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1. The Physics of
Diagnostic Ultrasound
FRCR Physics Lectures
Mark Wilson
Clinical Scientist (Radiotherapy)
Hull and East Yorkshire Hospitals
NHS Trust
mark.wilson@hey.nhs.uk
Session 1 & 2
2. Session 1 Overview
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Session Aims:
• Basic physics of sound waves
• Basic principles of image formation
• Interactions of ultrasound waves with matter
5. Basic Physics
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Sound Waves
• Sounds waves are mechanical pressure waves which propagate
through a medium causing the particles of the medium to oscillate
backward and forward
•The term Ultrasound refers to sound waves of such a high frequency
that they are inaudible to humans
• Ultrasound is defined as sound waves with a frequency above 20 kHz
• Ultrasound frequencies used for imaging are in the range 2-15 MHz
• The velocity and attenuation of the ultrasound wave is strongly
dependent on the properties of the medium through which it is travelling
6. Basic Physics
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Wave Propagation
• Imagine a material as an array of molecules linked by springs
• As an ultrasound pressure wave propagates through the medium, molecules
in regions of high pressure will be pushed together (compression) whereas
molecules in regions of low pressure will be pulled apart (rarefaction)
• As the sound wave propagates through the medium, molecules will oscillate
around their equilibrium position
7. Basic Physics
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Power and Intensity
• A sound wave transports Energy through a medium from a source. Energy is
measured in joules (J)
• The Power, P, produce by a source of sound is the rate at which it produces
energy. Power is measured in watts (W) where 1 W = 1 J/s
• The Intensity, I, associated with a sound wave is the power per unit area.
Intensity is measured in W/m2
• The power and intensity associated with a wave increase with the pressure
amplitude, p
Intensity, I p2
Power, P p
8. Basic Physics
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Frequency (f):
Number of cycles per second
Unit: Hertz (Hz)
Speed (c):
Speed at which a sound wave
travels is determined by the
medium
Unit: Metres per second (m/s)
Air – 330 m/s
Water – 1480 m/s
Av. Tissue – 1540 m/s
Bone – 3190 m/s
9. Basic Physics
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Wavelength ():
Distance between consecutive
crests or other similar points on
the wave
Unit: Metre (m)
A wave from a source of
frequency f, travelling through a
medium whose speed of sound is
c, has a wavelength
= c / f
11. Basic Principles of Image Formation
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Pulse-Echo Principle
) ) ) ) )
D
) ) ) )
) ) ) )
)
)
Source of sound
Distance = Speed x Time
2D = c x t
Sound reflected at boundary
Reduced signal amplitude
No signal returns
12. Basic Principles of Image Formation
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Pulse-Echo in Tissue
• Ultrasound pulse is launched into the first tissue
• At tissue interface a portion of ultrasound signal is transmitted into the second
tissue and a portion is reflected within the first tissue (termed an echo)
• Echo signal is detected by the transducer
Transducer
Can transmit
and receive US
Tissue 1 Tissue 2 Tissue 3
13. Basic Principles of Image Formation
B-Mode Image
• A B-mode image is a cross-sectional image representing tissues and organ
boundaries within the body
• Constructed from echoes which are generated by reflection of US waves at
tissue boundaries, and scattering from small irregularities within tissues
• Each echo is displayed at a point in the image which corresponds to the
relative position of its origin within the body
• The brightness of the image at each point is related to the strength
(amplitude) of the echo
• B-mode = Brightness mode
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14. Basic Principles of Image Formation
B-Mode Image Formation
A 2D B-mode image is formed from a large number of B-mode lines, where each
line in the image is produced by a pulse echo sequence
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Transducer
15. Basic Principles of Image Formation
Arrays
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Linear Curvilinear Phased
Rectangular FOV
Useful in applications
where there is a need
to image superficial
areas at the same time
as organs at a deeper
level
Trapezoidal FOV
Wide FOV near
transducer and even
wider FOV at deeper
levels
Sector FOV useful for
imaging heart where
access is normally
through a narrow
acoustic window
between ribs
16. Basic Principles of Image Formation
B-Mode Image – How Long Does it Take?
