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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 (%) = 
{(Z2Z1)/(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 goreturn time = 
(1.54mm/microseconds X goreturn time)/2


In soft tissue
max imaging depth PRP(micros) = 
imaging depth(cm) X 13micros/cm


Quality factor =

main frequency/bandwidth


Relate Qfactor 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 =

(VmaxVmin)/Vmax
V=velocity 

PI =

(VmaxVmin)/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 realtime, Bmode 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)/crosssectional 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

grayscale 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
