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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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118 Diagnostic ultrasound: imaging and blood ow measurements
N scatterers
Scanning direction
d pressure due to
process, as opposed to the delay-sum-detection-sampling process in
analog systems. As was discussed, a drawback of the digital beamformers is their cost, which increases with the number of array elements and
electronic channel counts. Currently digital beamformers in commercial
scanners sample the data at 60 to 80 MHz to 10 to 12 bits.
Mathematically the beamforming function can be summarized by the
following equation (Thomenius, 1996):
N
N
=−−+
()
et AAVt tt
i
ri tj
∑∑
j
==
11
ri tj
2()
rt
(4.3)
c
where e(t) is the summed echo waveform at the summing amplier, V(t)
is the transmitted waveform, N is the number of array elements, r(t) is the
focal distance at a particular time, Ari and A
for reception at channel i and transmission at channel j, and Δttj and Δt
are the weighting functions
tj
ri
are, respectively, the time delays applied during transmission and reception to elements j and i. For uniform excitation and receive weighting,
Atj = 1 and Ari = 1. For systems that use xed transmission focusing, this
equation is reduced to
N
=−+
()
et Vt t
∑
=
1
i
2()
rt
ri
(4.4)
c
4.1.3 Speckle
B-mode ultrasonic images exhibit a granular appearance, called speckle
pattern, which is caused by the constructive and destructive interferences
of the wavelets scattered by the tissue components as they arrive at the
transducer surface, as shown in Figure 4.16 (Wagner et al., 1983; Shung
and Thieme, 1993). The speckle pattern becomes more obvious at higher
frequencies. Figure4.17 shows an image of a layer of the human vocal cord
tissue obtained in vitro at 47 MHz. This speckle appearance very much
Detector
V
Figure 4.16 The signal detected at a transducer or element is the summation of all
scattered echoes generated by the scatterers in the ultrasound beam.
Signal detected at detector
n = N
V= AΣp
n
n = 1
Scattere
ejθn
nth scatterer
119Chapter four: Gray-scale ultrasonic imaging
2
r0
πσ
V
eV
4
Distance (mm)
Depth (mm)
9
5
6
7
8
456
78
Figure 4.17 An ultrasound image of a human vocal cord tissue at 47 MHz.
resembles the speckle pattern that results from laser scattering by a rough
surface. If the incident ultrasound beam is totally coherent like the laser
beam, the speckle carries no information about the microstructure of the
tissues. Fortunately, ultrasonic scanners use partially coherent incident
waves, i.e., pulses. Thus, the speckle patterns exhibited by tissues do contain useful information about the structures of the tissues, which can be
used clinically for tissue differentiation.
The resemblance between laser and ultrasound speckles has been
extensively analyzed (Wagner et al., 1983). The histogram of the video
signals or echo amplitude returned from tissues or the number of occurrences plotted as a function of the amplitude of these echoes V follows a
Rician distribution, shown in Figure4.18, similar to the distribution of the
magnitude of a phasor V = X + jY with a uniform phase, as illustrated in
Figure4.19(a) and (b). The symbol σ2 denotes the variance of the real component X or imaginary component Y. This means that the signal contains
random and ordered components. If there are no ordered components, the
histogram should follow a Rayleigh distribution given by
2
V
−
()
PV
V
=
2
σ
2
V
fo
2
≥
where V2 = X2 + Y2 and σ
2
, the variance of the magnitude of a phasor
V
V, = (2 – π/2)σ2 = 0.42σ2. Here σ2 = <X2> – <X>2. The symbol <X> denotes
the mean of X. It can be easily found that <V> = 1.91σV. This means the
signal-to-noise ratio for a Rayleigh distributed signal should be a constant at 1.91.
120 Diagnostic ultrasound: imaging and blood ow measurements
Rayleigh distribution
Random walk of a phasor
θ
Y
(a)
Probability density function
1/(2π
(b)
2
|V|
2
2σ
V
e
2
P(|V|)
Rayleigh
P(|V|) =
σV = variance of the magnitude of V
Rician
|V|/σ
|V|= (X
V
|V|
2πσ
V
2+Y2)1/2
Figure 4.18 Histograms or probability density function (PDF) of echo amplitude
from biological tissues follow a Rician distribution (dashed line), a special form of
which is the Rayleigh distribution (solid line). P(V) is the probability density at an
amplitude V and σ is the variance of V.
Figure 4.19 (a) Random walk problem of a phasor. (b) Uniformly distributed
probability density function for the phase of a phasor.
P1e
n=N
n=1
j
jθ
n
V=X+jY = |V|e
jθ
2
jθ
P2e
1
=AΣPne
X
)
0
2π
θ
121Chapter four: Gray-scale ultrasonic imaging
Tissue mimicking phantom
st
Speckles degrade spatial resolution
Cyst Ultrasound image of the cy
Figure 4.20 Speckles degrade spatial resolution.
