94
Dynamics of the Vascular System
increased elastic moduli, and accounts for the dispersion
of
wave
velocity.
Finally, the wall and fluid viscosities attenuate the pulse wave. The
extent of attenuation, or the degree of damping, is greater at higher
frequencies.
For instance, the pulse at the femoral artery no longer
exhibits the characteristic high frequency features of the aortic pulse.
a
smooth waveform is seen. The pulse reaching the arterioles is
normally
so
damped that its waveform appears sinusoidal.
In summary, pressure and flow pulses are modified as they travel
away from the heart due to
(1)
wave reflections,
(2)
geometric
nonuniformity,
(3)
elastic nonuniformity, and (4) damping.
4.2.2
Vascular
Impedance
to
Blood
Flow
The impedance of the total
systemic vascular tree, or the input
impedance to the arterial system, is defined as the complex ratio by
harmonic of pressure to flow. This
is
so
defined when the pressure and
flow waveforms are measured at the entrance to the arterial system,
namely,
at
the root or the aorta or ascending aorta. Impedance can also
be measured at different parts of the circulation. For instances, when
pressure and flow are measured at the femoral artery, then the vascular
impedance
so
obtained represents that of the impedance of the femoral
arterial vascular bed.
Vascular impedance has both a magnitude and a phase for each
harmonic. Since pressure and flow are generally not in phase, the
impedance possesses a phase angle within
90".
This is attributed to the
time delayed arrival between the pressure pulse and the flow pulse.
When the particular pressure harmonic leads the flow harmonic, then the
phase angle between them is positive.
Conversely, when the pressure
harmonic lags behind the corresponding flow harmonic, then the phase is
negative. Phase difference in the frequency domain, therefore, refers to
time delay in the time domain.
The harmonic contents
of
pressure and flow waveforms can be
obtained through Fourier analysis, as shown in Chapter
3.
Pulsatile
blood pressure waveform can be considered an oscillatory part with
sinusoidal components oscillating at different harmonic frequencies, no,