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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5814_Библиотеки_им_академика_М_И_Перельмана
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251Chapter eleven: Methods for measuring speed, attenuation, absorption
00
xx
yield the attenuation coefcient if beam diffraction loss can be appropriately compensated. The advantage of the xed path method over the variable path method is that there is no need to correct for beam diffraction.
The xed path method uses the same arrangement shown in Figure11.3
for measuring ultrasound attenuation in uids. Assuming that the attenuation coefcients in the reference liquid and the sample liquid are α0 and
α, and p0 and p1 are the pressures before and after the carriage movement,
it is straightforward to show that
α=α+1ln
0
xpp
1
(11.13)
0
This approach is not suitable for measurements on biological tissues.
A substitution method has been developed to overcome this problem and
is still the most reliable and most popular at present. An arrangement
similar to that shown in Figure 11.2 is used. Since the detecting device
must have a small aperture to minimize the phase cancellation effect or
aperture averaging effect (Busse and Miller, 1981), typically in attenuation measurements a hydrophone is preferred as a receiver. This arrangement is depicted in Figure11.6. The signals displayed on the oscilloscope
received by the hydrophone without and with a specimen in the path,
assuming that the scope has the capability of Fourier transform, as a function of frequency, are given by
−α
x
−α −α−α
()2
Oscilloscope
0
(11.14)
m
(11.15)
=
() ()
Vf Rfe
at
=
() ()
Vf Rfee T
bt
x
Source
Transducer
Tissue
x
m
Amplifier
Hydrophone
Figure 11.6 Experimental block diagram for in vitro ultrasound attenuation
measurements.
252 Diagnostic ultrasound: imaging and blood ow measurements
α−
V
eT
()
V
Te
t
1st Phase
where Rt is the transfer function of the experimental system, including
the electronic and ultrasonic components, T is the acoustic transmission
coefcient at the tissue-water interface, and α0 and α are the attenuation
coefcients in the reference liquid and the sample. Dividing Equation
(11.14) by Equation (11.15),
a
=
V
b
x
α−
() 2
0
m
(11.16)
Since the transmission coefcient between a liquid and a soft tissue
approaches 1, Equation (11.16) can be simplied to
a
=
V
b
x
α−α
0
m
e
(11.17)
Equation (11.17) shows that the attenuation coefcient of the sample
can be determined from a measurement of tissue specimen thickness xm
and the ratio of the detected signals if the attenuation coefcient of the
reference liquid is known. The advantage of this method is that there is
no need to know the experimental system transfer function Rt( f ). Unlike
velocity measurements, the accuracy of thickness measurement is not as
critical a factor in attenuation measurements. Specimen thickness, xm, can
be measured manually or with time-of-ight measurements.
11.2.1.2 Transient thermoelectric method
As was mentioned in Chapter 2, ultrasonic attenuation in tissues consists
of two terms, absorption and scattering. Since in the medical ultrasound
range, from 2.5 to 15 MHz, scattering loss is minimal, the transient thermoelectric method (Schwan, 1969; Parker, 1983) that measures absorption
is also useful for measuring attenuation. In this method, a thermocouple
is embedded in the volume of tissue of interest exposed by a rectangular acoustic pulse of known intensity; the temperature rise caused by the
acoustic pulse measured by the thermocouple is shown in Figure11.7. If
∂T/∂t
mperature, T
nd
2
Phase
t
0
Time,
Figure 11.7 Temperature increase measured by a thermocouple after exposure to
a pulse of ultrasound in a tissue.
253Chapter eleven: Methods for measuring speed, attenuation, absorption
()
0
T
t
Skin Surface
Transducer
ermo
the diameter of the thermocouple wire is sufciently small, the approximately linear rise in temperature in the second phase is related to the
absorption coefcient ~α by the following equation:
CJ
∂
p
α=
ITt
(11.18)
∂2
t
0
where Cp, J, and I are, respectively, the specic heat at constant pressure
of the tissue, the mechanical-heat conversion factor (4.18 joule/cal), and
acoustic intensity.
