FRCR US Lecture 2 - hullrad Radiation Physics

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The Physics of

Diagnostic Ultrasound

FRCR Physics Lectures

Session 3 & 4

Mark Wilson

Clinical Scientist (Radiotherapy) [email protected]

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Session 3 Overview

Session Aims:

• Recap

• Image Artefacts

• Contrast Agents

• Introduction to Doppler US

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Recap

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Recap

• The term Ultrasound refers to high frequency 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 velocity and attenuation of the ultrasound wave is strongly dependent on the properties of the medium through which it is travelling

= c / f c =

k /

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Recap

• Diagnostic ultrasound utilises the pulse-echo principle

Source of sound

)

)

D

Pulse

)

Echo

)

)

Sound reflected at boundary

Distance = Speed x Time

2D = c x t

• Each pulse-echo sequence produces one line of the image

• Several pulse-echo sequences are needed to compose a full image frame.

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Recap

Ultrasound waves undergo the following interactions:

• Reflection

• Scatter

• Refraction

• Attenuation and Absorption

• Diffraction

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Recap

Reflection

z

1 p i

, I i p r

, I r p t

, I t z

2

Intensity Reflection Coefficient (R)

R =

I r

I i

=

(

Z

2

Z

1

Z

1

+ Z

2

)

2

Acoustic Impedance z =

 

k

Acoustic Impedance z =

c

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Recap

Reflection

• Strength of reflection depends on the difference between the

Z

two materials values of the

• 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

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Recap

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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Recap

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

c

1 c

2

(>c

1

)

i t

Snell’s Law sin (i) sin (t)

= c

1 c

2

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Recap

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

Intensity, I

• Attenuation increases linearly with frequency

High freq.

• Limits frequency used – trade off between penetration depth and resolution

I = I

o

e

-

d

Where

 is the attenuation coefficient

Low freq.

Distance, d

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Recap

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 log

10

(I

2

/ I

1

)

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Image Artefacts

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Artefacts

Image Artefacts

When forming a B-mode image, a number of assumptions are made about ultrasound propagation in tissue. These include:

• Speed of sound is constant

• Attenuation in tissue is constant

• Ultrasound pulse travels only to targets that are on the beam axis and back to the transducer

Significant variations from these conditions in the target tissues are likely to give rise to visible image artefacts

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Artefacts

Range Errors

• The distance,

d

, to the target is derived from the time elapsed between transmission of the pulse and receipt of the echo from the target,

t

• In making this calculation the system assumes that

t

= 2

d

/ c, where the speed of sound is constant at 1540 m/s

• If the speed of sound in the medium between the transducer and target is greater (or less) than 1540 m/s, the echo will arrive back at the transducer earlier (or later) than expected for a target of that range

Fat c = 1420 m/s

Tissue c = 1540 m/s

Target

Displayed at

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Artefacts

Refraction

Refraction of the ultrasound beam as it passes between tissues with a different speed of sound can result in objects appearing at an incorrect position in the image

Medium 1 c

1

Medium 2 c

2

> c

1

Target

Displayed at

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Artefacts

Attenuation Artefacts

• During imaging the outgoing pulse and returning echoes are attenuated as they propagate through tissue, so that echoes from deeper targets are weaker than those from similar superficial targets

• Time Gain Compensation (TGC) is applied to correct for such changes in echo amplitude with target depth

• Most systems apply a constant rate of compensation designed to correct for attenuation in typical uniform tissue

• The operator can also make additional adjustments to compensate via slide controls that adjust the gain applied specific depths in the image

• TGC artefacts may appear in the image when the applied compensation does not match that actual attenuation rate in the target tissue

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Artefacts

Acoustic Enhancement

• Occurs when ultrasound passes through a tissue with low attenuation

• Echoes from deeper lying tissues are enhanced due to the relatively low attenuation in the overlying tissue

• This occurs because the TGC is set to compensate for the greater attenuation in the adjacent tissues

Image of renal cyst

Low attenuation

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Artefacts

Acoustic Shadowing

• Occurs when ultrasound wave encounter a very echo dense (highly attenuating) structure

