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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5783_Библиотеки_им_академика_М_И_Перельмана.pdf
Material Speed
Acoustic impedance
1520 1.52 x 10
6 Transcranial Doppler Ultrasound: Physical Principles
101
6.2.1 Speed ofUltrasound inTissue
The speed of sound in tissue is important for a number of reasons. It must be known
in order to convert the time delay between the transmission of a pulse and the subsequent reception of echoes into physical distances, it determines the maximum rate
at which pulses can be transmitted (it is usually necessary to wait until all the relevant echoes from one pulse return to the transducer before another is transmitted),
it determines the wavelength of the ultrasound (and hence resolution), it determines
the amount of refraction that takes place at tissue interfaces, and it is needed to
convert Doppler shift frequencies into tissue velocities. The speed of sound in tissue
depends on the elastic properties and density of the tissue, and in general the less
compressible the tissue the higher the speed of sound, so that, for example, ultrasound propagates much more rapidly through bone than through soft tissue.
Table6.1 gives approximate values for the speed of sound in some relevant tissues.
The important thing to note from this table is that, with the exception of air and
bone, all the values are very similar, at around 1540ms
value for air is much lower, but since ultrasound does not propagate through air this
is of little signicance; the value for bone is much higher, which is of some relevance when performing transcranial examinations. Taking the value of 1540ms−1 as
representative, it is easy to calculate that it takes pulses of ultrasound approximately
6.5μs to travel 1cm, and therefore, to convert the delay between the transmission
of a pulse and the reception of an echo into a depth (remembering that it will take
13μs for a round trip of 1cm). Ultrasound scanners do this automatically, but it
should be noted that a scanner has no way of telling what tissues the pulse has travelled through, and must use the same conversion factor for all acoustic paths.
Because the speed of sound is much higher in bone than soft tissue, the apparent
thickness of bone will be less than half its actual thickness. This may not matter
−1
(metres per second). The
Table 6.1 Speed of sound and acoustic impedance of some common materials
(metres per second)
Air
Aqueous humour
Blood
Bone
Brain
Fat
Lens of eye
Muscle
Soft tissue average
Vitreous humour
330 0.0004 x 10
1500 1.50 x 10
1570 1.61 x 10
3500 7.80 x 10
1540 1.58 x 10
1450 1.38 x 10
1620 1.84 x 10
1580 1.70 x 10
1540 1.63 x 10
(rayls)
6
6
6
6
6
6
6
6
6
6
102
()
()
g/II
Material Attenuation
0.7
D. H. Evans
when making transcranial measurements on the brain through a relatively small
aperture because it may simply mean the entire image is shifted, but where there are
signicant variations in the thickness of bone underlying the transducer it can introduce undesirable distortions into the image of the brain. Knowing the speed of ultrasound enables us to calculate the wavelength (given by sound speed divided by
frequency) which gives us an idea of the best spatial resolution available from the
technique, and which in soft tissue will be approximately 0.77mm at 2MHz and
0.1mm at 15MHz.
6.2.2 Attenuation ofUltrasound by Tissue
As ultrasound propagates through tissue, it is attenuated; that is to say the energy in
the beam is reduced. This happens through two main mechanisms: absorption and
scattering. Absorption is the conversion of the mechanical energy in the beam into
heat (which will cause a temperature rise in the tissue– see section on ultrasound
safety), while scattering is the process by which energy is redirected out of the
beam. In most soft tissue, the most important mechanism is absorption, but in blood
scattering dominates. Attenuation varies from tissue to tissue, and is strongly frequency dependent. It is usually measured in decibels (dB), and may be written as
(Eq.6.1):
AttenuationdB
=−
10
lo
10 0
x
where I0 is the initial intensity and Ix is the nal intensity. Thus, if the nal intensity
is one-tenth of the initial intensity, the attenuation is said to be −10dB; likewise
reductions in intensity to be one-hundredth and one-thousandth of the initial intensity would be written as −20 dB and -30 dB respectively. Typical values of the
attenuation of 1MHz ultrasound in some biological materials are given in Table6.2.
