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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