1. TTK4165 Color Flow Imaging Hans Torp Department of Circulation and Medical Imaging NTNU, Norway Hans Torp NTNU, Norway

2. Color flow imaging Estimator for velocity and velocity spread power, mean frequeny, bandwidthEstimator for velocity and velocity spread power, mean frequeny, bandwidth Color mapping and visualizationColor mapping and visualization Clutter filteringClutter filtering Scanning strategiesScanning strategies

3. Data acquistion in color flow imaging Beam k-1Beam k Beam k+1 Number of pulses in each direction 3 – 15 Frame rate reduction compared to B-mode

4. 2D Color flow imaging 1. Limited information content in the signal, i.e. short observation time, low signal-to-noise ratio, and low Nyquist velocity limit. 2.Insufficient signal processing/display. Full spectrum analysis in each point of the sector is difficult to visualize.

5. Signal power: Mean frequency: Bandwidth:

6. Taylor expansion of exp-function

7. Autocorrelation method Power, meanfreq., bandwidth derived from sample mean autocorrelation estimator

8. Scatter diagram of the autocorrelation estimator with lag m=1 for three different signals. To the right, a narrow band signal with center frequency ω 1 =π/2 to the left, a slightly more broadband signal with ω 1 =3π/2, and in the middle, high-pass filtered white noise. Autocorrelation method

9. Estimation error is minimum when correlation is maximum Hans Torp NTNU, Norway Correlation magnitude Correlation angle ~Velocity Matlab-demo: AcorrEst.m

10. Estimator properties

11. Normalized Autocorrelation function  (1) = R(1) / R(0)

12. Color mapping types Hans Torp NTNU, Norway Power Doppler (Angio) Brightnes ~ signal power Color flow Brightnes ~ signal power Hue ~ Velocity Color flow ”Variance map” Hue & Brightnes ~ Velocity Green ~ signal bandwidth

13. Color scale for velocity and - spread Power Band width Aortic insufficiency Hans Torp NTNU, Norway

14. Color flow imaging Mitral valve blood flow Normal mitral valve Stenotic mitral valve Hans Torp NTNU, Norway

15. Autocorrelation method Sensitive to clutter noise Phase angle of R(1) substantially reduced due to low frequency clutter signal Clutter filter stopband much more critical than for spectral Doppler

16. Clutter filter in color flow imaging? Beam k-1Beam k Beam k+1

17. Doppler Signal Model Signal vector for each sample volume: Signal vector for each sample volume: x = [x(1),…,x(N)] T Signal = Clutter + White noise + Blood x = c + n + b Typical clutter/signal level: 30 – 80 dBTypical clutter/signal level: 30 – 80 dB Clutter filter stopband suppression is critical!Clutter filter stopband suppression is critical! Zero mean complex random processZero mean complex random process Three independent signal components:Three independent signal components: Hans Torp NTNU, Norway -0.6-0.4-0.200.20.40.6 0 20 40 60 80 100 Blood velocity [m/s] Doppler spectrum [dB] Clutter Blood

18. Approaches to clutter filtering in color flow imaging IIR-filter with initialization techniquesIIR-filter with initialization techniques Short FIR filtersShort FIR filters Regression filtersRegression filters

19. IIR filter with initialization Chebyshev order 4, N=10 Power [dB] Frequency 00.10.20.30.40.5 -80 -60 -40 -20 0 Frequency response Steady state Step init. Discard first samples Projection init* *Chornoboy: Initialization for improving IIR filter response, IEEE Trans. Signal processing, 1992

20. FIR Filters Discard the first M output samples, where M is equal to the filter orderDiscard the first M output samples, where M is equal to the filter order Improved amplitude response when nonlinear phase is allowedImproved amplitude response when nonlinear phase is allowed 00.10.20.30.40.5 -80 -60 -40 -20 0 Power [dB] Frequency Frequency response, order M= 5, packet size N=10     M k k k zbzH 0 )( Linear phase Minimum phase

21. Regression Filters Subtraction of the signal component contained in a K-dimensional clutter space: Signal space Clutter space b1b1 b2b2 b3b3 x y c y = x - c Linear regression first proposed by Hooks & al. Ultrasonic imaging 1991 x = [x(1),…,x(N)]

22. Why should clutter filters be linear? No intermodulation between clutter and blood signalNo intermodulation between clutter and blood signal Preservation of signal power from bloodPreservation of signal power from blood Optimum detection (Neuman-Pearson test) includes a linear filterOptimum detection (Neuman-Pearson test) includes a linear filter y = Ax Any linear filter can be performed by a matrix multiplication of the N - dimensional signal vector xAny linear filter can be performed by a matrix multiplication of the N - dimensional signal vector x This form includes all IIR filters with linear initialization, FIR filters, and regression filtersThis form includes all IIR filters with linear initialization, FIR filters, and regression filters * Matrix A Input vector xOutput vector y

