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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3921_Библиотеки_им_академика_М_И_Перельмана
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13.2 Ultrasound Fundamentals 295
of this equation, it can be shown that
λ =
c
f
(13.3)
Assuming linearity, Eq. (13.2) has harmonic solutions of the form
p
(
r, t
)
= Re
P
(
r
)
· e
jωt
(13.4)
in which P represents a complex spatially dependent solution to the diffraction
integral for specific aperture boundary conditions. A complete examination of
diffraction is beyond the scope of this chapter, but P(r) can be thought of as
the spatial distribution of pressure arising from the transmission of ultrasound
from a particular transducer aperture. It therefore takes into account the effects
of focusing and propagation. Equation (13.4) is further complicated by the fact
that ultrasound scanners use short pulses with significant bandwidth necessitating
an integral over frequency to determine the spatial and temporal distribution
of ultrasound. Figure 13.1 shows a typical low-pressure ultrasound pulse that is
suitable for imaging. Note that the pulse is confined to a few cycles (Figure 13.1a)
centered at a frequency of 30 MHz with bandwidth extending from <20 MHz to
>40 MHz as shown in Figure 13.1b. Equations (13.2) and (13.3) assume linearity
as discussed above, but when beams with high peak pressures are transmitted into
tissue nonlinear effects can become important and can, in fact, be exploited to
improve image quality. Nonlinearity arises from the fact that the speed of sound
expressed in Eq. (13.2) is itself a function of pressure and acoustic velocity. Acoustic
velocity, v, in this case is distinct from speed of sound in that it represents the
actual velocity of the molecules arising from the acoustic pressure. A more accurate
nonlinear representation of speed of sound in Eq. (13.2) is given by
c = (c
0
+ βv)
2
(13.5)
where
β = 1 +
B
2A
(13.6)
and B/A represents the ratio of the second- and first-order terms in the expansion
of the expression for pressure. B/A is often referred to as the nonlinear parameter in
ultrasound and ranges in value from about 5 for water to about 12 for fatty tissues.
Nonlinear propagation has a significant and cumulative effect on the propagation
of ultrasound at relevant power levels. Essentially, the regions of compression
travel slightly faster than the regions of rarefaction causing the wave to sharpen
up, ultimately leading to a shock front. This leads to the generation of harmonics
in the pulse spectrum. Modern ultrasound instruments routinely exploit nonlinear
propagation to perform ‘‘tissue harmonic imaging’’ to improve the quality of
ultrasound images.
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296 13 High Frequency Ultrasound for the Visualization and Quantification of the Microcirculation
−0.4
−0.2
0.0
0.2
0.2 0.3 0.4 0.5 0.6
0.4
Relative amplitudeRelative amplitude (dB)
Time (µs)
−40
−35
−30
−25
−20
−15
−10
−5
0
0 20 40 60 80 100
Fre
q
uenc
y(
MHz
)
BW = 80%
(a)
(
b
)
Figure 13.1 Transmitted waveform from a 30 MHz array
probe measured at the elevation focus of the transducer
(VisualSonics MS400). The temporal length of the pulse is
confined to a few cycles of 30 MHz ultrasound, while the
spectrum shows a very wide bandwidth of ∼80% leading to
high axial resolution.
13.2.1
Resolution
The ultimate imaging performance of any ultrasound scanner is determined by
the frequency, geometry of its transducer, and tissue properties in accordance
with the laws of diffraction. These issues are reviewed by Foster et al. [4] who
described the trade-offs between resolution, penetration, and system dynamic
range. The resolution of the image is determined by the beam distribution (lateral
direction) and the pulse bandwidth (axial direction). Simple expressions for lateral
resolution (R
lat
), axial resolution (R
ax
), and depth of field (DOF) for a spherical
radiator at the focus are
R
lat
= λ
focal length
diameter
=
λ(f−number) (13.7)
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13.2 Ultrasound Fundamentals 297
R
ax
=
1
2
c
BW
(13.8)
DOF = 7
λ(f−number)
2
(13.9)
where
λ is the average wavelength, c is the speed of sound (1.5mmµs
−1
), and
BW is the bandwidth of the transducer (megahertz). The ratio of the focal length
to the diameter is often referred to as the f-number. Equation (13.7) is valid only
for a focused transducer in the focal zone or for an unfocused transducer at axial
distances beyond the far-field transition. Depending on the choice of frequency
and f-number, the resolution can vary over several orders of magnitude. Thus, a
typical clinical system with a center frequency of 5 MHz, an f-number of 2, and
bandwidth of 2.5 MHz will have lateral resolution of 0.6 mm and axial resolution
of 300 µm. By comparison, a micro-ultrasound scanner with similar geometry but
with a center frequency of 50 MHz will have lateral and axial resolutions of 60 and
25 µm, respectively.