With the exception of water, the attenuation coefcients for higher frequencies may
be obtained approximately by multiplying the attenuation at 1 MHz by the frequency in MHz. For example, the attenuation in soft tissue at 2MHz would be
Table 6.2 Attenuation
coefcients for some
biological materials at
1MHz. The values at a
higher frequency may be
obtained approximately by
multiplying by the frequency
in MHz (note however that
for water the value should be
multiplied by the square of
frequency)
Blood
Bone
Brain (adult)
Brain (infant)
Fat
Muscle
Water
Soft tissue average
coefficient at 1 MHz
(dB cm–1)
0.2
10
0.8
0.3
0.6
1.5
0.002
(6.1)
6 Transcranial Doppler Ultrasound: Physical Principles
103
1.4dBcm−1, and at 10MHz would be 7dBcm−1. The strong frequency dependency
of attenuation is the factor that limits the highest frequency that can be used in any
particular situation (ideally we would always use the highest frequency possible
because the shorter the wavelength, the better the spatial resolution). The higher the
attenuation coefcient, the higher the frequency, and the deeper the target, the
smaller will be the returning echoes. We are able to obtain very high-resolution
images of arteries like the extra-cranial carotid arteries because they are relatively
supercial and the overlying tissue has a relatively low attenuation coefcient; the
same is not true for deep vessels. The rapid attenuation of ultrasound by bone means
that if we wish to insonate through the skull, we have to use relatively low ultrasound frequencies (note, however, that the poor resolution we obtain when imaging
the brain is a result of both using a low frequency and the distortion of the ultrasound beam by the skull bone).
6.2.3 Ultrasound Behaviour at Acoustic Boundaries
Ultrasonic imaging is reliant on variations in the acoustic properties of tissues to
generate the echoes that reveal the range and direction of target structures. The
behaviour of sound when it encounters a change in acoustic properties depends on
the relative dimensions of the ultrasound wavelength and the target in its path. If the
target is small compared with the wavelength (such as the case with a red blood cell
or the inhomogeneities in the parenchyma of an organ), then the wave is said to be
scattered. If the target is large (such as the case at the interface between two organs),
then the wave is said to be reected or refracted. Both types of behaviour are important in ultrasonic scanning. In the case of scattering, the incident energy is retransmitted in all directions (though not necessarily equally), while in the case of
reection and refraction, the energy remains conned to a well-dened, reected
and transmitted beam.
Figure 6.1a, b illustrate the behaviour of ultrasound at a plain boundary for perpendicular and non-perpendicular incidence respectively. In the rst case, a proportion of the ultrasound is reected directly back to the source (the angle of incidence
and reection are both equal to zero), and a proportion continues along the original
path. In the second case, the angle of incidence and reection are also equal, but not
to zero, and therefore, the reected wave does not return to the transducer (this is
why it is much easier to image large surfaces that are perpendicular to the ultrasound beam). In the second case, there is also a transmitted wave, but its direction
depends both on the angle of incidence and the relative speeds of ultrasound on
either side of the boundary. The relationship between the angle of the incident wave
θ
and the transmitted wave θt is given by Eq.6.2:
i
sin
θ
c
i
1
=
sin
θ
c
2
t
(6.2)
104
a
Scattered
D. H. Evans
Fig. 6.1 (a) Reection of
Interface
ultrasound at a plane
boundary (perpendicular
incidence). (b) Reection
and refraction of
ultrasound at a plane
boundary (non-
Source
Incident
Z
Z
1
2
Transmitted
perpendicular incidence).
(c) Scattering of ultrasound
by a target with dimensions
smaller or comparable to
Reflected
the ultrasound wavelength
b
Source
Incident
θ
i
θ
r
Reflected
Interface
Z
1
Z
2
Transmitted
refracted
θ
t
c
Source
Incident
where c1 is the sound speed before the boundary and c2 the speed after the boundary.
If the speeds of sound on either side of the boundary are similar, the direction of
propagation changes very little, but if they are dissimilar then the direction may
change signicantly (i.e. it is said to be refracted). Refraction effects are particularly
important at interfaces between soft tissue and bone (recall the speed of sound in
bone is 2 to 3 times higher than in soft tissue), and can lead to considerable distortion as an ultrasound beam propagates through the skull. The proportion of energy
reected at a boundary depends on the difference in the acoustic impedance on the
two sides of the boundary and for normal incidence may be written (Eq.6.3):
ZZ
ZZ
21
21
6 Transcranial Doppler Ultrasound: Physical Principles
105
I
r
α
==
r
I
i
−
+
(6.3)
where Ii and Ir are the incident and reected intensities, and Z1 and Z2 are the acoustic impedance of the tissue before the boundary and after the boundary, respectively.
