Ultrasound Imaging
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Ultrasonic waves
Interaction with tissue
Tissue properties
Production and detection of ultrasound
Fields of ultrasound transducers
Image formation
Resolution in ultrasound images
Electronic focusing
Real time imaging
Doppler ultrasound
Demonstration of ultrasound
technology, meet in IAHS lobby,
Thursday, November 15, 1230.
Download class notes at
www.science.mcmaster.ca/medphys/courses
Further reading (available electronically at McMaster)
PNT Wells, Ultrasonic imaging of the human body, Reports
on Progress in Physics 62 671-722 (1999).
The Ultrasound Spectrum
WAVELENGTH
IN WATER
1.5 mm
0.015 mm
l f = 1500 ms -1
FREQUENCY
1 GHz
In water
Ultrasound microscopy
100 MHz
0.15 mm
10 MHz
1.5 mm
1.0 MHz
15 mm
0.1 MHZ
Medical imaging
Therapeutic applications
0.02 MHz (20 kHz, hearing threshold)
Description of Ultrasonic Waves
• In general, both compressional and shear waves can
propagate in a solid, but soft tissue will support only
compressional waves.
• While there are minor differences in the velocity of
ultrasound in soft tissues, the value 1540 meters per
second is assumed in image reconstruction. The variation
of velocity with frequency ( i.e. dispersion) can also be
ignored. A round trip of 1 cm takes 13 microseconds in
tissue.
• The product of wavelength and frequency is equal to the
wave velocity, so in soft tissue the wavelength of 10 MHz
ultrasound is 0.15 mm. The wavelength plays an
important part in determining the ultimate resolution that
can be achieved with an imaging system.
• The energy transported by the wave per unit time per
unit area is referred to as the intensity. The usual units
are Watts per square centimeter. The average intensity in
diagnostic applications is below 100 mW cm -2, but the
peak intensity can be much higher.
Propagation of Ultrasonic Waves
Absorption
This occurs even when the wave propagates in a homogeneous
medium such as a tank of water. For simple fluids, the main
mechanism is viscous loss. For complex media, such as tissue.
“relaxation processes” in which acoustic energy is coupled to
changes in molecular conformation are important. Both
mechanisms are dependent on frequency - viscous losses vary
as f2 and relaxation losses somewhere between linear and
quadratic dependence.
Scattering
Scattering of the ultrasonic wave does not take place unless
the wave encounters a change in acoustic impedance. For our
purposes, the acoustic impedance is Z = ρc where ρ is the
density and c is the speed of sound. For water Z is 1.48 X 106
kg m-2 s -1 and most soft tissues are within a ten per cent of this
value. Note that the acoustic impedance of compact bone (e.g.
the skull) is about five times higher and that of air is lower by a
factor of 3,700.
The physical process of scattering depends in a complex way
on the size of the inhomogeneity and its acoustic impedance
relative to the surrounding medium.In general, the fraction of
incident energy scattered by the inhomogeneity will increase
with both of these quantities.
Two special cases for scattering
#1 Object much smaller than the wavelength
A classic example is scattering by a single red blood cell, of
diameter about 10 microns. In this regime the scattering is
approximately the same in all directions, and the scattering
cross-section is proportional to f4. This is analogous to
Rayleigh scattering of light by small particles.
#2 Large object with a “smooth” boundary
In this case the incident wave is reflected and refracted at
the surface analogous to the behavior of a light wave at a
discontinuity in refractive index.
θ
θ
Specular reflection
Z1
Z2
φ
For the simple case of normal incidence the intensity reflection
coefficient is R = [(Z2 - Z1)/(Z2 + Z1)]2
Implications of Specular Reflection
Consider a soft tissue/bone interface. The intensity reflection
coefficient is (7.80 - 1.63)2 / (7.80 + 1.63)2 = 0.42. In other
words, the transmission is 58%. This means that if we were
trying to use ultrasound to image the brain, we would only get
33% of the incident intensity into the brain, and only 33% of the
scattered intensity out of the brain.
100%
SKIN
This is one reason that
ultrasound is not used
58%
to image the adult brain,
33%
but it is used in infants
where the skull is not
BRAIN yet calcified. The reflection
coefficient at gas/tissue
SKULL
interfaces is even larger,
so ultrasound is not useful
in imaging the lung. This also
explains why a coupling gel is
used during ultrasound exams.
The gel fills the space
between the transducer
and the skin and prevents
reflection by trapped air.
TRANSDUCER
SKIN
COUPLING GEL
Attenuation
Together, absorption and scattering result in attenuation of the
ultrasound wave. The intensity falls off exponentially with
distance. We could express this as exp (-μx) using a linear
attenuation coefficient μ, but with ultrasound it is conventional
to express the attenuation coefficient in dB cm-1.
Digression on the decibel
The decibel scale is a way to represent the ratio of two intensities.
