46
Dynamics
of the
Vascular
System
diameter of the blood vessel is small as compared to the pulse
propagation wavelength.
This is justified during the large part
of
the
cardiac cycle. At peak flow rates in early systole however, the ratio of
vlc is large (but not exceeding
l),
turbulence may ensue to produce
nonlinear effects.
Reynolds number from eqn. (3.1.12) is seen to vary with body length
dimensions, or the diameter
of
the aorta. One question immediately
arises is that the resulting Reynolds numbers calculated for large
mammals, such as the horse, show that turbulence may occur for a large
portion
of
the systole in the aorta. But this may not necessarily be the
case. It has been well documented that turbulence may not exist even for
Reynolds number greatly exceeding the critical value of
2,000.
It is only
established that for Reynolds number under
2,000,
turbulence does not
normally occur.
Again, this value was established under steady flow
conditions in rigid tubes.
The
arterial blood flow
exhibits
pulsatile
characteristics
and
peripheral outflow
occurs mostly in diastole.
In systole during
ventricular ejection, the aorta distends as a reservoir to accommodate the
flow as described by the classic windkessel model of the arterial system.
In concert with the pulsation, this compliance of the aorta acts to protect
the peripheral vascular beds from sudden surges in pressure and flow.
The compliance, defined as the ratio of change in volume due to a
change in pressure,
C
=
dV1dP
(3.1.13)
is proportional to body weight.
A
larger volume change occurs in
the aorta
of
a larger mammal and the longer effective length of the
aorta and a much slower heart rate, all help to reduce the tendency
of turbulence to reside in too large
a
portion
of
systole.
3.1.4
Elastic and Viscoelastic Properties
of
Blood Vessels
Many investigators have examined elastic properties of arteries. It is found
that the stress-strain or length-tension relationship is nonlinear and thus
does not obey Hooke's law. Arterial elasticity increases with extension and
