Introduction to Ultrasound Physics

Vassilis Sboros

Medical Physics and Cardiovascular SciencesUniversity of Edinburgh

Transverse waves

•Water remains in positionDisturbance traverse producing more wave along the pathDisturbance travel at 90o of water movement, hence transverse

Longitudinal wave

•Particles remains in positionDisturbance travel at 0o of particle movement, hence longitudinal

Sound-Mechanical wave

Generated by piezoelectric crystals

Single reflection

Sound-Mechanical wave

Frequency

• 1Hz = 1 cycle per second• Sound 20 Hz – 20 kHz• Ultrasound > 20kHz• Diagnostic Ultrasound 1-50 MHz• Ultrasound Therapy 40kHz-1MHz

Some definitions

• Wavelength• Phase• Velocity of sound • Acoustic impedance• Reflection• Scattering• Refraction• Absorption• Attenuation

Wavelength λ

c : velocity of sound (ms-1)

ν : frequency (Hz)

For ctissue= 1540 m/s cair = 330 m/s

ν=1MHz, λ=1.54mm λ=0.33mm

ν=3MHz, λ=0.51mm

ν=10MHz, λ=0.15mm

νλ c=

Phase

a) Angle of cycle rotation

b) Phase difference between identical waves

Pressure

• Positive – compression, negative –rarefaction

• Units 1 Pa = N / m2

Intensity (time)

Units W / m-2

Velocity of sound c

κ : stiffness (Pa)

ρ : density (Kg/m3)

ρκ=c

cair = 330 m/s

cwater= 1480 m/s

ctissue= 1540 m/s

cfat = 1450 m/s

cblood= 1570 m/s

cbone= 3500 m/s

Acoustic impedance Z

cu

pZ ρ==

p : pressure (Pa)

u : particle velocity (m/s)

Reflection

2211

2211

21

21

1

2

cc

cc

ZZ

ZZ

p

p

ρρρρ

+−=

+−=

pmuscle/ pblood= 0.03

pfat / pmuscle= 0.10

pbone/ pmuscle= 0.64

pmuscle/ pair = 0.99

Reflection

a) Smooth surface

b) Small particle

c) Rough surface

Scattering

General case for reflection

λ >> particle size = Rayleigh scattering

λ ~ particle size = Mie scattering

λ << particle size = reflection

Refraction

AttenuationAttenuation = scattering + absorption

Absorption = conversion to heat

Intensity decays exponentially

Frequency dependant

Interference

a) Constructive interference – waves in phase

b) Destructive interference – waves in antiphase

Multiple ultrasound sources

Plane disk transducer

Intensity (space)

Frequency Spectrum

a) Time domain

b) Frequency domain (FFT)

Nonlinear propagation

At high ultrasound pressure• Time domain –

asymmetrical pattern

• Frequency domain (FFT) –Harmonic frequencies

Bibliography

• McDicken W.N. Diagnostic Ultrasonics Churchill Livingstone New York

1991.

• Barnett E., Morley P. Clinical Diagnostic Ultrasound Blackwell

Scientific Publications, Oxford 1985.

• Meire H.B., Cosgrove D.O., Dewbury K.C., Farrant P. Clinical Ultrasound a comprehensive text: Abdominal and General Ultrasound Vol.2 Churchill Livingstone New York 2001.

The Engineering of

Ultrasound Imaging

Vassilis Sboros

Medical Physics and Cardiovascular Sciences

University of Edinburgh

Transducer Engineering -

Piezoelectric materials

• Positive Voltage = compression

• Synthetic ceramic - Lead Zirconate Titanate (PZT)– High sensitivity

– High acoustic power

– Easy to micromachine

– Impedance 20x tissue

• Thickness = λ/2 - resonance– Resonance due to internal reflection

– Determines transmit frequency

Transducer Engineering –

Backing layer

• PZT Impedance 20x

tissue

– Duration of pulse difficult

to control due to internal

ringing

• Backing layer = absorber

– High impedance

– Reduces ringing

Transducer Engineering –

Matching layer

• PZT Impedance 20x tissue

– Only 20% of energy transmitted to tissue

• Matching layer = impedance matching

– Impedance lower than PZT and higher than tissue

– Remove some ringing

• 1 layer 2x sensitivity

– λ/4 thickness

– Constructive interference towards tissue

– Destructive interference towards PZT

Transducer Engineering –

Frequency bandwidth vs sensitivity

• High sensitivity = specific dimensions for Backing, PZT and Matching layers

– Frequency band is narrow

– Resolution low

• >1 Matching layers

– Decreasing impedance

• Bandwidth 2x (60% to 120%)