The question about whether the speckle is a friend or foe has been
debated for many years. On one end, speckles provide diagnostic information for the clinicians to make a diagnosis. A clear example is that different organs exhibit different speckle or textural patterns, and tumors
frequently exhibit different speckle patterns from normal tissues. On the
other end, speckles degrade spatial resolution of the imaging system, as
illustrated in Figure4.20. Smaller objects may be obscured by the speckles. The most optimal resolution appears to smooth out somewhat the
speckle pattern while maintaining as much as possible the spatial resolution and the frame rate. Frame averaging via spatial compounding
or frequency compounding has been studied and implemented in commercial scanners. Spatial or frequency compounding describes a signal
processing scheme in which multiple frames are acquired either at different imaging angles or spatial positions or at different frequencies and
subsequently averaged to form one frame of image. Figure4.21 shows a
thyroid image obtained with spatial compounding in which the speckle
pattern is minimized.
Figure 4.21 Compounded ultrasound image of a thyroid. (Courtesy of Philips
Ultrasound.)
122 Diagnostic ultrasound: imaging and blood ow measurements
s
o
y domains
h
imaging system
4.1.4 Image quality
Image quality may be assessed merely by observing the image in a
highly subjective manner. The most objective way of assessing the image
quality of an ultrasound system is to use the receiving operator characteristics (ROC) curves (Shung et al., 1992), where the human involvement
is included. In order for the conclusion to be statistically meaningful,
many subjects need to be studied to obtain a measurement in which
both inter- and intraobserver variations are considered. Although this
approach is the most desirable, it is very complicated and expensive.
Simpler but quantitative measures such as spatial resolution and contrast resolution are often preferred. Spatial resolution can be assessed
by imaging standardized targets or phantoms consisting of point or
wire targets embedded in water or tissue-mimicking materials. Spatial
resolution measured in this way depends strongly upon the instrument
settings. A more convenient approach is to determine the point spread
function of the system.
4.1.4.1 Point spread function
The point spread function of an imaging system (Shung et al., 1992) is the
spatial point response, which is the inverse spatial Fourier transform of
the spatial transfer function of an imaging system if it can be treated as
a linear system, as shown in Figure4.22. Suppose that the point spread
function and the spatial transfer function of an imaging system can be
denoted as h(x) and H(ν), respectively, where x and ν are vectors represent-
ing spatial distances with a unit of cm and spatial frequencies with a unit
of cycles per cm. The input (the object to be imaged), S, and output (the
image acquired by the imaging system), O, are related by the following
equation in the spatial frequency domain:
O(ν) = H(ν)S(ν) (4.5)
s(x), S(υ) o(x), O(υ)
x,υ: Distance in 3D, spatial frequency in 3D (cycles/cm)
(x), S(υ) = inputs in the spatial and spatial frequency domains
(x), O(υ) = outputs in the spatial and spatial frequenc
(x), H(υ) = impulse response and transfer function of the
Figure 4.22 An imaging system is treated as a linear system.
Imaging system
h(x), H(υ)
123Chapter four: Gray-scale ultrasonic imaging
hd
om
gg
om
1
h(x
)
1
System II
System I
x
Figure 4.23 Point spread functions of two imaging systems represented by grayscale distributions as a function of one spatial dimension. System I has a narrow
point spread function, and therefore better spatial resolution than system II.
In the spatial domain their relationship is given by
∞
() ()*()()( )
==−χ χ
ohss
xxxxx
∫
−∞
(4.6)
where * denotes convolution.
The point spread function of an ultrasound system can be assessed
by imaging a small point target embedded in a homogeneous gel medium
or a point target suspended in a water bath and mapping the gray level
of the image. Figure4.23 shows the gray level of such an image as a function of one dimension of the spatial vector, x, represented by x1. System I,
which has a shaper point spread function, should have a better resolution
than system II. In ultrasonic imaging, the point spread function or lateral
resolution is typically assessed by a wire phantom, which consists of ne
wires arranged along a line embedded in a tissue-mimicking material,
shown in Figure4.24.
4.1.4.2 Contrast
Spatial resolutions of an imaging system are also affected by other
parameters, including noise and the contrast of the object to be imaged.
Figure4.25 shows a spherical void with scattering property, which may be
represented by ηo, the backscattering coefcient as discussed in Chapter 2,
surrounded by a background medium with backscattering coefcient ηm.
The object contrast may be dened as
The image contrast is dened as
γ=
o
γ=
i
η−η
(4.7)
η
0
−
(4.8)
g
0
124 Diagnostic ultrasound: imaging and blood ow measurements
Wire Phantom
Ultrasound Image
Linear Array
η = backscattering coefficient, g = gray level
Array
Azimuth
1.5 mm
Z
20 µm
Tungsten wires
0.65 mm0.65 mm
0.65 mm0.65 mm
1.5 mm
1.5 mm
1.5 mm
Figure 4.24 Spatial resolution of an ultrasonic imaging system is frequently
assessed with a wire phantom.
where go and gm denote the video signals or gray levels of the object and
background. A good imaging system would enhance or accentuate the
object contrast. The minimum contrast required for an imaging system to
detect the object of a specic size in the presence of image noise is called
contrast resolution.
