Ultrasound Physics Flashcards
- PARAMETERS FOR SOUND
Medium must be elastic for compression and rarefaction to occur
Pressure wave can be plotted as a sine wave
c = λf
Molecules not moving through the whole wave, just oscillating about their position and allowing energy to propogate
Speed of sound is INDEPENDANT of frequency
Time of one full cycle = Time Period = 1 / frequency
What determines the ultrasound speed?
DEPENDANT ON MATERIAL THROUGH WHICH IT TRAVELS
Elastic Property = how readily does it return to original state, how stiff is it
Inertial Property = Force required to move sound through - the denser the object - the more energy required for sound to propagate
Sound travels FASTER through LOWER DENSITIES
DRY AIR > HUMID AIR
Stiffness measured by Bulk’s modulus = B
Density = ρ
As density increases, the speed of sound decreases
Higher density = SLOWER Sound Waves
BUT
Higher density = Bulk Modulus also increases for most things
So speed of sound actually increases but due to the higher Bulk Modulus or STIFFNESS
Areas of rarefaction are actually NEGATIVE pressure measured in pascals (Pa)
As pressure increases = POWER INCREASES ^ 2
Relative intensity scale - Decibels = dB
Ultrasound attenuation is EXPONENTIAL AND NOT LINEAR - so logarithmic scale is helpful
dB = 10 x log ratio
Doubling intensity = +3dB
Having intensity = -3dB
Soft tissue attenuation
e.g.
= frequency x 0.5(dB/cm) / MHz
e.g. 2MHz probe = 1dB/cm drop
After 3cm = 3dB drop = so intensity is HALVED
Multiple sound waves = constructive or destructive interference depending on whether or not they are IN or OUT of phase
Beams converge on a focal point
US beam has varying intensities
When it converges onto a smaller area = beam intensity is higher
Highest intensity = Spatial Peak Intensity
Average of whole beam = Spatial Average Intensity
Temporal average = pulse average + also factoring in DUTY FACTOR
- PULSE ECHO BASICS
You need to use PULSE ECHO ultrasound in order to image. Transmit and then WAIT to RECEIVE.
Remember - the pulse is NOT perfect / uniform
Range Equation
T = (2 x Depth, d) / Speed of sound, c
T = 2D/c
D = Tc /2
Machine uses the TIME in order to plot the DEPTH
remember:
speed = distance / time
distance = speed x time
2 x depth (round trip for echo) = speed x time
depth = (speed x time) /2
Differences in material impedance will determine how much is reflected
REMEMBER SOFT TISSUE AVERAGE = 1540m/s
PULSE DURATION
Pulse duration =
#cycles x T or
#cycles / f
SPATIAL PULSE LENGTH
Length of pulse as it moves through space
SPL = #cycles x λ
You have to lengthen your RECIEVE TIME for DEEPER structures to avoid interference.
So setting depth = changes receive time.
Pulse repetition period = time between the start of the successive pulses
Inverse relationship between pulse repetition period and frequency
Not to be confused with WAVE period and frequency
DUTY FACTOR
Time you are transmitted pulse out of entire time you are acquiring image
= Pulse Duration / Pulse Repetition PERIOD
- ACOUSTIC IMPEDANCE
You can get reflection with partial transmission
Complete reflection of sound wave
Specular reflection
Non-specular reflection
Refraction if speed of sound varies with material and incident wave is at an angle
Scattering = US Wave interactions with objects SMALLER THAN THE WAVELENGTH
- small sound waves in ALL directions
Z = Acoustic impedance = tissue specific property
Product of density ρ and speed of sound C
Density ρ = Kg per metre CUBED
c = metres per second
= Kg / metre ^2 s
OR RAYLS
As speed is a function of the Bulks modulus aka stiffness
Acoustic Impedance is also a function of stiffness
= Kg / metre ^2 s
OR RAYLS
Can think of it like connecting springs over either differing or similar stiffness’s
- REFLECTION
3 Main categories: Perpendicular, Specular and Non-specular
Most soft tissue surfaces = not perfectly smooth and are therefore NON-SPECULAR REFLECTORS
(kind of like a reflection from a broken mirror!)
