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

Transcription

1 Background II Signal-to-Noise Ratio (SNR) Pulse Sequences Sampling and Trajectories Parallel Imaging 1

2 SNR: Signal-to-Noise Ratio Signal: Desired voltage in coil Noise: Thermal, electronic Noise Thermal dominates, depends on coil, patient size SNR = average signal / σ Gaussian noise (FT is gaussian) Signal Signal σ σ is for gaussian in real and imaginary signal components N averages = sqrt(n) increase Magnitude noise is Rician; can obtain σ 2

3 SNR SNR is the major limitation for MRI Low SNR High SNR 3

4 Averaging Noise is uncorrelated When adding two signals: Signal portion M adds, to 2M Noise variance σ 2 adds, increases to 2σ 2 Noise σ increases by square-root of 2 SNR changes from M/σ to 1.4 M/σ SNR increases with square-root of #averages 4

5 What are Examples of Averaging? NEX - simple averaging Decreased bandwidth/pixel (longer A/D time) Increased FOV Phase-encode direction Slice direction (3D) Readout direction (longer readout, same BW!) Increased matrix - but changes resolution! 5

6 Imaging Factors Influencing SNR Voxel size (spatial resolution) Acquisition time (NEX, BW) Polarization or Field strength RF coil Subject size Pulse sequence and parameters Receive Electronics (Ideally insignificant) 6

7 Voxel Size Example Full High Resolution 2x Increase (all 3 axes) 4x Increase (slice) 7

8 SNR and Field Strength 1.5T 3.0T Sagittal T 2 RARE: SNR Ratio = 1.7 8

9 Coil Sensitivity Coil Signal decreases further from coil Noise volume increases with coil size Smaller coils also limit FOV and aliasing Larger coils not ideal Target Region Sensitive Volume 9

10 SNR vs Resolution vs Scan Time High SNR SNR Voxel Volume T acq 10 High Resolution (Small Voxels) Short Scan Time

11 SNR Efficiency Often want to compare SNR of different sequences If times differ, comparison can be made fair by use of SNR efficiency: SNR = SNR p Tscan In many cases: SNR = SNR p TR 11

12 SNR Question Compare the SNR efficiency of two pulse sequences, assuming the signal level is constant: Spin Echo, 8echoes, khz bandwidth, TR=100ms SNR / r Simple gradient echo, 62.5 khz bandwidth, TR=5ms =0.050 SNR / 1 p = Signal level would NOT be constant, so this is harder! 12

13 Pulse Sequences Gradient Echo Sequences Spin Echo Sequences Preparation Sequences (We will expand on these a lot!) 13

14 Pulse Sequences and k-space RF k y G z k x G x 3D k-space G y k y k z Acq. k x 14

15 Sequence Questions Which Gradient parts in 2DFT can overlap? Generally ramps k-space area (min time) vs. frequency mapping (plateaus) Which is usually bigger, x-dephaser or y-phase-encode? x-dephaser: usually xres>yres, and x dephaser accounts for readout ramps For 50mT/m and 200mT/m/ms gradients, what is the duration where the fastest gradient to achieve a given area changes to trapezoidal? RF G z G x 0.5ms (0.25 ms full-scale rise time) G y Acq. 15

16 Gradient-Echo Pulse Sequence Flip Angle RF TE ~ 1+ ms G z Slice-Select Gradient Refocusing Gradient?? G y Phase- Encode Gradient Readout Gradient? G x Dephaser Gradient Signal Gradient Echo 16

17 RF-Spoiled Gradient Echo Contrasts Gradient Spoiled Balanced SSFP

18 Spin Echo Pulse Sequence RF 180º TE ~ 8+ ms G z G y G x Signal 18

19 Basic Spin Echo Considerations Pros: Refocusing pulse reverses dephasing Image acquired at spin echo increases signal Cons: Increased RF power deposition (SAR) Longer echo times than gradient echo (GRE) 19

20 Spin Dephasing and Spin Echoes Frequency variations cause dephasing (T2 ) Results in signal loss (T2*) Refocus spins to spin-echo (T2) Gradient-Echo Image B1 Spin-Echo Image 20

21 Spin-Echo-Train Imaging RF Signal k y k y k x k x 21 PD-weighted k-space T2-weighted k-space

22 Proton-Density and T2-weighted Spin Echo Proton Density Weighted T2 Weighted 22

23 Fast Recovery (FR) or Driven Equilibrium RF 180º 180º 180º 90º -90º... G z... Fast-Recovery... G y G x Signal 23

24 Magnetization Preparation Mag Prep... Imaging Sequence Mag Prep Examples: Prepare contrast Image rapidly before steady-state evolves Fat Saturation Inversion - Recovery Myocardial Tagging T2-prep Magnetization Transfer 24

