Appendix 2: Relationships Between the 4 Elastic Constants for a Linear Isotropic Material
3.3 Viscous Behaviour of Blood
3.3.5 Viscous Behaviour in Other Parts of the Cardiovascular System
From a rheological point of view, the cardiovascular system may be divided into the heart, arteries, microcirculation and veins. Table3.3 summarises the viscous Fig. 3.18 Effect of non-Newtonian viscosity model on the bulkflowfield. Simulatedflow in the carotid bifurcation was undertaken using a Newtonian and non-Newtonian viscous model. There are differences in velocity profile and in iso-velocity contours. Reprinted from Journal of Biomechanics, Vol. 32, Gijsen FJH, van de Vosse FN, Janssen JD; The influence of the non-Newtonian properties of blood on the flow in large arteries: Steady flow in a carotid bifurcation model; pp. 601–608, Copyright (1999), with permission from Elsevier
features of blood in these various compartments. The heart is associated with high Reynolds numberflow involving considerable mixing and the treatment of blood as a homogeneous Newtonianfluid with a high-shear viscosity is usually reasonable.
Flow in the veins is generally of low Reynolds number (<500), soflow is mostly laminar. In vivo evidence from ultrasound identifies the presence of rouleaux in venous flow (Cloutier et al. 1997; Wang and Shung 2001) suggesting that the
(a) atherosclerotic plaque
(b) saccular aneurysm
(c) fusiform aneurysm Fig. 3.19 Vortex production
in arterial disease which is associated with low shear and can provide suitable conditions for red cell aggregation.aAtherosclerotic plaque—a vortex is present in the post-stenotic region which may be stable or which may be shed downstream.bBerry aneurysm—a stable vortex is present.cFusilar aneurysm— a vortex ring may be generated which propagates downstream during the cardiac cycle
non-Newtonian properties of blood are important. Flow in the microcirculation is complex and covered in detail in Chap. 8, building on the discussions of the Fahraeus and Fahraeus–Lindqvist effects covered in Sect.3.3.3.
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Chapter 4
The Arterial System I. Pressure, Flow and Stiffness
Peter R. Hoskins and D. Rodney Hose
Learning outcomes
1. Describe the main constituents of an artery.
2. Describe the organisation of elastin and collagen in the artery.
3. Describe the stress–strain (pressure–diameter) behaviour of arteries.
4. Discuss the stress–strain behaviour of arteries in terms of the mechanical properties of elastin and collagen.
5. Describe pressure–time and velocity-flow waveforms in different arteries.
6. Describe the Windkessel model.
7. Discuss how the Windkessel model produces velocity–time and pressure–time waveforms.
8. Describe pressure wave propagation.
9. Define the Moens–Korteweg equation for pressure wave velocity.
10. Discuss how pressure–time and velocity–time waveforms in arteries arise from pressure wave propagation and reflected waves.
11. Describe laminar, turbulent and disturbedflow in arteries.
12. Describe axial and rotatingflow in arteries.
13. Discuss fully developedflow and non-fully developedflow in arteries.
This chapter will explore basic biomechanics of arteries concentrating on pressure, flow and stiffness. Here the emphasis will be on normal function. Abnormal function and disease will be considered in later chapters. In the appendix at the end of the chapter is a table of the values of key quantities in different arteries.
P.R. Hoskins (&)
Edinburgh University, Edinburgh, UK e-mail: [email protected]
D.R. Hose
Sheffield University, Sheffield, UK
©Springer International Publishing Switzerland 2017 P.R. Hoskins et al. (eds.),Cardiovascular Biomechanics, DOI 10.1007/978-3-319-46407-7_4
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