56
Dynamics
of
the
Vascular System
The trigonometric
representations of the above series give the
following:
N
f(t)
=
c0
+
Ccn
COS(~U,~
-
en)
(3.2.10)
n=l
where the harmonic magnitude and phase are represented
by
c,
=JW
and
I
bn
en
=
tar-
-
an
(3.2.1 1)
(3.2.12)
In terms of pulsatile pressure waveforms, the Fourier series can be
written as:
Thus, Fourier series representation of a periodic pressure waveform is the
summation of
a
mean
pressure
component
and
its
sinusoidal or
cosinusoidal harmonic components.
A
similar Fourier series representation can be written for the flow
waveform:
Figure 3.2.2 gives an example of the summation of Fourier components
that provides the re-synthesis
of
the aortic pressure waveform. For the
aortic pressure waveform, 10 harmonics are sufficient to accurately
reconstruct the waveform.