• Nearly all of the sound is reflected, resulting in an acoustic shadow

• This occurs because the TGC is set to compensate for the lower attenuation in the adjacent tissues

Image of Gallstone

High attenuation

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Artefacts

Reverberation Artefact

• Reverberation artefacts arise due to reflections of pulses and echoes by strongly reflecting interfaces

• Occur most commonly where there is a strongly reflecting interface parallel to the transducer face

• Involves multiple reflections - Initial echo returns to reflecting interface as if it is a weak transmission pulse and returns a second echo (reverberation)

Interface

Reverberation

Transducer

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Artefacts

Attenuation Artefacts

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Artefacts

Attenuation Artefacts

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Contrast Agents

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Contrast Agents

Ultrasound Contrast Agents

• Ultrasound contrast agents are gas-filled micro-bubbles which are injected into the blood stream

• Micro-bubbles will give increased backscatter signal due to the large acoustic impedance mismatch between the gas-filled bubble and surrounding tissue

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Contrast Agents

Ultrasound Contrast Agents

• Micro-bubble suspension is injected intravenously into the systemic circulation in a small bolus

• The micro-bubbles will remain in the systemic circulation for a certain period of time

• Ultrasound waves are directed on the area of interest and when the micro-bubbles in the blood flow past the imaging window they give rise to increased signal

• Allows detection of blood flow where it would otherwise not be seen

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Contrast Agents

Ultrasound Contrast Agents

Name

LEVOVIST

SONOVIST

DEFINITY

OPTISON

SONOVUE

SONAZOID

ALBUNEX

Capsule

Palmitic acid

Cyano-acrylate Air

Lipid

Albumin

Perfluoropropane

2

 m

2

 m

Octafluoropropane 3.7

 m

Phospholipids

Surfactant

Albumin

Gas

Air

SF

6

Fluorocarbon

Air

Bubble

Size

3-5

 m

2-3

 m

3.2

 m

4

 m

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Contrast Agents

Targeted Contrast Agents

• Targeted contrast agents are under preclinical development

• They retain the same general features as untargeted micro-bubbles, but they are outfitted with ligands that bind to specific receptors expressed by cell types of interest

• Micro-bubbles theoretically travel through the circulatory system, eventually finding their respective targets and binding specifically

• If a sufficient number of micro-bubbles have bound to the target area, an increased signal will be seen

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Doppler Ultrasound

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Doppler Ultrasound

The Doppler Effect

• The Doppler effect is observed regularly in our daily lives, e.g. it can be heard as the changing pitch of an ambulance siren as it passes by

• The Doppler effect is the change in the observed frequency of the sound wave (

f

r

) compared to the emitted frequency (

f

t

) which occurs due to the relative motion between the observer and the source

• Consider three situations

- Source and observer stationary

- Source moving towards observer

- Source moving away from observer

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Doppler Ultrasound

Source and observer stationary

Source

)

)

)

)

)

Observer

f

r

= f

t

The observed sound has the same frequency as the emitted sound

(Note: Frequency is the number of cycles per second)

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Doppler Ultrasound

Source moving towards observer

)

)

)

)

)

f

r

> f

t

Causes the wavefronts travelling towards the observer to be more closely packed, so that the observer witnesses a higher frequency wave than emitted

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Doppler Ultrasound

Source moving towards observer

)

)

)

)

)

f

r

< f

t

The wavefronts travelling towards the observer will be more spread out, so that the observer witnesses a lower frequency wave than emitted

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Doppler Ultrasound

The Doppler Effect

• The resulting change in the observed frequency from that transmitted is known as the

Doppler shift

• The magnitude of the Doppler shift frequency is proportional to the relative velocity between the source and the observer

• It does not matter if it is the source or the observer is moving

• The Doppler effect enables Ultrasound to be used to assess blood flow by measuring the change in frequency of the ultrasound scattered from moving blood

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Doppler Ultrasound

Ultrasound measurement of blood flow

• Transducer is held stationary and the blood moves with respect to the transducer