4a. Perpendicular reflection
Increasing acoustic impedance = larger proportion of reflection
R = Reflectance = (Difference / Sum ) ^2
Energy is conserved
So Total Energy Transmitted = 1 - Reflectance
[ONLY WORKS FOR PERPENDICULAR RELFECTION]
- REFRACTION
You get a mixture of specular reflection and transmittance
Incidence and reflecting angles are the same within the SAME tissue
Refraction angle change is determined by change of sound wave speed through the second tissue
The ratio of speeds is the same as the ratio of the sin of the angles about the normal
If it SLOWS = LARGER TRANSMITTED ANGLE
Another way to visualise this
- SCATTER
Mechanism of LOSS of sound wave AMPLITUDE
Interaction with material elements SMALLER than the WAVELENGTH
Scatter gives tissue its ECHOGENICITY
- ATTENUATION
Dependant on frequency, depth AND material
Higher frequency = Faster attenuation
Higher frequency = more tissue interactions per unit of time
Tissue and frequency dependence for attenuation
Remember this attenuation equation for soft tissue
Half value thickness = Tissue thickness to reduce signal intensity 50% = 3dB change
Dynamic range = how sensitive the probe is to listen for quiet echoes
- ULTRASOUND TRANSDUCER
8A. Piezoelectrical material
Soundwaves compress the material = induces a current = piezoelectric effect
REVERSE piezoelectric effect:
Run an ALTERNATING CURRENT through the material causing it to compress and rarefact
each crystal is a like a guitar string resonating at a set frequency
Known as RESONANT FREQUENCY
Determined by:
1. Speed of
RESONANT FREQUENCY
Determined by:
1. Speed of sound THROUGH PIEZOELECTRIC MATERIAL
2. MATERIAL THICKNESS
Thinner = HIGHER Frequencies
Thicker = LOWER Frequencies
(Like a guitar string = shorter string -> higher frequencies)
Material thickness = HALF THE FREQUENCY
v = f λ
λ = v/f = c / 2(PZT)
8B. MATCHING LAYER
- Smooths transition from high frequency frame to soft tissue
- Acoustic impedance is intermediate or between the two
Ideal thickness = 25% of incident wavelength from probe
8C. DAMPING BLOCK
Sits behind PZT Crystal
Like a wet rag on a cymbal (from drum kit).
1. Helps to dampen the crystal once current has been turned off
2. Gives shorter pulse lengths + LONGER receive time for echo
So BETTER AXIAL Resolution
- BUT gives LESS UNIFORM pulses.
Quality factor = resonant frequency / actual RANGE of frequencies produced.
More dampening = BIGGER RANGE PRODUCED.
BIGGER RANGE = Increase in bandwidth
8D. PZT WIRING
Can programme the order in which the vibrate
Manipulate to interfere in such a way to create a CONVERGENT BEAM
SEQUENTIAL firing can also be used for BEAM STEERING
PIEZOELECTRIC EFFECT
Mechanical INTO ELECTRICAL energy
Current = converted into pixel value
and REVERSE…
PZT = Lead Zirconium Titanate crystal
Oxygen shares electrons with Titanium/Zirconium
Titanium/Zirconium is more relatively positive
CRYSTAL POLARISATION
If zirconium were to move = positive centre would move creating a more positive end = creating a dipole
That’s why you can’t autoclave, you would ruin the structure!
Compression - MOVES the positive centre - causing an electrical current
9A. ULTRASOUND MODES: A MODE
AMPLITUDE mode
YOU TAKE ONE LINE
SINGLE TRANSDUCER ELEMENT
Smaller scatter - gives echotexture
Amplitude of reflected waves = gives tissue boundaries
You can increase pulse repetition frequency for better solution, but you have to reduce to the receive time SO YOU LOSE DEPTH
You can use the time for echo to calculate depth
Depth = (time x speed of sound in tissue) / 2
9B. ULTRASOUND MODES: B MODE
BRIGHTNESS Mode
You scan a line, but each point one at a time like in A Mode
Needs to happen 24 times a second in order to look like a line!
9C. M MODE = MOTION MODE
Combines the two modes
Superimpose an A MODE SCAN LINE over a B MODE IMAGE
Plot the A Mode single row in that specific line
Remember the attenuation is related to depth and frequency of beam
So you need to COMPENSATE for the echoes that take longer and are coming from DEEPER STRUCTURES = TIME GAIN COMPENSATION.
Increased gain of the signal depending on how long it takes to come back, post processing
- Ultrasound probe types
Linear
Curved – Sector as part of a circle.
Phased array – few transducers.
Endo cavity probe
Endovascular Probe
Single Element – ONE PZT CRYSTAL
Arrays – long row of transducer elements – linear or phased
Linear array – 2 or 3 fire a time to get A Mode data which is stitched together.
Phased array – all are fired in different sequences to steer the beam in different ways.
ULTRASOUND BEAM PROFILES
The beam narrows to a point – focal spot
Then diverges into the far field
Focal Zone – region with the best resolution – the width IS HALF of the PROBE TRANSDUCER
Outermost wavelets with interfere with the inner most causing the wave to converge.
