Canvas Chapter Notes Flashcards
Define a sound wave?
A longitudinal pressure wave travelling at the speed of sound through a medium
Define pressure?
The force exerted from the excess density of molecules above or below the mean density of the medium as molecules get squashed and pulled apart
What is phase of a wave?
A point along the course of one period of the wave expressed as an angle
What is the pulse envelope?
The characteristic shape of the pulse, created by drawing a line through successive peaks and rarefactions
What is a spectrum?
A plot of magnitude against frequency (or time)
What does the spectrum of a sine wave look like?
A single vertical line (only 1 frequency)
What does an indefinitesimally short pulse look like for a) Time Domain and b) frequency domain spectrums?
Time domain = single vertical line
Frequency domain = horizontal line
What is the bandwidth of an infinitely short pulse?
Infinite bandwidth
What happens to bandwidth as pulse length increases?
Bandwidth decreases
How does elasticity relate to stiffness?
Elasticity = 1 / stiffness
Do materials generally differ more in density or stiffness?
Stiffness - therefore stiffness is a better guide to predicting speed of sound than density
How do you calculate speed of sound in a material?
c = Sqrt( k / p)
k = stiffness
p = density
What is characteristic impedance?
The response of molecules in a medium to the excess pressure in the wave (assuming a simple plane wave)
- it is a measure of how fast a molecule in a medium moves in response to the excess pressure of the sound wave
How is acoustic impedance related to energy loss?
It is not
What is intensity of ultrasound?
Power per unit area
What is the frequency domain spectrum of a) short pulse b) long pulse
a) a wider bell-shaped curve
b) a narrow bell-shaped curve
What is the relationship between time domain and frequency domain?
They are reciprocal
What determines the size of an echo at an interface?
Differences in characteristic impedance
What is power?
The rate at which energy is transferred
What is intensity?
Power per unit area
What is specular reflection?
Reflection at a plane interface between two tissues with different acoustic impedance
When does Rayleigh scattering occur?
When sound encounters microscopic structures much smaller than a wavelength
What is a coherent imaging technique?
Where the phase of the waves may be fully specified at each point in space
- lasers and ultrasound are coherent techniques
- light bulbs are not
What do coherent imaging techniques give rise to?
Speckle patterns
What is attenuation?
The process by which intensity of a wave or pulse decreases with distance from the source
- equivalent to resistance
What are boundary losses?
Energy reflected away from the beam at interfaces (specular reflection)
What are the 3 mechanisms that give rise to attenuation?
- Absorption - conversion of sound to heat
- Scattering - energy diverted out of the beam
- Beam divergence - depends on beam shape = spreading out
(not strictly attenuation)
How does attenuation increase with depth?
It increases exponentially
How does frequency impact attenuation?
High frequencies are absorbed and scattered more
What is a point source?
A sound wave source that is much smaller than a wavelength of sound
- it spreads out in all directions
- e.g. when you speak, the wavelength is bigger than the size of your mouth - sound spreads out in all directions
What are plane parallel waves?
Waves that only propagate in one direction
What is the Fresnel Zone?
The Near zone
What is the equation for Fresnel Zone length?
D = a**2 / wavelength
D = length
a = half aperture width
What is the Fraunhoffer Zone?
The far field
What is the equationfor spread in the beam in the far field?
sin(theta) = wavelength / a
a = half aperture width
theta = half the angle of spread
For a square transducer
What is the effect of a large aperture for a given wavelength?
Uniform beam with long near field and small spread in the far field
What is the last axial maximum?
The last central intensity peak within the near field
What are Huygens sources?
Many point sources next to each other - acts as a straight beam at the centre but beams diverge at the edges
What is the unit and symbol for bulk modulus / stiffness?
Pascals (Pa) and Kappa (K)
How does speed of sound relate to density and stiffness?
c = Sqrt(K / p)
K = stiffness
p = density
How does greater density impact speed of sound?
Increased density decreases speed of sound
What is the percentage reflected intensity at soft tissue - soft tissue boundary?
1% or less
What is the percentage reflected intensity at bone - soft tissue boundary?
50%
What is the equation for refraction?
Sin(theta2) / Sin(theta1) = c2 / c1
What is the reflection coefficient and symbol?
Z, is the relative intensity of sound that is reflected at a boundary
What does the angle of refraction depend upon?
Angle of incidence and speed of sound
What is the percentage reflected intensity at air - soft tissue boundary?
100%
When does Rayleigh scattering occur?
When target size «_space;wavelength
What 2 factors impact ISB?
- Pulse length
- Doppler angle
How does frequency of sound relate to scattering and absorption?
Higher frequency = higher scattering and higher scattering = higher attenuation
What is the resonant frequency of a PZT transducer?
The frequency at which it vibrates when a voltage is applied across it
Why is damping of transducers needed?
