Ultrasound Physics Flashcards
Sound is a traveling variation in ______.
Pressure
Sound involves ______ motion in the medium through which it travels.
Mechanical
What are the 3 acoustic variables?
Pressure
Density
Particle vibration
- they are the quantities that vary in a sound wave
What are rarefactions & compressions?
Rarefactions = regions of low pressure & density
Compressions = regions of high pressure & density
What is density?
Density = concentration of matter (mass per unit volume)
Sound is a _______, _________ wave in which back-and-forth particle motion is parallel to the direction of travel
Mechanical, longitudinal
If the up and down motion of a water surface is perpendicular to the direction of wave travel it is what type of wave?
Transverse or shear wave
What is the definition of frequency? And what is it’s unit?
Freq = # of cycles that occur in 1 second
Hertz (1 Hz =1 cycle/sec)
1 kHz = 1000Hz
1 MHz = 1,000,000Hz
The positive and negative halves of a pressure cycle correspond to what, respectively?
Regions of compression & rarefaction
(Higher pressure = denser medium & vice versa)
What is the definition of period? And what is it’s unit?
Period = time it takes for 1 cycle to occur
Common unit for period = microseconds ( 1 microsecond = 0.000001 second) e.g. the period for 5MHz U/S = 0.2 microseconds
What is the equation for period?
T (period in microseconds) = 1/ freq (Mhz)
If the period decreases, what happens to freq?
If period decreases –> freq increases.
If freq inc –> period dec
What is the definition of wavelength? what is the common unit of wavelength?
Wavelength = length of SPACE/DISTANCE that 1 cycle takes up
Aka the length of cycle from front to back
Millimeters (1 mm = 0.001m)
For a propagation speed of 1.54 mm/s and a freq of 5MHz, what is the wavelength?
0.31mm
(Eq:: wavelength = propagation speed [mm/us] / freq [MHz])
What is propagation speed (c)? What is it’s unit?
The speed with which a waves moves through a medium
Units = m/s and mm/microsecond
What is the relationship between wavelength, propagation speed, & freq?
Wavelength = propagation speed (mm/microsecond) / freq (MHz)
If wavelength increases —> freq ________
Decreases
What primarily determines propagation speed?
The medium, specifically it’s stiffness (hardness)
What is stiffness?
Stiffness = resistance of a material to compression
Stiffer media –> HIGHER sound speeds (gas < liquid < solid)
What is the average propagation speed in soft tissues?
1540 m/s or 1.54 mm/microsecond
Shear waves travel ______ in comparison to longitudinal waves.
More slowly
The average propagation speed in fat is approximately what percentage in comparison to soft tissue?
~6% lower
Propagation speed in any medium depends on the ______ and ______ of the medium.
density (p) and stiffness
Density = mass density = mass per unit volume
Stiffness aka hardness or bulk modulus of elasticity (B)
What is the equation to for propagation speed?
c (m/s) = [ B (N/m^2) / density (kg/ m^3) ] ^ 0.5
*In general, stiffness differences dominate the effect on propagation speed more than mass density (therefore solids have higher propagation speeds than liquids)
How does propagation speed affect pressure and therefore the overall wave shape?
Higher pressure portions of the wave travel faster than lower pressure portions –> non sinusoidal shape
What is the term for propagation in which speed depends on pressure & changes wave shape?
Nonlinear propagation
- nonlinear propagation results in additional freq that are even & odd multiples of the fundamental freq ( a continuous - not pulsed - sinusoidal waveform is characterized by a SINGLE freq [this freq equals the # of cycles/second]
- while the shape becomes less sinusoidal, the harmonic become STRONGER
What is pulse repetition freq (PRF)? What is the common unit of measurement?
PRF = # of PULSES that occur in 1 second
kHz ( 1kHz = 1000Hz)
What is the pulse repetition period (PRP)? What is the common unit of measurement?
PRP = time from the beginning of 1 pulse to the beginning of the next
Milliseconds (0.001 seconds)
What is the formula for PRP?