- NEAR FIELD GEOMETRY
Distance between transducer and focal spot
Near field distance for the array = just the elements that are firing NOT whole array
- FAR FIELD GEOMETRY
The divergent angle GETS SMALLER
if diameter or frequency increases
Soo wider and higher frequency probes are LESS DIVERGENT
SO YOU GET MORE SIGNAL COMING BACK
Increasing diameter or frequency:
1. Increases focal depth
2. Decreases the divergence
- SIDE LOBES
When PZT contracts and expands they so in ALL DIMENSIONS
These cause SEPARATE WAVES to be propagated
TO REDUCE Side lobes
- DAMPEN US Wave
- NARROW Transducer elements to LESS THAN HALF the wavelength
- REDUCE AMPLITUDE of the peripheral waves
- GRATING LOBES
Additional OFF FIELD LOBES
Multi element transducer ray - wave interference
- FOCUSING AND STEERING
A) Using focusing ACOUSTIC LENS on the front side of the transducer
B) Curved transducer array can also manipulate the focal depth
C) Changing depth by using different widths e.g. just red, or red and orange or all of them would increase depth. Separate focal zones
D) Electronic focusing - delaying firing the central transducer elements will:
- increase angle of focus
- SHORTEN THE DEPTH
- FOCAL DEPTH:
Changing depth by using different widths would increase depth. Separate focal zones
D) Phased arrays, manipulating the DELAY of the CENTRAL transducers
ELECTRONIC FOCUSING:
BIGGER DELAY = SHORTER FOCAL DEPTH
STEERING:
Timing transducer firing
You can also steer and focus
Spatial Compounding
Adjusting angle of beam to acquire different areas - different lenticular pictures
- AXIAL RESOLUTION
Ability to differentiate two objects in the axial plane
Dependant on spatial pulse length = #cycles x wavelength
Need to wait for pulses to return but also need to differentiate between the pulses
When you have enough spacing:
When you don’t
Axial Resolution = 50% of SPL
- LATERAL RESOLUTION = BEAM WIDTH
Differentiating the axial plane
Near field depth is dependant on transducer width and frequency
Function of beam width
Lateral resolution improves approaching focal zone as width reduces
Large delay of central transducers = MORE SHALLOW FOCAL DEPTH
You can can compound different phrases to increase the depth of which you are in focus
Comes at cost of TEMPORAL RESOLUTION as you have to take THREE FRAMES
Improve LATERAL resolution by getting ride of SIDE LOBES
SIDE LOBES makes beam WIDER
- DAMPEN BEAM TO REDUCE Side lobes
- Make transducer elements THINNER - smaller side lobes
- Redice AMPLITUDE at the EDGES of the probe
- ELEVATIONAL RESOLUTION
The beam HEIGHT
ALSO NARROWS at focal zone
Adding additional transducers in elevational plane
1.5 D = More columns than rows
2 D = Equal numbers of columns and rows
Axial resolution allows you to cannulate vessels
In terms of what is best:
1. Axial resolution
2. Lateral resolution
3. Elevational resolution
- TEMPORAL RESOLUTION
To create ONE B-MODE frame
- Multiple A lines are stitched together
frames / sec = 1 / Time (frame)
Time (frame) = # scan lines x Time (line)
Time (line) =
speed = distance / time
time = distance / speed
= 2 X Depth (cm) / Speed of sound in tissue
SO INCREASING DEPTH increases time for one line
As pulse repetition time is longer
To IMPROVE TEMPORAL RESOLUTION
- Reduce line density or lines per degree
- Or keep density and narrow FOV
- Reduce depth
- Reduce number of focal zones
- DOPPLER SHIFT
Difference between frequency received and transmitted
Blood moving TOWARDS probe = high received frequency
AWAY = lower frequency
Doppler Equation
= 2 x frequency of US pulse x
speed of blood / (speed of blood + speed of sound in tissue)
as speed of blood is negligible you can shorten the equation
Probe is measuring speed at an angle
Make a right angle triangle
SOH CAH TOA
You can then rearrange the equation
With a 0 angle, Cos alpha = 1- so measurement is directly proportional to velocity of blood.