To create short pulses to give good resolution
What is the purpose of transducer matching layers?
There is a large impedance difference between the hard, rigid PZT and soft body tissue - so transmitted intensity will be low
- matching layer enables sound to be transmitted into the body more efficiently
What are general properties of matching layers
- Impedance between PZT and the body
- 1/4 of a wavelength thick
Why are matching layers 1/4 of a wavelength thick?
The wave reflected at the body interface will have its phase inverted - by having 2 * 1/4 wavelength, the wave will then be reflected by the matching layer in-phase and will superposition
Why do transducers use multiple matching layers?
Each layer has an impedance of the geometric mean of those on either side
- this allows matching over a wider range of frequencies as contained in a short pulse of sound
What are advantages of wide-bandwidth transducers?
- Short pulses = good spatial resolution
- Potential for complex pulse shapes
- Harmonic imaging at higher frequencies possible
- The same transducer can use different frequencies for imaging and Doppler
What characteristics make a good wideband transducer?
(4 reasons)
- Good damping in the backing layer
- Very good matching to body impedance
- PZT thickness chosen for middle of the wideband range
What causes spread in the elevation scan plane?
Beam width - side lobes present in elevation and scan plane
How many dimensions does a basic linear array have?
1
What is a 1.5D array?
The transducer element is divided into 3 in the elevation plane
- this can improve image quality
Why do multiple focal zones reduce frame rate?
Each focus requires a separate transmitted pulse - frame rate doubles with 2 focal zones and triples with 3
What is receive focus?
The receiving shape for echoes coming from different ranges
-is implemented by introducing a receive delay to particular transducer elements
What happens to the shape of the received wave as we add more harmonics?
It gets closer to square in shape
What characteristics of waveforms indicate it is composed of higher harmonics?
Sharply rising/falling edges
What is non-linear propagation?
The concept that the speed of sound at peak pressure is slightly higher than the speed of sound at rarefaction
- peaks more faster than troughs
Why does harmonic imaging give better resolution?
Higher frequency gives better resolution
What are the two ways we can use harmonic information to form an image?
- Using a filter method - remove transmit frequency from the received signal = shorter received pulse
- Pulse inversion method - requires 2 transmit pulses of opposite phase transmitted in sequence. The echoes from the pulse are added together
Improves signal to noise ratio of b-mode and reduces side lobe artefacts and reverberation are reduced
Improves contrast resolution when on
What are the pros and cons of harmonic imaging?
Pros: - better resolution at higher frequency
- removes clutter from the image
Cons: - weaker echoes at 2nd harmonic so penetration is poorer
How are harmonics used in practice?
A combination of second and first harmonics to give overall improvements of image quality without losing penetration
How are modern scanners adaptable?
They can:
- alter the transmit shape
- change the transmit power
- change the timing of pulses
- change the aperture used
These factors can be changed between each pulse - no two pulses need be the same
What does the adaptability of pulses allow?
- Dynamic multi-zone focusing
- Steering
- Coded excitation to improve signal to noise ratio of weak signals
- Control of pulse phase, for harmonic imaging
- Mixed B-mode and Doppler imaging
What is the beam former?
It controls exactly what pulse: shape, timing and phase are produced by each element in the transducer
What are typical PRFs?
1000’s per seconds
Why is TGC needed?
Attenuation
What is analogue to digital conversion?
Converts the analogue amplitude of a returning echo signal to the nearest integer value at set time intervals (bins) - this is then stored as a sequence of numbers
What are the advantages of digitising?
- No further risk of introducing noise or distortion into the signal
- Powerful computing can be done = image processing
- Easy storage in memory
How are raw echoes turned into images
ADC - analogue digital conversion
- often done by digitizing the r.f signal
What is echo signal rectification?
Turning the signal all positive
What is envelope detection?
Rectification and low pass filtering together
How are the dynamic ranges of echoes fitted into the range of the display monitor?
Grey scale mapping / compression
How can non-linear amplification improve image quality?
It can enhance the echoes of interest e.g. low level echoes or mid range echoes
What is compound scanning?
When multiple beams are sent out at different angles = allows more sides of objects to be perpendicular to the beam
What are the 4 main assumptions of ultrasound imaging?
- The speed of sound is constant in the body
- Attenuation in tissue is constant
- The beam axis is straight throughout the range of the beam
- The ultrasound beam is indefinitely thin
When do artefacts occur?
When the assumptions of ultrasound are not met
What are examples of speed of sound artefacts?
- Refraction - causes image distortion
- Axial misplacement
What are examples of attenuation artefacts?
- Poorly adjusted TCG
- Acoustic shadowing
- Post-cystic enhancement
- Poor skin contact
What are some examples of reflection artefacts?