PRP (ms) = 1 / PRF (kHz)
If PRP decreases, what happens to PRF?
PRP decreases while PRF increases b/c when more pulses occur in 1 second, the time between them decreases
What is pulse duration (PD)?
Pulse duration is the time it takes for one pulse to occur
What is pulse duration (PD) equal to? / what is the formula?
PD = period (T, the time for 1 cycle) x # of cycles in the pulse (n)
PD = T (microseconds) x n
- expressed in microseconds
What occurs to PD if the # of cycles is decreased? what about if the freq is increased?
Pulse duration DECREASES if the # of cycles is decreased
Pulse duration DECREASES if the freq is increased (inc freq reduces the period)
Slower pulses _________ image quality
Improve
What is duty factor (DF)?
DF = the fraction of time that pulsed U/S is on
- In CW U/S the DF = 1 (b/c U/S is on 100% of the time)
DF is the _______ of the _____ that the sound is on
fraction; PRP
Higher PRFs —> ______ DF
Increased DF (b/c less listening time between pulses)
What is the effect on DF is the PRF is increased? what is the period is increased?
Inc PRF –> Inc DF
Inc period –> Inc DF
What is the equation for DF?
DF = PD / PRP
DF = PD (microseconds) x PRF (kHz) / 1000 (KHz/MHz)
….this factor of 1000 converts KHz to MHz to be consistent with microseconds of PD
DF for Doppler ultrasound is ______in comparison to sonography?
Higher (0.5 - 5%) b/c of longer PDs
(typical sonography ranges from 0.1-1.0% DF)
What is spatial pulse length (SPL)? What is the unit?
SPL = length of a pulse from front to back
Millimeters (mm)
If freq is increased, what happens to SPL? What if # of cycles increases?
SPL decreases (b/c wavelength decreases with inc freq)
If # of cycles inc –> Inc SPL
The actual # of cycles that occur in 1 second in pulsed U/S depends on the _____.
DF
If the DF is 0.01 and the freq is a 5MHz pulsed wave, what is the actual # of cycles per second?
0.01 DF = 1%
0.01 x 5,000,000 = 50,000 cycles/second
What is bandwidth?
Range of freq contained in a pulse
How does a few # of cycles affect the bandwidth?
Fewer # of cycles = shorter pulses –> higher # of freq = broader bandwidth
What is fractional bandwidth?
Fractional bandwidth = Bandwidth / operating freq
_______ and ______ are indicators of strength of the sound.
Amplitude; intensity
What is amplitude?
Amplitude = maximum variation that occurs in an acoustic variable aka how far a variable gets away from its normal, undisturbed value
What is power?
Power is the rate of at which energy is transferred from one part of a system to another
What is the equation for power? What is the unit of measurement?
Power = Energy transferred / time required to transfer energy
Watts (W) & milliwatts (mW)
What is intensity?
Intensity = the rate at which energy passes through a unit area
What is the equation for intensity? What are the units of measurement?
Intensity = power [mW] / area (over which power is distributed) [cm^2]
Miliwatts per centimeter squared (mW/ cm^2)
What happens to the intensity if the power is increased? Area is increased? Area is decreased?
Inc intensity
Dec intensity (power less concentrated)
Inc intensity (power more concentrated)
Intensity is proportional to __________
Amplitude^2
If amplitude is double, intensity is ________.
Quadrupled
Intensity = Amplitude^2
(and vice versa, if amplitude is halved, intensity is quartered)
Intensity is NOT constant across a sound beam, but is usually highest in the ______ and falls off near the ________. Also, intensity is NOT constant within pulses, but rather starts out _____ and then _______ towards the end of the pulse.
Center; periphery
High; decreases
What is the relationship between temporal average intensity, pulse average intensity, and DF.
I(TA) = I(PA) x DF
As an unfocused sound beam travels through a medium, the _______ and _______ will decrease. This is termed __________.
Amplitude; intensity; attenuation
What is absorption?
