Arterial and Venous Fluid Dynamics
The majority of these lecture notes are taken from the author’s chapter “Blood flow in arteries and veins”, in the book “Perspectives in Fluid Mechanics” edited by G K Batchelor, H K Moffatt and M G Worster, published by Cambridge University Press, 2000.
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The majority of these lecture notes are taken from the author's chapter "Blood flow in arteries and veins", in the book "Perspectives in Fluid Mechanics" edited by G K Batchelor, H K Moffatt and M G Worster, published by Cambridge University Press, 2000. Other parts come from his own book, Pedley (1980).
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The Cardiovascular System
Material transport from one part of the body to another, in vertebrates or other large animals, involves fluid (liquid or gas) flowing along and across the walls of systems of tubes. The most widely studied tube systems are the mammalian cardiovascular and ventilatory systems. The purposes of studying the mechanics of physiological flows can be summed up under four headings: ( 1) pure physiology, or understanding how animals work; (2) pathophysiology, or understanding how they go wrong, i.e. the origins and development of diseases; (3) diagnosis, or working out how to infer what has gone wrong from (relatively) simple and non-traumatic measurements, for example of blood pressure; (4) cure, which in the mechanical context usually means bioengineering, and which here includes vascular and other surgery as well as the design of prosthetic devices. Different scientists and practitioners will have different motivations, but the basic mechanical principles are clearly the same for all. In the mechanical context (2, 3 and 4 above) it is worth remarking that disease of the arteries, notably atherosclerosis, causes around 50% of the deaths in modem western society, through heart attacks and strokes, and drastically lowers the quality of life of those elderly patients who suffer reduced blood flow to the legs through constriction or blockage (stenosis) of the femoral (thigh) arteries. Fluid mechanical factors are strongly implicated in the development of atherosclerosis (atherogenesis) as well as its effects, because the distribution of wall shear stress (WSS) in arteries is linked to atherogenesis. What follows is a very brief review; for more detail see Giddens et al. (1993), Friedman (1993) and Fry (1987), for excellent treatments. The results of several in vivo studies show that, if a normal artery, with an intact endothelium, is altered so that the mean wall shear stress (WSS) changes, then over a period of months the artery wall remodels itself to restore the mean WSS to its normal value (Zarins et al. 1987). The normal shear stress, as estimated from the assumption of Poiseuille flow, is usually in the range
G. Pedrizzetti et al. (eds.), Cardiovascular Fluid Mechanics © Springer-Verlag Wien 2003
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T.J. Pedley
1-2 N m - 2 , the actual value depending on the species and the vessel. Such long-term adaptation is thought to be important during angiogenesis and growth, determining artery diameters in response to flow rate demands. The only signal related to flow rate that the endothelial cells could detect is the WSS. If it rises, then the response of the vessel is to increase its luminal diameter while retaining the same wall thickness. However, if the WSS falls below about 1 N m - 2 , t
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