Download - Scattering from Individual Red Blood Cells
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Scattering from Individual Red Blood Cells
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Scattering from Ensembles of Red Blood Cells
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Scattering from Ensembles of Red Blood Cells
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The Doppler EffectMoving source
‘Pulse-echo’:
Moving receiver
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Continuous wave Doppler System:getting directionality I
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Continuous wave Doppler System:getting directionality II
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Pulsed wave Doppler: Approach
Question: what is really being measured here?
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Pulsed wave Doppler: Basic Equations
]
2[2sin
2)(
cd
tfcd
teAtr oo
o
]2)1(2
[2sin2)1(2)(
PRF
oo
PRF
oi cf
vicd
tfcf
vicd
tetr
2),(),()( tzQjtzIFFTfS audioaudio
PRFDoppler
PRF
DoppleroDM f
iff
ifcd
tetI 12sin)1(2
)(
cvf
f oDoppler
2
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Pulsed wave Doppler:Signals
Reference oscillator
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Measurement limitations: aliasing
0 2 4 6 8 10 12 14 16 18 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6Audio data set - quadrature
Pulse Number
Dep
th -
in s
ampl
es
RF data set
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
1400
1600
IF data set - quadrature
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
1400
1600
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1Audio data set - quadrature
Pulse Number
Dep
th -
in s
ampl
es
RF data set
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
IF data set - quadrature
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
0 2 4 6 8 10 12 14 16 18 20-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6Audio data set - quadrature
Pulse NumberD
epth
- in
sam
ples
RF data set
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
1400
1600
IF data set - quadrature
Pulse Number
Dep
th -
in s
ampl
es
2 4 6 8 10 12 14 16 18 20
200
400
600
800
1000
1200
1400
1600
Well sampled At Nyquist (PRF/2) Aliased
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Measurement limitations: depth vs velocity limits
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Measurement limitations: velocity resolution limits
Velocity resolution Frequency resolution
Fres = 1/(total time) = PRF/(N) where N=number of pulses
Using the Doppler equation…
Vres = c*PRF/(2*Ftrans*N)
Increasing N therefore improves resolution, but total time must be less than that of expected changes to flow (e.g. due to cardiac cycle)
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Measurement limitations: pulse length
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Measurement limitations: tranverse motion
Fundamental trade-off between localization and velocity resolution
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A closer look at spectra and their relation to hemodynamics
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Measurement limitations: tranverse motion
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Measurement of Haemodynamic indices
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Colour flow: how it works
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Colour flow: The autocorrelation function
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Colour flow: how it works
1
1
1
1
)1(Q)(Q)1(I)(I
)1(I)(Q)1(Q)(Iarctan
4ˆ N
n SSSS
N
n SSSS
Tx
PRFmean
nnnn
nnnnf
cfv
PRFDoppler
PRF
DoppleroDM f
iff
ifcd
tetI 12sin)1(2
)(
2),(),()( tzQjtzIFFTfS audioaudio
Demodulated Audio (time domain) Audio (freq. domain)
For pulsed wave Doppler we had:
And calculated full spectra (i.e. velocity distributions in a time window) with:
For colour flow, we use the autocorrelator to calculate the mean velocity (Jensen ’96):
N=# pulsesIs=Iaudio
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Power Doppler: how it works
1
122 )(Q)(Iˆ
11 N
n SSmean nnP N
Demodulated Audio (time domain) Audio (freq. domain)
For power Doppler, we use the audio frequency data to calculate the mean power:
N=# pulsesIs=Iaudio
The power is proportional to the volume of moving blood
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Colour flow: ‘clutter’ filtering(a) Doppler Spectrum at 5 MHz
Dop
pler
Pow
er
Doppler Frequency (velocity)
Fmax
(b) Doppler spectrum at 50 MHz
Tissue
Blood
NoiseDop
pler
Pow
er
Doppler Frequency (velocity)
Fmax
Tissue
Blood Noise
Prior to power and velocity estimation, a high pass filter (e.g. FIR, IIR, regression) is applied to remove the tissue signals
- the ‘clutter’ filter can have a fundamental impact on flow detection
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Flow imaging processing overview
- Ensembles generally 4-16 pulses along a beam direction
- process repeated across image plane
RawData
‘ensemble’
Power est.
Clutterfilter
VelocityEst.
PowerEst.
VarianceEst.
Thresholding/Flow
decision
Bscan
Velocityimage
Powerimage
Varianceimage
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Colour flow: limitations
- noise and small number of pulses results in vessel detection limits
- ‘flash’ artefacts due to transient tissue/transducer motion
- filtering results in increased loss of slower flow
As with pulsed-wave Doppler: -aliasing -depth vs velocity limits (more stringent due to 2D image acquisition)