– Little loss in sensitivity

1D – Single Plane disk transducer

2D beams – Array transducers

a) Linear

b) Curvilinear

c) Trapezoidal

d) Sector

e) Radial

Transducer Engineering –

Lens

• Single element

– Focus has high sensitivity and resolution

• Linear Array

– Electronically in scan plane

– Only in elevation plane

• Phased Array

– Mild in scan plane

– Stronger in elevation plane

Linear Array Transducers

• 128 elements

– Binary processing

• Choice of frequency

– Penetration vs resolution or attenuation vs frequency

• Dimensions ~ 1/f

– ~1.3λ width per element (83mm @3MHz)

– ~30λ height - elevation(15mm @3MHz)

Linear Array Transducers

• Active group of elements

– Finite beam per element

– Transmit fixed (~20)

– Receive (<20 to >20 as depth increases)

– Electronic focus

Linear Array Transducers

• Transmit Electronic Focus

– Transmission timing

– One focus

– Controllable

Linear Array Transducers

• Receive Electronic Focus

– Electronic delay

– Depth ~ element number

– Multiple foci

– Not controllable/automatic

– High resolution at all depths

Linear Array Transducers

Transmit Multiple focus

Linear Array Transducers

1.5D array

for improved elevation focus

Linear Array Transducers

Transmit Apodization

Curvilinear Array Transducers

• Sector scanning

– Wider field

– Linear array structure

– Active element number reduced -Poorer resolution

Phased Array Transducers

• Sector scanning

– Narrow acoustic window

• Narrower elements

– All elements used (transmit and receive)

– Shorter near field per element

– Wider far field per element

– Beam steering ±45o

Linear/Phased Array Transducers

Compounding – Reduction of noise

Persistence – Reduction of frame rate

Matrix Array Transducers

Endocavity Array Transducers

a) Curvilinear – transvaginal

b) Curvilinear – Transvaginal, transrectal

c) Bi-plane – Transrectal(prostate)

d) Phased array –Transoesophageal (heart)

Intravascular Array Transducers

• Curvilinear/convex 360o

• High frequency (30MHz)

• Vessel wall

phantom

A-mode (transmission)

A-mode

Eye A-mode

B-mode scanning

Eye B-mode

B-mode

Formation of B-mode image

B-mode

B-mode

Transmit gain and power

B-mode

Time gain compensation

(TGC)

Compensate for attenuation

B-mode

Analogue to digital conversion

limited values – memory

binary system

sampling rate (40MHz)

digital processing

B-mode

Digital signal Rectification Enveloping

B-mode

Compression

Accommodate in the image

low and high echoes

B-mode

Image memory

B-mode

Interpolation

Linear?