1. Minimum time for one line = (2 x depth) / speed of sound = 2D / c seconds
2. Each frame of image contains N lines
3. Time for one frame = 2ND / c seconds
E.g. D = 12 cm, c = 1540 m/s, Frame rate = 20 frames per second
Frame rate = c / 2ND
N = c / 2D x Frame rate = 320 lines (poor - approx half of standard TV)
Additional interpolated lines are inserted between image lines to boost image
quality to the human eye
4. Time is very important!!!
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17. Basic Principles of Image Formation
Time Gain Compensation (TGC)
• Deeper the source of echo Smaller signal intensity
• Due signal attenuation in tissue and reduction in initial US beam intensity by
reflections
• Operator can TGC use to artificially ‘boost’ the signals from deeper tissues
(like a graphic equaliser)
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18. Basic Principles of Image Formation
M-Mode Image
• Can be used to observe the motion of tissues (e.g. Echocardiography)
• One direction of display is used to represent time rather than space
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Transducer at fixed point Time
Depth
19. Basic Principles of Image Formation
M-Mode Image of Mitral Valve
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22. Ultrasound Interactions
Speed of Sound, c
• The speed of propagation of a sound wave is determined by the medium it is
travelling in
• The material properties which determine speed of sound are density, (mass
per unit volume) and elasticity, k (stiffness)
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Atom / Molecule
Bond
23. Ultrasound Interactions
Speed of Sound, c
• Consider a row of masses (molecules) linked by springs (bonds)
• Sound wave can be propagated along the row of masses by giving the first
mass a momentary ‘push’ to the right
• This movement is coupled to the second mass by the spring
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m m m m
K K K
Sound wave
24. Ultrasound Interactions
• Stiff spring will cause the second mass to accelerate quickly to the right and
pass on the movement to the third mass
• Smaller masses are more easily accelerated by spring
• Hence, low density and high stiffness lead to high speed of sound
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m m m m
K K K
Small masses (m) model a material of low density linked by springs of high
stiffness K
25. Ultrasound Interactions
• Weak spring will cause the second mass to accelerate relatively slowly
• Larger masses are more difficult to accelerate
• Hence, high density and low stiffness lead to low speed of sound
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M M M M
k k k
Large masses (M) model a material of high density linked by springs of low
stiffness k
Speed of Sound c = k /
26. Ultrasound Interactions
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Material C (m/s)
Liver 1578
Kidney 1560
Fat 1430
Average Tissue 1540
Water 1480
Bone 3190
Air 330
27. Ultrasound Interactions - Reflection
Reflection of Ultrasound Waves
When an ultrasound wave travelling through one type of tissue encounters an
interface with a tissue with different acoustic impedance, z, some of its energy
is reflected back towards the source of the wave, while the remainder is
transmitted into the second tissue
- Reflections occur at tissue boundaries where there is a change in acoustic
impedance
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Transducer
z1
z2
28. Ultrasound Interactions - Reflection
Acoustic Impedance (z)
• The acoustic impedance of a medium is a measure of the response of the
particles of the medium to a wave of a given pressure
• The acoustic impedance of a medium is again determined by its density, ,
and elasticity, k (stiffness)
• As with speed of sound, consider a row of masses (molecules) linked by
springs
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m m m m
K K K
Sound wave
29. Ultrasound Interactions - Reflection
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• A given pressure is applied momentarily to the first small mass m
• The mass is easily accelerated to the right and its movement encounters little
opposing force from the weak spring k
• This material has low acoustic impedance, as particle movements are
relatively large in response to a given applied pressure
m m m m
k k k
Small masses (m) model a material of low density linked by weak springs of low
stiffness k
30. Ultrasound Interactions - Reflection
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• In this case, the larger masses M accelerate less in response to the applied
pressure
• Their movements are further resisted by the stiff springs
• This material has high acoustic impedance, as particle movements are
relatively small in response to a given applied pressure
M M M M
K K K
Large masses (M) model a material of high density linked by springs of high
