Physics & Hemodynamics Flashcards
What is the Doppler Equation?
Change in frequency = blood flow velocity * Cosine theta * 2 * transmitted frequency / velocity of ultrasound in soft tissue
dF = VCos(theta)2*Ft/c
There is a 2 in the equation because two Doppler shifts occur.
What is the velocity of ultrasound in soft tissue?
1540 meters/second
1.54mm/microsec
What do wall filters do?
Wall filters filter out part of the doppler shift (filter velocities)
What is the high pass wall filter and what is it used for?
The high pass wall filter filters out low velocities and allows high velocities to pass (used for CFD).
What is the low pass wall filter and what is it used for?
The low pass wall filter filters out high velocities and allows low velocities to pass (used for TDI).
What signals are present in tissue doppler? Which wall filters are used?
Low velocity, high amplitude signals (high pass filter off, low pass filter on).
What signals are present in color flow doppler? Which wall filters are used?
High velocity, low amplitude signals (high pass filter on, low pass filter off)
What parameter is determined by both ultrasound source and medium?
Wavelength
Order of ultrasound speed through different tissues? What two parameters affect the velocity?
(fastest) Bone > soft tissue > fat > lung > air (slowest)
Velocity determined by density and stiffness of the medium (faster in stiffer media, slower in denser media)
What is power doppler? What information does it provide?
Only signifies the presence of a Doppler shift. Does not include information on direction or speed (i.e. no velocity information).
What are other names for power doppler?
Energy mode or color angio
What is the Nyquist limit?
The maximum doppler shift that can be measured before aliasing occurs
Aliasing occurs when the deltaF (Doppler shift) > 1/2 PRF
Equation for the Nyquist limit
Nyquist limit = 1/2 PRF
What are the following parameters for M Mode?
X-axis
Y-axis
Frame rate
Brightness
X-axis = time
Y-axis = depth
Frame rate = 1000
Brightness = strength of the returning signal (stronger reflector = brighter on screen)
What is wavelength?
The distance between two identical points in adjacent cycles of a waveform signal
What is spatial pulse length? What type of resolution does it determine?
The length of a single pulse (a measure of DISTANCE)
SPL = wavelength x number of cycles in the pulse
Axial resolution = 1/2 SPL
What parameter determines axial resolution?
Spatial pulse length
Axial resolution = 1/2 SPL
What are the synonyms for axial resolution?
Longitudinal, axial, radial, range, depth (LARRD)
What parameter determines lateral resolution?
Beam width
What are the synonyms for lateral resolution?
Lateral, angular, transverse, azimuthal (LATA)
What is spatial resolution?
The ability to accurately create images of small structures in their correct anatomic position
(The ability to distinguish the space between two individual points)
What is the frequency of ultrasound?
> 20,000 Hz (20kHz)
Diagnostic ultrasound is usually in the range of 2-15 MHz
What is frequency?
The number of cycles per second
What is temporal resolution? What mode of echo has the best temporal resolution?
The ability to accurately determine the position of a structure at a particular instant in time
M-mode has the best temporal resolution.
What is power? What is it proportional to?
Power is the rate of energy transfer by the ultrasound beam or the rate at which work is performed.
Measured in watts (J/sec).
Proportional to amplitude^2
What is intensity?
Power per unit area
This is what can cause tissue damage and is responsible for the bioeffects of ultrasound.
Proportional to amplitude^2
What is gain?
Signal amplification
What is compression?
A reduction in the differences between signals, leading to a smaller dynamic range
(Compression decreases dynamic range so that the signals can be processed by the TEE machine)
What is dynamic range?
The ratio between the largest and smallest values the signal can assume
I.e. the range of signals the ultrasound machine can process
What are the five functions of an ultrasound receiver (listed in order of occurrence)?
1) Amplification
2) Compensation
3) Compression
4) Demodulation
5) Rejection
What is rejection?
Elimination of very low amplitude signals in 2D ultrasound (reduces noise)
What are synonyms for rejection?
Threshold and suppression
What are 5 ways to decrease or eliminate aliasing artifact?
1) Use CWD instead of PWD
2) Use a lower transmitted frequency (Ft)
3) Decrease depth of the sample gate
4) Increase PRF
5) Change baseline
What is an L wave?
Wave between the E and A waves indicated impaired relaxation and elevated LA pressure on MVI PWD
What is pressure half time?
The amount of time it takes to go from the maximum pressure gradient to 1/2 that maximum pressure (~71% decrease in velocity)
Which ultrasound parameters are depth dependent?
Pulse repetition period and pulse repetition frequency (dependent on listening time)
Nyquist limit is therefore depth dependent (1/2 PRF)
Which mode of ultrasound creates the greatest thermal intensity?
Pulse wave Doppler (maximum heating spatial peak temporal average)
What is mechanical index? What is the equation for it?
The strength of the US beam and the beam’s ability to produce cavitation of contrast material. High MI = strong beam.
