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 90 o of water movement, hence transverse
Longitudinal wave Particles remains in position Disturbance travel at 0 o 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
Wavelength Phase Velocity of sound Acoustic impedance Reflection Scattering Refraction Absorption Attenuation Some definitions
Wavelength λ λ = c ν For c tissue = 1540 m/s ν=1mhz, λ=1.54mm ν=3mhz, λ=0.51mm ν=10mhz, λ=0.15mm c air = 330 m/s λ=0.33mm c : velocity of sound (ms -1 ) ν : frequency (Hz)
Phase a) Angle of cycle rotation b) Phase difference between identical waves
Pressure Positive compression, negative rarefaction Units 1 Pa = N / m 2
Units W / m -2 Intensity (time)
Velocity of sound c c = κ ρ κ : stiffness (Pa) ρ : density (Kg/m 3 ) c air = 330 m/s c water = 1480 m/s c tissue = 1540 m/s c fat = 1450 m/s c blood = 1570 m/s c bone = 3500 m/s
Acoustic impedance Z Z = p u = ρ c p : pressure (Pa) u : particle velocity (m/s)
Reflection 2 2 1 1 2 2 1 1 2 1 2 1 1 2 c c c c Z Z Z Z p p ρ ρ ρ ρ + = + = p muscle / p blood = 0.03 p fat / p muscle = 0.10 p bone / p muscle = 0.64 p muscle / p air = 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
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) 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 vssensitivity 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 vsresolution or attenuation vs frequency Dimensions ~ 1/f ~1.3λwidth 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 ±45 o
Linear/Phased Array Transducers Compounding Reduction of noise Persistence Reduction of frame rate
Matrix Array Transducers
EndocavityArray Transducers a) Curvilinear transvaginal b) Curvilinear Transvaginal, transrectal c) Bi-plane Transrectal (prostate) d) Phased array Transoesophageal(heart)
Intravascular Array Transducers Curvilinear/convex 360 o 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 = f S -f O Doppler shift = f d = f S -f O Speed = v f d ~v
Doppler ultrasound Transducer Blood Transmission T Scattering R Reception R
Case 1. Blood stationary Transmission T Scattering R Reception R f r = f t
Case 2. Blood moving away from transducer Transmission T Scattering R Reception R f r < f t
Case 3. Blood moving towards transducer Transmission T Scattering R Reception R f r > f t
General case f t v f r = f t + f d f d = 2 f t v/c
Some values Transmit frequency Speed of sound Speed of blood 4 MHz 1540 m/s 1 m/s Doppler shift = 5194 Hz Hear Doppler signal
Doppler ultrasound Transmission Scattering Reception f t f r
Doppler ultrasound f t + f d f t θ v f d = 2 f t v cos θ/c
Cosine function 1.0 0.8 Cosine 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 70 80 90 Angle (degrees)
40 80 ο ο 60 ο
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) Doppler signal processor Display T R 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 Arcuateartery External iliac Internal 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 Doppler signal processor Display T R Tissue Blood Tissue Blood
Amplitude Received signal T R Blood Tissue From tissue (Clutter) From blood Tissue 4.999 5.000 5.001 5.002 Frequency (MHz) Blood
Amplitude Demodulation 4.999 5.000 5.001 5.002 Frequency (MHz) -1000 0 1000 2000 Frequency (Hz) Demodulation removes underlying transmit frequency
High pass filter Lost blood signal -1000 0 1000 2000 Frequency (Hz) -1000 0 1000 2000 Filter frequency thresholds Filtering removes the clutter signal
Amplitude 10ms Time Spectrum analysis Doppler frequency Time Spectrum analysis estimates all the frequencies present in the Doppler signal
Transducer Signal processor Received signal 4.999 5.000 5.001 5.002 Frequency (MHz) Demodulator High pass filter Spectrum analysis Doppler signal -1000 0 1000 2000 Display 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 Doppler signal processor Display Sensitive region Gate depth Gate length
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 f d Maximum Doppler frequency shift which can be estimated is half the prf f d(max) = prf/2
Waveforms in disease Local disease (Atherosclerosis) Downstream disease (placental disease)
Atherosclerosis Jet Turbulence
Max velocity Quantification 1. Peak velocity
Measurement of blood velocity I. Transducer θ v v = c f d 2f t 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 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 Linear array Colour box 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
Colour image (mean Doppler frequency) Blood-tissue discriminator B-mode image
Colour image (mean Doppler frequency) Blood-tissue discriminator B-mode image
No blood tissue discriminator
With blood tissue discriminator
Colour modes Variance Colour processor Mean frequency Power 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 amplitude 40 o 90 o 60 o Doppler frequency Clutter filter
Angle dependence
Aliasing
Aliasing Doppler amplitude 3m/s 4m/s 1m/s 2m/s 3m/s Aliasing limit Doppler frequency Aliasing limit
Jet Recirculation