stiffness K
Acoustic Impedance z = k
Acoustic Impedance z = c
Can also be shown
31. Ultrasound Interactions - Reflection
Amplitude Reflection Coefficient (r)
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r =
Z2 – Z1
Z1 + Z2
z1 z2
pi , Ii pt , It
pr , Ir
pi
pr
=
32. Ultrasound Interactions - Reflection
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Intensity Reflection Coefficient (R)
R =
Z2 – Z1
Z1 + Z2
Ii
Ir
= ( )
2
• Strength of reflection depends on the difference between the Z values of the
two materials
• Ultrasound only possible when wave propagates through materials with
similar acoustic impedances – only a small amount reflected and the rest
transmitted
• Therefore, ultrasound not possible where air or bone interfaces are present
Intensity Transmission Coefficient (T)
T = 1 - R
33. Ultrasound Interactions - Reflection
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Interface R T
Soft Tissue-Soft Tissue 0.01-0.02 0.98-0.99
Soft Tissue-Bone 0.40 0.60
Soft Tissue-Air 0.999 0.001
34. Ultrasound Interactions - Reflection
Reflection at an Angle
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z1 z2
i
r
• For a flat, smooth surface the angle of
reflection, r = the angle of incidence, i
• In the body surfaces are not usually
smooth and flat, then r i
35. Ultrasound Interactions - Scatter
Scatter
• Reflection occurs at large interfaces such
as those between organs where there is a
change in acoustic impedance
• Within most organs there are many small
scale variations in acoustic properties
which constitute small scale reflecting
targets
• Reflection from such small targets does
not follow the laws of reflection for large
interfaces and is termed scattering
• Scattering redirects energy in all
directions, but is a weak interaction
compared to reflection at large interfaces
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36. Ultrasound Interactions - Refraction
Refraction
When an ultrasound wave crosses a tissue boundary at an angle (non-normal
incidence), where there is a change in the speed of sound c, the path of the
wave is deflected as it crosses the boundary
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c1 c2 (>c1)
i
t
Snell’s Law
sin (i)
sin (t)
c1
c2
=
37. Ultrasound Interactions - Attenuation
Attenuation
• As an ultrasound wave propagates
through a medium, the intensity
reduces with distance travelled
• Attenuation describes the reduction in
intensity with distance and includes
scattering, diffraction, and absorption
• Attenuation increases linearly with
frequency
• Limits frequency used – trade off
between penetration depth and
resolution
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Distance, d
Intensity, I
Low freq.
High freq.
I = Ioe- d
Where is the attenuation coefficient
38. Ultrasound Interactions - Attenuation
Absorption
• In soft tissue most energy loss (attenuation) is due to absorption
• Absorption is the process by which ultrasound energy is converted to heat in
the medium
• Absorption is responsible for tissue heating
Decibel Notation
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Decibel, dB = 10 log10 (I2 / I1)
Attenuation and absorption is often expressed in terms of decibels
39. Ultrasound Interactions - Diffraction
Diffraction
• Diffraction is the process by which the ultrasound wave diverges (spreads out)
as it moves away from the source
• Divergence is determined by the relationship between the width of the source
(aperture) and the wavelength of the wave
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Low Divergence
Aperture small compared to
High Divergence
Aperture large compared to
41. Session 2 Overview
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Session Aims:
• Construction and operation of the ultrasound transducer
• Ultrasound instrumentation
• Ultrasound safety
43. Ultrasound Transducer
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Transducer
• The transducer is the device that converts electrical transmission pulses into
ultrasonic pulses, and ultrasonic echo pulses into electrical signals
• A transducer produces ultrasound pulses and detects echo signals using the
piezoelectric effect
• The piezoelectric effect describes the interconversion of electrical and
mechanical energy in certain materials
• If a voltage pulse is applied to a piezoelectric material, the material will
expand or contract (depending on the polarity of the voltage)
• If a force is applied to a piezoelectric material which causes it to expand or
contract (e.g. pressure wave), a voltage will be induced in the material
45. Ultrasound Transducer
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Transducer
• A transducer only generates a useful ultrasound beam at one given frequency
• This frequency corresponds to a wavelength in the transducer equal to twice
the thickness of the piezoelectric disk – This is due to a process known as
Resonance!
