EPI Bildgebung. German Chapter of ISMRM. Doktorantentraining. Freiburg 30 Mai - 1 Juni 2001

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1 EPI Bildgebung German Chapter of ISMRM Doktorantentraining Freiburg 30 Mai - 1 Juni 2001

2 Review of k-space and FT The EPI sequence Technical requirements Choice of the readout waveform ramp sampling regridding trajectory measurement The N/2 ghost phase correction with reference image-based correction regridding effects Off-resonance effects (distortions) field inhomogeneity and Maxwell shifts unwarping methods Slowing down interleaving ghosting and phase correction echo-time shifting Speeding up half-ft paralell methods Application examples

3 MRI: FOURIER ENCODING ACQUI- SITION FT RAW DATA (k - space) IMAGE (r - space)

4 MRI: SCANNING STRATEGIES RF sample k y G x G y k x k y k y RF k y G x k x G y

5 RF STANDARD MRI: LOW DUTY CYCLE TR GS GR GP ACQ

6 Echo-Planar Imaging (EPI) RF G z G x G y TR ACQ k x High duty cycle Instantaneous Mz sampling k y

7 Some useful maths

8 CONVOLUTION TAPE RECORD f g f g HEAD PROFILE ( + f g)( x) = f ( z) g( x z) dz CONVOLUTION THEOREM [ f g] [ f ] FT[ g] FT =FT

9 SAMPLING DISTRIBUTIONS Single sample - Dirac's delta: + δ( x a) f( x) dx= f( a) a f(x) x Equidistant sampling Bracewell's "shah" III( x ) = δ( x n) + n= + III( x ) f( x) dx= f( n) n= Correct notation: (x)

10 Properties of (x) III( k ) III(x) k x x 1 [ III( x ) III ( x 1) ] III( + 1 2) FT k x 1 a III k a = δ ( k na) III(ax) k a 1/a x

11 DISCRETE FT dk e k s ld k Nd kn i l / 2 ) ( ) ( π δ = Π = Nd n k s Nd k d k ) ( ) III( FT "sampled signal" = = 1 2 / 2 / / 2 ~ N N l N n l i l n e s s π s l = s(ld) x x s(k) Π ( ) d k III =

12 DISCRETE FT(2) k k FT III( ) Π s( k) = d Nd III( d x) sinc( Nd x) ~ s ( x) FOV = 1/d RESOLUTION = 1/Nd

13 TECHNICAL REQUIREMENTS Goal: EPI 128x128, 2x2mm resolution total time 82ms, without ramp sampling. Example of a whole-body gradient coil:* efficiency: mt/m/a L = 170 µh R = 40 mω ms signal bandwidth: (0.32ms/128) -1 = 400 khz gradient: 1/(2mm * 0.32ms) = 15.6 khz/cm = 36 mt/m current: 36/0.075 = 480 A voltage: 170uH*480A/0.16ms = 510V peak heating power: (480A) 2 * 40mΩ = 9.2 kw * Bruker BGA55 (55 cm)

14 READOUT SHAPE G amplitude t = 2G/slew + 1/(G*resol) duration t FASTEST WAVEFORM: plateau = 2*ramp

15 RAMP SAMPLING G +50% k-space range r 2r r G -25% time G 2-30% time

16 EFFECT of NON-EQUIDISTANT SAMPLING G(t) k FFT: ALL POINTS WITHOUT RAMPS

17 REGRIDDING S l CONVOLUTION KERNEL W ~ S = S W ( k k ) k k l l l l Needed: k l distribution (trajectory)

18 REGRIDDING - A CLOSER LOOK non-equidistant distribution: W ( k) ( k kl ) / D( k) l sampled signal: W ( k) s( k) = δ sampling density regridded signal: image: convolution kernel [ K( k) ( W ( k) s( ))] III( k / k0) k ~ ~ III( xk0) x [ K( x) ( W ( x) ~ s ( ))] FOV depends on initial sampling density image intensity needs correction

19 REGRIDDING - NYQUIST CONDITION GRADIENT n samples k-space FT IMAGE DOMAIN ~ W (k) W ( x ) G Gp/2 Gp/2 nπ /2 samples sampling rate >= G max / FOV FIELD OF VIEW

20 MEASUREMENT OF k-space TRAJECTORY Onodera et al. J. Phys. E 20, 416 (1987) k k 0 Echo centre: k = -k 0 time k 0 k(t) plot

REGRIDDING WITH A MEASURED TRAJECTORY 50 g(t) 40 30 20 k(t) 10 1 6 11 16 21 26 31 36 41

21 REGRIDDING WITH A MEASURED TRAJECTORY 50 g(t) k(t) RAW REGRID (TRAPEZE) REGRID (MEASURED)

22 THE GHOST N/2 GHOST EVEN ODD G x (t) DATA db(x,y) 2DFT p + Q(x,y+N/2) Q(x,y) 2DFT Q(x,y) = A + Bx + CAN BE CORRECTED f(x) + Cy + CAN BE ADJUSTED g(x,y)? IMAGE

