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105 Cards in this Set

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Nyquist Criterion
f(sampling)>=2f(signal)
f must be the highest freq in the signal
reconstructed f = f(signal)
period X frequency
1
power is proportional to
amplitude**2
intensity =
power/area
intensity is proportional to
power
AND
amplitude**2
speed =
frequency X wavelength
pulse duration =
# cycles X period
OR
# cycles/frequency
SPL =
# cycles in each pulse X wavelength of each cycle
PRF X PRP =
1
DUTY FACTOR (%) =
(pulse duration/PRP) X 100
For Raleigh scattering
Intensity is proportional to
FREQUENCY**4
total attenuation =
attenuation coefficient X distance
attenuation coefficient =
frequency/2
impedance (Rayls) =
density X propagation speed
OR
density X (freq X wavelength)
For reflection
the strength of the echo received when incident angle is at or near 0 is
stronger
For normal or oblique incidence
Incident intensity =
reflected intensity + transmitted intensity
For normal incidence
IRC (%) =
{(Z2-Z1)/(Z2+Z1)}**2 X 100
OR
reflected (aka echo) intensity/incident intensity
For normal incidence
ITC (%) =
(transmitted intensity/incident intensity) X 100
OR
1- IRC
For Raleigh scattering
intensity is proportional to
particle radius
For oblique incidence
incident angle =
reflected angle
For reflection
echo strength is inversely related to
the impedance difference at the boundary
For attenuation
as distance increases
amplitude and intensity decrease
Angle of transmission =
sin -1 [sin inc. angle X xmit prop speed)/inc prop speed]
Refraction
(only oblique incidence)

if a)speed med1< speed med2
OR
b)speed med1 > speed med2
OR
c) speed med1 = speed med1

relate incident and transmit angles
assume the propagation speeds of med1 and med2 are different
a)incident angle < xmit angle
b)incident angle > xmit angle
c)no refract xmit angle=inc angle
decreased damping
(decreases ? AND
increases ?)
decreases pulse duration(# cycles X period) and Q
AND
increases bandwidth and axial resolution
Snell's law
sin(transmission angle)/sin(incident angle) =
prop. speed in med2/prop. speed in med1
For spatial resolution
increasing frequency
decreases ?
AND
increases ?
decreases penetration
AND
improves spatial resolution
In soft tissue
max imaging depth
PRF(Hz) =
77,000/imaging depth(cm)
In soft tissue
depth of a reflector in terms of go-return time =
(1.54mm/microseconds X go-return time)/2
In soft tissue
max imaging depth
PRP(micros) =
imaging depth(cm) X 13micros/cm
Quality factor =
main frequency/bandwidth
Relate Q-factor to bandwidth
Wide bandwidth = lo Q value
Narrow bandwidth = hi Q value
axial resolution(mm)=