- Mirror Image artefacts
- Reverberation
What are some examples of beam shape artefacts?
Slice thickness artefact
What is the approximate temporal resolution of the human eye?
25 fps
What two factors determine frame rate?
- The number of ultrasound lines / beams
- Depth of image
What is reverberation?
Multiple reflection between parallel surfaces
What is contrast resolution?
The ability to detect one target against another
What is the Doppler shift?
The change in frequency between the transmitted and received soundwaves
Why is there the factor of 2 in the Doppler equation?
There have been 2 Doppler shifts: one on the way out and one on the way back
What is one assumption of the Doppler effect?
The target velocity is much smaller than the speed of sound in tissue
How does sign of velocity change in the Doppler equation?
v is positive for targets moving towards the transducer and negative for targets moving away
What is the cross-over region of a CW transducer?
The sensitive region where transmit and receive beams cross over
What produces high and low Doppler frequencies?
High - flow towards transducer
Low - flow away from the transducer
What algorithm converts from time domain to the frequency domain?
Fourier Transform
How do velocity profiles of slow and fast moving blood differ?
Slow - parabolic flow
Fast - plug flow
What is an advantage of CW doppler?
It can detect very high velocities with no aliasing
What is high PRF mode?
It doubles the PRF and Nyquist limit by creating 2 sample volumes - one at half target depth = can be problematic if there is a vessel here
Why are PW Doppler pulses generally longer (6-7 cycles) than B-mode?
The transmit frequency needs to be well defined in order to accurately detect changes due to moving targets
Why do shorter Doppler pulses (i.e. to look at narrow regions of vessels) causes Doppler frequencies to be less well defined?
Intrinsic spectral broadening (ISB)
- multiple Doppler shifts from varying velocities of blood
- is intrinsic to the machine and cannot be avoided
What is the impact of a highly focused beam on PW spectrum?
The same as a short pulse - ISB
Targets moving across the beam will give Doppler signal whose amplitude rapidly increases and then decreases as target moves across the beam
- Rapidly changing signals produce wide spectrums in the frequency domain
How much can ISB impact velocities?
+/- 10%
Why is an ideal Doppler angle of 45 - 60 degrees used in practice?
< 45 can lead to poor penetration in practice
What is pulsatility index (PI)?
Measure of how pulsatile a waveform is - high for pulsatile, low for damped or resistive
PI = (PSV - EDV) / average of peak envelope
What is resistive index (RI)?
Measure of ratio of EDV to PSV
- High EDV indicates low resistance and gives low RI value
When does waveform ghosting / spectral trace reflection occur?
In very superficial vessels e.g. ankle vessels
- may also occur if the gain is too high
How can weak PW signals be amplified?
Reduce the steer of the beam and heel-toe the probe
What is the difference between side lobes and grating lobes?
Grating lobes are a special type of side lobe
They are both caused by the spreading out of energy from the main beam that is reflected back
- Grating lobes generally have larger amplitudes than side lobes
Does all of the energy stay within the main transducer beam?
No
How do grating lobes appear?
At the wrong location but in the same direction as the main ultrasound beam
How can you practically adjust for attenuation?
Adjust TGC
How can you correct for edge dropout practically?
Turn on CT scanning or compound scanning or heel-toe the probe
When do comet tail artefacts occur?
When there is reflection between 2 very closely spaced reflectors - usually between metallic objects
What is a resonance/ring down artefact?
Used in CEUS - vibration of very small structure e.g. gas bubbles - highly echogenic
What is phase aberration artefact and what may cause it?
It is the same as smearing vaseline on the lens and can be caused by a layer of subcutaneous fat
How can you reduce mis-registration/distortion/phase aberration artefacts in obese patients?
Turn of CT and compound scanning. Turning on tissue harmonic imaging might help
What artefact may cause twin-image artefacts e.g. of aorta?
Refraction
How can refraction artefacts be overcome?
Changing the beam angle
What are the 3 main ways to reduce aliasing?
- Adjust scale
- Decrease depth
- Use a lower frequency probe
How can motion artefacts appearon a spectral trace?
As bright chunks of spectral near the baseline
What does each colour pixel show?
The mean frequency shift/velocity in that area
How many transmission pulses are needed for each colour line?
7 - 10
What impacts frame rate?
Length and width of colour box and line density and depth
How is lateral resolution calculated?
LR = beam width / 2
What is the equation for beam width?
Beam width = wavelength x focal length / aperture size
How is pulse length calculated?
PL = n x wavelength
n = number of cycles
What is greyscale mapping?
Converts the huge range of echo intensities from reflected tissue into 128 or 256 grey scale bins
- can be done in a linear, curved or sigmoidal manner
Do colour or B-mode pulses have wider bandwidth?
B-mode as they have shorter pulses
When do we see display monitor flicker?