• The ultrasound waves transmitted by the transducer strike the moving blood, so the frequency of the ultrasound experienced by the blood is dependent on whether the blood is stationary, moving towards or away from the transducer

• The blood then scatters the ultrasound, some of which travels in the direction of the transducer and is detected

• The scattered ultrasound is Doppler frequency shifted again as a result of the motion of the blood, which now acts as a moving source

• Therefore, a Doppler shift has occurred twice between the ultrasound being transmitted and received back at the transducer

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Doppler Ultrasound

Ultrasound measurement of blood flow

Doppler frequency shift, f d

= f r

f t

=

2 f c t v cos

Target direction

f

r

= received frequency

f

t

= transmitted frequency c = speed of sound v = velocity of blood

= angle between the path of the ultrasound beam and the direction of the blood flow (angle of insonation)

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Doppler Ultrasound

Ultrasound measurement of blood flow

• The detected Doppler shift also depends on the cosine of the angle

 between the path of the ultrasound beam and the direction of blood flow

• The operator can alter

 by adjusting the orientation of the transducer on the skin surface

• Desirable to adjust

 to obtain the highest Doppler frequency shift cos

1

0

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90

Doppler Ultrasound

Ultrasound measurement of blood flow

If the angle of insonation of the ultrasound beam is known it is possible to use the Doppler shift frequency to estimate the velocity of the blood using the Doppler equation

v = c f d

2 f t cos

In diseased arteries the lumen will narrow and the blood velocity will increase

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Doppler Ultrasound

Ultrasound measurement of blood flow

A

1

V

1

A

2

Narrowing in artery

V

2

The flow (Q) remains constant

Q = A

1

V

1

= A

2

V

2

A = Area

V = Velocity

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Break

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Session 4 Overview

Session Aims:

• Continuous Wave Doppler US

• Pulsed Wave Doppler US

• Harmonic Imaging

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Doppler Ultrasound

Continuous Wave and Pulsed Wave Doppler

• Doppler systems can be either continuous wave or pulsed wave

• Continuous wave (CW) systems transmit ultrasound continuously

• Pulsed wave (PW) systems transmit short pulses of ultrasound

• The main advantage of PW Doppler is that Doppler signals can be acquired from a known depth

• The main disadvantage of PW Doppler is that there is an upper limit to the Doppler frequency shift which can be detected

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Doppler Ultrasound

Continuous Wave (CW) Doppler

• In a CW Doppler system there must be separate transmission and reception of ultrasound

– transducer with two separate elements

• The region from which Doppler signals are obtained is determined by the overlap of the transmit and receive ultrasound beams

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Doppler Ultrasound

Pulsed Wave (PW) Doppler

• In a PW Doppler system it is possible to use the same transducer element for both transmit and receive

Transducer

• The region from which Doppler signals are obtained is determined by the depth of the gate and the length of the gate, which can both be controlled by the operator

Gate depth

Gate length

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Doppler Ultrasound

Ultrasound signal received by transducer

The received ultrasound signal consists of the following four types of signal:

• echoes from stationary tissue

• echoes from moving tissue

• echoes from stationary blood

• echoes from moving blood

The task for the Doppler system is to isolate and display the Doppler signals from blood, and remove those from stationary and moving tissue

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Doppler Ultrasound

Ultrasound signal received by transducer

• Doppler signals from blood tend to be low amplitude (small reflected echo) and high frequency shift

(high velocity)

Amplitude

• Doppler signals from tissue are high amplitude (large reflected echo) and low frequency shift (low velocity)

• These differences provide the means by which signals from true blood flow may be separated from those produced by surrounding tissue

Tissue

Blood

Frequency

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Doppler Ultrasound

Doppler signal processing

Transducer

Signal processor

Demodulator

High-pass filter

Frequency estimator

Demodulation

Separation of the Doppler frequencies from the underlying transmitted signal

High-pass filtering

Removal of the tissue signal

Frequency estimation

Calculation of Doppler frequency and amplitudes

Display

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Doppler Ultrasound

Demodulation

• The Doppler frequencies produced by moving blood are a tiny fraction of the transmitted ultrasound frequency