INCREASING DOPPLER ANGLE = REDUCTION IN DOPPLER SHIFT
At very steep angles you also get REFRACTION
So we try to keep between 30-60 degrees
You can see above 60 there is an exponential loss of accuracy
You get more of a doppler shift with
- Higher transmitted frequency from the probe
- Higher veolcity of moving oject
- Smaller angles
Velocity of blood can be calculated using
Without dampening
You’ll have a tighter/narrower band of resonant frequencies
BUT it would take ages to die down
WITH DAMPENING
SHORTER spatial pulse length allows a receive time in order to measure
- CONTINUOUS WAVE DOPPLER
- Continuous emission with one PZT
- Second one receiving continually
Doppler shift is within audible range
DUPLEX DOPPLER
- B Mode image
- Two crystals laterally using pulse echo
However this would only SUMMATE different signals as you can’t tell depth
Receive time required to listen for echoes
- PULSED WAVED DOPPLER
- Create B Mode image
- Select an an active area to look for the doppler shift
SPECTRAL PULSE WAVE
You select a region WITHIN your area of interest.
You set your gate size
And correct the angle
You’re pulse repetition time is the SAME AS ONE LINE OF A MODE DATA
So MAX doppler shift measurable =
HALF OF YOUR PULSE REPETITION FREQUENCY
- POWER PULSE WAVE DOPPLER
Does NOT take into account DIRECTION only MAGNITUDE
Better for LOW FLOW states
- SPECTRAL DOPPLER
- B-Mode image acquired
- Region of interest
- Choose an A LINE of data and then the GATE
- Set the angle correction
X = Time scale = SWEEP SPEED
Y = VELOCITY
Baseline = 0 Velocity line
Spectral line thickness = the SPREAD of velocities you are measuring
Gate needs to be centred in the lumen
And wide as possible to get representative average velocity
RESISTIVE INDEX
Difference between peak and end diastolic velocity / peak systolic velocity
If EDV is positive, RI < 1
If EDV = 0, RI = 1
If EDV is negative, RI >1
A stenosis within the vessel
- flow can be much higher / turbulence and generate aliasing
Tardus parvus
Very top waveform
https://radiopaedia.org/articles/tardus-parvus?lang=gb
- ALIASING
Wen peak systolic velocity is HIGHER than the scale
OR
If you are too deep, and the pulse reputation length is TOO LONG, so pulse repetition frequency is not high enough to measure the higher velocities.
NYQUIST LIMIT
When sampling is too low you cannot tel direction.
So to overcome this
- Increase your scale
- Lower base line
- Use a higher frequency probe
- Find a shallower vessel
You can also measure high velocities with continuous wave doppler
Ways of addressing aliasing
- Tissue Harmonic Imaging
Only listening for harmonic frequencies
Frequency transmitted is the fundamental frequency based on thickness of pizzoelectric material
Harmonic frequencies are integer multiples of the resonant frequency
These form standing waves with nodes
Speed dependant on Bulk’s modulus (B) and density (ρ)
In areas of compression, the box modulus or stiffness is higher, so sound passes faster.
Inverse for rarefraction so slower.
So not a perfect sinusoidal wave = NON LINEAR BEHAVIOUR
Micro bubbles will expand and contract at the harmonic frequency
As you get deeper you get more harmonics being recieved
of 1st, 2nd, 3rd… order
Harmonic frequency formation is only at the most intense past the beam so only at the centre
Detection of harmonic frequencies can be plotted with depth.
Higher order frequencies will attenuate and may not reach the US transducer
Harmonic frequencies, only a occur at tissue boundaries
By selecting for these, you can eliminate scatter giving better resolution and contrast
Narrow bandwidth of initial wave required in order to work out resonant frequencies
Generally, a wide receiver bandwidth is used to acquire pulse echoes and scatter
Machine can fast Fourier transform to pull out relevant frequencies in “Harmonic Mode”
Another way to require just the harmonic frequencies:
- PULSE INVERSION HARMONICS
- 2 inverted waves that reflect and destructively interfere so no detected
BUT harmonic waves are IN PHASE as its from vibrating tissue boundaries so CONSTRUCTIVELY INTEREFERE
- POWER MODULATION HARMONICS
Two different waves of different amplitudes
Lower amplitude = not intense enough so no harmonic frequency reflected
Fundamental frequency waves = constructively interfere = but computer can fourier these out
LEAVING ONLY HARMONIC FREQUENCIES
Harmonic frequencies occur only with high beam intensity and a boundaries, based on non-linear wave properties
BENEFITS:
Better SNR + contrast
Less scatter and noise
Intense positive beam is narrower = better lateral resolution
27A. REFRACTION
Refraction occurs when the incident angle is not 90°
Emergent angle is larger if faster (think accelerating away from normal)
or narrower if slows up
EDGE SHADOWING
Some of the incident sound will be reflected off the edge at an angle
Some of the sound making it in will be refracted. But creates a void not receiving any sound waves.