When the frame rate is reduced below 25Hz
What is the difference between frame rate and temporal resolution?
Frame rate is the number of frames displayed per second.
Temporal resolution is the ability to CAPTURE motion, does not involve the processing and display
What is the grey level of a spectral waveform?
The number of RBCs that reflect that particular velocity or frequency shift
How does sample volume impact frequency resolution?
Wide SV: long pulse, narrow bandwidth, better frequency resolution
Narrow SV: short pulse, wide bandwidth, worse frequency resolution
What can a small sample volume cause?
Intrinsic Spectral Broadening (ISB)
What is dynamic range?
The ratio of highest to lowest echo strength (voltage)
What does persistence do?
Sends multiple pulses and averages frames - temporal resolution may be an issue
What is autocorrelation?
The processing of a colour image that converts the spectrum of frequency shifts at each point to one value at output
How does autocorrelation work?
It compares the phase from the speckle pattern produced by the ultrasound pulses
Does size or depth of a colour box have a bigger impact on frame rate?
Box size
How can THI improve resolution?
It can improve contrast resolution
- reduces speckle
Why does post-cystic enhancement occur?
The ultrasound machine assumes for constant attenuation. There is very little attenuation in fluid - hence there is over-compensation post-cyst
What is Reynold’s number?
A number that describes when turbulence will occur
Above which Reynold’s numbers will there be turbulence?
> 2000 - 2500
Explain Poiseuille’s law in words?
Resistance to flow depends on the geometry (mainly radius) and viscosity
And a pressure difference will cause fluid to flow in a steady manner
Explain the Bernoulli equation in words?
Energy is conserved - there is no perpetual motion
What is the unit for viscosity (u)?
Pascal seconds (Pa s)
or Kg m-1 s-1
Does Reynold’s number have units?
No - it is a ratio
What are the units for pressure?
Pa
Pascals
What is the SI unit for energy?
Joules J
What does viscosity depend on?
The temperature and haematocrit of blood
What is the impact of temperature on blood viscosity?
Decreased temperature causes increased viscosity
What is density?
Mass / volume
What are the 3 causes of inertial losses?
- Acceleration
- Deceleration
- Change of direction
What is the largest site of reflection in the arterial tree?
The arterioles
What is Anisotropy?
The phenomena of attenuation (or other properties such as speckle pattern) varying depending on the orientation of the target to the ultrasound beam or image plane
Why do short pulses have a range of frequencies centering around fmid?
Other frequencies are produced as the wave starts/stops
What gives approximate bandwidth of a pulse?
Bandwidth = +/- 2 x 1/pulse length
What is the equation for bulk modulus? (K)
regarding pressure and volume
K = -V (change in P / change in V)
- note the minus sign occurs because the volume decreases with an increase in pressure
How does speed of sound in a material relate to bulk modulus?
c = Sqrt ( K / p)
Describe characteristic acoustic impedance?
The quantity for how easily a molecule in a medium moves in response to a given change in acoustic pressure
- It is NOT resistance to a sound wave
What is the equation for acoustic impedance at a molecular level?
Z = Excess pressure / Particle velocity
What is the equation for Z in a material?
Z = Sqrt ( p K)
What does the total scattered power of a target depend upon?
- Target size (area) - to the power of 6
- Frequency - to the power of 4
What is superposition?
Waves in phase adding together
How do absorption and scattering change with frequency?
Low frequencies are attenuated more (90%) than scattered (10%) energy loss
- high frequencies are absorbed and scattered more = poor penetration
How do you narrow the beam for a transducer with a narrow aperture?
Increase the frequency
What is the beam profile for a large aperture for a given wavelength?
Uniform beam with long near field and small spread in the far field
What is dynamic range?
The difference in signal strength between the weakest and strongest echo
What is interpolation?
Using a smaller number of scan lines to improve frame rate
- the gaps between lines are filled by synthetic data
What are twinkle artefacts?
Artefacts arising from calcified vessels or stones
How is an ultrasound image constructed?
Echoes are generated from reflection and scattering from irregularities in tissue (changes in acoustic impedance)
What 2 key pieces of information are needed to display an echoes position?
- The range (distance) of the target from the transducer
- The direction of the target from the transducer - i.e. the position and orientation of the ultrasound beam
What is a wave?
The transfer of energy due to local displacement of particle (but no net movement)
Are shear waves longitudinal or transverse waves?
Transverse waves
What is phase and its units?
The position within a cycle of oscillation
- measured in degrees
How does pressure change when a medium is compressed?
It increases in the positive direction
What is the excess pressure?
The difference between actual pressure and mean ambient pressure
What is peak excess pressure?
The amplitude of a wave
How is stiffness calculated?
The ratio of stress to strain
What is stress or pressure?
The force per unit area
What is strain?