B-mode

Reading of image memory to

form display

Gray scale

Ultrasound Imaging Modes

• Real-time 2D imaging

– Good spatial resolution

– Good temporal resolution

– Good Penetration

Heart scan

Ultrasound Imaging Modes

• 3D and 4D

– Good spatial resolution

– Poor temporal resolution

– OK Penetration Foetal scan

Heart scan

Doppler Ultrasound

Pete Hoskins and Vassilis Sboros

Medical Physics and Cardiovascular Sciences

University of Edinburgh

Doppler ultrasound

• Principles of Doppler

• CW/PW Doppler

• Doppler systems (spectral, duple, colour) and controls

• Principles of contrast imaging

Doppler effect

patient

Doppler system

Controls

Doppler effect

Change in pitch is proportional to speed of source

Change in pitch = fS - fO

Doppler shift = fd = fS - fO

Speed = v

fd ~ v

Doppler ultrasound

T

R

TransducerBlood

R

Transmission

Scattering

Reception

Case 1. Blood stationary

T

R

R

Transmission

Scattering

Reception

fr = ft

Case 2. Blood moving away from transducer

T

R

R

Transmission

Scattering

Reception

fr < ft

Case 3. Blood moving towards

transducer

T

R

R

Transmission

Scattering

Reception

fr > ft

General case

v

fr = ft + fd

ft

fd = 2 ft v/c

Some values

• Transmit frequency 4 MHz

• Speed of sound 1540 m/s

• Speed of blood 1 m/s

• Doppler shift = 5194 Hz

• Hear Doppler signal

Doppler ultrasound

Transmission Scattering Reception

ftfr

Doppler ultrasound

θ v

ft

ft + fd

fd = 2 ft v cos θ/c

Cosine function

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90

Angle (degrees)

Co

sin

e

80ο 40ο60ο

Some more values

• Transmit frequency 3-5 MHz

• Velocity 0-3 m/s

• Angle 40-80 degrees

• Speed of sound 1540 m/s

• Doppler frequency shift 0-15 kHz

• Audio range 0-20 kHz

• Can hear Doppler shift frequencies

Doppler systems

• Spectral display

• Colour flow

Spectral display

Frequency

shift (kHz)

Time (s)

baseline

Colour flow

‘Triplex’ display

Summary of systems and main controls

• 2 main types of system are

– Spectral Doppler

– Colour flow

• main controls for spectral Doppler adjust:

– position of sensitive region

– beam direction

– spectral Doppler display

• main controls for colour flow adjust:

– size and depth of colour box

– beam direction

– colour display

Spectral Doppler

Frequency

shift (kHz)

Time (s)

baseline

Spectral Doppler - continuous wave (CW)

TR

Sensitive region

Transducer

Doppler signal

processor

Display

• Separate transmit and receive

elements

• Emits ultrasound continuously

• Receives ultrasound continuously

• Doppler signals from sensitive region

Stand alone CW Doppler system:

features

• No B-mode image

• No depth discrimination

• Use for vessels at defined location

• Use for vessels with characteristic waveform shapes

• Obstetric applications - umbilical arteries

• Peripheral vascular application - carotid, lower limb

CW spectral Doppler examples

Arcuate artery External

iliac

Internal iliac Umbilical

2 vessels in beam

Pulsed wave (PW) Doppler systems

Gate depth

Gate length

Sensitive

region

Doppler signal

processor

Display

• Emits ultrasound in pulses

• Depth discrimination

• Sensitive region depth and length set by user

Stand alone PW Doppler system - features

• No B-mode image

• Depth discrimination

• Use for vessels at defined location

• Use for vessels with characteristic waveform shapes

• Transcranial

Duplex system

B-mode + PW Doppler = Duplex

Duplex system - features

• B-mode and PW Doppler

• depth discrimination

• all cardiovascular applications

• basis for all modern Doppler systems

System components and signal processing

TR

Doppler signal

processor

Display

Tissue

BloodTissue

Blood

Received signal

Frequency (MHz)

4.999 5.000 5.001 5.002

Am

pli

tud

e

From

tissue

(Clutter)

From

blood

TR

Tissue

Blood

Blood

Tissue

Frequency (Hz)

-1000 0 1000 2000

Frequency (MHz)

4.999 5.000 5.001 5 .002

Am

pli

tud

e

Demodulation

Demodulation removes

underlying transmit frequency

Frequency (Hz)

-1000 0 1000 2000

Filter frequency

thresholds

Lost blood

signal

-1000 0 1000 2000

High pass filter

Filtering removes the

clutter signal

Time

Amplitude

10ms

Time

Doppler

frequency

Spectrum analysis

Spectrum analysis

estimates all the

frequencies present

in the Doppler signal

Transducer

Display

Spectrum analysis

Demodulator

High pass filter

Signal processor

Frequency

(MHz)4.999 5.000 5.001 5 .002

-1000 0 1000 2000

Received signal

Doppler signal

Spectral display

Cut-off filter

Filter low

Filter high

End diastolic

flow

Loss of end

diastolic flow

Typical filter values

• Obstetrics 80-100Hz (little arterial movement)