These two parameters are interrelated. A system with superior resolution for high-contrast objects may not be capable of maintaining the same
resolution as the contrast is reduced.
Side lobes and grating lobes produced by a single-element transducer
or array, discussed in Chapter 3, are undesirable because they would cause
η
m
η
Phantom
Figure 4.25 Diagram denoting a spherical void phantom with a scattering property different from the surrounding medium and the corresponding image.
g
m
o
g
o
Image
125Chapter four: Gray-scale ultrasonic imaging
Phased array
Spherical void phantom
Image
Figure 4.26 Side lobes and grating lobes generated by arrays produce artifacts
and degrade contrast resolution.
artifacts and degrade the contrast resolution of an ultrasonic imaging system. This is illustrated in Figure4.26. There is a spherical void in the phantom. Instead of producing one image of the void, two more images are
generated by the grating lobes. In addition, the echoes resulting from the
side lobes or grating lobes will contribute to the echoes generated by the
main lobe or beam. For a void with no scatterers, these echoes produced
by the side or grating lobes will appear in the void, reducing the contrast
between the void and the surrounding medium.
4.1.4.3 Noises
There are two sources for noises in an ultrasonic imaging system: acoustic noises produced by the transducer/array and spurious acoustic interactions and electronic noises produced by the imaging system itself.
Acoustic noises may result from the cross talk among elements in an array
and between the active element(s) and the support structures, from spurious reections and refractions, and from grating and side lobes. The electronic noises are generated by the cross-coupling of cables and electronic
components and active devices themselves. Typically acoustic noises are
larger than electronic noises and more troublesome.
4.1.5 Phase aberration compensation
In commercial scanners, the sound velocity in tissues is assumed to be a
constant. This could cause image degradation if the sound velocity of a
region of tissues deviates substantially from this assumed value, as illustrated in Figure4.27. It is known that fat and skin have velocities that differ
appreciably from 1540 m/s. Transmitted wavefront is distorted as it propagates through skin, fat, and other tissues. Confounding this problem, the
arrival times of retuned echoes are distorted again. The predetermined
time delays calculated with the assumed velocity in the beamformer may
not be sufciently accurate to achieve proper focus. This issue is especially severe when imaging obese patients. Various methods have been
used to compensate for this aberration caused by the phase difference of
126 Diagnostic ultrasound: imaging and blood ow measurements
Phase Aberration: caused by the assumption that
Transmitted wave front
Skin
et
Echo-waveforms
sound velocity in tissue is a constant
Time delays calculated contain slight errors
Fat Lobule
Target
Linear Array
Figure 4.27 Source of phase aberration in ultrasonic imaging.
the pulses arriving at the transducers or arrays (Flax and O’Donnell, 1988;
Nock and Trahey, 1989). One method uses a region of a tissue with prominent features, e.g., a blood vessel, as a target. Figure4.28 describes how
this can be achieved. The arrival times of all returned echoes at each element of an array or pulses returned from a target are adjusted via crosscorrelation of the echo waveform with a reference waveform. This concept
will be described in detail again in Chapter 6. Another method compensates for the velocity difference by adjusting the delays of the arriving
echoes until the brightness from a region of tissues is maximized. These
methods have all been demonstrated to be capable of improving image
quality under certain conditions. Their capability is limited because the
f(z)
Cross-correlation
g(z)
Skin
Fat Lobule
z
Targ
z
Linear Array
Figure 4.28 Phase aberration compensation can be carried out by cross-correlating
the returned echo waveforms.
Liver Ultrasound
Technically Challenging Patient
Female - 330 Ibs
127Chapter four: Gray-scale ultrasonic imaging
Conventional Technology
Failed Exam
Figure 4.29 The quality of a phase aberration-compensated liver image is drastically improved. (Courtesy of Philips Ultrasound.)
PureWave Crystal Technology
Tissue Aberration Correction
Coded Beamforming
Successful Exam
phase difference in the elevational plane cannot be compensated. Further,
they slow down the frame rate. These approaches may play a more signicant role if phase aberration compensation is implemented on multidimensional arrays. Figure4.29 shows the image improvement obtained with the
implementation of phase aberration correction on an obese patient.
4.1.6 Clinical applications
There are numerous clinical applications of B-mode ultrasound because it is
noninvasive and can display 2D cross-sectional images of anatomical structures in real time. It is used in obstetrics for monitoring the status of a fetus,
in gynecology for diagnosing problems in the ovary, in general radiology
for diagnosing liver tumors and gall bladder diseases, in vascular surgery
for detecting arterial stenosis and deep vein thrombosis and characterizing
atherosclerotic plaques, and in cardiology for diagnosing valvular diseases
and monitoring the integrity of cardiac wall functions, to name just a few.
4.2 M-mode and C-mode
In M-mode display, one intensity-modulated A-line or B-line is swept
across the monitor as a function of time at a rate much slower than the
pulse repetition frequency (PRF) of the A-line, as illustrated in Figure4.30.
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