The fractional change in thickness
What are the units of strain?
No units, is a ratio
What are the units of stiffness?
Pascals
K = stress / stiffness
= Pa / no units
What are the units of stress?
Pascals (N/m*2)
Why is speed of sound faster in bone than tissue, even if it is twice as dense?
It has a stiffness 10x greater
What is the equation for acoustic impedance (Z) relating to local particles?
Z = P / v
- P = LOCAL pressure
- V = LOCAL particle velocity
What is acoustic impedance analogous to?
Electrical Impedance
What is the general acoustic impedance of a material given by?
z = Sqrt(pk)
- acoustic impedance increases with both density and stiffness
also
z = pc
How does acoustic impedance change with a) stiffness b) density?
Increases in both density and stiffness will cause an increase in acoustic impedance
How does total particle pressure and total particle velocity change across an interface of changing acoustic impedance?
Total particle pressure and total particle velocity must be continuous
How much reflection occurs at soft tissue-soft tissue interfaces?
~1%
What percentage reflection occurs at soft tissue - fat interface?
~10%
What percentage reflection occurs at soft tissue - air boundary?
99.9%
How does frequency impact reflection coefficient?
It does not
What is diffuse reflection?
The reflection at a rough interface where ultrasound is scattered reflected.
What transducer properties cause diffraction of waves?
An aperture smaller than the wavelength
What is the equation for NFL?
NFL = a^2/wavelength
What is non-linear propagation?
The theory that high-pressure (compressions) areas of the wave propagate faster than rarefactions
- rarefactions start to catch up with compressions
- compressions become taller and narrower and rarefactions become lower in amplitude and longer
How do harmonics of short pulses appear?
They appear as repeats of the pulse spectrum around the fundamental frequency, rather than narrow spectral lines
What happens to the shape of a pulse as it travels further into a medium?
As the pulse travels further, higher frequency components are attenuated more rapidly than low-frequency components and the pulse shape becomes more rounded as the overall amplitude is reduced.
How does harmonic imaging work?
The fundamental frequency is ignored and only forms images using the second harmonic part of the pulse
- the ultrasound beam is narrower and suppresses artefacts such as side lobes
- Can use: 1. Pulse inversion method or 2. High-pass frequency filter
How does scattering relate to angle of incidence?
It is independent of angle of incidence
What is specular reflection?
Reflection at a smooth, mirror-like surface
What does reflection at an interface depend on?
Mismatches in:
1. Acoustic impedance
2. Density
3. Speed of sound
What is non-linear propagation concerned with? (2 reasons)
- Steepening in the shape of the ultrasound pulse
- Generation of harmonics at multiples of the fundamental frequency
What does DICOM stand for?
Digital imaging and Communications in Medicine
What is DICOM?
A set of protocols of how to do/manage various operations and formats relating to medical imaging
How does DICOM display different levels of brightness?
It uses the concept of just noticeable difference (JND) between luminance levels of the display
How does DICOM use a Test Target to measure contrast detectability?
It uses a Test Target
- is a square image of 8 horizontal or vertical sinusoidal bands across the image
- for different background grey levels, the amplitude of the bands is adjusted and increased above the background level until you can just notice the bands
What is the non-linear response of the human eye?
The human eye needs a greater range of contrast at low light levels in order to detect change than it does at high levels of illumination
How does the DICOM scale overcome the non-linear response of the human eye?
It specifies a compensation curve for displays to give a ‘perpetually linearised’ image
- ensures contrast detectability within dark areas is the same as in the bright areas of the image
What is the DICOM standard for colour display in ultrasound images?
There is currently no equivalent DICOM standard for colour images
What are other external factors that may impact image quality?
Angle of viewing (e.g. oblique)
Background room lighting
Viewing distance
How is energy carried by a wave related to amplitude?
Energy is proportional to amplitude squared
- intensity is also proportional to amplitude squared
- amplitude can also be thought of as pressure
What is bandwidth?
Within a pulse, no two cycles are the same, unlike a pure Sine wave where every cycle is identical
- generally most of the pulse looks like a sine wave just at each end the amplitude falls to zero
- the spectrum has a bandwidth centred about a central frequency
How is elasticity related to stiffness?
Elasticity = 1 / Stiffness
Why are we more interested in intensity of ultrasound, not energy or power?
Energy is not transmitted equally in all directions
- we are more interested in power per unit area (intensity)
What are the energy losses at boundaries?
There are none
How does acoustic impedance relate to speed of sound?
Z = pc
What is the equation for ratio of reflected intensity (Ir) to incident intensity (It)?
Ir / It = ((Z2 - Z1) / (Z2 - Z1))^2
What is Poiseuille’s Equation?
Change in pressure = (8uLQ) / (Pi r^4)
What is Poiseuille’s Equation?