The frequency-dependent attenuation of ultrasound limits the total ultrasound
path in tissue to about 600 wavelengths round trip or a maximum depth of 300
wavelengths. On the basis of this criterion, imaging 10 –30 mm of mouse or human
tissue suggests minimum wavelengths of 33 µm (45 MHz) to 100 µm (15 MHz),
respectively. This range is ideal for imaging of mice and rats. Note that fixing the
bandwidth at 50% results in axial resolution approximately twice that of lateral
resolution but that this is only true over a comparatively narrow DOF. This leads
to one of the central issues in ultrasound, which is how to sweep the focus over
the entire field of view in an effective manner. Generally, this problem is solved
by the use of a linear array of transducers in which the delay patterns of transmit
and receive are manipulated to achieve a focus that dynamically sweeps from near
to far. Dynamic focusing and phased linear arrays are firmly entrenched as the
dominant technology for ultrasound imaging.
13.2.2
Reflectivity and Signal Strength
Signal strength or brightness in ultrasound images is determined by the reflectivity
of the tissues being imaged. From a theoretical point of view, prediction of
the reflected signal requires solution of the inhomogeneous wave equation and
detailed knowledge of the mechanical properties of tissue. In particular, the acoustic
impedance, Z, defined as the product of density and speed of sound
Z = ρ
0
c (13.10)
is critical in determining reflectivity. In general, two regimes are important: (i)
reflection at surfaces with dimensions
λ and (ii) situations where the reflector
dimension is
λ. The latter situation is referred to as Rayleigh scatter. In regime
1, ultrasound waves are reflected from large interfaces such as that between the
liver and kidney and are governed by a reflection coefficient defined by
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298 13 High Frequency Ultrasound for the Visualization and Quantification of the Microcirculation
R =
(Z
2
− Z
1
)
(Z
2
+ Z
1
)
(13.11)
where Z
2
and Z
1
are the acoustic impedances of the tissues forming the interface.
In soft tissues, values of the reflection coefficient are in the range of ∼0.0001–0.1
but can become very significant in the presence of bone or air. In the scatter
regime, reflectivity is more complex. In the simplest situation (Rayleigh scatter),
the scattered pressure from a solid sphere of radius a is given by
D
(ϕ)
=
k
2
a
3
3
κ − κ
0
κ
0
+
3ρ − 3ρ
0
2ρ + ρ
0
Cosϕ
(13.12)
where k is the wave number in the medium, κ is the compressibility of the
particle, and ϕ is the scattering angle. Not surprisingly, the amplitude of the
pressure scattered by a small sphere is strongly dependent on size, frequency (via
k), compressibility, density, and scattering angle. Red blood cells are generally
considered to be Rayleigh scatterers, but this assumption begins to break down at
some of the higher frequencies discussed here.
13.2.3
Doppler Quantification of Blood Flow
Ultrasound is well established as a means of measuring blood flow or, more
precisely, blood velocity using the Doppler principle. Scattering of ultrasound from
moving red blood cells leads to a shift in the frequency of scattered ultrasound in
comparison to the frequency of the insonifying pulse. The expression for velocity
of blood flow, v,isgivenby
v =
f
d
c
(2 f
0
Cos(θ))
(13.13)
where f
d
is the Doppler frequency shift, f
0
is the insonifying frequency, c is the
local speed of sound, and θ is the angle between the axis of beam propagation
and the flow velocity vector. Doppler information may be displayed in a variety
of ways to contribute functional information on the flow of blood in the vascular
system. Pulsed Doppler is used to display blood velocity as a function of time
(the Doppler waveform) at a particular location in space. This is very useful for
the detailed evaluation of local hemodynamics but is not helpful for mapping the
vasculature. To perform this function, the display of the average velocity calculated
on a pixel-by-pixel basis using Doppler estimators is performed. The latter mapping
is referred to as color flow imaging. Since velocity is a vector, color flow images are
encoded with flow toward the transducer represented in shades of red and flow away
from the transducer in shades of blue. Another important display method involves
integrating the power in the Doppler spectrum for each pixel and displaying this
information as a ‘‘Power Doppler’’ image. Such displays are linearly proportional
to blood volume and are displayed on an orange to yellow scale superimposed on
the grayscale ultrasound image.