∂
denotes the slope of the temperature rise as a
t
∂
function of time at time = t0. The rst phase of temperature rise cannot
be used because of the heat exchange occurring between the tissue and
the wire. For this method to be valid, the wire diameter has to be small
(<75 μm), the half-power beam width has to be greater than 3 mm, to
minimize the heat loss by conduction to the surrounding regions, and
the temperature rise < 1°. These guidelines restrict the application of the
technique to high-frequency and tightly focused beams. A pulse decay
technique where the viscous heating artifact is minimized has been
developed to overcome these problems (Parker, 1983). In this method,
a Gaussian intensity prole is assumed for the ultrasound beam (see
Figure2.8) and the beam is scanned across an embedded thermocouple
of 51 μm diameter thermojunction, as shown in Figure11.8. The intensity prole is assumed to be
2
x
x
0
=−()
Coupling Medium
ermocouple
couple Wire
Figure 11.8 A transducer is scanned across a thermocouple embedded in a tissue.
Ix Ie
z
(11.19)
m
Tissues
x
254 Diagnostic ultrasound: imaging and blood ow measurements
2Tt
T
where x0 is a measure of the beam width. After an exposure of duration
Δt and assuming no signicant heat conduction during the duration, the
temperature distribution along x should be
2
x
x
=−()
Tx Te
0
(11.20)
m
where
α
CJ
p
I
(11.21)
m
=
m
from Equation (11.18). The temperature decay at a point x at a function of
time following exposure has been found theoretically (Parker, 1983) to be
2
x
(,)
kt x
4/ 1
d
T
=
Txt
−
m
0
kt x
4
+
0
d
e
+
(11.22)
At x = 0 or on the beam axis,
=
(0,)
Tt
m
kt x
4/ 1
+
d
0
(11.23)
where kd is the thermal diffusitivity of the medium surrounding the heat
sensor and equals 1.5 × 10–3 cm2/s for soft tissues. Using Equation (11.23),
Tm can be estimated from the time history of the temperature decay on the
axis given x0 estimated from Equation (11.19) following a measurement of
the beam prole. Here it is assumed that the beam prole measured in
a water bath is similar to that in tissues and not affected by attenuation.
Then from Equation (11.21) the absorption coefcient β can be estimated
since Im, Δt, Cp, and J are all known. The advantage of this method over
the transient thermoelectric method for highly focused beam was clearly
demonstrated by Parker (1983).
11.2.2 In vivo methods
In vitro methods for attenuation measurements are difcult to be imple-
mented in vivo. A few approaches have been studied for in vivo esti-
mation of attenuation and can be classied into two categories: loss of
amplitude methods and frequency shift methods (Greenleaf, 1986). The
central idea for both is treating the tissue as a uniform distribution of
255Chapter eleven: Methods for measuring speed, attenuation, absorption
Depth of Penetration
Echo Amplitude
-αz
p0e
z
Figure 11.9 The echo amplitude scattered from a tissue decreases as a function of
depth of penetration. The solid line denotes the tted curve.
scatterers. If the difference in transducer beam characteristics at different depths in a tissue can be adequately compensated, the difference in
echo amplitude from tissues at different depths of the same volume is
related to the attenuation coefcient of the tissue and the separation in
depth.
11.2.2.1 Loss of amplitude method
This method is illustrated in Figure11.9, where the amplitude drop as a
function of depth of penetration of the ultrasound beam or time of ight
of the pulse is shown. If beam diffraction can be adequately compensated,
the drop should be exponential and a curve tting algorithm may be used
to estimate the attenuation coefcient.