If Z1 and Z2 are similar, then most of the energy is transmitted and little reected; if
Z1 and Z2 are very dissimilar, then the converse is true. Values of acoustic impedance
for some relevant tissues are given in Table6.1. It can be seen that the values for
most soft tissues are very similar, but that air has a very low value and bone has a
relatively high value. The result of this is that the percentage of energy reected at
soft tissue interfaces is of the order of 1%, but that, at soft tissue/bone interfaces,
approximately 50% of the energy is reected. The impedance of air is so low that
effectively no transmission at all takes place at a soft tissue/air interface. The low
acoustic impedance of air is the main reason why it is impossible to image through
air and why it is essential to exclude air from the interface between the transducer
and the skin.
Figure 6.1c illustrates the phenomenon of scattering. Scattering is important
because it is the process that allows us to image the parenchyma of organs and to
image blood ow. The scattering pattern and the amount of scattering that occur at
a target depend on the size of the target, and the distribution of compressibility and
density in the target volume. For targets that are very much smaller than the ultrasound wavelength, the wave is scattered more or less uniformly in all directions,
while for larger targets, the scattering pattern is more complex but still takes place
over a wide range of angles. For very small targets, such as red blood cells, the scattering is called Rayleigh scattering and is proportional to the fourth power of frequency; for larger targets, the scattered power still increases with frequency but less
rapidly so. The power returned to the ultrasound transducer by scattering is much
less than that returned by specular reectors, but is also much less angle dependent.
Therefore, echoes from the internal structure of organs and from blood are much
weaker than those from distinct boundaries, but do not change signicantly as the
angle of insonation changes.
6.3 Pulse-Echo Principles (B-Mode Techniques)
The basic principle behind B-scanning has been described in the introduction. A
B-mode display is essentially a cross-sectional image of the tissue in the scan plane,
built up using an echo ranging technique. A transducer transmits a short ultrasound
pulse into the tissue in a predetermined direction, then switches to receive mode and
gathers echoes due to reection or scattering in the tissue from that same direction.
Since the direction of transmission and reception and the time delay between pulse
transmission and echo reception are known, the position of any structure producing
an echo can be determined. The size of each of the echoes provides information
106
D. H. Evans
about the amount of ultrasound reected or scattered by the structure (although it is
necessary to compensate for the attenuation of the pulse by intervening tissue).
Once all the echoes have been received from depths of interest, then another pulse
is transmitted along a slightly different path, and the whole process repeated until
the required plane, perpendicular to the transducer face, has been interrogated. The
rate at which pulses can be transmitted (the pulse repetition frequency or PRF) is
limited by the speed of ultrasound in the tissue and the maximum depth of interest;
so, for example, if it is required to image to a depth of 10cm, it will be necessary to
wait 13μs × 10, that is, 130μs, before another pulse is transmitted. Clearly considerable processing by the ultrasound scanner is necessary to produce acceptable
images from the simple echo information described above, and the interested reader
is referred to Hoskins etal. [1] for further information.
6.4 Transducers
At one time the method used for scanning the ultrasound beam through tissue
involved physical movements within the transducer. All transducers for B-scan
imaging are now array transducers where the beam is steered electronically. There
are two basic types of arrays: linear arrays and phased arrays, both of which contain
a large number of very small piezoelectric elements capable of transmitting and
receiving ultrasound.
In linear arrays, each beam is generated using only a limited number of adjacent
array elements at any one time. Each successive beam is generated by selecting
another group of elements, so if the rst beam is generated using elements 1–8, for
example, then the second beam might be generated using elements 2–9 and so on.
Thus, the beam steps along the array. Linear array transducers produce rectangularor parallelogram-shaped elds where all the scan lines are parallel to each other, and
are the transducers of choice for imaging the extra-cranial carotid arteries.
In phased arrays, each beam is generated using most or even all of the elements
at the same time. Each successive beam is generated by steering the direction of
transmission and reception by appropriate phasing of the signals applied to the
transducer elements. Phased arrays produce sector-shaped elds where the scan
lines are not parallel to each other and are the transducers of choice for intracranial
imaging because their small footprint, which allows them to be used with the limited acoustic windows available in the skull.
Modern ultrasound systems not only move the beam electronically, but dynamically vary their aperture (the number of elements used) and apodisation (relative
weighting of the contribution of different elements), and also use electronic focussing on both transmit (multiple-zone focussing) and receive (dynamic focussing) to
achieve excellent lateral resolution in the scan plane. Some modern transducers also
use more than one row of elements to improve the focussing in the elevation plane
(i.e. the out of plain dimension or the slice thickness).