Change in pressure = (8uLQ) / (Pi r^4)
How does lowering frequency impact speckle pattern?
It makes it coarser
What are boundary loses?
Energy reflected away from the beam at interfaces
How is energy lost through absorption?
Sound energy is converted to heat - making molecules vibrate in a disordered and random way i.e. not coherent
What are the units for attenuation coefficient/
dB cm-1 MHz-1
Why can’t you image through bone?
50% of energy is reflected and the rest is quickly attenuated
What is Snell’s Law?
n1 sin(theta1) = n2 sine(theta2)
Why is a large pulse wave sample advantageous?
It reduces ISB
What is TIC?
The thermal index for when the ultrasound is near bone and
What are the 2 main classifications of ultrasound imaging hazards?
Thermal and non-thermal
What are the two main types of thermal hazards?
- Tissue heating - can cause cell death
- Transducer self-heating - can cause erythema + burning
What are the 2 main types of Non-thermal hazards?
- Radiation force - energy absorbed by tissue. This can cause streaming - the movement of particles
- Cavitation - oscillation of small gas bodies or bubbles
What are the two types of cavitation?
- Stable Cavitation - causes microstreaming
- Collapse cavitation - can cause physical damage and free radicals
What factors determine whether cavitation can occur?
- Are there free gas bodies - called cavitation nuclei
- The pulse shape and frequency of ultrasound
What do thermal effects depend on?
The average energy input (or intensity) to the tissue
What do cavitation effects depend on?
The amplitude and length of individual pulses and the presence of cavitation nuclei - gas bodies
What causes bubble collapse during cavitation?
Magnitude of negative pressure experienced during rarefaction - influences likelihood of collapse
- the transition from large positive pressure to large negative pressure
What is the FDA limit for scanner MI output?
1.9
How does frequency impact MI?
Lower frequency increases MI
What are the two distinct risks of using contrast agents in CEUS?
- Pharmacological risk - associated with injected substance
- Risk of physical effects - gas bodies being insonated in tissue
What do potential bio-effects of CA depend upon?
Rarefactional pressure amplitude
Agent dose
Agent delivery
Imaging mode
Tissue properties
Clearing pulse - bursting bubbles
How does energy relate to pressure?
Energy is proportional to pressure amplitude squared
Why is energy carried by a sound wave always positive?
It is proportional to pressure amplitude squared
What are some of the variables that are not ideal in terms of the haemodynamics of blood vessels?
- branches and curves
- flexible and distensible
- Uneven multidimensional flow
- gravity
- feedback systems
- assumes constant temperature
- volume changes
What is the equation for volume flow?
Q = v * A
What is Poiseuille’s formula?
Change in P = (8* mean v * L * u) / r^2
in a rigid tube:
change in P = (8 * Q * L * u) / Pi * r^4
What is Poiseuilles Law?
Change in P = 8QLu / Pi*r^4
What is the formula for Reynolds number?
Re = p v L / u
Re = 2rpv/u
Is also the ratio of inertial to viscous losses
What is viscosity?
The internal friction in a fluid
What is polycythemia?
Too many RBCs, u increases
How does dialysis impact viscosity?
RBCs can be smashed up, u decreases
What are the 3 main forms of pressure within the circulation?
- Dynamic pressure - work done by heart contraction (120mmHg)
- Static pressure - residual, if dead. Generally small, 5-10mmHg
- Hydrostatic pressure - due to gravity
What equation relates pressure and height?
P = -p g h
- note is negative because pressure decreases as h increases
What is the equation for energy density (Bernouilli Equation)?
Energy density = P - pgh + 1/2 p v^2
OR, P - pgh + 1/2 p v^2 (before) = P - pgh + 1/2 p v^2 (after)
How do velocity and pressure relate with the Bernouilli Equation?
If v increases, P decreases
If v decreases, P increases
What are the 4 main causes of inertial losses?
- High flow rates
- Changes in diameter
- Sharp changes in direction
- Angles
What are streamlines?
Lines drawn tangent to the direction of flow
Which vessels are physiologically effected by hydrostatic pressure?
Arteries and veins
T/F: There are no inertial losses in a straight tube with constant flow
F
T/F: In laminar flow, the boundary vessel extends throughout the vessel
T
T/F In laminar flow, there is no flow just next to the vessel wall
T
T/F In plug flow, there is no flow just next to the vessel wall
T
Which arteries are most likely to experience turbulence?
Large arteries with high flow velocities e.g. aorta
Are we likely to get plaque build up at high or low shear surfaces?
Both - bifurcations are the most common site
What is Ptm?
Transmural pressure - difference between inside and outside of the vesse;
What is Laplace’s law?
T = Ptm * r
Tension = transmural pressure * radius
What parameter gives the best indication of perfusion to the foot?