• E.g. If transmitted frequency is 4 MHz, a motion of 1 m/s will produce a

Doppler shift of 5.2 kHz, which is less the 0.1% of the transmitted frequency

• The extraction of the Doppler frequency information from the ultrasound signal received from tissue and blood is called demodulation

• In PW Doppler, need the PRF to be at least twice the maximum

Doppler shift frequency in order to avoid ‘aliasing’ (not a problem in CW)

• Aliasing is an artefact introduced by under-sampling in which high frequency components take the alias of a low frequency component

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Doppler Ultrasound

High-pass Filtering

Amplitude

Tissue

High-pass

Filtering

Amplitude

Frequency

Blood

Frequency

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Blood

Doppler Ultrasound

Frequency Estimation

• A spectrum analyser calculates the amplitude of all the frequencies present within the Doppler signal

• In the spectral display the brightness is related to the amplitude of the

Doppler signal component at that particular frequency

Frequency shift

Time

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Doppler Ultrasound

Aliasing

Original signal

Aliased signal

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Doppler Ultrasound

Aliasing

Aliased signal

Increased PRF

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Doppler Ultrasound

Duplex Imaging

• Duplex imaging combines Doppler information with a real-time B-mode image

• This produces a 2D representation of the direction and velocity of the blood flow on a grey-scale image

• In a typical display blood flowing towards the transducer is coded as red and blood flow away from the transducer is coded blue

Red

– towards transducer

Blue

– away from transducer

Green - Variance

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Doppler Ultrasound

Doppler Displays

– Spectral Doppler

• Available in CW and PW Doppler

• Detailed analysis of distribution of flow

• Examine change in flow with time

Frequency shift or

Velocity

Time

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Doppler Ultrasound

Doppler Displays

– Colour Doppler

• Available in PW Doppler only

• Superimposed Doppler information on underlying B-mode image

• Overall view of flow in region

• The sign (direction), mean Doppler shift (mean velocity) and variance

(turbulence) of Doppler spectrum are usually colour-coded and displayed

Red

– towards transducer

Blue

– away from transducer

Green - Variance

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Doppler Ultrasound

Doppler of Common Carotid Artery

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Doppler Ultrasound

Blockage in Carotid Artery

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Doppler Ultrasound

Renal Colour Doppler

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Doppler Ultrasound

Doppler Displays

– Power Doppler

• In a Colour Doppler image the magnitude of the frequency shift colour encodes the pixel value and assigns a colour depending on blood flow direction

• This Doppler signal processing places a restriction on the motion sensitivity since the signals received must be extracted to determine the velocity (magnitude of Doppler shift) and direction (phase shift)

• Power Doppler encodes the strength of the Doppler shifts (amplitude, intensity, power) with colours and ignores directional (phase) information

• In Power Doppler the magnitude of the Doppler signal is displayed rather than the Doppler frequency shift (e.g. the density of the red blood cells is depicted rather than their velocity)

• Power Doppler therefore exhibits increased sensitivity to slow flow rates at the expense of directional and quantitative flow information

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Doppler Ultrasound

Suspicious dark lesion

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Doppler Ultrasound

Power Doppler

– Circle of Willis

Suspicious dark lesion

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Doppler Ultrasound

Prostate Cancer

Suspicious dark lesion

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Harmonic Imaging

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Harmonic Imaging

Introduction

• Harmonic imaging of tissue is useful in suppressing weak echoes caused by artefact (acoustic noise) which cloud the image and make it difficult to identify anatomical features.

• These echoes (often called clutter) are particularly noticeable in fluid filled areas (e.g. heart or cyst) and are a common problem when imaging large patients.

• Harmonic imaging is possible by utilising harmonic frequencies of the ultrasound pulse.

