TTK4165

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

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

3. Beam k-1 Beam k Beam k+1 Data acquistion in color flow imaging 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. Autocorrelation method Scatter diagram of the autocorrelation estimator with lag m=1 for three different signals. To the right, a narrow band signal with center frequency ω1=π/2 to the left, a slightly more broadband signal with ω1 =3π/2, and in the middle, high-pass filtered white noise.

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

10. Estimator properties

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

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

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

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

15. Autocorrelation methodSensitive 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. Beam k-1 Beam k Beam k+1 Clutter filter in color flow imaging?

17. Doppler Signal Model 100 Clutter 80 60 Blood Doppler spectrum [dB] 40 20 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Blood velocity [m/s] Hans Torp NTNU, Norway • Signal vector for each sample volume: x = [x(1),…,x(N)]T • Zero mean complex random process • Three independent signal components: Signal = Clutter + White noise + Blood x = c + n + b • Typical clutter/signal level: 30 – 80 dB • Clutter filter stopband suppression is critical!

18. Approaches to clutter filteringin color flow imaging • IIR-filter with initialization techniques • Short FIR filters • Regression filters

19. 0 Steady state -20 Step init. Discard first samples -40 -60 -80 0 0.1 0.2 0.3 0.4 0.5 IIR filter with initialization Frequency response Power [dB] Projection init* Frequency Chebyshev order 4, N=10 *Chornoboy: Initialization for improving IIR filter response, IEEE Trans. Signal processing, 1992

20. M å - k = H ( z ) b z k = k 0 Linear phase Minimum phase 0 0.1 0.2 0.3 0.4 0.5 FIR Filters • Discard the first M output samples, where M is equal to the filter order • Improved amplitude response when nonlinear phase is allowed 0 -20 Power [dB] -40 -60 -80 Frequency Frequency response, order M= 5, packet size N=10

21. Subtraction of the signal component contained in a K-dimensional clutter space: b3 Signal space x y b2 c Clutter space b1 Regression Filters x = [x(1),…,x(N)] y = x - c Linear regression first proposed by Hooks & al. Ultrasonic imaging 1991

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

23. Frequency response Linear Filters y = Ax • Definition of frequency response function = power output for single frequency input signal 1 2 Ho w = ; -p < w < p ( ) Ae w N [ ] T w w - i i ( N 1 ) = e 1 e e L w 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. Hans Torp NTNU, Norway FIR filter matrix structure FIR filter order M=5 Packet size N=10 Output samples: N-M= 5 + Improved clutter rejection Increasing filter order - Increased estimator variance

25. Subtraction of the signal component contained in a K-dimensional clutter space: b3 Signal space x y b2 c æ ö K å H = - ç ÷ y I b b x Clutter space i i b1 è ø = i 1 Regression Filters y = x - c A Choise of basis function is crucial for filter performance

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

27. DFT Set low frequency coefficients to zero Inverse DFT 0 0.1 0.2 0.3 0.4 0.5 Fourier Regression Filters Frequency response 0 -20 Power [dB] -40 -60 -80 Frequency N=10, clutter dim.=3

28. Legendre polynom basis functions b0 = b1 = b2 = b3 = Gram-Schmidt process to obtain Orthonormal basis functions -> Legendre polynomials

29. 0 -20 -40 -60 -80 0 0.1 0.2 0.3 0.4 0.5 Polynomial Regression Filters b0 = Frequency responses, N=10 b1 = Power [dB] b2 = b3 = Frequency

30. Regression filter bias Magnitude and phase frequency response Polynomial regression filterpacket 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 needed • Obtained by increased packet size or lower PRF • Beam interleaving permits lower prf without loss in framerate

32. scanning direction Color flow scanning strategies time B-mode scanning Electronic scanning continuous acquisition + no settling time clutter filter + High frame rate - low PRF (=frame rate) 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

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

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

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

36. 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 Minimum detectable Doppler shift Clutter filter cutoff frequency: fc > N*FR (transit time effect mechanical scan) Frame rate FR =1 Hz FR = 10 Hz FR=20 Hz Width (# beams) N=30 30 Hz 300 Hz 600 Hz N=70 70 Hz 700 Hz 1400 Hz

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

38. Periferal vessel imaging with fo= 10 MHz Mechanical scanning: fc = 1400 Hz ~ 108 mm/sec. 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=30 30 Hz 300 Hz 600 Hz N=70 70 Hz 700 Hz 1400 Hz 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 flowContinuous sweep acquisition + Brachial artery