Pressure
What happens to pressure if velocity increases?
Pressure decreases
What is pressure drop proportional to?
Mean velocity
What is Darcy’s law?
Rf = 8Lu / Pi r^4
Generally, what form of energy is highest in arteries?
Generally PE > KE
- but with very high velocity flow, inertial losses can overtake frictional losses
What is Reynolds equation?
Re = 2 rp meanv / u
(is the ratio of inertial to viscous losses)
What are the thresholds for Reynolds values?
< 2000 is laminar flow
2000 - 2500 is a disturbed intermediate flow
Re >2500 is turbulent
What are the 4 assumptions based on the Bernoulli equation?
- fluid is incompressible
- fluid is ideal
- flow is incompressible
- flow is one dimensional
What is the strength of focusing?
The ratio of the aperture width to the beam width at the focus
What is the equation for focus strength?
a / W = a^2 / (F*lambda)
a = aperture width
W = focal width
F = focal length
What is the focal zone?
Where beam width < 2 * the focal width
What happens to focal width as aperture size increases?
Focal width decreases, with small spread in the far field
What conditions are needed for strong focusing?
Wide aperture
How does beam steering impact aperture size?
It reduces it - causes more spread
Which hazard is in effect more at higher frequencies?
Heating
Heating is proportional to frequency
Which hazard is more important at lower frequencies?
Acoustic cavitation
Acoustic cavitation is proportional to 1 / Sqrt(f)
What are the units for TI and MI?
Decibels
What is acoustic dose rate?
Rate of absorption of energy per unit mass
What are the limits for TImax and MImax in the eye?
TI = 1
MI = 0.23
What are the limits for TImax and MImax in the body?
TI = 6
MI = 1.9
What are: TIS, TIB, TIC?
TIS = TI for soft tissue
TIB = TI for bone
TIC = TI for cranial bone
What are the 3 main non-thermal hazards?
- Acoustic cavitation - oscillation of bubbles
- Gas-body effects - complete reflection at air-bubble interface
- Radiation pressure - streaming and shear stress
How many MI values are there?
Just 1
What causes cavitation?
Contrast agents
Which 2D scanner controls do not affect TI and MI?
Gain, Dynamic range, TEQ/auto-optimize, MAPS
Which 2D controls affect TI and MI?
Power
Freeze
Frequency
Compounding
Depth
Focus
X-res
Write zoom
How can you reduce random errors?
Take repeat readings
How do random errors change with number of repeats (n)?
Random error is proportional to Sqrt(n)
How does a focused beam impact average velocity? and how can this impact be mitigated?
It can over-estimate average velocity (up to 30%)
- set range gate to straddle vessel and focus at range gate
How many dimensions can an ultrasound beam be focused in?
3
- scan plane, elevation plane and steering plane
Generally, what is the difference between the weakest and strongest echo?
10^5
How does lower frequency impact MI and TI?
Lower frequency increases TI MI
What is a hazard?
Anything that can cause harm
How are energy and pressure related?
Energy is proportional to pressure squared
What is viscous diffusion?
The process of the boundary layer spreading from the wall to the centre of the vessel
What is inlet length?
Length after entrance that it takes for flow to become parabolic
What is Laplace’s Law?
T = Ptm * r
S = Ptm *r / h
How is K calculated?
K = -V change in P / change in V
- is minus because an increase in pressure causes a decrease in volume
What is Moens-Korteweg Equation?
Pulse wave velocity equation
What are equations for Z?
z = pc = Sqrt(pK) = 1/A Sqrt(pEh / 2r) = local P / local v
What is PI?
(PSV - EDV) / Mean V
What is RI?
(PSV - EDV) / PSV
How is bandwidth measured?
Full width at half maximum
What does a high and low Z mean?
High = large pressure, little response
Low = little pressure, large response
What happens to Z and pulse wave velocity with age?
Z and PWV increase due to the increase in E (stiffness) of vessels (Moens-korteweg Eq)
What is Snells Law?
Sin(theta2) / Sin(theta1) = c2 / c1
What is the interference of waves with a 180 degree phase difference?
Cancellation
What is the interference of waves with a 90 degree phase difference?
1.5x superposition
What is the interference of waves with a 360 degree phase difference?
2x superposition
What is the interference of waves with a 270 degree phase difference?
0.5x cancellation
What is the equation for spread in the far field?
Sin(theta) = wavelength / a
- theta = half angle of spread, a = half aperture width
What are Huygens wavelets?
Many individual point sources next to each other. Plane parallel waves at the centre but beam divergence at edge
Which aspect of the beam can be focused?
Only the near field
When would you not get grating lobes?
When the spacing between individual elements is < 1 wavelength
What are the units for attenuation coefficient?
dB cm-1 MHz-1
What is a point source?
