100
Dynamics
of
the
Vascular
System
where p2 is the distal pressure, p1 is the proximal pressure,
y
is
the
propagation constant and z is along the longitudinal axis of the artery in
the direction of pulse propagation. The propagation constant obtained
under such circumstances, is known as the “true” propagation constant,
since it is not influenced by wave reflections. It is a complex variable,
thus has both magnitude and phase. It encompasses both the attenuation
coefficient,
a,
and the phase constant,
p:
y=a+jP
(4.3.2)
The attenuation coefficient dictates the amount of damping imposed on
the propagating pressure pulse due to both viscosity of the blood and
viscosity of the arterial walls.
The phase constant arises because of the finite pulse wave velocity, c.
In other words, the pressure pulse travels at finite velocity and therefore,
takes finite amount of time to go through each arterial segment.
Pulse
wave velocity at any given frequency is given by:
w
c=-
P
(4.3.3)
Thus, pulse wave velocity varies with frequency. This arises, because
different harmonic component travels at different velocity, known as
harmonic dispersion. Li et al.
(1981)
have shown that that true phase
velocity increases at low frequencies and reach
a
somewhat constant
value at high frequencies, usually beyond the third harmonic. Anliker et
al.
(1
968)
utilized high frequency artificial waves, essentially unaffected
by reflections, to obtain phase velocity and attenuation in the dog aorta.
4.3.2 Foot-to-Foot
Velocity
Pulse wave velocity has been popularly approximated by the so-called
“foot-to-foot” velocity.
Here, one simply estimates the pulse wave
velocity from the transit time delay (At)
of
the “onset” or the “foot”
between two pressure pulses measured at
two
different sites along an
artery or the pulse propagation
path.
This requires
again, the