MI = peak negative pressure / √frequency
(MI indicates the beam’s ability to cause cavitation-related bioeffects; thought a reasonable proxy for micromechanical damage)
What mechanical index will generate harmonics?
MI >0.1
What is quality factor?
QF = RF/BW
Lower QF = better image quality
Bandwidth = range of frequencies emitted in a pulse (6-11MHz = 5)
What is SPTA? What is the maximum SPTA recommended to avoid thermal injury for an unfocused US beam? For a focused beam?
Spatial peak temporal average intensity
Unfocused: < 1W/cm2
Focused: <100mW/cm2 (0.1W/cm2)
What 3 processes cause attenuation?
- reflection
- scattering
- absorption
What is Rayleigh scattering?
Form of organized scatter when the beam encounters objects smaller than its wavelength and is redirected equally in all directions.
Is increased with increasing frequency to the 4th power.
What is the attenuation coefficient?
The number of decibels of attenuation when sounds travels 1cm
Units: dB/cm
In soft tissues, the attenuation coefficient = 1/2 frequency
AC = 1/2 F
What has the highest acoustic impedance?
The piezoelectric crystal
Piezoelectric crystal > matching layer > gel > skin
What are the units of acoustic impedance?
Rayls (Z)
Density * velocity
Z=p*V
What is the maximum allowable mechanical index per the FDA?
1.9
What type of wave is sound waves?
Sound is a mechanical longitudinal wave.
Sound travels via a series of compressions and rarefactions in molecules of the medium it travels through.
What is amplitude? How are power and intensity related to amplitude?
The difference between the average acoustic variable and the peak acoustic variable
Power and intensity are related to amplitude^2
What mechanical index creates the strongest harmonics?
MI>1
What beam frequency and strength (high vs low) causes:
1) a low mechanical index 2) a high mechanical index
Low mechanical index: high frequency transducer, low beam strength
High mechanical index:
low frequency transducer, high beam strength
MI = peak negative pressure / √frequency
What determines wave properties involving time?
Only the source of the beam
Remember: SECONDS = SOURCE
What is the pulse repetition period?
PRP = pulse duration + listening time
(Time from beginning of one pulse to the beginning of the next pulse)
What ultrasound time parameters are ALSO dependent on depth?
Pulse repetition period and pulse repetition frequency (because they include listening time, and listening time is depth dependent)
Less depth = less listening time = more pulses can be sent per second = higher pulse repetition frequency = higher Nyquist limit and better temporal resolution
What is frame rate? What does it depend on?
Frame rate = number of frames per second (number of images per second)
Higher PRF = higher frame rate
Higher frame rate = better temporal resolution
What determines the velocity of ultrasound in tissue? How does stiffness and density affect velocity?
The medium only
- As stiffness increases, velocity increases (i.e. as elasticity decreases)
- As density increases, velocity decreases
A less dense, less elastic tissue will have a higher US velocity
What are the advantages and disadvantages of higher frequency ultrasound?
Advantage: better axial resolution
Disadvantages: greater attenuation, less harmonics
What is impedance?
Acoustic resistance to sound traveling through a medium
Impedance = density x velocity
Z=PxV
Determined by the medium only
Unit: Rayls
Velocity is determined by density and elasticity, and elasticity is inversely related to stiffness. So Z is affected by velocity, density, elasticity, AND stiffness
What is the Curie temperature for ultrasound?
Around 360 C
Beyond this point, the material becomes depolarized and loses its piezoelectric properties (i.e. the transducer no longer works)
What does backing material do in the transducer?
Acts as a damper to decrease ringing, allowing the probe to generate short, clean pulses.
- Decreases spatial pulse length and pulse duration (improves axial resolution)
- Increases bandwidth
- Decreases quality factor (good!)
- But also decreases sensitivity to reflected echoes
What is the purpose of the matching layer?
To prevent a large reflection at the interface of the mucosa and PZT
- Has an acoustic impedance between that of mucosa and the PZT
For imaging, should the quality factor be higher or lower?
Lower quality factor used for imaging
What is bandwidth?
The difference between the lowest and highest frequencies in a pulse
What is the equation for resonant frequency for pulsed US?
RF=V/2T
V= velocity
T = thickness
Where does the best lateral resolution in an ultrasound beam occur?
At the point of focus
What is the ultrasound beam focus point?
Focus = location of the minimum diameter of the beam
What is the near field? What is it also called?
The distance from the transducer to the point of focus
Aka: Near Zone, Fresnel Zone
Equation for length of the near field (Ln)
Ln=r^2/lambda
r=radius of crystal
lambda=wavelength
What is the far field? What is it also called?
The distance past the point of focus
Aka: Far Zone, Fraunhofer Zone
How is beam divergence affected by:
- crystal diameter
- crystal frequency
Crystal diameter: larger diameter = less divergence (deeper focal length)
Crystal frequency: higher frequency = less divergence (deeper focal length)
What are the two steps of demodulation?
