Introduction to Ultrasound Physics
Vassilis Sboros
Medical Physics and Cardiovascular Sciences
University of Edinburgh
Transverse waves
•Water remains in position
Disturbance traverse producing more wave along the path
Disturbance travel at 90o of water movement, hence transverse
Longitudinal wave
•Particles remains in position
Disturbance 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
λ=
c
ν
For ctissue = 1540 m/s
ν=1MHz, λ=1.54mm
ν=3MHz, λ=0.51mm
ν=10MHz, λ=0.15mm
c : velocity of sound (ms-1)
ν : frequency (Hz)
cair = 330 m/s
λ=0.33mm
Phase
a)
b)
Angle of cycle rotation
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
c=
ρ
κ : stiffness (Pa)
ρ : density (Kg/m3)
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
p
Z = = ρc
u
p : pressure (Pa)
u : particle velocity (m/s)
Reflection
p2 Z1 − Z 2 ρ1c1 − ρ 2 c2
=
=
p1 Z1 + Z 2 ρ1c1 + ρ 2 c2
pmuscle / pblood = 0.03
pfat / pmuscle = 0.10
pbone / pmuscle = 0.64
pmuscle / pair = 0.99
Reflection
a)
b)
c)
Smooth surface
Small particle
Rough surface
Scattering
General case for reflection
λ >> particle size = Rayleigh scattering
λ ~ particle size = Mie scattering
λ << particle size = reflection
Refraction
Attenuation
Attenuation = scattering + absorption
Absorption = conversion to heat
Intensity decays exponentially
Frequency dependant
Interference
Multiple ultrasound sources
a) Constructive interference – waves in phase
b) Destructive interference – waves in antiphase
Plane disk transducer
Intensity (space)
Frequency Spectrum
a)
b)
Time domain
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)
b)
c)
d)
e)
Linear
Curvilinear
Trapezoidal
Sector
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
Controls
Doppler system
patient
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
Transducer
Blood
Transmission
T
Scattering
R
Reception
R
Case 1. Blood stationary
Transmission
T
Scattering
R
Reception
R
fr = ft
Case 2. Blood moving away from transducer
Transmission
T
Scattering
R
Reception
R
fr < ft
Case 3. Blood moving towards
transducer
Transmission
T
Scattering
R
Reception
R
fr > ft
General case
ft
v
fr = ft + fd
fd = 2 ft v/c
Some values
• Transmit frequency
• Speed of sound
• Speed of blood
• Doppler shift
• Hear Doppler signal
4 MHz
1540 m/s
1 m/s
=
5194 Hz
Doppler ultrasound
Transmission
ft
Scattering
Reception
fr
Doppler ultrasound
ft + fd
ft
θ
v
fd = 2 ft v cos θ/c
Cosine function
1.0
Cosine
0.8
0.6
0.4
0.2
0.0
0
10 20 30 40 50 60 70 80 90
Angle (degrees)
80ο
60ο
40ο
Some more values
•
•
•
•
Transmit frequency
Velocity
Angle
Speed of sound
3-5 MHz
0-3 m/s
40-80 degrees
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)
baseline
Time (s)
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)
baseline
Time (s)
Spectral Doppler - continuous wave (CW)
Display
R
T
Doppler signal
processor
Transducer
Sensitive region
• 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
Internal iliac
External
iliac
Umbilical
2 vessels in beam
Pulsed wave (PW) Doppler systems
Doppler signal
processor
Display
Sensitive
region
Gate depth
• Emits ultrasound in pulses
Gate length
• 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
Display
R
T
Doppler signal
processor
Tissue
Tissue
Blood
Blood
T
Received signal
Tissue
Blood
Amplitude
R
From
tissue
(Clutter)
From
blood
4.999
5.000
5.001
Frequency (MHz)
Tissue
Blood
5.002
Amplitude
Demodulation
4.999
5.000 5.001
Frequency (MHz)
5 .002
-1000
Demodulation removes
underlying transmit frequency
0
Frequency (Hz)
1000
2000
Lost blood
signal
High pass filter
-1000
0
1000
2000
-1000
0
1000
Frequency (Hz)
Filter frequency
thresholds
Filtering removes the
clutter signal
2000
Amplitude
10ms
Time
Spectrum analysis
Doppler
frequency
Time
Spectrum analysis
estimates all the
frequencies present
in the Doppler signal
Transducer
Received signal
4.999 5.000 5.001
5 .002
Signal processor
Demodulator
High pass filter
Doppler signal
-1000
Spectrum analysis
Display
Spectral display
0
1000
2000
Frequency
(MHz)
Cut-off filter
Filter low
End diastolic
flow
Filter high
Loss of end
diastolic flow
Typical filter values
• Obstetrics
• Vascular
• cardiology
80-100Hz (little arterial movement)
150-200 Hz (some arterial pulsation)
300Hz+
(valves and myocardium)
Pulsed wave (PW) Doppler
Doppler signal
processor
Sensitive
region
Gate depth
Gate length
Display
Doppler signal
CW
PW
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)
Atherosclerosis
Jet
Turbulence
Quantification 1. Peak velocity
Max velocity
Measurement of blood velocity I.
Transducer
θ
v
v = c fd
2ft cos θ
Measurement of blood velocity II.
Measurement of blood velocity III.
Standard table
Diameter
stenosis (%)
0
Peak systolic
velocity (cm/s)
< 90
0 - 15
< 100
15 - 50
< 125
50 - 80
> 135
80 - 99
> 230
Downstream disease
Uterine artery
Fetus
Placenta
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
Peak systolic marker
End diastolic 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
Sector
Colour
box
Linear array
Colour
box
• Image built up line by line
• Each line consists of adjacent sample volumes
Colour flow system components
Display
B-scan
processor
Colour flow
processor
Spectral Doppler
processor
Beamformer
Transducer
Transmitters
Colour flow processor
Demodulator
Clutter
filter
Doppler
statistic
estimator
Post
processor
Blood tissue
discriminator
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
• ‘Persistence’ or ‘Frame-averaging’
– Reduces noise
– ‘lag’ in image
High persistence
Low persistence
Value =
0.4 frame 1
+ 0.3 frame 2
+ 0.2 frame 3
+ 0.15 frame 4
+ 0.10 frame 5
Value =
0.6 frame 1
+ 0.4 frame 2
Blood-tissue discriminator
Colour
image
(mean
Doppler
frequency)
B-mode
image
Blood-tissue discriminator
Colour
image
(mean
Doppler
frequency)
B-mode
image
No blood tissue discriminator
With blood tissue discriminator
Colour modes
Colour
processor
Variance
Mean frequency
Colour Doppler
Power
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 amplitude
40o
60o
90o
Doppler frequency
Clutter filter
Angle dependence
Aliasing
Aliasing
Doppler
amplitude
3m/s
4m/s
1m/s
2m/s
3m/s
Doppler frequency
Aliasing
limit
Aliasing
limit
Jet
Recirculation