Is much smaller than the wavelength of sound - beam diverges in all directions
What is the equation for the NFL?
NFL = a^2 / wavelength
a = half aperture width
What is the typical attenuation coefficient of soft tissue?
0.7db cm-1 MHz-1
What is axial resolution dependent on?
Pulse length and therefore frequency, number of cycles and wavelength
How does increasing frequency impact NFL?
It increases NFL
What do zero-crossing detectors display?
(Sqrt(mean v))^2
What is the duty factor?
Pulse duration / PRF
What factor usually limits frame rate?
The speed of sound, c
What is the range equation?
c = 2d / t
What is the vmax without aliasing equation?
c^2 / 8d ft Cos(theta)
What is the wave shape when all harmonics are added?
Pure square wave
What are the 2 ways of utilising harmonics?
- High-pass filter - removes fundamental frequency
- Pulse inversion method - 2 pulses of opposite phase are transmitted in sequence - cancel out
What are the disadvantages of using harmonics?
Weaker echoes so penetration is poor
How does attenuation change with depth?
It increases exponentially
What are the 2 causes of ISB?
- Finite pulse length = range of frequencies
- Different doppler angles, not known, edge vs mid
What generates harmonics?
The non-linear propagation of ultrasound waves, whereby the peaks (compressions) travel faster than troughs (rarefactions) which distorts the waves and generates multiples of the fundamental frequency
What is Darcy’s Law?
P = QR
What is the Wormersley parameter?
The ratio of inertial to viscous forces for pulsatile flow (like Re but for pulsatile flow)
What does a high Wormersley parameter indicate?
Inertial forces dominate
What does a Wormersley parameter below 1 indicate?
Viscous forces dominate
How is Young’s Modulus, E, calculated?
stress / strain
How are mmHg and Pa related?
1 mmHg = 133.3 Pa
How are pressure and velocity related?
Increase in velocity decreases pressure
What is a Newtonian fluid?
One whose viscosity is not impacted by shear rate
What 2 components contribute to boundary layer formation?
- Fluid viscosity
- no-slip condition next to vessel wall
What is the equation for beam width at the focus?
W = F * wavelength / a
F = focal length
a = half aperture width
What is the focal zone?
Focal zone is where beam width is < 2x the width at the focus
What happens to wave amplitude when it is reflected at an interface of high to low impedance?
Amplitude is negative
When does phase inversion occur at an interface?
When we go from high to low impedance (negative amplitude of reflection) then the phase is inverted. e.g. at probe-skin interface
What does the movement of a target between pulses cause?
A phase difference between the two pulses
How does density impact absorption coefficient?
Increased density e.g. bone causes increased absorption coefficient
What is temporal peak intensity?
The highest intensity found within a pulse
What is temporal average intensity?
The intensity averaged across the whole pulse cycle - including the dead time between pulses
What is the pulse average intensity?
Intensity averaged across the whole pulse cycle, not including dead time
What are the two main classes of hazard?
Thermal and non-thermal
What are the two types of cavitation?
Stable cavitation - causes microstreaming
Collapse cavitation - causes physical damage and free radicals
What are the two groups of non-thermal effects?
Non-cavitational and cavitational
What is radiation force?
Energy absorbed by the tissue in the direction of ultrasound propagation
What is cavitation?
The compression and stretching of molecular gas structures when ultrasound passes through them
How can bubble collapse cause chemical damage during cavitation?
Bubble collapse causes extremely high localised pressure and temperature increases. This causes large mechanical stresses on the surrounding medium and potentially creates free radicals which can cause chemical damage
What do thermal effects depend on?
The average energy input to the tissue
What do non-thermal effects depend on?
The amplitude and length of the individual pulses
- particularly the negative pressure experienced during rarefaction
What causes bubble collapse?
The transition from a large negative pressure to a positive pressure
What are the simplest for of contrast agents for CEUS?
IV saline that has been shaken up
How are harmonics generated during CEUS?
At high intensities, contrast agent mechanical oscillation becomes non-linear = easier for bubbles to expand than contract. They then radiate harmonics
How does B-flow visualise flow?
It analyses the speckle pattern and compares at different times using code-excitation
- speckle pattern should remain the same when there is no movement = zero signal
- speed and turbulence = greater signal detection
What is the maximum number of transmit focal zones possible for each pulse?
1
One pulse is needed per focal zone
Name some different artefacts?
Post-cystic enhancement
Speckle
Acoustic shadowing
Refraction
Reflection
Comet-tail
slice thickness
What are 6 assumptions of ultrasound?
- Speed of sound is constant in the body
- Attenuation is constant and uniform
- The beam axis is straight throughout the range of the beam
- Later echoes result from targets at greater depth
- The ultrasound beam is infinitely thin
- The image is acquired instantly
