the physics of diagnostic ultrasound frcr physics lectures mark wilson clinical scientist...

The Physics of The Physics of Diagnostic UltrasoundDiagnostic Ultrasound

FRCR Physics LecturesFRCR Physics Lectures

Mark WilsonClinical Scientist (Radiotherapy)

Hull and East Yorkshire Hospitals

NHS Trust

[email protected]

Session 1 & 2

Session 1 OverviewSession 1 Overview


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Session Aims:

• Basic physics of sound waves

• Basic principles of image formation

• Interactions of ultrasound waves with matter

Basic PhysicsBasic Physics


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Wave Motion



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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



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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



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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 p2Power, P p



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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



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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

Basic Principles of Basic Principles of Image FormationImage Formation


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Basic Principles of Image FormationBasic Principles of Image Formation


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Pulse-Echo Principle

) ) ) ) )D

) ) ) )

) ) ) )

)

)

Source of sound

Distance = Speed x Time2D = c x t

Sound reflected at boundary

Reduced signal amplitude

No signal returns



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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

TransducerCan transmitand receive US

Tissue 1 Tissue 2 Tissue 3


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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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


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


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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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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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


M-Mode Image of Mitral Valve


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Ultrasound Ultrasound Interactions in MatterInteractions in Matter


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Ultrasound InteractionsUltrasound Interactions

• Reflection

• Scatter

• Refraction

• Attenuation and Absorption

• Diffraction


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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


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 mK K KSound wave


• 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 mK K K

Small masses (m) model a material of low density linked by springs of high stiffness 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


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M M M Mk k k

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

Speed of Sound c = k /



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Material C (m/s)

Liver 1578

Kidney 1560

Fat 1430

Average Tissue 1540

Water 1480

Bone 3190

Air 330

Ultrasound Interactions - ReflectionUltrasound 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

z1z2


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 mK K KSound wave



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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 mk k k

Small masses (m) model a material of low density linked by weak springs of low stiffness k



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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 MK 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 = cCan also be shown


Amplitude Reflection Coefficient (r)


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r =Z2 – Z1

Z1 + Z2

z1 z2

pi , Ii pt , It

pr , Ir

pi pr =



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Intensity Reflection Coefficient (R)

R =Z2 – Z1

Z1 + Z2Ii 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



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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


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

Ultrasound Interactions - ScatterUltrasound 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 - RefractionUltrasound 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=

Ultrasound Interactions - AttenuationUltrasound 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- dWhere is the attenuation coefficient

Ultrasound Interactions - AttenuationUltrasound 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

Ultrasound Interactions - DiffractionUltrasound 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 DivergenceAperture small compared to

High DivergenceAperture large compared to

BreakBreak


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Session 2 OverviewSession 2 Overview


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Session Aims:

• Construction and operation of the ultrasound transducer

• Ultrasound instrumentation

• Ultrasound safety

Ultrasound Ultrasound TransducerTransducer


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Ultrasound TransducerUltrasound 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



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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



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Beam Shape – Diffraction

NEAR FIELD FAR FIELD

NFL

a

Near Field Length, NFL = a2 / a = radius of transducer = Wavelength



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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!!



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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



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Beam Focusing

aW

F

Beam width at focus, W = F / a

At focal point:

• Maximum ultrasound intensity

• Maximum resolution



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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



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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



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Beam Shape - Overlapping Groups of Elements

Fire elements1-5 together

And then…

Fire elements2-6 together

And so on…

Near field length increases as (N)2



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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



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Array Focussing

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

Time delays



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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



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Resolution

Resolution in three planes

Axial Slice Thickness

Lateral



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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

InstrumentationInstrumentation


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Transmitter Clock

TGC Generator Transducer Beam Controller

AD Converter

Signal Processor Image Store

Archive Display

x, y

z



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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


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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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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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

LiverHeart


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 SafetyUltrasound Safety


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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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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

http://images.google.co.uk/imgres?imgurl=http://i.treehugger.com/images/2007/5/24/thermometer.gif&imgrefurl=http://www.treehugger.com/2007/05/20-week/&h=364&w=269&sz=5&hl=en&start=5&tbnid=opsVGIry9_HLgM:&tbnh=121&tbnw=89&prev=/images%3Fq%3Dthermometer%26gbv%3D2%26hl%3Den



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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)



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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



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Soft-Tissue Thermal Index (TIS)

Soft tissue

Maximum temperature

Bone-at-Focus Thermal Index (TIB)

Soft tissue

Maximum temperatureBone



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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



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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



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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



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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



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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

The EndThe End


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the physics of diagnostic ultrasound frcr physics lectures mark wilson clinical scientist...

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