Application of Time-Frequency Analysis : Diagnostic Doppler Ultrasound

DATE ： 2013/12/12REPORTER ：林宗民

Outline1. Basic Concepts

2. Doppler Signal

3. Spectral Doppler

4. Doppler Image(Color Doppler, Power Doppler)

5. Conclusion

UltrasoundLongitudinal waveFrequency > 20 KHzDiagnosis Ultrasound ： 1~13 MHzVelocity ：343m/s in air1540m/s in tissue6420m/s in aluminum

http://i299.photobucket.com/albums/mm288/wasi142/Biological%20classification/waves.jpg

Doppler EffectFrequency shift due to relative movement.

Doppler frequency ： fd = f – f0

Ultrasound Image – B modeBrightness-mode

Backscattered image

Tomography

http://content.answcdn.com/main/content/img/McGrawHill/Encyclopedia/images/CE757525FG0010.gif

Doppler Signal, xd(t) = iFT{ fd = fr – ft}

Typically ~kHz in diagnosis Doppler ultrasound.

Continuous Wave Pulse WaveMeasuring the time-varying

Doppler shiftTransmitting several pulses and

sampling received signals

Doppler Signal

Doppler SignalContinuous Wave

Transmitting monochromatic wave.

Transmitted signal spectrum

Doppler SignalContinuous Wave

Transmitting monochromatic wave.

Received signals from moving tissue plus static tissue.

Received signal spectrum

fstatic

fmoving

Doppler SignalContinuous Wave

Transmitting monochromatic wave.

Received signals from moving tissue plus static tissue.

Demodulation and filtering.

Doppler signal spectrum

fstatic

fmoving

Doppler SignalContinuous Wave

Transmitting monochromatic wave.

Received signals from moving tissue plus static tissue.

Demodulation and filtering.

Doppler signal spectrum

fmoving

Doppler SignalPulse Wave

Transmitting several pulses.

Multi-gate sampling.

Doppler SignalPulse Wave

Transmitting several pulses.

Multi-gate sampling.

Doppler signal

Spectral Doppler (Sonogram)

Continuous wave or Pulse wave

Combining B-mode ultrasound with pulsed wave Doppler

STFT has been commonly used.Unbalanced Sampling with ↑50% overlap.

http://en.wikipedia.org/wiki/File:SpectralDopplerA.jpg

2, ( ) fnS Q

j pmt f

p nS Q

X n m w nS p x p e

Simulation AnalysisSimulated Doppler signal.

Using STFT, Cohen’s class Distribution.Choi-Williams DistributionBessel DistributionCone-Shape Distribution

0 0.5 1 1.5 2 2.5 3-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (s)

Am

plitu

de (

mv)

Time (s)

Fre

quen

cy (

Hz)

Power Spectral Density S(t,f)

500 1000 1500 2000 2500 3000

50

100

150

200

250

300

350

400

450

500

Simulation Analysis

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

STFT

Conedistribution

Bessel Distribution

Choi-Williams Distribution

Simulation Analysis

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Time (s)

Fre

quen

cy (

Hz)

0.05 0.1 0.15 0.2 0.25 0.30

500

1000

1500

2000

2500

Conedistribution

Bessel Distribution

Choi-Williams Distribution

STFT Choi-Williams Bessel Distribution Cone Distribution0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Method

Cor

rela

tion

coef

ficie

ntSTFT

Color DopplerCombining B-mode and Doppler signal.

Pulse Wave Multi-gate system.

Velocity and direction of blood flow are the desire information.

2 spatial dimension +1 temporal dimension amount computation.

Auto-correlation method for calculating average frequency.

Power DopplerCombining B-mode and Doppler signal.

Pulse Wave Multi-gate system.

Total power of Doppler signal.

Indicating the flow density information.

Not T-F analysis

ConclusionImage is 3-D signals. It’s not proper to use T-F analysis.

Spectral Doppler is 1-D signals. T-F analysis has been used to measure the blood flow.

In practice, diagnosis signals are more complex than simulated signals, and more noise. Statistic methods are used.

Reference“The Difference Between Colour Doppler Velocity Imaging and Power Doppler Imaging,” W. N. McDicken and T. Anderson, Eur

J Echocardiography(2002)3,240–244

“Time-Frequency Analysis for Doppler Ultrasound signals,” 陳宗銓 , http://djj.ee.ntu.edu.tw/Tutorial_Time-Frequency%20Analysis%20for%20Doppler%20Ultrasound%20Signals.docx.

“Physics and instrumentation of Diagnostic Medical Ultrasound,” PETER FISH, 1990.

“Evaluation of fetal arrhythmias from simultaneous pulsed wave Doppler in pulmonary artery and vein,” Julene S Carvalho, Federico Prefumo, Valentina Ciardelli, Shanthi Sairam, Amarnath Bhide, Elliot A Shinebourne, 2007.

“The Physical Principles of Doppler and Spectral Analysis,” Peter N. Burns, PhD, J Clin Ultrasound 15567-590. NovemberlDecember 1987.