Blood flow
Principle
Blood flow in arteries can be characterized by the combination of three
key phenomena:
·
internal laminar (or sometimes turbulent) flow, with
and without flow irregularities due to a stenosis, a curvature or a
bifurcation;
·
pulsatile flow, diminishing from aorta to capillaries.
·
compliant arterial wall boundaries;
Each of them has a dramatic effect on the flow pattern.
More Info
For aorta flow and geometry the entrance effect due to the aortic valve
(see Entrance effect and entrance
Length), characterized by the entry length, is at least
In the bend, there is strong asymmetry due to the centripetal forces at
the outer curvature. Branching causes also entry phenomena such as asymmetries
in the velocity patterns (see Flow in bifurcations). Also
complicated secondary flows perpendicular at the axial flow direction may occur,
and even flow separation, all of which are far more difficult to analyze than
simple steady-state fully developed Poiseuille flow. Secondary flows in
curvatures and bifurcations are characterized by a swirling, helical component
superimposed on the main streamwise velocity along the tube axis. In fact, all
the larger arteries of the circulatory system, including the epicardial
coronary vessel, are subject to entrance effects.
In large vessels the inertia character overwhelms the viscid character.
The inertance can be expressed as L = ρ∙l/A,
where ρ is the density, l the tube length and A the wetted tube
area.
Furthermore, flow in the larger arteries is, in general, not Poiseuille
flow due to the pulsatile character, especially in the aorta. In the ascending
aorta of large mammals viscous effects of the entrance region are confined to a
thin-walled boundary layer. The core is characterized as largely inviscid,
caused by the heavy pulsatile character. These factors, together with specific
density and viscosity are comprised in the Womersley number, which can be
considered as the pulsatile version of the Reynolds number. With high numbers
inertia dominates, yielding a rather well flat flow front. With low numbers
viscosity dominates, yielding parabolic-like flows, however skewed towards the
outer wall. An example for this is the flow in the left common coronary artery.
In other coronary arteries the Reynolds
numbers are much lower, the viscous effects are more dominant and flow is
laminar. The velocity profile in many regions will be more like a parabolic
Poiseuille flow, except that there will be skewing of this profile due to vessel
curvature and branching. Also, significant entrance effects may result in the
blunting of the velocity profiles.
Although there have been numerous fluid-dynamic studies of secondary
flow phenomena, instrumentation limitations have prevented in vivo
observations.
An additional complication introduced by the geometry of the arterial
system is flow separation from and reattachment to the wall, causing
recirculation zones. This phenomena in pulsatile flows is an extremely complex.
Literature
Author: N. Westerhof, Mark I.M. Noble, Nikos Stergiopulos. Snapshots of hemodynamics:
an aid for clinical research and graduate ducation, 2004, Springer Verlag.
http://mss02.isunet.edu/Students/Balint/bloodflow.html.