If the two intensities are I1 and I2, we can express the ratio as
dB ratio = 10 log10 (I1 / I2)
so if the attenuation coefficient is, for example, 1 dB cm-1, after
transmission through 10 cm of tissue the intensity will be reduced
by 10 dB, or a factor of 10. After 20 cm it would be reduced by
20 dB or a factor of 100.
Frequency dependence
The attenuation coefficient is a function of ultrasound frequency.
As shown on the next diagram, the coefficient is roughly
proportional to frequency for a variety of tissues. In fact, a good
rule-of-thumb is that the attenuation coefficient for soft tissue is
1 dB cm-1 MHz-1. Note the implications: at 1 MHz, transmission
through 10 cm of tissue reduces intensity by a factor of 10, but at
10 MHz, transmission through 10 cm of tissue reduces intensity
by a factor of 10,000,000,000! This frequency-dependent
attenuation imposes limits on the performance of imaging systems.
Generation and detection of ultrasound
Both rely on the piezoelectric effect, first discovered in the late
1800’s. Certain natural crystals (e.g. quartz) undergo a change
in physical size when an electric field is imposed on the crystal.
+
-
This change can launch an acoustic wave in the surrounding
medium. These materials also demonstrate a reciprocal
piezoelectric effect: a voltage is generated across the crystal
which is proportional to the applied pressure. This pressure
can result from an acoustic wave incident on the crystal. The
resulting voltage can be detected and amplified, so we have a
means of detecting acoustic waves as well as generating them.
In medical applications, the same “transducer” is used to
generate acoustic waves and to detect the waves scattered
by tissue. Synthetic materials demonstrate a much more
efficient conversion of electrical to acoustic energy. Most
medical transducers are fabricated from a ceramic material:
lead zirconate titanate, or PZT.
A transducer has a natural resonant frequency corresponding
to a wavelength (in the material) that is twice the transducer
thickness. For PZT, a 1 mm thick transducer resonates at 2
MHz. While resonance contributes to efficient energy conversion,
it may be detrimental in other ways.
POWER
PRESSURE
Most ultrasound imaging is based on the localization of “echoes”
or scattered waves from structures within the tissue. Intuitively,
we would expect that it is easier to figure out where a short pulse
came from because longer pulses would lead to temporal overlap
in the echoes and greater ambiguity about their source. Hence
it is generally desirable for the source to emit a short pulse, but
this is not what we get from a resonating transducer:
TIME
FREQUENCY
PRESSURE
POWER
The emitted pulse lasts a long time and looks like a pure “tone”.
This corresponds to a narrow frequency spectrum. If the
transducer is “damped” so that it does not resonate, the pulse is
much shorter, and the spectrum is correspondingly broad.
TIME
BANDWIDTH
FREQUENCY
This diagram shows a single element transducer with electrical
connections and mechanical damping. Note also the matching
layer. This is fabricated of material with an acoustic impedance
between that of the PZT crystal (very high) and tissue. Its
thickness is one quarter wavelength. It can be shown that this
maximizes power transfer from the PZT to the tissue in the same
way anti-reflective coatings work on glasses and other optics.
Note also, that the PZT crystal is shaped like a spherical shell.
This results in a focussed wave. Similar results could be achieved
with an acoustic lens
As discussed later, single element transducers are no longer
used in medical imaging. Multi-element arrays offer potential
for electronic focussing and real-time imaging.
Acoustic fields of ultrasonic transducers
A very small transducer (compared to the ultrasound wavelength)
would act like a point source (and detector). This would be
useless for imaging because we would not be able to direct the
ultrasound pulse to a specific region, nor would we be able to tell
which direction echoes were coming from.
Let’s consider a larger transducer as shown below. We can
conceptually divide the transducer into many small elements, all
vibrating in phase. Each emits a spherical wave, but at some
arbitrary point in the tissue, these waves do not arrive in phase
because the distance to each element is different. In order to
calculate the resulting field we must consider the possibility of
interference and sum all of the waves taking into account their
relative phase. This is exactly what you do to calculate the
diffraction pattern from a single slit in optics, and the same sort
of integral appears in the acoustic problem.
AXIS OF SYMMETRY
P
This diagram shows the amplitude of the pressure field when
the disk transducer vibrates at a single frequency. Close to the
transducer in the “near field” there is a complex interference
pattern. In the “far field” we see a well-defined peak on the axis
of the transducer. The peak broadens and decreases in size
as we move farther from the transducer.
Mathematically, we can show that the amplitude of the acoustic
pressure wave is proportional to
2 J1 (k a sin θ)
where k = 2π/λ
k a sin θ
J1 is first order
Bessel function
We can do the same calculation for a focused transducer with
the geometry shown below:
Focal plane
P
a
r
z
In the focal plane the pressure amplitude is proportional to
2 J1 (kr / 2f)
(kr / 2f)
where f = z / 2a is called
the f - number or f#
Note that the amplitude peak becomes narrower as we decrease
λ (i.e. increase frequency) or as we decrease the f - number.