11.2.2.2 Frequency shift method
The frequency shift method can be accomplished either in the frequency
domain by measuring the spectral difference or in the time domain by
estimating the zero-crossing of the echo waveform, which was discussed
in Chapter 5. This method is illustrated in Figure 11.10. Two regions, A
and B, at different depths, of an A-line echo waveform are windowed for
Fourier analysis, shown in Figure11.10 (a) and (b). Various time window
functions, e.g., Hamming, Blackman, and Henning windows, may be
used to minimize spectral distortion. The two spectra are then divided
to yield the slope of the attenuation curve shown in Figure 11.10(c) if
beam diffraction can be adequately compensated. In logarithmic scale,
the difference in the spectra yields the attenuation coefcient as a function of frequency. This process has to be repeated many times before any
256 Diagnostic ultrasound: imaging and blood ow measurements
(a)
Echo Amplitude
Magnitude
on B
Log Magnitude
(c)
B
A
Depth of Penetration
Spectrum of Region A
Spectrum of Regi
Frequency
(b)
Difference of spectra
Frequency
z
Figure 11.10 (a) The scattered echoes from two regions of a tissue, A and B, can
be windowed for spectral or zero-crossing analysis. (b) Spectra of echoes from
regions A and B. (c) The difference of the two spectra in log scale can be tted with
a line to estimate the attenuation coefcient.
257Chapter eleven: Methods for measuring speed, attenuation, absorption
2( )
as
meaningful results can be obtained because biological tissues are far from
being homogeneous.
The shift in center frequency of the transmitted pulse can also be
estimated from determining the zero-crossing of the echo waveform.
Attenuation coefcients of normal liver and fatty liver with values
from 0.45 to 0.5 dB/cm-MHz and from 0.6 to 0.8 dB/cm-MHz, respectively, have been reported from in vivo measurements on humans with
these methods.
11.3 Scattering
The measurement of the scattering properties of tissues is of paramount
importance because an ultrasonic image is formed from both specularly
reected echoes from tissue boundaries and diffusely scattered echoes
from tissue parenchyma.
11.3.1 In vitro methods
The scattering properties of a medium can only be measured under two
extreme cases: scatterer size >> wavelength and scatterer size << wavelength. As was discussed in Chapter 2, for a distribution of scatterers, only
if the scatterer concentration n is very small is the intensity attenuation
coefcient given by
α= σ+σ
A measurement of the attenuation coefcient would yield σs, assuming σs >> σa. This condition is satised only for large scatterers whose size
is >> wavelength. Therefore, only under the case where the scatter concentration is extremely small and the scatterer size is >> wavelength can
the scattering cross section be obtained from measuring the attenuation
coefcient of the medium. Several methods, however, have been developed to measure the scattering properties of a medium for a distribution
of small scatterers whose size is << wavelength (Shung and Thieme, 1993).
The simplest is the narrowband substitution method, which was developed by Sigelmann and Reid (1973).
Suppose that a volume of tissue is insonied by an ultrasound beam as
illustrated in Figure11.11. Both the transducer and the tissue are immersed
in saline solution in a water tank. The transducer is located a distance of
R from the tissue and saline interface. Saline is preferred over water for
a tissue sample to prevent permeation of water into the tissue. Here it
is assumed further that R is >> transducer aperture and wavelength, so
n
(11.24)
258 Diagnostic ultrasound: imaging and blood ow measurements
22
00
P
Rz
()
22
00
Iz V
Rz
Tissue
Saline
V
z
R
0
Figure 11.11 Experimental block diagram for in vitro ultrasound backscattering
measurements.
that at z > R the transducer can be treated as a point source. Under these
conditions, the intensity of ultrasound beam at R + z0 is
0
−α −α
=
()
Iz
Rz
()
e
2
+
0
(11.25)
where P0 denotes the total power emitted by the transducer, the term
P0/(R + z0)2 is the spherical spreading of the energy emitted by a point
source, α0 is the attenuation coefcient in saline, and α is the attenuation
coefcient in the tissue. If the transmitted ultrasound is a series of bursts
at a frequency of f with a very narrow bandwidth, the intensity of the scattered wave from a region of tissue can be selected by time gating, which
is illustrated in Figure4.34 for measurement.
η
−α −α
=
(0)
I
s
()
Rz
e
2
+
0
(11.26)
where V is the scattering volume, bounded by the beam width at R + z0
and duration of the gate τ, = Scτ/2, c is the sound velocity in the tissue,
S is the beam cross section at z0, and η is the backscattering coefcient
dened in Chapter 2. It should be noted that η = nσb, where σb is the backscattering cross section for very small n. However, for biological tissues,
as was discussed in Chapter 2, σb is typically so small that it is impossible
to measure. In order to alleviate this problem, the backscattering coefcient, which represents the intensity scattered into one solid angle in
the backward direction per unit incident intensity with a unit of 1/cm-sr,
is used. For this denition to be valid, the scattering from one unit of
volume of scatterers must be so weak that there is no multiple scattering.
