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Biomedical Signal and Image Processing
This can potentially cause the wave front to distort during propagation through the
tissue; however, the wave number is often assumed to be the same for all directions
to simplify the solution.
At this point, it is important to note that even though in the strict theoretical sense,
one can attempt to find the wave equation in all points of an inhomogeneous medium
such as biological tissue. If such a wave equation was available, one could have used
the equation to form very informative images of the biological system under study.
However, the trick is in the fact that, in order to generate the wave equation, one
needs to know the exact characteristics of all the points in the tissues under study.
In reality, if we knew the characteristic information about the structure of the tissue,
there was no need for imaging! All tomographic attempts described in this chapter
are indeed directed toward finding the acoustic features of the tissue. This means
that while knowing the general form of the wave equation might help in understanding the problem, the actual equation is never available, and therefore we need to
resort to tomographic methods to analyze the tissue.
Next, the physics of the main ultrasound characteristics that are used for medical
imaging applications, i.e., attenuation and reflection, is further described.
16.4.3 ATTENUATION
Once the sound waves leave the ultrasound probe, they travel through the adjoining
tissue in which the waves will be attenuated. Since the ultrasound transducer can
only detect sound waves that ultimately reach the crystal, the absorption of sound in
the body tissue decreases the intensity of sound waves that can be detected. Hence,
the deeper the region of interest is located, the more difficult the detection process
becomes. Absorption of sound waves is due to the conversion of the ultrasound
energy into motion, which translates into heat energy. This is due to the friction of
cells and structures sliding over each other, and the friction of this movement transforms the mechanical energy also into heat energy.
Attenuation in the pressure signal, dP, is directly proportional to the incident
pressure, P, the distance over which the absorption takes place, dz, and the tissuespecific attenuation factor, α. In other words,
dP = aPdz
(16.7)
Solving this equation for P in the case of a plane wave, we have
( )
− z
P z = P 0 exp[ a ]
(16.8)
Equation 16.8 is known as the Beer–Lambert–Bouguer law of attenuation. In this
equation, the attenuation coefficient α (which is often expressed in neper/m or
neper/cm) varies from one tissue to another, and P 0 is the pressure at z = 0.
Table 16.1 lists a variety of acoustic properties for some selected tissues. These
properties include the speed of propagation, the acoustic impedance, and the attenuation coefficient.
Biomedical Signal and Image Processing
This can potentially cause the wave front to distort during propagation through the
tissue; however, the wave number is often assumed to be the same for all directions
to simplify the solution.
At this point, it is important to note that even though in the strict theoretical sense,
one can attempt to find the wave equation in all points of an inhomogeneous medium
such as biological tissue. If such a wave equation was available, one could have used
the equation to form very informative images of the biological system under study.
However, the trick is in the fact that, in order to generate the wave equation, one
needs to know the exact characteristics of all the points in the tissues under study.
In reality, if we knew the characteristic information about the structure of the tissue,
there was no need for imaging! All tomographic attempts described in this chapter
are indeed directed toward finding the acoustic features of the tissue. This means
that while knowing the general form of the wave equation might help in understanding the problem, the actual equation is never available, and therefore we need to
resort to tomographic methods to analyze the tissue.
Next, the physics of the main ultrasound characteristics that are used for medical
imaging applications, i.e., attenuation and reflection, is further described.
16.4.3 ATTENUATION
Once the sound waves leave the ultrasound probe, they travel through the adjoining
tissue in which the waves will be attenuated. Since the ultrasound transducer can
only detect sound waves that ultimately reach the crystal, the absorption of sound in
the body tissue decreases the intensity of sound waves that can be detected. Hence,
the deeper the region of interest is located, the more difficult the detection process
becomes. Absorption of sound waves is due to the conversion of the ultrasound
energy into motion, which translates into heat energy. This is due to the friction of
cells and structures sliding over each other, and the friction of this movement transforms the mechanical energy also into heat energy.
Attenuation in the pressure signal, dP, is directly proportional to the incident
pressure, P, the distance over which the absorption takes place, dz, and the tissuespecific attenuation factor, α. In other words,
dP = aPdz
(16.7)
Solving this equation for P in the case of a plane wave, we have
( )
− z
P z = P 0 exp[ a ]
(16.8)
Equation 16.8 is known as the Beer–Lambert–Bouguer law of attenuation. In this
equation, the attenuation coefficient α (which is often expressed in neper/m or
neper/cm) varies from one tissue to another, and P 0 is the pressure at z = 0.
Table 16.1 lists a variety of acoustic properties for some selected tissues. These
properties include the speed of propagation, the acoustic impedance, and the attenuation coefficient.