Biomedical Engineering Reference
In-Depth Information
laminar and turbulent flow. First, laminar flow facilitates the acceleration of
the blood flow to reach peak flow velocity. Later, the transition from laminar
flow to turbulent flow appears as early phase in the deceleration phase soon
after the peak velocity. In such situations, the transition flow depends upon the
curvature and radius of a vessel. This flow generates forces parallel to the vessel
wall termed as 'shear force'. For example, shear forces are common at the points
of atherosclerotic plaque in the arterial wall. The shear force can be represented
as:
s
=
ηδv/δ
r
where
η
is coefficient of viscosity and
δv/δ
r
is the radial variation
of velocity in the vessel. In the vessel, the shear force is greater close to the
vessel wall. The reason for this is that the radial spatial variation in velocity is
largest there.
In humans, laminar flow is common in veins and capillaries. This flow varies
due to respiratory motion and arterial contractions. The flow velocity in the veins
varies on the order of 10-20 cm/sec. In the arteries, blood flow is pulsatile with
Reynolds number
>
7000. In blood vessels, turbulence is rarely observed. How-
ever, turbulence may be seen in large arteries and systolic motion in the heart.
Typical flow velocities in large arteries vary from zero in the end-diastolic phase
of cardiac cycle to 50-100 cm/sec in the mid-systole. Larger spatial variations
in flow velocity are also observed at the vessel walls near vascular bifurcation
sites at which atherosclerotic plaque appears. In arteries, blood flow in cardiac
chambers is pulsatile because cardiac chambers are large open spaces. In these
chambers,
R
0
is large and inflow and outflow of blood result in vertex formation
and also in large spatial velocity variations. This flow characteristic is known as
'cine ventriculography'. Vertex formation is related to rapid inflow and outflow
of blood in the cardiac chambers. In the diastolic phase, little flow and small
volume changes are observed as short-lived phase. This short-lived phase of
cardiac cycle depends on the heart rate. These are common in patients with low
heart rates. In these patients blood is approximately stagnant during late dias-
tole, while systolic events are less affected by heart rate. At heartbeats above
70 beats per minute, patients show appearance of vortices and spatial variation
in flow velocity in cardiac chamber. These spatial variations affect systole and
diastole. On the other hand, microvascular circulation occurs at flow velocities
0.5-1.0 cm/sec and is pulsatile in the arterioles up to the precapillary sphincter.
It is continuous in the capillaries and venules distal to it. Vessel walls experience
high shear forces. Microcirculation vessels do form a network of vessels with
changing orientation inside the vessel.