259Chapter eleven: Methods for measuring speed, attenuation, absorption
2
44
00
AS cP
R
Rz
Reflecting Surface
T
ceiver
Otherwise, Equation (11.26) is not valid. Here it is assumed that individual
scattering volumes are independent so as to allow the use of the product ηV to represent the total scattered intensity from a volume of V. The
denition of scattering coefcient may be extended to dense distributions
of smaller scatterers (Shung and Thieme, 1993), where scatterers are correlated. Biological tissues may be approximated as dense distributions of
small scatterers because in the medical ultrasound frequency range the
wavelength is typically much greater than the sizes of tissue components.
The power received by the transducer of aperture size A can be
obtained by substituting Equation (11.25) into Equation (11.26), assuming
R >> z0,
ητ
=
P
s
4
0
−α −α
e
(11.27)
The backscattering coefcient can be estimated from Equation (11.27)
by measuring S, P0, α, and α0 since all other parameters are known. The
cross section of the beam S at the site of measurement may be measured
precisely with a hydrophone or simply approximated by its –3 dB contour. The transmitted acoustic power P0 is difcult to estimate because
the transfer functions of the electronic and acoustic systems must be
known. For practical purposes, the need for this knowledge is eliminated
by performing an additional procedure that measures the reected power
from an ideal at reector at the position where scattering measurement
is made. This is made possible by considering Figure11.12, which shows
a at reector is placed at a distance of R from the transducer, assuming
R + z0 ~ R. For a nonfocused transducer, it is possible to make the approxi-
mation that in the far eld of the transducer, the transducer can be treated
ransducer
Imaginary Re
R R
Figure 11.12 Diagram illustrating the mirror theory when a wave is impinging
on a at reecting surface.
260 Diagnostic ultrasound: imaging and blood ow measurements
4
AP
R
2
PPSc
2
24
Pe
as a point source located at the center of the transducer aperture. Applying
the mirror theory, the transducer as a receiver would appear as if it were
located at a distance 2R from the source. The power received from the
reector by the transducer of aperture size A is then
Γ
0
R
−α
4
=
P
r
0
e
2
(11.28)
where Γ is the reectivity of the reector and approaches 1. Assuming
Γ ~ 1 and dividing Equation (11.27) by Equation (11.28),
s
r
ητ
z
−α
4
0
=
e
2
R
(11.29)
Rearranging this equation, it can be found that
RScP
s
z
α
4
0
η=
2
e
(11.30)
P
τ
r
Equation (11.30) can be converted into dB scale by taking the log of both
sides of the equation and multiplying by 10, that is,
−α
z
η= −τ+−−
10log10log 10log(2)(10log 10 log)10log( )
RScP
sr
0
(11.31)
From this equation, it is easily seen that the backscattering coefcient, η,
can be calculated by merely measuring the difference in the scattering
power and reected power in dB if all other terms are known.
This method has been used to measure the scattering properties of
a number of tissues (Shung and Theiem, 1993). Results for several tissues
are given in Table2.1. As indicated earlier, the mirror theory is invoked to
calculate the reected power from a at reector. This approach is valid
only for a nonfocused transducer. When a focused transducer is used,
error will result (Yuan and Shung, 1986). The reason for this is illustrated
in Figure11.13, which shows that for a focused transducer, the imaginary
point source is not located at R from the reector. Not recognizing this
crucial assumption in utilizing the substitution method has resulted in a
large discrepancy in data reported in the literature for the backscattering
coefcient of tissues.
A wideband pulse may be transmitted instead of a burst consisting of several cycles in scattering measurements. Following Fourier
transform, the backscattering coefcient over a frequency band can
be obtained by sacricing the signal-to-noise ratio. A more accurate
substitution method, that does not involve any approximation and is
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