by the author for his so-called “hybrid” implicit-explicit 2D FSI approach [6], which solved for the transpiration velocities simultaneously with the rest of the velocity field, and then iteratively updated the wall position based on those wall velocities.
 
9
9Different conclusions may be drawn for other vascular territories depending on, say, the curvature of the inlet or the Reynolds number (i.e., entrance length), so the interested reader is encouraged to review the literature and/or perform their own tests specific to their application of interest.
 
10
10This differential compliance may serve to act as a kind of low pass filter to smooth the transients of the cardiac cycle and thus ensure a more quasi-steady supply of blood to the brain vs. other cerebral vascular territories.
 
11
11Although blood exhibits a variety of non-Newtonian properties, as briefly discussed later, in the large artery hemodynamics literature the term “non-Newtonian” often explicitly or implicitly refers to shear-thinning properties alone. Many shear-thinning models have been proposed, as recently reviewed by [29].
 
12
12Poise is the cgs unit of dynamic viscosity, named for Poiseuille. 1 Poise = 1 dyne-s/cm2 =0.1Pas. The cgs unit for kinematic viscosity is the Stokes, equivalent to cm2/s, and is often calculated from the dynamic viscosity assuming a blood density of 1.06 g/cm3.
 
13
13For example, the ~ 3-μm RBC-free plasma layer adjacent to the arterial wall has an appreciable effect on the apparent viscosity of blood (i.e., the Fahraeus-Lindqvist effect) for arteries below ~ 0.25mm radius [28], namely a two-order-of-magnitude scale difference.
 
14
14Turbulence caused by the external compression of an artery is thought to give rise to the so-called Korotkoff sounds used for blood pressure measurement. Noises (“bruits”) can also be detected by a stethoscope placed over a stenosed superficial vessel like the carotid artery, or intracranial aneurysms, which may also harbor turbulent flow [40].
 
15
15Reynolds stresses are terms that arise from time averaging of the Navier-Stokes equation after decomposition of the velocity into mean and fluctuating components. They are not stresses in a physical sense, but rather embody the effects of the fluctuating velocities on the mean flow.
 
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Metadaten
Titel
Assumptions in modelling of large artery hemodynamics
verfasst von
David A. Steinman
Copyright-Jahr
2012
Verlag
Springer Milan
Buch
Modeling of Physiological Flows

Print ISBN: 978-88-470-1934-8

Electronic ISBN: 978-88-470-1935-5

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-88-470-1935-5_1