• Choice of frequency is important – remember that attenuation increases with
increasing frequency
• Image resolution increases with frequency
• Therefore, there is a trade-off between scan depth and resolution for any
particular application
46. Ultrasound Transducer
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Beam Shape – Diffraction
NEAR FIELD FAR FIELD
NFL
a
Near Field Length, NFL = a2 / a = radius of transducer
= Wavelength
47. Ultrasound Transducer
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Beam Shape - Diffraction
• In the near field region the beam energy is largely confined to the dimensions
of the transducer
• Need to select a long near field length to achieve good resolution over the
depth you wish to scan too
• Near field length increases with increasing transducer radius, a, and
decreasing wavelength,
• Short wavelength means high frequency – not very penetrating
• Large transducer radius – Wide beam (poor lateral resolution)
• Trade-off between useful penetration depth and resolution!!
48. Ultrasound Transducer
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Beam Focusing
• An improvement to the overall beam width can be obtained by focusing
• Here the source is designed so that the waves converge towards a point in
the beam, the focus, where the beam achieves its minimum width
• Beyond the focus, the beam diverges again but more rapidly that for an
unfocused beam with the same aperture and frequency
49. Ultrasound Transducer
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Beam Focusing
a
W
F
Beam width at focus, W = F / a
At focal point:
• Maximum ultrasound intensity
• Maximum resolution
50. Ultrasound Transducer
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Beam Focusing
For a single element source, focusing can be achieved in one of two ways:
1) A curved source
A curved source is manufactured with a radius of curvature of F and
hence produces curved wave fronts which converge at a focus F cm from
the source
F
Source Focus
51. Ultrasound Transducer
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Beam Focusing
For a single element source, focusing can be achieved in one of two ways:
2) An acoustic lens
An acoustic lens is attached to the face of a flat source and produces
curved wave fronts by refraction at its outer surface (like an optical lens).
A convex lens is made from a material with the lower speed of sound
than tissue.
Source Focus
Lens
52. Ultrasound Transducer
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Beam Shape - Overlapping Groups of Elements
Fire elements
1-5 together
And then…
Fire elements
2-6 together
And so on…
Near field length increases as (N)2
53. Ultrasound Transducer
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Array Focusing
Waves from outer elements 1 and 5 have
greater path lengths than those from other
elements
Therefore signals do not arrive simultaneously
at the target and reflections do not arrive at all
elements at the same time
54. Ultrasound Transducer
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Array Focussing
Introduce time delays to compensate for extra
path length on both transit and receive
Time delays
55. Ultrasound Transducer
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Multiple Zone Focussing
• Fire transducer several times with different focus to compile better image
• However, more focus points decreases frame rate
56. Ultrasound Transducer
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Resolution
Resolution in three planes
Axial Slice Thickness
Lateral
57. Ultrasound Transducer
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Resolution
Resolution Depends on Typical Value (mm)
Axial Pulse length 0.2 - 0.5
Lateral Beam width 2 – 5
Slice Thickness Beam height 3 - 8
• Higher frequency improves resolution in all three planes
• Slice thickness is a hot topic for improvement – 2D arrays
59. Instrumentation
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Transmitter Clock
TGC Generator Transducer Beam Controller
AD Converter
Signal Processor Image Store
Archive Display
x, y
z
60. Instrumentation
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Clock
• Command and control centre
• Sends synchronising pulses around the system
• Each pulse corresponds to a command to send a new pulse from the
transducer
• Determines the pulse repetition frequency (PRF)
PRF = 1 / time per line = c / 2D
Where c is speed of sound and D is maximum scan depth
If there are N lines, then Frame Rate = c / 2ND
61. Instrumentation
Transmitter
• Responds to clock commands by generating high voltage pulses to
excite transducer
Transducer
• Sends out short ultrasound pulses when excited
• Detects returning echoes and presents them as small electrical
signals
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62. Instrumentation
AD Converter
• Converts analogue echo signals into digital signals for further
processing
Needs to:
• Be fast enough to cope with highest frequencies
• Have sufficient levels to create adequate grey scales (e.g. 256 or 512)
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63. Instrumentation
Signal Processor
Carries out:
• TGC application
• Overall gain
• Signal compression – fits very large dynamic range ultrasound signal
on to limited greyscale display dynamic range
• Demodulation – removal of the carrier (ultrasound) frequency
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Grey level
Input Amp
Linear
Liver
Heart
64. Instrumentation
Image Store
• Takes z (brightness) signal from processor
• Positions it in image memory using x (depth) and y (element position)
information from beam controller
• Assembles image for each frame
• Presents assembled image to display
• Typically have capacity to store 100-200 frames to allow cine-loop
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66. Ultrasound Safety
Hazard and Risk
• Hazard describes the nature of the danger or threat (e.g. burning,
falling, etc)
• Risk takes into account the severity of the potential consequences
(e.g. death, injury) and the probability of occurrence
• There are two main hazards associated with ultrasound:
- Tissue heating
- Cavitation
• But is there any risk???
