Introduction to Acoustics

λ1 = c1 / fus
θ1
λ2 = c2 / fus
λ1 / sin θ1 = λ2 / sin θ2
θ2
θ1
c1 / sin θ1 = c2 / sin θ2
Fig. 21.9 Refraction of ultrasound as it passes from one
material to another. Dark brown: incident compressional
wavefronts and wave vector incident at angle θ1. Light
brown: reflected compressional wavefronts and wave vector
reflecting at angle θ1. Gray: transmitted compressional
wave. The interfacial shear wave increases in intensity as
the ultrasound beam cross section coherently contributes
to the wave; attenuation of the shear wave causes a rapid
decrease in amplitude outside the beam
the interface. This capillary wave is subject to high attenuation.
Because tissue has an interface on every cell
boundary and every tissue boundary, this mechanism is
responsible for some of the conversion of incident ultrasound
power into heat as ultrasound propagates into
tissue. It is important to notice that the propagation speed
of the capillary wave is not the same as that of the component
of the compressional wave directed along the
interface, so the capillary wave is out of phase with the
ultrasound wave, contributing to the transfer of energy
into the capillary wave. Outside the ultrasound beam,
the capillary wave takes on its conventional wavelength
(cs/ f ), where f is the ultrasound frequency. The propagation
speed of the capillary wave (cs) is proportional
to the interfacial tension.
21.3.3 Diagnostic Ultrasound Propagation
in Tissue
Diagnostic ultrasound uses ultrasound frequencies of
1–30MHz. (MHz = cycles per µs). The speed of ultrasound
in most tissues is near 1.5mm/µs (1500 m/s).
There are some notable exceptions. In bone the speed is
between 3.5mm/µsand4mm/µs, and in air the speed is
0.3mm/µs. In cartilage the speed is 1.75 mm/µswhich
of course varies with composition. In fat the speed is
Medical Acoustics 21.3 Basic Physics of Ultrasound Propagation in Tissue 851
1.45 mm/µs(Table21.3). In muscle, the speed of ultrasound
varies by about 1.5%, depending on the angle of
propagation to fiber orientation.
Although most authors focus attention on ultrasound
frequency, ultrasound wavelength may be more convenient
for understanding the important issues. There are
three issues of importance:
• Ultrasound cannot resolve structures smaller than
the wavelength.
• Scattering and attenuation [21.42] both depend on
ultrasound wavelength and its relationship to the size
of the scatterers.
• The focusing properties of ultrasound beam patterns
and the formation of side-lobes depend on the ratio
between the wavelength and the width of the
transducer.
21.3.4 Amplitude of Ultrasound Echoes
Red blood cells (erythrocytes) are 0.007 mm in diameter
and about 0.001 mm thick. The largest cells in the
body, nerve axons, may be 1 m long, but their diameter is
about 0.001 mm. A liver cell is about 0.04 mm in diameter.
The smallest structures imaged by ultrasound in
clinical practice are layers less than 1 mm thick, such
as the media lining major arteries (the intima-media
thickness, IMT) [21.43], corneal layers (with 30 MHz
ultrasound) and skin surfaces. However, these structures
can only be observed in the range (depth) direction
because resolution is best in that direction. Lateral resolution
is dependent on the numeric aperture of the
ultrasound beam pattern and the relationship between
the object of interest and the focus as well as the ultrasound
wavelength. Only the ultrasound wavelength
affects depth resolution. The result is that ultrasound
images are anisotropic, with much better resolution in
the depth direction than in the lateral direction. The image
is delivered to the examiner as a pictorial map in
two dimensions. In our optical experience, resolution is
equal in the two dimensions. Therefore, we expect that,
if we can see detail in one dimension, we can also see the
detail in the other, even when we cannot. This gives the
impression that ultrasound has higher resolving power
in the lateral direction than it in fact does. This is particularly
important in measurements such as the IMT and
measuring the thickness of the atherosclerotic cap. Such
structures can only be visualized when the ultrasound
beam is oriented perpendicular to the structure.
To identify tissues and organs, the lateral dimensions
must by at least 10 wavelengths wide. This
Part F 21.3