Rectification and Smoothing
Rectification: turns all negative voltages positive
Smoothing: places an envelope around signals to smooth them out
What is a reverberation artifact?
Caused by the beam ricocheting between two strong reflectors, creating multiple, equally-spaced reflections in the image
Aka: ringdown artifact, comet tail
What is a refraction artifact?
When the beam is bent prior to striking the reflector
The machine assumes the beam travelled in a straight line, so the image will be placed to the side and deeper than the true reflector
How is scattering related to frequency?
Scattering is directly related to frequency (higher frequency beam = greater scattering)
What is the equation for Snell’s law?
n1sin(theta1) = n2sin(theta2)
The ratio of the sine of the angles of incidence and transmission is equal to the ratio of the refractive index of the materials at the interface.
When refraction occurs, if the incident velocity is higher than the transmitted velocity, how is the incident angle related to the transmitted angle?
If Vi>Vt, then the incident angle is > transmitted angle
V1/V2 = sine(theta 1)/sine(theta2)
Sine increases as angle increases
What conditions must be met for refraction to occur?
Oblique incidence (not 90 degrees) AND the transmitted velocity must be different from the incident velocity
What is line density? How is it related to temporal resolution?
Line density = number of scan lines/image
As line density increases, temporal resolution decreases.
What is the most common composition of a piezoelectric crystal in a TEE probe?
Lead zirconate titanate (PZT)
What determines the frequency of CWD? What about PWD?
For CWD, frequency = frequency of electrical excitation voltage applied to the to the crystal.
For PWD, frequency = V/2T (need to know the thickness of the crystal and the velocity of sound in the crystal)
What is the intensity reflection coefficient?
The % of ultrasound intensity that is reflected at the interface of two media
= (incident intensity-transmission intensity)/incident indensity x100%
Affected by acoustic impedance, medium density, stiffness, and the velocity of ultrasound
What is duty factor?
A unitless number describing the amount of time that the ultrasound machine is producing sound.
Increasing PRF increases DF.
What is responsible for Doppler determinations of blood flow velocities?
Rayleigh scattering
What is the effect of focusing an ultrasound beam on:
- focal zone
- far field divergence
- beam diameter
- focal depth
- smaller focal zone
- increased far field divergence
- reduced beam diameter in near field
- shallower focal depth
Note: narrower beam = better lateral resolution
What two factors determine beam divergence? Are the relationships inverse or proportional?
Crystal diameter and frequency of sound (which is determined by V/2T)
Crystal diameter and frequency are both INVERSELY related to beam divergence
What is the optimal thickness of the PZT crystal?
1/2 wavelength
What is the optimal thickness of the matching layer?
1/4 wavelength
What is the piezoelectric effect and reverse piezoelectric effect?
Piezoelectric effect: conversion of sound to electrical signal
Reverse piezoelectric effect: conversion of electrical signal to sound
Reverse piezoelectric effect happens first, piezoelectric effect happens second
What is the ALARA principle?
“As low as reasonably achievable”
Minimize patient exposure to ultrasound
- If image is too dark, increase GAIN first
- If image is too bright, decrease POWER first
What is the shortcut for calculating wavelength from MHz?
Divide 1.54 by the frequency in MHz
Velocity = 1.54mm/microsecond
1 MHz = 1 cycle/microsecond
Equation for duty factor
DF = pulse duration / PRP x100
Order of attenuation in tissues (greatest to least)
Main mechanism of attenuation?
Air > Lung and bone > Muscle > Soft tissue > Fat > Blood/fluid > Water
Absorption is primary mechanism in air, lungs, bone
Beam divergence equation
Sin(beam divergence angle) = 1.2 * lambda / d
d=diameter
Beam divergence increases with smaller diameter crystal and lower frequency sound
Remember shorter focal length = greater divergence with depth
What is Huygen’s principle?
A large active element can be thought of as millions of tiny distinct sound sources
Each point on a wavefront is the source of spherical waves
What is backing material composed of?
May be composed of tungsten powder and araldite
How do you calculate Qp/Qs?
- Calculate Qp (use radius main PA and VTI through PA)
- Calculate Qs (radius LVOT and VTI through LVOT)
Then divide Qp by Qs (stroke volume through pulmonary artery / stroke volume through LVOT)
How do you calculate AR regurgitant volume using stroke volume?
Total volume into LV = volume out through AV + regurgitant volume
Therefore, regurgitant volume = stroke volume LVOT - stroke volume MV
How do you calculate stroke volume (general equation)?
Volume = area x distance
Therefore, SV = area x VTI
What is the equation for regurgitant fraction?
RF = regurgitant volume / stroke volume through valve
Simplified Bernoulli’s equation
Driving pressure - pressure in receiving chamber = 4V^2
How is dp/dt calculated?
Slope of LV pressure rise from 4-36mmHg
(slope from MR velocity = 1 to MR velocity = 3)
Therefore, dp/dt = 32/dt
What is the equation for velocity of circumferential shortening?
VcF=FS/ejection time