Absorption = conversion of sound to heat
Attenuation can occur by what 3 means?
Absorption; reflection; scatter
What is the dominant factor that contributes to attenuation of sound in soft tissues?
Absorption
Scatter occurs when sound encounters ____ ______ and _____ _______.
tissue surfaces; heterogeneous tissues
The generation of echoes by the ______ and ______ of sound is crucial to image production.
Reflection; scattering
What is the unit of measurement of attenuation?
Decibel (dB)
What is the attenuation coefficient? and what are its units?
Attenuation coefficient = attenuation that occurs with EACH centimeter the sound wave travels
Units = dB/cm
3 dB corresponds to an intensity ratio of ______.
10dB corresponds to an intensity ratio of ____.
3dB = intensity ratio of 1/2 (aka 50% reduction in intensity)
10dB = intensity ratio of 1/10 (aka 90% reduction in intensity)
What is the formula to determine attenuation in dB?
Attenuation (dB) = attenuation coefficient (dB/cm) x L (cm)
L = path length (aka how far the sound has traveled in cm)
If path length increases, attenuation _______. If freq increases, attenuation _______.
Increases; increases
_____dB of attenuation per centimeter for each MHZ of freq
0.5
What is the average attenuation coefficient (dB/cm) in soft tissues?
Attenuation coefficient (dB) = 1/2 x freq (MHz) x L (cm)
If 4MHz U/S with 10mW/cm^2 intensity is applied to a soft tissue surface, what is the intensity 1.5cm into the tissue?
1) Multiple freq by 1/2 to yield attenuation coefficient of 2 dB/cm.
2) Multiple attenuation coefficient by (2 dB/cm) by path length (1.5cm) to yield an attenuation of 3 dB.
3) An attenuation of 3dB corresponds to an intensity ratio of 0.5. (aka 50% of the original intensity remains after sounds travels through this path).
4) Multiple intensity ratio (0.5) by original intensity (10mW/cm^2) to yield end intensity of 5mW/cm^2
With respect to perpendicular incidence, sound may be _________ or ________. Most often, _______ occur.
reflected back into 1st medium; transmitted into 2nd medium; both
True or false, in the case of perpendicular incidence the transmitted sound changes direction.
False
When discussing incidence, the intensities of the reflected sound (the echo) & the transmitted sound depend on the ____________ at the boundary and the _________ of the media on either side of the boundary.
Incident intensity; impedances
What is the definition of impedance?
Impedance determines how much of an incident sound wave is reflected back into 1st medium & how much is transmitted into 2nd medium
What is the formula for impedance? And what are its units?
Impedance = density (p) of a medium x propagation speed
Rayls (z)
z = p (kg/m^3) x c (m/s)
What happens to impedance if density increases? If propagation speed increases?
Increases; increases
The sum of the reflection and transmission coefficients must equal ____.
One (e.g. 100%)
The _____ the difference between the impedances, the _____ the echo.
Greater; stronger
If media impedances are the same, what happens?
No echo is produced
For impedances of 40 and 60 rayls, determine the intensity reflection (IRC) & transmission coefficients (ITC) .
IRC = [ 60 - 40 / 60 + 40] ^2
= (20 / 100) ^2
= (0.2) ^2 –> 0.04
ITC = 1 - 0.04 –> 0.96
_____ angle always equals the ______ angle.
Reflection; transmission
A change in the direction of sound when it crosses a boundary is called ____.
Refraction
If the propagation speed in the 2nd medium is GREATER than the 1st medium, the transmission angle is ______ than the incidence angle
greater
Propagation speed (c)
c1 < c2 –> Incidence angle < transmission angle
c1 > c2 –> incidence angle > tranmission angle
What are the two requirements for refraction to occur?
1) Oblique incidence
2) Different propagation speed on either side of the boundary
What is scatter?
The redirection of sound in many directions by rough surfaces or by heterogeneous media
How do contrast agents produce echoes?
