The Physics of Diagnostic Ultrasound FRCR Physics Lectures

1
The Physics of Diagnostic UltrasoundFRCR Physics
Lectures
Session 1 2

• Mark Wilson
• Clinical Scientist (Radiotherapy)

mark.wilson_at_hey.nhs.uk
Hull and East Yorkshire Hospitals
NHS Trust
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Session 1 Overview

• Session Aims
• Basic physics of sound waves
• Basic principles of image formation
• Interactions of ultrasound waves with matter

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Basic Physics
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Basic Physics

• Wave Motion

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Basic Physics

• 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

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Basic Physics

• 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

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Basic Physics

• 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

Power, P ? p
Intensity, I ? p2
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Basic Physics

• 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

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Basic Physics

• 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
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Basic Principles of Image Formation
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Basic Principles of Image Formation

• Pulse-Echo Principle

D
Source of sound
)
Sound reflected at boundary
)
)
)
)
Distance Speed x Time
2D c x t
)
)
)
)
)
Reduced signal amplitude
)
)
)
)
)
No signal returns
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Basic Principles of Image Formation

• Pulse-Echo in Tissue

Tissue 1
Tissue 2
Tissue 3
Transducer Can transmit and receive US

• 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

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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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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

Transducer

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Basic Principles of Image Formation

• Arrays

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
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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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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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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

Time
Transducer at fixed point
Depth
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Basic Principles of Image Formation

• M-Mode Image of Mitral Valve

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Ultrasound Interactions in Matter
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Ultrasound Interactions

• Reflection
• Scatter
• Refraction
• Attenuation and Absorption
• Diffraction

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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)

Atom / Molecule
Bond
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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

Sound wave
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Ultrasound Interactions
Small masses (m) model a material of low density
linked by springs of high stiffness K

• 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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Ultrasound Interactions
Large masses (M) model a material of high density
linked by springs of low stiffness k
M
M
M
M
k
k
k

• 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

Speed of Sound c ? k / ?
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Ultrasound Interactions
Material C (m/s)
Liver 1578
Kidney 1560
Fat 1430
Average Tissue 1540
Water 1480
Bone 3190
Air 330
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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

z2
z1
Transducer
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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

Sound wave
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Ultrasound Interactions - Reflection
Small masses (m) model a material of low density
linked by weak springs of low stiffness k

• 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

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Ultrasound Interactions - Reflection
Large masses (M) model a material of high density
linked by springs of high stiffness K
M
M
M
M
K
K
K

• 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

Acoustic Impedance z ? ?k Acoustic Impedance z
?c
Can also be shown
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Ultrasound Interactions - Reflection
z1
z2
pi , Ii
pt , It
pr , Ir

• Amplitude Reflection Coefficient (r)

Z2 Z1
pr
r

pi
Z1 Z2
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Ultrasound Interactions - Reflection

• Intensity Reflection Coefficient (R)

• 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
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Ultrasound Interactions - Reflection
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
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Ultrasound Interactions - Reflection

• Reflection at an Angle

• 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

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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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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

c2 (gtc1)
c1
Snells Law
sin (i)
c1
i

c2
sin (t)
t
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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

Intensity, I
Low freq.
High freq.
Distance, d
I Ioe- ?d
Where ? is the attenuation coefficient
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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

Attenuation and absorption is often expressed in
terms of decibels
Decibel, dB 10 log10 (I2 / I1)
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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

High Divergence Aperture large compared to ?
Low Divergence Aperture small compared to ?
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Break
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Session 2 Overview

• Session Aims
• Construction and operation of the ultrasound
  transducer
• Ultrasound instrumentation
• Ultrasound safety

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Ultrasound Transducer
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Ultrasound Transducer

• 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

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Ultrasound Transducer

• Transducer

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Ultrasound Transducer

• 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

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Ultrasound Transducer

• Beam Shape Diffraction

a
NEAR FIELD
FAR FIELD
NFL
Near Field Length, NFL a2 / ?
a radius of transducer ? Wavelength
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Ultrasound Transducer

• 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!!

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Ultrasound Transducer

• 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

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Ultrasound Transducer

• Beam Focusing

F
a
W
Beam width at focus, W F? / a

• At focal point
• Maximum ultrasound intensity
• Maximum resolution

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Ultrasound Transducer

• Beam Focusing
• For a single element source, focusing can be
  achieved in one of two ways
• 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

Source
Focus
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Ultrasound Transducer

• 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.

Lens
Focus
Source
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Ultrasound Transducer

• Beam Shape - Overlapping Groups of Elements

Fire elements 1-5 together
Fire elements 2-6 together
And then
And so on
Near field length increases as (N)2
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Ultrasound Transducer

• 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
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Ultrasound Transducer

• Array Focussing

Time delays
Introduce time delays to compensate for extra
path length on both transit and receive
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Ultrasound Transducer

• Multiple Zone Focussing

• Fire transducer several times with different
  focus to compile better image
• However, more focus points decreases frame rate

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Ultrasound Transducer

• Resolution
• Resolution in three planes

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Ultrasound Transducer

• 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

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Instrumentation
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Instrumentation
Clock
Transmitter
TGC Generator
Transducer
Beam Controller
x, y
AD Converter
z
Signal Processor
Image Store
Archive
Display
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Instrumentation

• 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
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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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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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Instrumentation
Grey level

• 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

Liver
Heart
Linear
Input Amp
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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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Ultrasound Safety
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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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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

Rate of energy absorption per unit volume q
2??I Where ? absorption coefficient, ?
frequency, I intensity
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Ultrasound Safety

• 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)

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Ultrasound Safety

• 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

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Ultrasound Safety
Soft-Tissue Thermal Index (TIS)
Maximum temperature
Soft tissue
Bone-at-Focus Thermal Index (TIB)
Maximum temperature
Bone
Soft tissue
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Ultrasound Safety
Cranial (or Bone-at-Surface) Thermal Index (TIC)
Maximum temperature
Soft tissue
Bone
All three TI values depend linearly on the
acoustic power emitted by the transducer
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Ultrasound Safety

• 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

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Ultrasound Safety

• 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

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Ultrasound Safety
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
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Ultrasound Safety

• 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

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The End
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