### Application of Time-Frequency Analysis : Ultrasound Doppler Imaging

```Application of Time-Frequency Analysis :
Diagnostic Doppler Ultrasound
DATE：2013/12/12
REPORTER：林宗民
Outline
1.
Basic Concepts
2.
Doppler Signal
3.
Spectral Doppler
4.
Doppler Image(Color Doppler, Power Doppler)
5.
Conclusion
Ultrasound
Longitudinal wave
Frequency > 20 KHz
Diagnosis Ultrasound：1~13 MHz
Velocity ：
 343m/s in air
 1540m/s in tissue
 6420m/s in aluminum
http://i299.photobucket.com/albums/mm288/
wasi142/Biological%20classification/waves.jpg
Doppler Effect
Frequency shift due to relative movement.
Doppler frequency： fd = f – f0
fd =
−2vcosθ
c
f0 , v ≪ c
Ultrasound Image – B mode
Brightness-mode
Backscattered image
Tomography
http://content.answcdn.com/main/content/img/McGrawHill/Enc
yclopedia/images/CE757525FG0010.gif
Doppler Signal
Doppler Signal, xd(t) = iFT{ fd = fr – ft}
Typically ~kHz in diagnosis Doppler ultrasound.
Continuous Wave
Pulse Wave
Measuring the time-varying
Doppler shift
Transmitting several pulses and
Doppler Signal
Continuous Wave
Transmitting monochromatic wave.
Transmitted signal spectrum
Doppler Signal
Continuous Wave
Transmitting monochromatic wave.
Received signals from moving tissue plus static
tissue.
fstatic
fmoving
Doppler Signal
Continuous Wave
Transmitting monochromatic wave.
Received signals from moving tissue plus static
tissue.
Demodulation and filtering.
fstatic
fmoving
Doppler signal spectrum
Doppler Signal
Continuous Wave
Transmitting monochromatic wave.
Received signals from moving tissue plus static
tissue.
Demodulation and filtering.
fmoving
Doppler signal spectrum
Doppler Signal
Pulse Wave
Transmitting several pulses.
Multi-gate sampling.
Doppler Signal
Pulse 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.
X  n t , m f  
nS Q
 w  (nS  p)  x  p  e
p  nS Q
 j 2 pm  f

http://en.wikipedia.org/wiki/File:SpectralDopplerA.jpg
Simulation Analysis
Simulated Doppler signal.
fMax (kHz) = 3.5 sin 2πf1 t + 1,
0s ≤ t ≤ 0.3s
Using STFT, Cohen’s class Distribution.
Choi-Williams Distribution
4000
Bessel Distribution
3000
Cone-Shape Distribution
2000
Amplitude (mv)
Power Spectral Density S(t,f)
500
450
400
Frequency (Hz)
350
1000
0
-1000
300
-2000
250
-3000
200
150
-4000
100
50
500
1000
1500
Time (s)
2000
2500
3000
0
0.5
1
1.5
Time (s)
2
2.5
3
2500
2500
2000
2000
Frequency (Hz)
STFT
Frequency (Hz)
Simulation Analysis
1500
1000
500
1000
0.05
0.1
0.15
Time (s)
0.2
0.25
0
0.3
2500
2500
2000
2000
1500
1000
500
0
Choi-Williams
Distribution
500
Frequency (Hz)
Bessel
Distribution
Frequency (Hz)
0
1500
0.05
0.1
0.15
Time (s)
0.2
0.25
0.3
1500
Cone
distribution
1000
500
0.05
0.1
0.15
Time (s)
0.2
0.25
0.3
0
0.05
0.1
0.15
Time (s)
0.2
0.25
0.3
2500
2500
2000
2000
Frequency (Hz)
STFT
Frequency (Hz)
Simulation Analysis
1500
1
0.9
1000
1500
Choi-Williams
Distribution
1000
500
0
0.05
0.1
2500
Correlation coefficient
0.8
500
0.7
0.6
0.5
0.15
0.2
0.25
0
0.3
0.05
0.1
Time (s)
0.4
0.15
Time (s)
0.2
0.25
0.3
2500
0.3
2000
2000
0.2
0
STFT
Frequency (Hz)
Bessel
Distribution
Frequency (Hz)
0.1
1500
1000
500
0
1500
Cone
distribution
Choi-Williams Bessel Distribution Cone Distribution
Method
1000
500
0.05
0.1
0.15
Time (s)
0.2
0.25
0.3
0
0.05
0.1
0.15
Time (s)
0.2
0.25
0.3
Color Doppler
Combining 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 Doppler
Combining B-mode and Doppler signal.
Pulse Wave  Multi-gate system.
Total power of Doppler signal.
Indicating the flow density information.
Not T-F analysis
Conclusion
Image 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_TimeFrequency%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.
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