Early work demonstrating Doppler detection of blood flow changes with breast
tumors began 20 years ago. Since then, attempts have been made to correlate
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13.3 Instrumentation 299
conventional ultrasound Doppler findings with tumor stage and/or patient
prognosis. It is, however, clear that these methods are sensitive only to large vessel
flow, that is, arterioles and venules larger than about 50 µm. This situation has
recently changed with the introduction of three important innovations in the field
of ultrasound imaging: (i) the development of a generation of new microbubble
(MB) contrast agents, (ii) the development of new nonlinear signal processing
tools to permit effective separation and display of the echo from the microvascular
pool, and (iii) the development of micro-ultrasound and high-frequency Doppler,
which enable noninvasive imaging of microscopic structure and blood flow with
unprecedented spatial resolution.
13.3
Instrumentation
The growing demand for imaging tools in the biological community led
to successful commercialization of micro-ultrasound in the early 2000s [5]
(Figure 13.2a). These systems were based on mechanically scanned single-element
transducers operating in the 15 –80 MHz range and provided resolution in the
(a)
(b)
(c) (d)
Figure 13.2 High frequency
micro-ultrasound imaging systems devel-
oped over the past 10 years have enabled
effiecient, high resolution, quantitative anal-
ysis of animal models of disease. Earlier
systems (a) relied on mechanically steered
single element scanheads (b). More re-
cently, fully beamformed scanners (c) have
been developed using novel high frequency
arrays (d). The latter devices use no me-
chanical actuation and improve the depth
of field of the imaging system.
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300 13 High Frequency Ultrasound for the Visualization and Quantification of the Microcirculation
40–200 µm range depending on frequency and aperture configuration according
to Eqs. (13.7–13.9). Photographs of the scanner and scanhead of the mechanical
scanner are given in Figure 13.2a and b, respectively. The scanhead contains the
high-frequency transducer in a sealed liquid-filled compartment that is coupled to
the mouse skin using an ultrasound gel. Remarkably, these probes were capable
of reaching frame rates in excess of 100 Hz. Several hundred peer-reviewed papers
using the single-element-scanned micro-ultrasound platform have now been
published. Overviews related to applications of micro-ultrasound in developmental
biology in mice are available [6–10] in the area of cardiovascular research [11–14]
and in the area of cancer [15–19]. While single-element systems have fared well
in the market, they suffer from serious limitations in DOF. This is due to the fact
that the single transducer has a fixed focus in space analogous to a camera with a
fixed focus lens. In addition, single elements are limited in their ability to provide
functional maps of Doppler blood flow in real time and in their ability to image
contrast agents. In 2009, systems based on linear transducer array technology
were finally introduced to solve these problems [20]. Arrays offer the flexibility to
change the point of focus electronically as the ultrasound propagates back to the
sensor thus extending the DOF. The new imaging technology was commercialized
by VisualSonics and enables the frequency of systems based on linear transducer
arrays to be extended from 15 MHz to above 50 MHz. Photographs of the linear
array instrument and scanhead that currently defines the field of micro-ultrasound
imaging are shown in Figure 13.2c and d, respectively.