Due to the impedance mismatch between suspended particles & suspending medium (impedance of gas is MUCH LESS than that of the suspending liquid)
The distance to a reflector is calculated by the range equation, which is what?
d (mm) = 1/2 [ c (mm/us) x t (us)]
distance = 1/2 (propagation speed x ROUND TRIP
time)
What is the purpose of damping (backing) material?
Reduces pulse duration & spatial pulse length –> improves axial resolution
- Additionally, reduces U/S amplitude therefore decreasing the efficiency & sensitivity of the system (aka the ability to detect weak echoes….this is the tradeoff for better resolution)
What is purpose of the matching layer?
Improve sound transmission through tissues
Operating freq (resonance freq) is determined by what?
1) Propagation speed of the element material
2) Transducer element thickness
Operating/resonance freq is such that the _______ of the element corresponds to _______ a wavelength in the element material.
thickness; 1/2
____ elements –> higher frequencies
Thinner (b/c wavelength decreases while freq inc)
What is the equation relating resonance freq to transducer element thickness?
Freq = propagation speed (mm/us) / 2 x thickness
what is the advantage of voltage excitation when used selectively with wide bandwidth transducers?
Can operate the same transducer at more than 1 freq
Wide bandwidth transducers allow use of harmonic imaging, which is what?
In harmonic imaging, echoes of 2x the freq ae sent into the body & received to improve the image
Reducing the # of cycles in ultrasound pulses _______ their bandwdth.
Broadens
The width in the scan plane determines the _______resolution.
Lateral
What does the width perpendicular to the scam plane determine?
The extent of the section thickness artifact
Bea width at any location depends on _______, _______, and _______.
Wavelength
Aperture
Distance from the transducer
While the element or lens is increasingly curved, the focus moves ______ to the transducer.
Closer
(this causes beam width at the focus to decrease)
The limit of beam narrowing depends on _______, _______, and ________.
Wavelength
Aperture
Focal length
For a rectangular aperture, how does one calculate the minimum beam width?
Focal beam diameter =
2 ( wavelength x focal length) / aperture
Beam width narrows to ___ the disk diameter at the near zone length and then ______ to the disk diameter at twice the near zone length.
1/2
widens
Why do lenses focus?
B/c the propagation speed through them is higher than in tissues
_______at the surface of the lens forms the beam so that a focal region occurs.
Refraction
The ______ is the size of the group of elements energized to produce each pulse.
Aperture
Multiple focal zones can be acquired leading to improved detail resolution, however this degrades what?
Temporal resolution ( b/c the frame rate is reduced due to the multiple pulses per scan line)
An Increased or decrease in the curvature of the delay pattern moves the focus ______ or _______, respectively.
Shallower; deeper
To maintain the same focus beam width at increasing focal lengths, the aperture must be _______.
Increased
What is apodization and how does it work?
Reduces the effect of grating lobe artifact.
Outer elements are driven at lower amplitudes than inner elements (downside is loss of resolution)
Axial and lateral resolution depend on the ______ and ______ of the ultrasound pulses, respectively.
Length; width
What is axial resolution?
The minimum reflector separation required along the direction of sound travel to produce separate echoes.
What is the most important factor for determining axial resolution?
Spatial pulse length
What is the formula for determining axial resolution?
AR (mm) = SPL (mm) / 2
How are the number of cycles in each pulse reduced?
Transducer damping
What is lateral resolution?
The minimum reflector separation in the direction perpendicular to the beam direction that can produce 2 separate echoes
(this is equal to the beam width)
What is the equation for lateral resolution?
LR (mm) = beam width (mm)
To avoid ______ _______, all echoes from one pulse must be received before the next pulse is emitted.
Echo misplacement
Imaging depth (aka penetration) in cm multiplied by PRF (kHz) must not exceed _____ if echo misplacement is to be avoided
77 cm/ms
While operating frequency is reduced & penetration increases –> PRF is _____to avoid echo misplacement
Reduced
Power ratio (dB) = ???