25 Fat-Saturated FSE RF 90º 180º 180º... G z... G y Fat-Sat... G x Signal 25

26 Fat Saturation (Magnetization Preparation) Fat Saturated T1w FSE 26

27 Inversion-Recovery TI 180º 180º RF 1 Signal 0-1 Fat suppression based on T 1 Short TI Inversion Recovery (STIR) 27

28 Sampling & Point-Spread Functions PSF = Fourier transform of sampling pattern Just 1 s as samples, mostly a matter of scaling Lots more you can do with this...! k-space Sampling Point-Spread Function Fourier Transform Extent Spacing Width FOV 28

29 Partial Fourier Acquisition/Reconstruction k y k y k x k x k y k x 29

30 Alternate k-space Trajectories k y k y k y k x k x k x Cartesian EPI Spiral k y k y k x k x Radial Projection 30

31 Parallel Imaging Coils have limited sensitivity Unalias based on known sensitivities (SENSE) Limited sensitivity results in k-space correlations k y Fill in missing k-space (GRAPPA) k x Build up FOV with coil arrays 31

32 Basic Parallel Imaging: PILS (Parallel Imaging with Localized Sensitivities) Griswold 2000 Consider 2 coils Each sensitive to exactly 1 breast Each coil uses a reduced FOV Readout but simultaneous acquisition Combination allows full image in less time 32

33 SENSE: Unalias Image Sensitivity 1 (S 1 ) Sensitivitiy 2 (S 2 ) Pruessmann 1999 SENSE Image A A A B B B Coil 1 Signal (C 1 ) Coil 2 Signal (C 2 ) When it fails A A B B 33

34 SENSE: Brief Mathematics At each pixel Using Coil 1: Using Coil 2: C1 = S1A x A + S1B x B C2 = S2A x A + S2B x B A B A If we know S1 and S2 at A,B and signals C1 and C2, A = S1B C2 - S2B C1 B = S2A C1 - S1A C2 B S2AS1B - S2BS1A S2AS1B - S2BS1A More complicated with more than 2 coils If denominator is small, noise amplification Just a matrix inversion or pseudoinverse 34

35 SENSE Calibration Low-resolution images from each coil Divide images by RMS image or body coil image Challenge: coil sensitivity in area of low signal k phase k read Low Resolution Image 35

36 Parallel Imaging: k-space Approaches Sodickson 1997 (SMASH), Griswold 2002 (GRAPPA) Acquire reduced FOV, and some calibration lines Fill in missing lines to extend the FOV k y k x 36

37 GRAPPA: Coil Sensitivities and k-space Reduced Image Extent Correlated Pixels k y k y k y k x k x k x Correlated k-space Reduced k-space Extent 37

38 GRAPPA Calibration Fully-sampled central k-space Griswold 2002 Find data correlation between lines/coils Note: data-driven vs model (SENSE) Not just image vs k-space! k phase Coil 2 Coil 1 Coil 3 k read 38 Repeat for all calibration points and all coils

39 GRAPPA Synthesis Use kernel information to synthesize data Repeat for all coils Combine coils and reconstruct Coil 2 Coil 1 k phase Coil 3 Griswold 2002 k read 39

40 Accelerated Parallel Imaging & Noise Full 2x 3x 4x Constant Scan Time Full 2x 3x 4x Acceleration is in Left-Right Direction in Images 40

41 2D Parallel Imaging (for 3D Acquisitions) 3D imaging uses 2 phase-encode directions Can apply parallel imaging in 2 directions Note: Readout is in S/I (head-foot) direction! Fully Sampled 2x A/P and 2x L/R 8-Channel Phased- Array Coil 4x A/P

42 Parallel Imaging Questions For synthesis which takes more multiplies to fill in one missing pixel, SENSE or GRAPPA? GRAPPA: kernel-size x (#coils) 2 Coil 1 Coil 2 Coil 3 SENSE: (#coils) Which direction(s) do we want coil sensitivity variations most? Phase-encode (y, and if 3D, z as well) Readout ~ helps GRAPPA a little 42

43 Summary ~ Background Overview of NMR Hardware Image formation and k-space Excitation k-space Signals and contrast Signal-to-Noise Ratio (SNR) Pulse Sequences Sampling and Trajectories Parallel Imaging 43