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a Chapter 2 Physical Principles of Doppler Ultrasonography 11
T
Amplitude
Time
Fig. 2.4. Period of sound. The duration of one wavelength
of sound is its period. Horizontal axis represents the time
and the vertical axis the magnitude of pressure wave deflections
around the baseline
±
Fig. 2.7. Pressure amplitude of a sound wave. Horizontal
axis depicts distance or time. Vertical axis represents variations
in the acoustic pressure. The plus and minus signs indicate
the positive and negative fluctuations of the pressure,
respectively. P, the amplitude that is the maximum
change in the pressure above or below the baseline value
represented by the horizontal line
Fig. 2.5. Concept of pulse repetition frequency (PRF). The
illustration shows a PRF of 1 KHz (1,000 pulses per second)
sound wave at a location is the rate of flow of energy
per unit of cross-sectional area of the beam at that
location. It is therefore power divided by beam crosssectional
area. Pressure amplitude is measured using
a device called a hydrophone. Intensity (I) is derived
from the pressure amplitude (p) as they are directly
related:
I ˆ p 2 =c
Fig. 2.6. Pulse length, which is the distance in space occupied
by one ultrasound pulse. Horizontal axis represents
the distance and the vertical axis the pressure amplitude
For pulsed Doppler applications, the PFR limits the
highest velocity that can be measured without creating
the artifact known as aliasing. This subject is
further discussed in Chap. 3.
Amplitude, Power, Intensity
The maximum variation in pressure generated in a
medium by a propagating sound wave is called pressure
amplitude (Fig. 2.7). Pressure amplitude is directly
related to the amount of sound energy emanating
from a vibratory source. It is therefore a measure
of the strength of sound radiation. The rate of flow of
ultrasonic energy through the cross-sectional area of
the beam is expressed as its power. The intensity of a
Intensity is expressed by several descriptor parameters
based on its peak and average values.
For continuous-wave Doppler ultrasound, intensity
is measured as the spatial peak value (I sp ) and the
spatial average value (I sa ). The former is measured
usually at the focal point of the beam, the latter at
the cross-sectional location of the beam. For pulsed
Doppler ultrasound it is necessary to consider both
the spatial and the temporal intensity values. Both
peak and average values are measured in various
combinations, as follows: spatial peak temporal peak
(I sptp ), spatial peak temporal average (I spta ), spatial
average temporal peak (I satp ), and spatial average
temporal average (I sata ). Additional descriptors of
pulsed ultrasound intensity include the spatial peak
pulse average intensity (I sppa ), which is the intensity
at the spatial peak averaged over the pulse length.
These measures of sound energy of a transmitted
Doppler ultrasound beam are important for biosafety
considerations and are discussed in Chap. 6.
Ultrasound and Piezoelectric Effect
Audible sound frequency ranges from approximately
10 Hz to 20 KHz. Sound with a frequency of more
than 20 KHz is inaudible to the human ear and is