23 The N/2 ghost - linear case READOUT GRADIENT TRAJECTORY IMAGE

24 REFERENCE SCAN METHOD CALIBRATION PROCESSING G read 1. FT in readread 2. Apply exp(iφ(x)) to odd lines 3. FT phase direction S (k) e FT S (k) o R (x) e R (x) o Phase -1 Correction: exp(iφ(x)) = arg( R e(x) R o(x) )

25 IMAGE-BASED METHOD 1. FT in read direction 2. Split even and odd lines 3. FT in phase direction (even and odd): 4. Select a ghost-only line [ FOV 2 ] [ FOV 2 ] R ( x, y) = R( x, y) + R( x, y ± / ) e R ( x, y) = R( x, y) R( x, y ± / ) e o iφ( x) y : R( x, y ) = 0 & R( x, y ± FOV / 2) 0 5. Phase correction: g g g [ Ro ( x, yg) Re( x, y ) 1] φ( x) = arg g

26 GHOST CORRECTION - RESULTS ORIGINAL NON-LINEAR PHASE CORRECTION LINEAR PHASE CORRECTION

27 PERSISTENT GHOSTS LINEAR 1D PHASE CORRECTION

PHASE-SHIFT MAP 30 20 Q (deg) 10 0-10 -20 1 2 3 4 5 6

28 PHASE-SHIFT MAP Q (deg) f (rad) FIT: A + Bx + Cy + D(x 2 -y 2 ) + E 2xy

29 CORRECTION: LINEAR 1D 2nd ORDER 2D

30 CONTOUR GHOST EFFECT OF GRIDDING ERRORS simple regrid even-odd regrid

31 OFF-RESONANCE EFFECT - SPIN WARP time frequency SPIN DENSITY: FAT WATER k x k y x y IMAGE

32 OFF-RESONANCE EFFECT - EPI time frequency SPIN DENSITY: FAT WATER k x k y x y IMAGE

33 EPI: SUSCEPTIBILITY EFFECTS 5 mt/m 250 ms 10 mt/m 130 ms 16 mt/m 80 ms

34 MAXWELL SHIFTS (concomitant gradients) B x z = B z x because, without el. fields or currents: B = 0 field generated by "x-grad coil": xg zˆ + zgxˆ zg B B + xg 0 B = 0 2 ( B + xg) + ( zg) B + xg z G 2B 0 2 Maxwell shift at 1T, 20mT/m, z=10cm: 85 Hz

35 UNWARPING field map methods reference scan methods

36 UNWARPING CORRECTION ORIGINAL EPI 64x64 100kHz 3T

37 UNWARPING ORIGINAL CORRECTION REFERENCE EPI 256x256, 200kHz, 3T

38 EPI: SEQUENCE single shot multi-shot (interleaved)

39 INTERLEAVING t k y kx SINGLE SHOT MULTI SHOT

40 NUMBER OF INTERLEAVES:

41 EVEN-ODD ECHO SHIFT READOUT GRADIENT TRAJECTORIES SINGLE SHOT INTERLEAVED

42 ECHO-SHIFT ARTEFACT 1 SHOT 9 SHOTS

43 GHOSTING in Multi-Shot EPI image from even echoes: d = FOV/(2*n_shots) R ( x, y) = R( x, y) + A R( x, y + md) + B R( x, y + md) e m even m image from odd echoes: m odd m Re ( x, y) = R( x, y) + Am R( x, y + md) Bm R( x, y + md) e even m odd m iφ( x) Deriving φ(x) from the image? There should be no even ghosts - stability required! Only high order (week) ghosts can be used - high SNR required!

44 IMAGE BASED DEGHOSTING - ATTEMPT STABLE SIGNAL: only odd ghosts UNSTABLE SIGNAL: even and odd ghosts

45 SOLUTION: ALTERNATING TRAJECTORIES

46 IMAGE-BASED DEGHOSTING A STANDARD INTERLEAVING raw non-linear correction linear correction D ALTERNATING INTERLEAVING

Background II. Signal-to-Noise Ratio (SNR) Pulse Sequences Sampling and Trajectories Parallel Imaging. B.Hargreaves - RAD 229.

Background II. Signal-to-Noise Ratio (SNR) Pulse Sequences Sampling and Trajectories Parallel Imaging. B.Hargreaves - RAD 229. Background II Signal-to-Noise Ratio (SNR) Pulse Sequences Sampling and Trajectories Parallel Imaging 1 SNR: Signal-to-Noise Ratio Signal: Desired voltage in coil Noise: Thermal, electronic Noise Thermal