23. Frequency response Linear Filters y = Ax Definition of frequency response functionDefinition of frequency response function = power output for single frequency input signal 2 1 )(   Ae N HoHo   T Nii eee    )1( 1    Note 1. The output of the filter is not in general a single frequency signal (This is only the case for FIR-filters) Note 2. Frequency response only well defined for complex signals 

24. FIR filter matrix structure FIR filter order M=5 Packet sizeN=10 Output samples: N-M= 5 Increasing filter order + Improved clutter rejection - Increased estimator variance Hans Torp NTNU, Norway

25. Regression Filters Subtraction of the signal component contained in a K-dimensional clutter space:Subtraction of the signal component contained in a K-dimensional clutter space: xbbIy          K i H ii 1 Signal space Clutter space b1b1 b2b2 b3b3 x y c Choise of basis function is crucial for filter performance y = x - c A

26. Fourier basis functions n b (k)= 1/sqrt(N) e i*2π*k*n/N n= 0,.., N-1 are orthonormal, and equally distributed in frequency

27. Fourier Regression Filters DFT Set low frequency coefficients to zero Inverse DFT 00.10.20.30.40.5 -80 -60 -40 -20 0 Frequency Power [dB] Frequency response N=10, clutter dim.=3

28. Legendre polynom basis functions b 0 = b 1 = b 2 = b 3 = Gram-Schmidt process to obtain Orthonormal basis functions -> Legendre polynomials

29. Polynomial Regression Filters b 0 = b 1 = b 2 = b 3 = Power [dB] Frequency 00.10.20.30.40.5 -80 -60 -40 -20 0 Frequency responses, N=10

30. Regression filter bias Magnitude and phase frequency response Polynomial regression filter packet size = 10, polynom order 3. Severe bias in bandwidth and mean freq. estimator below cutoff frequency.

31. How to image low velocity flow Long observation time neededLong observation time needed Obtained by increased packet size or lower PRFObtained by increased packet size or lower PRF Beam interleaving permits lower prf without loss in framerateBeam interleaving permits lower prf without loss in framerate

32. Color flow scanning strategies B-mode scanning Mechanical scanning + No settling time clutter filter - low frame rate Electronic scanning Packet acquisition - Settling time clutter filter +flexible PRF without loss in frame rate Electronic scanning continuous acquisition + no settling time clutter filter + High frame rate - low PRF (=frame rate) scanning direction time

33. Color flow imaging with a mechanical probe v = W*FR Image width W Frame rateFR Sweep velocityv= W*FR Virtual axial velocity: vr= v*cotan(  ) vr v  Example: Image width W = 5 cm Frame rateFR =20 fr/sec Angle with beam  = 45 deg. Sweep velocityv= 1 m/s Virtual axial velocity: vr= 1 m/s vr > max normal blood flow velocities!

34. Color flow imaging with a mechanical probe v = W*FR Reflected wave does not hit the transducer Max Dopplershift 600 Hz ~ 0.21 m/sec

35. Color flow imaging with a mechanical probe W= N*b v = W*FR Beamwidth (Rayleigh criterion): b Effective number of beams: N =W/b Frame Rate: FR Signal from stationary scatterer N*Fr*t Clutter signal bandwidth: 2*N*FR Power spectrum Clutter filter cutoff frequency: fc > N*FR Frequency components < fc removed

36. Minimum detectable Doppler shift Frame rate FR =1 Hz FR = 10 Hz FR=20 Hz Width (# beams) N=3030 Hz300 Hz 600 Hz N=7070 Hz700 Hz1400 Hz Clutter filter cutoff frequency: fc > N*FR (transit time effect mechanical scan) Cardiac flow imaging: fo= 2 MHz, 15 mm aperture, beamwidth 3 mm 30 beams covers the left ventricle fc = 600 Hz ~ 0.21 m/sec. lower velocity limit

37. Atlanta, GA april 1986 Vingmed, introduced CFM The first commercial colorflow imaging scanner with mechanical probe Horten, Norway september 2001 GE-Vingmed closed down production line for CFM after 15 years of continuous production

38. Minimum detectable Doppler shift Clutter filter cutoff frequency: fc > N*FR Frame rate FR =1 Hz FR = 10 Hz FR=20 Hz Width (# beams) N=3030 Hz300 Hz 600 Hz N=7070 Hz700 Hz1400 Hz Periferal vessel imaging with fo= 10 MHz Mechanical scanning: fc = 1400 Hz ~ 108 mm/sec. Electronic scanning: fc = 30 Hz ~ 2.3 mm/sec. Packet acquisition (P=10): Frame rate = 35 frames/sec Continuous acquisition:Frame rate = 350 frames/sec

39. Combining tissue and flow Continuous sweep acquisition + Brachial artery