If the transducer emits a pulse (as it usually does) rather than a
continuous wave, the calculation is more complex because the
pulse contains energy at many frequencies. The general
features of the field are the same if we consider the frequency to
correspond to the average of the power spectrum. The sharp
maxima and minima of the interference pattern are not so
evident for pulsed excitation. Note that a focused transducer can
be used as a detector and that it will have the same directional
sensitivity.
…..so enough physics, how do you make images?
To obtain a complete image it is necessary to a “fill in the box”
by getting sufficient A scans. In the early days of ultrasound
imaging this was accomplished by moving a single element
transducer over the surface of the patient. Before considering
modern methods, it is instructive to examine the resolution
attainable with the older method.
Typical ultrasound image – note the high resolution at 12 MHz,
the “speckle” in the image, and the characteristic appearance
of the cyst in the thyroid gland.
Image courtesy of
GE Healthcare
Resolution in Ultrasound Images
Axial
direction
Consider the case of a rectilinear scan where parallel A scans
are obtained by translation of the transducer.
Lateral direction
The axial resolution is determined by the pulse length. This
is why it is important to have well-designed wide-band
transducers that emit a short pulse. Typical values of axial
resolution are 1 mm or less.
The lateral resolution depends on the focusing properties of the
transducer. It can be improved by increasing the frequency or
by decreasing the f#. The first option is limited by the clinical
requirements for penetration. In general, systems use the highest
frequency possible. For a small organ like the thyroid, a higher
frequency can be used than is possible with a large organ like the
liver. The second option is limited by the fact that stronger
focusing (i.e. lower f#) will result in a reduced “depth-of-field”.
This means that lateral resolution is rapidly degraded at depths
out of the focal plane.
Schematic illustration of the depth-of-field problem
Low f-number
transducer
Focal plane
High f-number
transducer
Electronic focusing
The depth-of-field problem can be overcome to some extent by
focusing the transducer at different depths for different parts of
the image. The concept is illustrated below:
Electronic focusing can be achieved with annular arrays or with
linear arrays of transducer elements. A lens can be used with a
linear array to provide some (fixed) focusing in the plane
perpendicular to the array.
Real time ultrasound imaging
A major advantage of modern systems is the ability to acquire
images in “real time”. Practically, this means that an image must
be obtained in a time comparable to persistence of human vision.
This requires about 30 images (or frames) per second. For a
frame rate F, there is a relationship between the number of A
scans in the image, L, and the maximum depth to be imaged, d.
In order to avoid ambiguity in echo location we require
1/F = 2 L d/c
where c is sound velocity
Clearly it is not possible to translate a transducer quickly enough
to get real time images. Early scanners overcame this problem by
using a rotating or rocking scanner:
Surface
Shaded area is the imaged region. Because of its shape, this
is sometimes called a sector scan.
Another way to do this would be to have an array of transducer
excited sequentially, so that each is used to get an A scan. The
problem with this approach is that a single element has very poor
lateral resolution. This can be overcome by using groups of
array elements to steer and focus the beam as shown below:
The implementation of these ideas requires sophisticated
electronics and fabrication techniques. Advances in these
technologies have allowed real time systems to become
small, portable, and cheap compared to other imaging methods.
Doppler ultrasound
The Doppler shift is a familiar phenomenon at audible frequencies.
The same thing happens when ultrasound is scattered by a moving
object such as a red blood cell.
Note: the factor of two appears in the equation because the
moving object “hears” a Doppler shift, as does the observer of the
scattered ultrasound.
For typical blood velocities and ultrasound frequencies, the
Doppler shift is in the kHz regime. In simple systems, this can
be presented to the operator as an audible signal.
POWER
Large signal from
stationary objects
Blood moving
away from the
transducer
Weak Doppler signals
due to blood moving
towards the transducer
FREQUENCY
The Doppler signal must be found in the “clutter” of signals from
stationary objects. This is one case where a narrow-band or cw
system is advantageous. One problem with such a system is that
it provides no depth resolution so it may be difficult to localize the
blood flow information. This is overcome in pulsed Doppler
systems that determine the Doppler shift as a function of depth.
Color flow imaging
Blood vessel
Consider the two signals above, acquired a short time apart
without moving the transducer. As expected, the signal from
stationary tissue is unchanged, but the signal from the blood
vessel has changed because a different arrangement of
scatterers fills the volume that contributes to the signal. The
faster blood is flowing, the greater the difference in the signals.
The “difference” can be mathematically quantified as a
correlation, and there is a relationship between this and the
blood flow velocity. This information can be obtained everywhere
in the image and overlaid as a color on the normal gray scale
image. Red and blue are used to code for direction of flow and
the brightness of the color is used to indicate velocity.
Example (from GE’s clinical image library) of color Doppler
study of carotid stenosis.
Instead of imaging flow velocity, another mode is “power Doppler”
where the integral of the power spectrum is displayed. This
increases sensitivity and allows imaging of organ perfusion
For example, this image (courtesy of GE) shows renal perfusion.