13.3.1
Imaging Protocols
Animals studied under approved protocols are positioned on an imaging plat-
form that presents the region to be imaged to a scanhead rigidly attached to a
mechanical positioning system as shown in Figure 13.3a. This allows hands-free
positioning and capture of the images. The animal is first anesthetized using a
2% isoflurane mixture in oxygen or air, and hair (if present) is removed using a
depilatory cream. The mouse is then restrained on the heated imaging platform
with surgical tape to maintain normal body temperature of the animal during
imaging. A warmed ultrasonic gel is applied to the mouse’s skin to couple the
scanhead and imaging commences. Key physiological parameters are captured
from the platform including heart rate, temperature, respiration, and ECG. These
signals are gathered through paw and temperature probes and integrated with the
real-time micro-ultrasound images. A typical imaging configuration is illustrated
in Figure 13.3a in which the system operator has a mouse on the imaging platform
with required instrumentation. A flexible but lockable arm holds the transducer
adjacent to the tissue to be imaged. In the background, the anesthesia delivery,
induction chamber, and monitoring equipment are shown on the right. Images
such as the one shown in Figure 13.3b show the results of an upper abdominal
image of an adult mouse. The depiction of organs and other vascular structures is
remarkably similar to human images made at much lower frequencies. Visible are
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13.3 Instrumentation 301
(a)
(b)
Figure 13.3 (a) The imaging system of
Figure 13.2c being used to image a mouse.
The mouse is anesthetized and lying on a
heated stage and is monitored for heart rate,
breathing, and, in some cases, blood pres-
sure. Scanning is preformed after removal of
hair (if necessary) and after the application
of a heated gel to the region of interest. The
Ultrasound scanhead is mounted on a ‘‘Rail
System’’ inside a biosafety cabinet to reduce
jitter in the image due to hand motion. (b)
Example of a still frame from a real-time
sequence of images of the abdominal region
of the mouse. This ‘‘B-scan’’ image shows,
from left to right, a section through the
kidney, adrenal gland, the vena cava, portal
vein, and the aorta.
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302 13 High Frequency Ultrasound for the Visualization and Quantification of the Microcirculation
the overlying liver, the right kidney, adrenal gland, vena cava, aorta, and portal vein.
An additional accessory to the imaging platform is an injection mount that allows
for the guidance of precise injections or biopsies in vivo through the real-time
imaging guidance of the micro-ultrasound system. For ultrasound contrast and
targeted imaging studies (described in detail in Section 13.3.2), MB agents such
as MicroMarker (VisualSonics, Toronto) or Definity (Lantheus, Montreal) can be
reconstituted according to manufacturer’s specifications and injected via tail vein
in volumes that typically do not exceed 100 µl.
13.3.2
Microbubble Contrast Agents
The introduction of ultrasound MB contrast agents has created a significant
opportunity for visualization of the microcirculation [21, 22]. Recent reviews of
the physics and imaging modes for contrast ultrasound are given by Ferrara et al.
[23] and Borden et al. [24]. Current generations of these agents consist of MBs,
which range in diameter from <1to5µm, rendering them suitable for intravenous
injection. A typical contrast agent consists of a thin flexible or rigid shell composed
of albumin, lipid, or polymer confining a gas such as nitrogen, or a perfluorocarbon.
The choice of shell and gas has an important influence on the properties of the
agent. While Eq. (13.5) indicates that nonlinear propagation of ultrasound results
in the creation of harmonics, scatter from MBs is governed by somewhat more
complex interactions that result in the creation of other spectral features unique
to MBs. The radial motion of the wall of an MB under insonation is most often
described by the Rayleigh– Plesset or Keller–Miksis equations as described in [23].
It is a fortunate coincidence of nature that insonation in the MHz frequency range
excites bubble resonance due to the compressible nature of the gas inside the
bubble. The frequency of this resonance is a function of the gas properties and the
shear modulus of the MB shell given by
f
o
=
1
2πa
e
3κp
o
+ 12G
s
d
Se
a
e
ρ
L
(13.14)
where f
o
is the resonant frequency, a
e
is the equilibrium bubble radius, κ is the
polytropic exponent of the gas, p
o
is the atmospheric pressure, G
s
and d
S
are
the shear modulus and thickness of the shell, respectively, and ρ
L
is the density
of the surrounding liquid [25]. With increased incident amplitudes, the bubbles
can be driven to oscillate asymmetrically resulting in the scattering of energy to
harmonic multiples of the transmit frequency (f
o
) and to noninteger multiples
of the fundamental such as 1/2f
o
,3/2f
o
,5/2f
o
, and so on. The component at 1/2
the fundamental is referred to as the subharmonic, while the other noninteger
harmonics are referred to as ultraharmonics.