Voltage ratio squared
I.e. If input voltage amplitude to an amplifier is 2mV and the output voltage is 200 mV, the voltage ratio is 200/2, or 100. The power ratio is 100^2 = 10,000
3 dB corresponds to a power gain of ?
10 dB corresponds to a power gain of ?
3 db = power gain x2
10 dB = power gain x 10
What is time gain compensation?
Equalizes differences in received echo amplitudes caused by different reflector depths (aka increased attenuation from greater imaging depths is compensated for)
The time gain slope can be expressed in what units?
Decibels of gain per cm of depth
The slope should correspond to the average attenuation coefficient in the tissue if properly adjusted
_____ and ______ determine the maximum imaging depth
Attenuation; maximum amplifier gain
What is the maximum amplifier gain determined by?
Noise
The _____ ________ of the digitizer is determined by the digitizing frequency
Temporal precision
Each cycle of voltage must be interrogated at least _____ to determine its frequency/
2 times
What is the average soft tissue attenuation?
0.5 dB/cm-MHz
(Average attenuation is 1dB/cm-MHz when the centimeter value is the distance from the transducer to the reflector; sound must travel twice this distance so the attenuation # doubles)
*Typical TCG slopes ~1 dB/cm-MHz
What are the 3 functions of a signal processor?
Amplitude detection
Bandpass filtering
Compression (dynamic range reduction)
A smaller dynamic range presents a _____ contrast image.
Higher
What is persistence?
The averaging of sequential frames (frame averaging) to provide a smoother image appearance & to reduce noise
Speckle reduction improves _______ _____ and _____ ______.
Dynamic range
Contrast resolution
Detail resolution is usually limited by _________ and _______ rather than by pixel density in the memory.
Spatial pulse length
Beam width
The analog-to-digital converter (ADC) is part of the ____ _____. And the digital-to-analog converter (DAC) is part of the ____ _______.
Beam former
Image processor
How does an a change in the number of bits per pixel affect contrast resolution?
More bits per pixel (more gray shades)–> improved contrast resolution
Greater # of shades or ______ dynamic range –> improved contrast resolution
Reduced
What is dynamic range?
The ratio of the largest to the smallest amplitude or power that a system can handle
- expressed in dB
Greater dynamic range values indicate what?
The ability to detect weaker echoes, aka greater sensitivity
What is frame rate?
The # of images stored per second
What is temporal resolution?
The ability of a display to distinguish closely spaced events in time & to present rapidly moving structures correctly.
-Expressed in milliseconds
If frame rate increases, temporal resolution _____.
Increases (less time elapses between one frame to the next)
What is the formula for PRF is there are more than 1 focuses?
PRF (Hz) = n x LPF x FR (Hz)
n = # of foci
LPF = lines per frame
FR = frame rate
Must occur to PRF if you want to increase the # of foci? Increase the # of LPF? Increase the FR?
PRF must increase in every instance
In order to avoid echo misplacement, what must occur to PRF if penetration increases?
PRF must decrease (must ensure that all echoes from one pulse are received before another pulse is emitted)
Lower operating frequency –> _____ penetration —> _____ PRF
Increased
Decreased
When image depth is increased, what happens to FR?
FR decreases
Echo misplacement is also called what?
Range ambiguity artifact
Temporal resolution in A and M modes is equal to what?
Pulse repetition period (b/c each pulse produces a new line of echo information)
What is harmonic imaging?
The fundamental (transmitted) frequency echoes are filtered out and the second harmonic frequency echoes are accepted
What are the 3 primary ways in which harmonic imaging improves image quality?
1) Harmonic beam much narrower –> improves lateral resolution [harmonics are generated only in the highest intensity portion of the beam]
2) Eliminates grating lobe artifacts [extra beams not strong enough to generate the harmonics]
3) Reduced/eliminated image degradation b/c harmonic beam is generated at a depth beyond were some artifactual problems occur (e.g. superficial reverberation)
What is spatial compounding?
Technique in which scan lines are directed in multiple directions by phasing so that structures are interrogated more than once by the U/S beam
