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a Chapter 2 Physical Principles of Doppler Ultrasonography 15
place when the size of the interface is smaller than
the incident sound wavelength. Such an interface is
known as a point target. In regard to Doppler shift,
the scatterer is significantly smaller than the wavelength
and is in motion. The Doppler-shifted ultrasound
reflecting from such a moving scatter propagates
in all directions (Fig. 2.13). Obviously, it also
reaches any receiving transducer at the source of
transmission. The process of scattered ultrasound returning
to the source-receiver is called backscattering.
It is well accepted that the primary sources of scattering
in blood are the circulating RBCs [10]. These
cells are so numerous that the contribution of the
other formed elements of blood, such as white blood
cells and platelets, to scattering ultrasound is inconsequential.
An RBC has a biconcave discoid shape with
a mean diameter of 7.2 lm and a mean thickness of
2.2 lm. In comparison, the wavelength of Doppler
ultrasound for diagnostic applications varies from
1540 lm to 154 lm, corresponding to 1±10 MHz
transducer frequency. As is apparent, the RBCs are
several magnitudes smaller than the wavelengths, so
they can be regarded as point targets. In reality, however,
circulating erythrocytes do not act as discrete
scatterers but as volumes of randomly distributed
point targets. The number of RBCs in such a scattering
volume fluctuates around a mean value and
causes fluctuations in the scattering power. Turbulent
blood flow increases fluctuations in the RBC concentration
and is therefore associated with increases in
the scattering power and consequently the power of
the Doppler shift signal [10]. In regard to whole
blood, it has been experimentally demonstrated that
the scattering power becomes maximum at a hematocrit
range of 25%±30% [10]. At higher hematocrit
values, the scattering behavior of blood becomes
more complex as the RBCs become too crowded and
can no longer be treated as randomly distributed
scatterers.
In addition to hematocrit, scattering is also affected
by the state of red cell aggregation. Spatial variations
in the flow field can result in changes in the
variance of red cell packing and backscattering cross
section which will influence the Doppler power at a
given frequency [11]. In this circumstance, the mean
Doppler frequency will not necessarily be proportional
to the mean flow through the sample volume
and may affect volumetric flow quantification and the
power mode display of color Doppler. Scattering is
also dependent on certain characteristics of the transmitted
ultrasound including the frequency and the
angle of insonation [12]. The phenomenon is a complex
subject and a comprehensive review is beyond
the scope of this chapter.
Magnitude of Doppler Shift
Relative velocities of the sound and the scatterers are
important determinants of the magnitude of the Doppler
frequency shift. In regard to blood flow, the
speed of RBCs is significantly less than the speed of
sound in a biologic medium. Consequently, the Doppler
shift is much smaller than the incident ultrasonic
frequency. Assuming a sound propagation speed of
1,540 m/s in soft tissues, the Doppler shift for a given
blood flow speed and the transducer frequency can
be calculated from the Doppler equation. This exercise
is illustrated in Table 2.2, which lists the Doppler
frequency shifts for most obstetric transducer frequencies
(2±7 MHz) at blood flow speeds of 25, 50,
and 75 cm/s. As is evident, the frequency shifts are
approximately 1/1,000 their corresponding transducer
frequencies. Furthermore, the Doppler shifted sound
Table 2.2. Doppler frequency shifts for various transducer
frequencies at three blood flow velocities and an insonation
angle of 08
Transducer
frequency (MHz)
Doppler shift at three flow
velocities (KHz)
Fig. 2.13. Phenomenon of scattering. d Scatter, k wavelength
of the incident beam. The large arrow shows the direction
of propagation of the incident ultrasound. The
smaller arrows radiating from d indicate the directions of
scattering. Note that scattering occurs when the wavelength
is much greater than the size of the reflector (kd)
at 25
cm/s
at 50
cm/s
at 75
cm/s
2 1.3 0.7 1.9
3 1.9 1.0 2.9
4 2.6 1.3 3.9
5 3.2 1.6 4.9
6 3.9 1.9 5.8
7 4.6 2.3 6.8