Scattering from Individual Red Blood Cells

Scattering from Ensembles of Red Blood Cells

Scattering from Ensembles of Red Blood Cells

The Doppler EffectMoving source

‘Pulse-echo’:

Moving receiver

Continuous wave Doppler System:getting directionality I

Continuous wave Doppler System:getting directionality II

Pulsed wave Doppler: Approach

Question: what is really being measured here?

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

Pulsed wave Doppler:Signals

Reference oscillator

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

Measurement limitations: depth vs velocity limits

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)

Measurement limitations: pulse length

Measurement limitations: tranverse motion

Fundamental trade-off between localization and velocity resolution

A closer look at spectra and their relation to hemodynamics

Measurement limitations: tranverse motion

Measurement of Haemodynamic indices

Colour flow: how it works

Colour flow: The autocorrelation function

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

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

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

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

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)