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a Chapter 3 Spectral Doppler: Basic Principles and Instrumentation 23
duces faster temporal changes in the blood flow speed
and in the power spectral density. A shorter temporal
length of the sample ensures spectral nonvariance.
However, the shorter the duration of the Doppler data
segment, the worse is the frequency resolution. A
signal segment of 5 ms gives a resolution of only
200 Hz, whereas increasing the duration to 20 ms improves
the resolution to 50 Hz. Prolonging the duration,
however, introduces uncertainty regarding the
constancy of the power spectrum density. Under this
circumstance, FFT processing does not function reliably,
as it is based implicitly on the assumption of
spectral constancy for the duration of the sample.
Intrinsic Spectral Broadening
When a single scatterer moves at a constant speed
across an ultrasound beam of limited width, the resultant
Doppler spectrum has a range of frequencies
instead of a single frequency. Because the phenomenon
of broadening the Doppler spectrum is caused
by the inherent properties of the measurement system,
it is known as intrinsic spectral broadening
(also transit time broadening). Spectral broadening
mostly encompasses the following phenomena: (1)
transit time broadening caused by the inhomogeneity
of the ultrasound field causing amplitude fluctuations
of the returning echo; this produces a range of frequencies
distributed around the centroid Doppler
shift frequency; (2) geometric broadening which results
from the changing angles of insonation incurred
by the scatterer as it moves across the beam; (3) nonstationery
broadening caused by the changes in velocity
during the sampling time; and (4) velocity gradient
broadening originating from the changes in velocity
within the sampling volume [8]. The problem of
spectral broadening is compounded by the contribution
from multiple moving RBCs traversing the ultrasound
beam. The RBCs do not act as discrete scatterers
but as volumes of randomly distributed scatterers.
The number of RBCs in such a scattering volume
in an ultrasonic field varies continually and randomly
around a mean value, which causes swings in
the scattering power. The consequences are similar to
the spectral broadening of the Doppler signal observed
with a single moving scatterer.
Spectral broadening is affected by the beam width,
pulse length, and angle of insonation. Wider and
more homogeneous beams, longer pulses, and smaller
angles of insonation narrow the spectral spread. Obviously,
the situation is worse with the short-gate
pulsed Doppler ultrasound applications, where a scatterer
can traverse only a part of the beam of a transmitted
short pulse. The consequent transit time
broadening effect generates a significant degree of
ambiguity regarding the true distribution of velocity
Fig. 3.6. Amplitude-frequency spectrum from a circulation
with a parabolic flow velocity profile. Top: Ideal spectrum
with an even distribution of amplitudes (scattering power)
at various frequencies, indicating erythrocytes traveling at
various speeds. Bottom: Effect of spectral broadening on
the maximum frequency defintion of the same spectrum.
ISB intrinsic spectral broadening
in the sample volume. The main clinical significance
of spectral broadening is that it potentially compromises
the prercision of the maximum frequency shift
envelope (Fig. 3.6). The mean frequency definition,
however, is not affected, as the distribution of the frequencies
around the mean shift is symmetric.
Analog Fourier Spectral Analysis
Analog fourier spectral analysis allows fast spectral
processing of the Doppler signals utilizing analog
techniques as opposed to the digital approach of FFT.
One such implementation, known as Chirp Z analysis,
is also a discrete Fourier transform-based method
and requires less computing power and offers a wide
dynamic signal processing range.
Autoregression Analysis
Although Fourier-based methods dominate, alternative
approaches for Doppler spectral processing are
available. These methods are theoretically capable of
eliminating many of the inherent disadvantages of the
FFT method. Kay and Marple comprehensively described
the autoregressive approach for spectral analysis
[9]. Such procedures have been widely used for
spectral analysis of speech and other periodic phe-