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67. Ultrasound Safety
Tissue Heating
• During a scan some of the ultrasound energy is absorbed by the exposed
tissue and converted to heat causing temperature elevation
• Elevated temperature affects normal cell function
• The risk associated with this hazard depends on the:
- Degree of temperature elevation
- Duration of the elevation
- Nature of the exposed tissue
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Rate of energy absorption per unit volume
q = 2I
Where = absorption coefficient, = frequency, I = intensity
68. Ultrasound Safety
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Tissue Heating
• Thermal effects in patient are complex
• Temperature increase will be fastest at the focus resulting in a temperature
gradient
• Heat will be lost from focus by thermal conduction
• The transducer itself will heat up and this heat will conduct into tissue
enhancing the temperature rise near the transducer
• The presence of bone in the field will increase the temperature rise
• Blood flow will carry heat away from the exposed tissues
• It is impossible to accurately predict the temperature increase occurring in the
body and a simple approach to estimate the temperature increase is used to
provide some guidance - Thermal Index (TI)
69. Ultrasound Safety
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Thermal Index (TI)
TI = W / Wdeg
W = Transducer power exposing the tissue
Wdeg = The power required to cause a maximum temperature rise of 1oC
anywhere in the beam
• TI is a rough estimate of the increase in temperature that occurs in the region
of the ultrasound scan
• A TI of 2.0 means that you can expect at temperature rise of about 2oC
• The difficulty with calculating the TI lies mostly in the estimation of Wdeg
• To simplify this problem there are three TIs
70. Ultrasound Safety
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Soft-Tissue Thermal Index (TIS)
Soft tissue
Maximum temperature
Bone-at-Focus Thermal Index (TIB)
Soft tissue
Maximum temperature
Bone
71. Ultrasound Safety
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Cranial (or Bone-at-Surface) Thermal Index (TIC)
Soft tissue
Maximum temperature
Bone
All three TI values depend linearly on the acoustic power emitted by the
transducer
72. Ultrasound Safety
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Does Temperature Rise Matter?
• Normal core temperature is 36-38oC and a temperature of 42oC is “largely
incompatible with life”
• During an ultrasound examination only a small volume of tissue is exposed and
the human body is quite capable of recovering from such an event
• Some regions are more sensitive such as reproductive cells, unborn fetus, and
the CNS
• Temperature rises of between 3 and 8oC are considered possible under certain
conditions
• There has been no confirmed evidence of damage from diagnostic ultrasound
exposure
73. Ultrasound Safety
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Cavitation
• Refers to the response of gas bubbles in a
liquid under the influence of an ultrasonic wave
• Process of considerable complexity
• High peak pressure changes can cause micro-
bubbles in a liquid or near liquid medium to
expand – resonance effect
• A bubble may undergo very large size variations
and violently collapse
• Very high localised pressures and temperature
are predicted that have potential to cause cellular
damage and free radical generation
74. Ultrasound Safety
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Cavitation
Micro-bubbles grow by resonance processes
Bubbles have a resonant frequency, fr, depending on their radius, R.
frR 3 Hz m
This suggests that typical diagnostic frequencies (3 MHz and above) cause
resonance in bubbles with radii of the order of 1 micrometer
75. Ultrasound Safety
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Mechanical Index (MI)
• The onset of cavitation only occurs above a threshold for acoustic pressure
• This has resulted in the formulation of a mechanical index (MI)
• Mechanical index is intended to quantify the likelihood of onset of cavitation
MI = pr / f
where pr is the peak rarefaction pressure and f is the ultrasound frequency
• For MI 0.7 the physical conditions probably cannot exist to support bubble
growth and collapse
• Exceeding this threshold does not mean there will be automatically be
cavitation
• Cavitation is more likely in the presence of contrast agents and in the
presence of gas bodies such as in the lung and intestine