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Harmonic Imaging

The Ultrasound Pulse

• Ideally the US pulse would rise and fall very quickly and contain only one frequency (or wavelength)

• In reality the US pulse contains a finite range of frequencies (or wavelengths)

Actual

Ideal

Frequency

Frequency

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Harmonic Imaging

Spatial Pulse Length (SPL)

The spatial pulse length (in mm) is defined as

 n

Where

 is the wavelength and n is the number of cycles

A wider range of wavelengths and more cycles produces a longer SPL

Use a higher frequency and shorter US pulse to give smaller SPL and improved resolution

For Diagnostic US typical SPL values range from 0.3 to 1.0 mm

SPL

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Harmonic Imaging

Bandwidth

• Bandwidth describes the spread of

US frequencies the transducer can transmit/receive

• The frequency content may be specified in terms of the Q factor:

Q factor = F

0

/ (F

2

– F

1

)

• An increased bandwidth and a decreased SPL reduces the Q Factor

• High Q = pure ultrasound pulse

Amp

Freq

F

0 is the centre frequency and the lower and upper frequencies (F

2 and

F

1

) are at half the peak amplitude

(reduction of 3 dB)

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Harmonic Imaging

Side Lobes

• Ideally US pulse energy appears as a single front travelling in forward direction

• Some energy travels off in different directions called

side lobes

• The energy transmitted in side lobes can reduce image quality

(contrast and resolution)

Main lobe side lobes

Transducer

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Harmonic Imaging

Non-linear Propagation

• In the description of propagation of sound waves given in the first session the wave propagated with a fixed speed determined by the properties of the medium

• This is a good approximation to reality when the amplitude of the wave is small, but at higher pressure amplitudes the effects on non-linear propagation become noticeable

• The speed at which each part of the wave travels is related to the properties of the medium

and

to the local particle velocity, which enhances or reduces the speed

• In the high pressure (compression) parts of the wave this results in a slight increase in speed

• In the low pressure (rarefaction) parts of the wave this results in a slight decrease in speed

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Harmonic Imaging

Non-linear Propagation

• As the wave propagates into the medium the compression parts catch up with the rarefaction parts

• The compression parts become taller and narrower in amplitude, while the rarefaction become lower in amplitude

• The rapid changes in pressure in the compression parts of the wave appear in the pulse spectrum as high frequency components, these are multiples of the fundamental frequency F

0 known as Harmonics

Fundamental Frequency

F

0

Second Harmonic

2F

0

Third Harmonic

3F

0

Frequency

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Harmonic Imaging

Harmonic Imaging

• In harmonic imaging an US pulse is transmitted with fundamental frequency F

0 but due to non-linear propagation the returning echoes also contain energy at harmonic frequencies 2 F

0 and 3 F

0

.

• The imaging system ignores the fundamental frequency component of the echo and forms an image using only the 2 nd harmonic component.

• The effective ultrasound beam (the harmonic beam) is narrower than the conventional beam because non-linear propagation occurs most strongly in the highest amplitude parts of the transmitted beam (i.e. near beam axis).

• Weaker parts of the beam such as side lobes and edges of the main lobe produce little harmonic energy and are suppressed in relation to the central part of the beam.

• Harmonic imaging also reduces acoustic noise from weak echoes and reverberations.

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Harmonic Imaging

Transmit Pulse

Transducer

Bandwidth

Transmit

Pulse

Received Echo

Filtered Echo

F

0

Frequency

F

0

2F

0

2F

0

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Harmonic Imaging

Harmonic Imaging

• Harmonic imaging can only be performed with a wide bandwidth transducer which can respond to both the fundamental frequency and its 2 nd harmonic.

• The received echoes are passed through a filter which removes frequencies around F

0 and only allows through those near to 2F

0

.

• As ‘acoustic noise’ echoes are mainly at the fundamental frequency, they are suppressed giving a clearer image.

• To achieve good separation of the received 2 nd harmonic frequencies from the fundamental frequencies, the frequency spectra of the pulse and received echoes must be made narrower than in normal imaging.

• Reduction of the frequency range results in an increase in pulse length and a reduction in axial resolution.

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The End

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