6 Transcranial Doppler Ultrasound: Physical Principles
107
6.5 Artefacts
It is important that users of ultrasound instruments are aware of the many image
artefacts that can arise. Two of the most important types are described briey below.
6.5.1 Speed ofSound andBeam Deviation Artefacts
To generate ultrasound images, it is necessary to assume that the beam has followed
a straight path through the tissue, and that the speed of sound in the tissue is constant and known. Anything that invalidates these assumptions will lead to misregistration of targets. Beam direction may be changed either by refraction effects (i.e.
where the beam meets a boundary between two tissues with different ultrasound
velocities, at nonnormal incidence), or by very strong specular reectors that are not
at right angles to the beam. Deviations from the assumed velocity of sound will
make targets appear closer or farther away than they should. If the tissue with the
higher or lower velocity is a parallel-sided layer, then all the structures behind the
layer will be moved so as to appear closer or further from the transducer, which may
not matter. On the other hand, if the layer is not parallel sided or is incomplete, then
some parts of the structure behind the layer will be moved more than others, so that
a straight boundary might appear ragged. Strong specular reectors, not at right
angles to the beam, may act as acoustic mirrors completely redirecting the beam
direction away from that assumed by the machine.
6.5.2 Shadowing andFlaring Artefacts
Attenuation of ultrasound in bodily tissues is very signicant so that echoes returning from deep structures are always very much smaller than those returning from
similar supercial structures. In order to overcome this, ultrasound instruments
employ what is known as time gain compensation (TGC) to the returning echoes, so
that echoes from deeper structures are amplied more than those from supercial
structures. In order to do this, the instrument needs to assume an average rate of
attenuation in the tissue so it can calculate the appropriate gain to apply to echoes
from each depth. Shadowing and aring artefacts occur when the attenuation is
either underestimated or overestimated respectively. One common example of shadowing occurs behind an atheromatous plaque in the carotid artery, where the plaque
attenuates the ultrasound much more rapidly than soft tissue, and so the TGC does
not adequately compensate for the reduction in the size of the echoes returning from
behind the plaque. The converse effect can be seen when there is a cyst in the tissue.
The uid in a cyst does not attenuate ultrasound as rapidly as soft tissue, but the
TGC continues to increase gain with depth as though there is soft tissue present. The
108
vc
=−=
θ
=
θ
D. H. Evans
result of this is that the echoes from behind the cyst are amplied more than is
appropriate, and the region behind the cyst appears to be very highly reecting.
Although these are artefacts, they do in fact convey diagnostic information, in that
they reveal the presence of tissue with an unexpectedly high or low attenuation values.
6.6 Doppler Principles
If an observer is stationary relative to a source of waves, then the frequency the
observer measures is the same as the frequency transmitted. If, however, the observer
is moving towards or away from the source of waves, then a greater or lesser number of wave fronts will pass the observer in a given time interval, and so the observer
will measure a higher or lower frequency than that which was transmitted. This
effect is known as the Doppler effect after the Austrian physicist, Christian Doppler,
who rst described the phenomenon in 1842. In medical ultrasound, the targets do
not emit spontaneously, and therefore, to make use of this effect, it is necessary to
transmit ultrasound into the body, and to observe the change of frequency as the
wave is reected or scattered from the target. Under these conditions, it can be
shown [2] that the ‘Doppler frequency’, fd, i.e. the difference between the transmitted frequency ft and the received frequency fr, is given by Eq.6.4:
ffff
dtrt
2cos /
(6.4)
where v is the velocity of the target, c the velocity of sound in tissue and θ the angle
between the ultrasound beam and the direction of motion of the target. The velocity
of sound and the transmitted frequency are known in any situation, and therefore,
the velocity of a target can be found from Eq.6.5:
vf
Kcos
d
(6.5)
where K is a known constant (c/2ft). This equation may be used to monitor changes
in velocity, and if the angle θ can be determined, then absolute velocity may be
calculated. In practice, where blood ow is concerned, there will be many targets in
the Doppler sample volume with a range of velocities, and so the Doppler shift signal will contain a spectrum of frequencies. Figure6.2 shows the spectral display
(usually called a sonogram) of the Doppler signal recorded from an internal carotid
artery. The horizontal axis represents time, the vertical axis the Doppler shift frequency and the grey level of each pixel the power of the Doppler signal at the corresponding frequency and time.