(low value=better resolution)
SPL/2
OR
for soft tissue
(.77 X #cycles in a pulse)/frequency(MHz)
OR
for soft tissue
.77 X PD
OR
.77 X (# cycles in a pulse) X period
OR
low Q
OR
wide bandwidth
OR
reduced sensitivity
focal depth =
(diameter**2 X freq)/61.6
OR
diameter**2/(4 X wavelength)
lateral resolution =
beam diameter
(Time to make one frame) X (frame rate) =
1
(Time to make one frame) =
# pulses X PRP
? bits are in a byte
8
? bytes are in a word
2
? bits are in a word
16
formula for the number of gray shades
2**# of bits
Mechanical index =
peak negative pressure/
square root of frequency
pressure gradient =
flow X resistance
voltage =
current X resistance
Doppler shift (Hz) =
reflected frequency - transmitted frequency
Doppler Equation
(2 X speed of blood X transducer frequency X cos(theta))/propagation speed
measured velocity =
true velocity X cos(theta)
RI =
(Vmax-Vmin)/Vmax
V=velocity
PI =
(Vmax-Vmin)/Vmean
V=velocity
Nyquist Limit =
PRF/2
Larger the crystal thickness
the smaller the resonant frequency
Near field length increases
with increasing frequency and aperture
thereby narrowing the focus of a focused beam
Increasing frequency and aperture
narrows the focus of a focused beam
For spatial resolution
the shorter the SPL
the greater the spatial resolution
For spatial resolution
the shorter the PD
the greater the spatial resolution
axial resolution =
SPL/2
lateral resolution =
beam width
For lateral resolution
increasing the frequency
increases the resolution by decreasing the focus
For lateral resolution
increasing the aperture (or increasing curvature)
increases the resolution by decreasing the focus
Elevational resolution =
beam width perpendicular to the scan plane
For elevational resolution
increasing the delay of curvature
decreases the depth of focus
For elevational resolution
increasing the frequency
decreases the slice thickness
The best overall resolution is
axial
Multiple transmission foci results in
a long focus
decreased frame rate
and
decreased temporal resolution
Dynamic range =
Largest power of system/smallest power of a system
Largest power of system/smallest power of a system
Largest intensity of echoes of system/smallest intensity of echoes of a system
For A mode
x axis and y axis units
x axis depth
y axis echo amplitude
For M mode
x axis and y axis units
x axis time
y axis motion
For real-time, B-mode image formation
Echo brightness increases with
echo amplitude
Frame rate is proportional to
PRF
Frame rate is inversely proportional to
# lines per frame
Time to create 1 frame =
1/frame rate
Increasing the sector angle
increases the number of scan lines per frame
AND reduces the frame rate
Greater the imaging depth
reduces the PRF and frame rate
Temporal resolution depends on
frame rate
temporal resolution is degraded by these 3 factors
increased:
imaging depth
lines per fame
number of foci
Fluid viscosity causes these 2 things
flow resistance
energy loss
Poiseuille's equation
change in pressure/flow resistance = volumetric flow rate(Q)
Mean velocity across a vessel =
volumetric flow rate(Q)/cross-sectional area(A)
Venous resistance is proportional to
viscosity
AND
vessel length
Venous resistance is inversely proportional to
vessel diameter**4
Pressure =
1/volume
bulk modulus =
pressure change/volume change
Bulk modulus =
1/compressibility
The effect of stenosis on flow speed
increases flow speed
Doppler Equation
Doppler rfequency -transmitted frequency
OR
Operating frequency X {(2 X volume)/propagation speed}
Increasing beam angle does what to the Doppler shift
decreases Doppler shift
Increasing frequency does what to the Doppler shift
increases Doppler shift
Increasing flow velocity does what to the Doppler shift
increases Doppler shift
Flow direction towards the transducer causes a positive or negative Doppler shift
positive
Flow direction away from the transducer causes a positive or negative Doppler shift
negative
Sample volume width is determined by
the beam width
Sample volume gate is determined by
how long the gate is open
For color flow imaging
Increasing ensemble length does what to the frame rate
reduces
For color flow
Increasing the number of scan lines per frame does what to the frame rate
decreases
Sensitivity/specificity =
number of + correct test results/total number of positive test results
Negative predictive value =
number of correct negative test results/total number of negative test results
Positive predictive value =
number of correct positive test results/total number of positive test results
Accuracy =
number of correct test results/total number of test
Intensity and power values are lowest for
gray-scale anatomic imaging
Intensity and power values are highest for
pulsed Doppler
Mechanical Index =
Peak rarefractional pressure amplitude/sq root(operating frequency)
To correct aliasing
the Nyquist Limit is
(increased/decreased)
AND
the PRF is (increased/decreased/unchanged)
Both should be increased.
To sample for low blood flow use:
(High/low) wall filters
(High/low) PRF
Low PRF with low wall filters
Dynamic range calculation =
Divide larger voltage by smaller, count the number of zeroes in the resultant 10 factor and multiply by 20