IEEE Ultrasonic symposium 2002

Transcription

1 IEEE Ultrasonic symposium 2002 Short Course 6: Flow Measurements Hans Torp Department of Circulation and Medical Imaging TU, orway Internet-site for short course: Lecture 3: Color flow imaging Hans Torp TU, orway

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

3 2D Color flow imaging 1. Limited information content in the signal, i.e. short observation time, low signal-to-noise ratio, and low yquist velocity limit. 2. Insufficient signal processing/display. Full spectrum analysis in each point of the sector is difficult to visualize.

4 G(ω) B P ω1 ω Signal power: P = π π dω G( ω) Mean frequency: π 1 ω = 1 dωωg( ω) P π Bandwidth: B = 1 π 2 1 G P π dω ( ω ω ) ( ω)

5 im{r(1)} dω G( ω) exp(iω ) G( ω) exp(iω ) π - π re{r(1)} G(ω) - π ω π π R ) = iω ( 1) dω G( ω e P = R 0) = π π ( dω G( ω) π R(1) π iω 1 1 i( 1) i 1 = e ω ω ω dωg( ω) e Pe {1 2 B π 2 } Taylor expansion of exp-function

6 Autocorrelation method R(1) Pe {1 1 2 iω1 B 2 } Rˆ = 1 k = 1 z( k + 1) z( k * ) P = R(0) ω 1 arg { R(1) } R(1) B 2 1 R(0) Pˆ = ˆ ω = 1 Rˆ arg (0) { Rˆ (1) } Bˆ = 2 1 Rˆ Rˆ (1) (0) Power, meanfreq., bandwidth derived from sample mean autocorrelation estimator

7 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.

8 Estimation error is minimum when correlation is maximum Correlation angle ~Velocity ) e (R g l n a abs(r) x 10 6 Hans Torp TU, orway Correlation magnitude Matlab-demo: AcorrEst.m

9 Estimator properties Estimator properties = = = k k z R P 1 2 ) ( 1 (0) B P P Var 2 ) ( = + = k k z k z R 1 * ) ( 1) ( 1 ˆ (1)) ˆ ( ˆ1 R = angle ω B Var 2 1 ) ( ω

10 ormalized Autocorrelation function im{ρ(1)} i arrow band signal Broad band signal 1 re{ρ (1)} ρ(1) = R(1) / R(0)

11 Color mapping types Power Doppler (Angio) Brightnes ~ signal power Hans Torp TU, orway Color flow Brightnes ~ signal power Hue ~ Velocity Color flow Variance map Hue & Brightnes ~ Velocity Green ~ signal bandwidth

12 B-flow Doppler signal power added to B-mode image

13 Color scale for velocity and - spread LV Power y Ao LA H¹ H H x Band width Aortic insufficiency Hans Torp TU, orway

14 Color flow imaging Mitral valve blood flow ormal mitral valve Stenotic mitral valve Hans Torp TU, orway

15 Autocorrelation method Sensitive to clutter noise im{r(1)} dω G( ω) exp(iω ) G( ω) exp(iω ) π - π re{r(1)} G(ω) - π ω π Phase angle of R(1) substantially reduced due to low frequency clutter signal Clutter filter stopband much more critical than for spectral Doppler

16 How to perform clutter filter in color flow imaging? Beam k-1 Beam k Beam k+1 Raw signal from beam k Signal after high-pass filter Lost settling time Signal discontinuity causes ringing in highpass filters

17 Approaches to clutter filtering in color flow imaging IIR-filter with initialization techniques Short FIR filters Regression filters

18 General Linear Filters A general linear filter is described by a matrix multiplication of the - dimensional signal vector x In color flow imaging =packet size (number of pulses per beam) y = Ax The matrix rows are a set of (possibly) different FIR- filters for each time instant Definition of frequency response function: Ho 1 2 ) = Ae where (ω ω e ω [ ] iω i( 1) ω T = 1 e Le

19 FIR Filters H( z) = M k= 0 b k z k Power [db] Frequency responses, order = 5 Linear phase Minimum phase Discard the first M output samples, where M is equal to the filter order Improved amplitude response when nonlinear phase is allowed Frequency

20 IIR Filters Matrix formulation of IIR filter: H ( z) M = k = 0 k= 0 k b k z a k z k y = C v(0) + D x v(0) is initial filter state Initialization techniques: zero: v(0) = 0 step: v(0) = x(0) v step ( ) projection: v(0) = - (C T C) -1 C T B x

21 Highpass IIR Output Transient 1 x = sin ωt Amplitude 0 Time y = C v(0) + D x zero init. step init. projection init.

22 IIR Zero and Step Initialization 0 Frequency response Very poor stop-band attenuation Power [db] Steady state Step init. Last /2 samples of zero init. A more sophisticated initialization technique is needed Frequency Chebyshev order 4, =10

23 IIR Projection Initialization 0 Frequency response The signal component in the transient subspace is removed -20 Power [db] -40 Steady state Projection init. A = ( I - P transient ) B Frequency Chebyshev order 4, =10 Sufficient stop-band width at the cost of increased transition width

24 Regression Filters Subtraction of the signal component contained in a K-dimensional clutter space: b 3 Signal space x y y = I K i= 1 b i H bi x b 1 Clutter space b 2

25 Fourier Regression Filters DFT Set low frequency coefficients to zero Power [db] Frequency response Inverse DFT Frequency =10, clutter dim.=3

26 Polynomial Regression Filters b 0 = 0 Frequency responses, =10 b 1 = b 2 = Power [db] b 3 = A b 0 = I P b k = 0, b1,.., b 1 k b T k -60 Legendre polynomial Frequency base

27 Frequency Responses 0 Power [db] Pol. reg. IIR proj. init. FIR min. phase Frequency Other quality measures for clutter filters than the frequency response?

28 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.

29 How to image low velocity flow Long observation time needed Obtained by incresed packet size or lower PRF Beam interleaving permits lower prf without loss in framerate

30 time scanning direction Color flow scanning strategies B-mode scanning Mechanical scanning + o 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)

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

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

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

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

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

36 Minimum detectable Doppler shift Frame rate Clutter filter cutoff frequency: fc > *FR Width (# beams) FR =1 Hz FR = 10 Hz FR=20 Hz =30 30 Hz 300 Hz 600 Hz =70 70 Hz 700 Hz 1400 Hz Periferal vessel imaging with fo= 10 MHz Mechanical scanning: Electronic scanning: Packet acquisition (P=10): Frame rate = 35 frames/sec Continuous acquisition: fc = 1400 Hz ~ 108 mm/sec. fc = 30 Hz ~ 2.3 mm/sec. Frame rate = 350 frames/sec

37 Combining tissue and flow Continuous sweep acquisition + Brachial artery