Under ‘ideal’ conditions, the spectrum of Doppler frequencies at any moment in
time would correspond to the distribution of velocities in the sample volume, but
there are a number of factors which distort the spectrum and limit the accuracy with
which the velocity distribution can be determined (note also that the shape of the
sample volume itself will mean that the ow within a vessel is unlikely to be
time
frequency
6 Transcranial Doppler Ultrasound: Physical Principles
Fig. 6.2 Sonogram of the Doppler signal from a normal internal carotid artery. The horizontal axis
represents time, the vertical axis Doppler shift frequency (or velocity), and the grey scale the power
of the Doppler shift frequency at the corresponding time and frequency. Three complete cardiac
cycles are shown
109
sampled uniformly, and therefore, the distribution of velocities in the sample volume may not exactly correspond to the distribution of velocities in the vessel). The
reader is referred to Evans and McDicken [2] for an in-depth discussion of these
effects, but the effect of ‘wall-thump’ lters is briey described here because of its
importance. As already mentioned, the signals reected by structures such as blood
vessel walls are orders of magnitude greater than those scattered by blood, and
therefore, it is necessary to reject such signals if we wish to study the motion of the
blood. This is possible because in general such solid structures move with much
lower velocities than those of blood ow, and therefore, these signals can be rejected
using a high- pass (wall-thump) lter. While this can be quite effective, the lter will
also reject the signals from slowly moving blood. This means that blood ow close
to a vessel wall cannot be studied, and that the mean blood ow velocity in a vessel
tends to be slightly overestimated, although is not usually a major problem as long
as the operator is aware of the effect.
6.6.1 Pulsed Wave Doppler
Early Doppler ultrasound devices were continuous-wave devices (that is to say they
both transmitted and received ultrasound continuously), but such devices had little
or no range resolution. Because in general it is important to be able to select signals
from a particular depth, nearly all ultrasound Doppler instruments now use pulsed
transmission. Pulses of ultrasound are transmitted at regular intervals, and after a
xed (but controllable) delay, a receive gate attached to the transducer opens for a
brief period of time and allows signals from a pre-determined range of depths to be
collected for Doppler processing. The delay between pulse transmission and the
opening of the receive gate determines the depth from which signal samples are collected, and the time for which the receive gate is open in combination with the
transmitted pulse length determines the sample volume length.
110
D. H. Evans
Pulsed wave (PW) ultrasound systems actually operate by measuring the rate of
change of phase of the returning ultrasound pulses rather than the Doppler shift
frequency per se and because of this are subject to the effects of aliasing. Aliasing is
the phenomenon that occurs when a moving object is not sampled sufciently rapidly to be able to reconstruct its true movement. If a Doppler signal is to be correctly
interpreted, then the rate at which it is sampled (i.e. the pulse repetition frequency)
(with certain caveats). Failure to respect this limit can lead to artefacts such as rapid
forward ow being interpreted as reverse ow. The obvious way to avoid this problem is to increase the PRF, but as we have already seen this is limited by the fact that
if we wish to avoid range ambiguity we must collect all the returning echoes of
interest before transmitting a subsequent pulse. It can be shown [2] that there is a
maximum range-velocity product limit given by Eq.6.6:
where z
is the maximum range a PW system can gather echoes from unambigu-
max
ously and v
zv cf
is the maximum velocity that can be unambiguously measured.
max
/cos=28
θ
tmaxmax
(6.6)
Therefore, it is possible to measure high velocities in supercial structures correctly
and low velocities in deep structures correctly, but not high velocities in deep structures. This limit is particularly troublesome in cardiac work where there may be
very high velocities through stenosed heart valves, but it is possible to encounter
aliasing in more supercial structures such as stenosed carotid arteries. Equation 6.6
reveals that one of the ways to avoid aliasing is to use a lower transmitted ultrasound
frequency, and this is one of the reasons why Doppler studies are often performed
at slightly lower frequencies than imaging studies.
6.6.2 Duplex Scanning
Duplex scanners are scanners that combine B-mode imaging with PW Doppler
measurements. The B-scan image is used to guide the Doppler beam and to place a
Doppler sample volume in a region of interest. Since blood vessels may be imaged,
the Doppler angle, θ, can also be measured (by assuming that the blood ow is parallel to the vessel wall) and, therefore, the Doppler shift frequency can be calibrated
in terms of blood ow velocity.
6.6.3 Colour Flow Imaging (CFI)
Colour ow imaging systems are similar to pulse-echo B-mode systems, except that
both the amplitude and the ‘Doppler shift’ on the returning echoes are measured.
Where no Doppler shift is detected, the usual grey-scale information is written to