• Vascular 150-200 Hz (some arterial pulsation)

• cardiology 300Hz+ (valves and myocardium)

Pulsed wave (PW) Doppler

Gate depth

Gate length

Sensitive

region

Doppler signal

processor

Display

CW

PW

Doppler signal

Aliasing

• Upper limit to detected velocity measured using PW

Doppler

Max Doppler

frequency shift

CW Doppler signal

PW Doppler signal

(lots of samples)

PW Doppler signal(2 samples/wavelength)

PW Doppler signal

(not enough samples)

Aliasing

Aliasing

• Doppler frequency shift estimated correctly when:

– at least 2 samples per wavelength

– prf > 2 fd

• Maximum Doppler frequency shift which can be

estimated is half the prf

– fd(max) = prf/2

Waveforms in disease

• Local disease (Atherosclerosis)

• Downstream disease (placental disease)

Jet TurbulenceAtherosclerosis

Quantification 1. Peak velocity

Max velocity

Measurement of blood velocity I.

Transducer

v

θ v = c fd

2ft cos θ

Measurement of blood velocity II.

Measurement of blood velocity III.

Standard table

Diameter Peak systolic

stenosis (%) velocity (cm/s)

0 < 90

0 - 15 < 100

15 - 50 < 125

50 - 80 > 135

80 - 99 > 230

Downstream disease

Fetus Placenta

Uterine artery

Spiral/arcuate

arteries

Abnormal placental development leads

to increase in resistance to flow

Umbilical waveforms

Quantification 2. Waveform shape.

Max

Mean

Min

Resistance index (RI) = (max-min)/max

Pulsatility index (PI) = (max-min)/mean

Estimation of RI

End diastolic marker

Peak systolic marker

Controls for CW, PW and duplex

– position of sensitive region (PW, duplex)

• gate length, gate depth

– beam direction (PW, duplex)

• Beam steering angle

– spectral Doppler display (CW, PW, duplex)

• gain

• Filter level

• Velocity scale

• Time scale

• Baseline

– Measurement (duplex)

• Beam-vessel angle

Colour flow

Colour flow image

• Display of 2D flow image superimposed on B-mode

image

Colour boxes

• Image built up line by line

• Each line consists of adjacent sample volumes

Sector Linear array

Colour

boxColour

box

Colour flow system components

Colour flow

processor

Display

Beamformer

B-scan

processor

Spectral Doppler

processor

Transducer Transmitters

DemodulatorClutter

filter

Doppler

statistic

estimator

Post

processorBlood tissue

discriminator

Colour flow processor

Clutter filter

clutter

blood

Frequency (MHz) Frequency (MHz)

Frequency estimation

• Fast Fourier Transform (64-128 data points)

– full frequency spectrum

• Autocorrelator (3 data points)

– mean frequency

– variance

– power

Post-processor

High persistence

Value =

0.4 frame 1

+ 0.3 frame 2

+ 0.2 frame 3

+ 0.15 frame 4

+ 0.10 frame 5

Low persistence

Value =

0.6 frame 1

+ 0.4 frame 2

• ‘Persistence’ or ‘Frame-averaging’

– Reduces noise

– ‘lag’ in image

Blood-tissue discriminator

B-mode

image

Colour

image

(mean

Doppler

frequency)

Blood-tissue discriminator

B-mode

image

Colour

image

(mean

Doppler

frequency)

No blood tissue discriminator

With blood tissue discriminator

Colour modes

Colour

processor

Mean frequency Power

Variance

Colour Doppler Power Doppler

Mean frequency: red-blue scale

Mean frequency + variance: red-blue +

green

Power: no B-mode in colour box

Power: with B-mode in colour box

Angle dependence

θ θ θ

Colour Doppler angle dependence

Power Doppler angle dependence

Angle dependence

Doppler frequency

Doppler amplitude40o

90o

60o

Clutter filter

Angle dependence

Aliasing

Doppler frequency

Doppler

amplitude

1m/s 2m/s 3m/s4m/s3m/s

Aliasing

limit Aliasing

limit

Aliasing

Jet

Recirculation