6
Dynamics
of
the Vascular System
Modern understanding of pressure-flow relationships came with the
inventions
of
fluid-filled
catheter-manometer
system
and
the
electromagnetic flowmeter. The simultaneous measurements of blood
pressure and flow have led to considerable advancement of the studies of
blood flow or hemodynamics. The catheter was introduced in man by
Forssmann
in
1929, and later advanced for catheterization
of
right heart
for pressure measurement by Cournand and Range in 1941 (Li et al.,
1976). Cournand and Forssmann shared the Nobel prize for medicine in
1956 for the invention leading to the advancement of modern day
catheterization for visualization of blood pressure waveforms in various
anatomical sites throughout the circulation.
The electromagnetic
flowmeter was introduced by Kolin in 1936. But ultrasonic transit-time
and Doppler flow velocity probes have taken center stage in modern
research and routine clinical measurements.
In an attempt to understand the function of the arterial system as a
whole, Hales
(1
733) concluded that in order for the arteries to accept the
large amount of blood ejected, or the stroke volume, the arteries must
behave like a temporary storage reservoir. Since the size of the aorta is
considerably smaller than that of the ventricle, the receiving aorta must
be elastic in order to perform the function as
a
reservoir. This
interpretation of the reservoir function of arteries became known later as
the windkessel theory which was vigorously pursued
a
century later by a
German physician Frank towards the end
of
the 19'h century. The
emphasis on the storage properties of the arteries modeled by Frank as a
single elastic tube implied that all pressure fluctuations in the arterial tree
should occur synchronously.
In
other words, the blood pressure pulse
should propagate with infinite velocity. The peripheral vessels, on the
other hand, are assumed rigid as stiff tubes. This gives rise to the lumped
compliance-resistance model of the arterial circulation. This windkessel
model lacks the description of the propagation characteristics
of
the
pressure pulse.
Blood pressure pulse propagation with finite wave velocity in a blood
vessel was considered over
two
centuries ago by Euler in
1775.
He
attempted to develop a formula for its calculation. The well-known
physicist Young in 1816, and also the Weber brothers in 1866,
apparently
solved for the propagation velocity in an elastic tube