The challenge of MB contrast imaging has been to develop specific pulse
sequences and signal processing that maximize detection efficiency for signals
arising from MBs while suppressing signals arising from tissue or nonlinear
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13.3 Instrumentation 303
propagation. This has generally required the development of pulse sequences in
which the phase difference and amplitudeof the insonifyingpulse is manipulated to
suppress or enhance particular linear and nonlinear components. For example, one
conceptually simple approach to separate linear from nonlinear signals is to send
an ultrasound pulse like the one in Figure 13.1a followed by a second identical pulse
shifted in phase by 180
◦
. When the echoes from these experiments are subtracted,
the result is zero for linear scatter and nonzero for nonlinear scatter. This technique,
known as pulse inversion imaging, was developed by Hope-Simpson and colleagues
[26] and is now a standard approach on clinical instruments. Techniques such
as harmonic imaging [27] and pulse inversion [26] exploit the second harmonic
(2f
o
) to provide greater contrast with respect to the surrounding tissue. Burns
and Hope-Simpson [28] patented the concept of combining phase and amplitude
processing for optimized nonlinear contrast imaging and Doppler. This idea was
further refined by Haider and Chiao [29] and evolved into commercially available
contrast pulse sequences (CPSs). Eckersley et al. [30] showed that phase and
amplitude modulation (PIAM) provided 14–18 dB enhancement of contrast signals
over linear scatterers for insonifying pulses having a center frequency of 2.5 MHz.
The detection of energy in the subharmonic and ultraharmonic frequency range
has also been explored by a number of investigators [31–35] and is of particular
interest because these signals arise only from MB interactions. At diagnostic
frequencies, PIAM processing retains an advantage over subharmonic imaging
in that resolution is not compromised. In the micro-ultrasound frequency range,
Needles et al. have shown optimal contrast imaging with amplitude modulation
approaches [36]. Figure 13.4 shows vials of commercially available MicroMarker
contrast available from VisualSonics (Figure 13.4a) and a dark field micrograph of
Definity (Lantheus Medical Imaging) showing MB sizes from 1 to ∼5 µm.
5 µm
(a) (b)
Figure 13.4 Effective blood pool tracers
consisting of lipid encapsulated gas mi-
crobubbles (MBs) have been developed for
clinical and preclinical ultrasound imag-
ing over the past several decades. (a)
MicroMarker contrast (VisualSonics) was
developed specifically for use in mice. It has
average particle size of about 2 µmandis
injected intravenously in very small quantities
of 50 µl containing ∼10
7
MBs. (b) Dark field
microscopy of microbubbles in solution.
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304 13 High Frequency Ultrasound for the Visualization and Quantification of the Microcirculation
13.4
Applications of Micro-Ultrasound in Studies of the Microcirculation
Doppler approaches enable visualization of vessels down to about 50 µm depending
on frequency as described in Section 13.2.3. This information can be displayed in a
number of formats including pulsed Doppler, color Doppler, and power Doppler.
Pulsed Doppler is a measurement at a particular spatial location in which blood
velocity is measured as a function of time. Therefore, it reports mainly on the
hemodynamics of flow. Color Doppler encodes the mean velocity of flow and is
presented as a color overlay on top of the grayscale image of anatomy. Flow toward
the transducer is usually encoded in shades of red and flow away in shades of blue.
Finally, power Doppler reports the integral of Doppler power and is a reflection of
the number of moving scatterers (red blood cells) and is therefore a representation
of blood volume. An example of a color flow and pulsed Doppler study of a mouse
kidney is given in Figure 13.5. Here, a color flow image (scout image) clearly
differentiates the renal vein and artery by means of its ability to color code flow
direction and average velocity. By placing a cursor in the renal artery and aligning
a direction vector with the flow axis, accurate flow velocity estimates based on
Eq. (13.13) can be made and automatically displayed in a dynamic plot of the pulsed
Renal artery
Renal vein
Figure 13.5 Color flow imaging (scout
image above) clearly differentiates the renal
vein of a mouse and artery by means of its
ability to color code flow direction and aver-
age velocity. By placing a cursor in the renal
artery and aligning a direction vector with
the flow axis, accurate flow velocity estimates
can be made and automatically displayed in
a dynamic plot of the ‘‘Doppler’’ waveform.
Here, the peak velocity is ∼600 mm s
−1
.
Further analysis based on waveform mea-
surements can then determine important
indices that reflect the health of the organ.
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