182
Dynamics
of
the Vascular System
critical to the accuracy
of
the recorded signals. These are discussed
in
Chapter
8.
6.3
Modeling and Collapsible Vessel Properties
6.3.1
Steady
Flow
in
Collapsible
Tubes
That veins collapse is commonplace.
The collapsibility is easily
demonstrated by applying even a slight pressure over superficial veins,
one can observe both venous pooling (bulging vein) and flow ceasation
due to occlusion.
Transmural pressure is the difference between
intravascular and extravascular or ambient pressure:
4
=e-e
(6.3.1)
We have seen that the veins have low pulse pressure oscillating with P,
close to zero.
The collapsible tube with flow is connected by rigid connections to
two
reservoirs. The tube is enclosed in a chamber, containing, say water
with an adjustable external pressure P,.
Such a resistor
is
first used by
Starling in his heart-lung machine (Knowlton and Starling, 1912) in
1912. The flow in this tube is governed by the pressure differences, PI-
P, and P2-Pe. The amount
of
flow is dependent on the cross-section of
the tube, and hence the transmural pressure.
If
the inlet pressure
PI
and
the external pressure
P,
were fixed, i.e. a constant PI-P,, then the flow
velocity increases with decreasing P2-P,.
But with this, the cross-
sectional area decreases, hence the volume flow which is the product of
velocity and cross-sectional area first increases, then becomes limited.
This flow-limiting phenomenon is well illustrated by Holt in 194
1.
Assume laminar flow at a large Reynolds number
so
that Bernoulli’s
equation holds:
12
Po
=
P+yP
(6.3.2)