27 B. MIRRORING
Sound from highly reflective boundaries can echo between objects, taking longer to reach probe.
Gives mirror image on the other side of the specular reflector
REFRACTIVE DUPLICATION
Refracted sound at a tissue boundary can then be reflected off an object taking a round trip / non-linear path
It will misregister the depth because of the longer echo and duplicate the object
Only way around it is to adjust probe so incident angle is perpendicular to surface, avoiding refraction
27 C. REVERBERATION
Wave from strongly reflecting surface then reflects off ultrasound probe
Can I go multiple times.
Resulting artefact is repeating lines of equal distance with intensity reducing with depth
27 D. RING DOWN
Occurs when fluid between microbubbles produces resonant frequencies
COMET TAIL
A type of reverberation between two highly reflective surfaces
27 F. SHADOWING
Ultrasound encounter is highly reflective or attenuating structure e.g. rib
So no echoes behind it
27 G. ENHANCEMENT
Passing through fluid filled structure not very attenuating
Successive pulses are therefore of a higher intensity
27 E. SIDE LOBES AND GRATING
Side lobes are due to radial expansion of transducer elements
Reflections from sidelobes can reach the probe and misregistered in those A lines
27 H. SPEED ERROR
compared to soft tissue average:
Sound travels FASTER in MUSCLE
Sound travels SLOWER in FAT
E.g. sound travelling through lipoma will be slower and the successive pulse from the next tissue boundary take longer
creating a deeper step in the boundary
the reverse is also true through a structure where it can past faster
creating a shallower step in the boundary
AMBIGUITY
When imaging short depths - short pulse repetition period
BUT still receive echoes from deeper structures!
In the field of view:
the ghost of the deepest structural appear darker as it comes from more attenuating deeper point
The pressure of peak points of compression can be measured in Pascal’s
Power is proportional to the square of pressure
Referring to power is the energy moving through tissues
the intensity is proportional to the power over area squared
intensity can be measured using
HYDROPHONES:
Microprobe OR Membrane
Has a PZT - measures intensity at single point
CALORIMETER:
to measure the energy of the entire wave
measures time taken to increase temperature by 1°
THERMOCOUPLE combines a hydrophone and a calorimeter
it has a fine probe but this time measuring temperature, calculating the intensity at that point within the beam
- BEAM INTENSITY: SPATIAL INTENSITY
- More intense at the focal spot where it narrows
- More intense through the centre of the beam due to constructive interference.
You can then plot the spatial intensity along the width of the ultrasound beam
Maximum = spatial peak intensity
AVG = special average intensity
Ratio between the two = BEAM UNIFORMITY RATIO (BUR)
- BEAM INTENSITY: TEMPORAL INTENSITY
PD = time energy is transmitted
Duty Factor = Pulse duration / pulse repetition period = % time energy is being transmitted
Pulse repetition frequency = higher transmits more energy
You can measure intensity during the pulse itself or during the pulse repetition period
Giving TEMPORAL INTENSITY
Maximum = Temporal Peak
AVG during Pulse Duration = Pulse Average
AVG during Pulse Repetition Period = Temporal Average
Spatial and temporal parameters are both used to look at BIOEFFECTS
SPATIAL AVERAGE - TEMPORAL AVERAGE INTENSITY
AVERAGE POWER
OVER ONE AREA OF THE BEAM
FOR ONE PULSE REPETITION PERIOD
Spatial and Temporal Averages can be used to work out the Spatial and Temporal Peaks
Special average is the spatial peak DIVIDED by the beam uniformity ratio:
SA = SP / BUR
Temporal average is the pulse average MULTIPLIED by the duty factor
TA = PA X DF
You can look at a range of different indices
Thermal:
Spatial Peak = at the most intense part of the beam
Temporal Average = what is the average energy experienced over the whole beam
Mechanical:
Spatial Peak = at the most intense part of the beam
Pulse Average = average energy during the pulse
As this maximum energy comes through that’s when rarefaction / cavitation can occur
- THERMAL INDEX
Attenuation: Scatter + Absorption / heat production
Thermal index = mathematical calculation = temperature rise given ultrasound parameters and beam geometry
TI = 1 = a uniform beam in increasing tissue temperature by 1°C
Most depended on duration
but also location, tissue type, transducer parameters and perfusion
Thermal index is highest at the spatial peak = at the focal point
Highest attenuation = NEAR FIELD = thermal index is high superficially
Scan for shorter periods
Move the probe
Lower PRF / Increase PRP
Lower PD
Use lower powers / frequencies
MI = Function of Peak rarefaction pressure / square rout of
