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Parallel Magnetic Resonance Imaging: Characterization and Comparison A Master of Science (M.S.) Thesis Defense Presentat

Parallel Magnetic Resonance Imaging: Characterization and Comparison A Master of Science (M.S.) Thesis Defense Presentation. Swati Rane Magnetic Resonance Systems Laboratory Department of Electrical Engineering. Outline. Introduction to Magnetic Resonance Imaging

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Parallel Magnetic Resonance Imaging: Characterization and Comparison A Master of Science (M.S.) Thesis Defense Presentat

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  1. Parallel Magnetic Resonance Imaging: Characterization and Comparison A Master of Science (M.S.) Thesis Defense Presentation Swati Rane Magnetic Resonance Systems Laboratory Department of Electrical Engineering Parallel MRI: Characterization and Comparison - Swati Rane

  2. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  3. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  4. Magnetic Resonance Imaging: Introduction • Technique to image biological structures using Nuclear Magnetic Resonance phenomenon. • Charged particles in the nuclei (protons) possesses spin and a magnetic moment which contributes to the MR signal. • At equilibrium, the magnetic moments cancel out. Parallel MRI: Characterization and Comparison - Swati Rane

  5. Spins and the Steady State Magnetic Field Z Y X • Under the action of a steady state magnetic field B0, the spins align in the direction of B0 and precess about the B0 axis with a frequency dependent on the strength of B0.- Larmor frequency. Parallel MRI: Characterization and Comparison - Swati Rane

  6. Spins and the RF Field Z Z Y Y X X • With the B0 field applied, if a RF field pulse, B1 is applied along the X axis with a frequency equal to the Larmor frequency (resonance), the net magnetization tips to the XY plane (on the Y axis). Tipping proportional to strength of RF pulse. Parallel MRI: Characterization and Comparison - Swati Rane

  7. Spin Relaxation Z Z Z Y Y Y X X X • B1applied for a short duration • Spins relax back to equilibrium along Z axis Parallel MRI: Characterization and Comparison - Swati Rane

  8. MR signal and k-space data k-space lines Inv. Fourier = transform Echo • Mxysignal does not become 0 instantly, the spins merely dephase • Can rephase spins to form a symmetrical MR signal -> echo • MR data (k-space) from scanner is a line by line acquisition of echoes • Inverse Fourier Transform of the data gives required image Parallel MRI: Characterization and Comparison - Swati Rane

  9. MR Signal Acquisition and Acquisition Time Reduction • Time required for every line in k-space depends on the properties of the protons -> Repetition Time TR (~ 100s of msec) • Total imaging time for N lines is NxTR -> very long • Imaging speed should be accelerated • to images tissues rapidly to study their dynamic interactions • to reduce artifacts caused by patient motion • to facilitate real time imaging • to allow blood oxygen level dependent (BOLD) functional MRI studies • to reduce patient inconvenience Parallel MRI: Characterization and Comparison - Swati Rane

  10. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  11. Acquisition Time and Pulse Sequences • Scan time has to be reduced for dynamic imaging • Achieved by reducing N, reducing TR • Reduction in TR achieved by new pulse sequences • Echo Planer Imaging (EPI) • Fast Spin Echo (FSE), etc TR reduced to 100s of µsec • PROBLEMS:Challenge for the hardware, artifacts, field inhomogeneity, chemical shift artifacts, RF pulse saturation, blur, etc Parallel MRI: Characterization and Comparison - Swati Rane

  12. Parallel MR Imaging • Other option: Reduce N • Achieved by Parallel MR Imaging • Parallel Imaging is a MR Imaging technique using an array of locally sensitive receivers to image an object. • Primary goals of Parallel MRI - Extend field of view (FOV) - Increase SNR • Used since the past decade for imaging tissue dynamics • Rapid imaging using parallel MRI achieved by • Subsamplingk-space • Image reconstruction by apriori information of coil sensitivities Parallel MRI: Characterization and Comparison - Swati Rane

  13. Basic Concept IFFT IFFT • k-spaceis subsampled = data is sampled below Nyquist rate • Subsampling along direction in which coils are differentially sensitive • Aliasing occurs due to subsampling Parallel MRI: Characterization and Comparison - Swati Rane

  14. Basic Concept (contd. ) Half FOV • Consider image with the field of view (FOV) as shown and two coils with the following sensitivities Full FOV Parallel MRI: Characterization and Comparison - Swati Rane

  15. Basic Concept (contd. ) PARALLEL MR Reconstruction subsample subsample Effective FOV Parallel MRI: Characterization and Comparison - Swati Rane

  16. Parallel Imaging: Key Points • Aliasing occurs as a result of subsampling • Parallel imaging algorithms aim at removing aliasing or regenerating the missed k-space lines using the coil sensitivities • Subsampling factor is limited theoretically by the number of coils • Parallel reconstruction techniques • SENSE (SENSitivity Encoding) • PILS (Partially Parallel Imaging with Localized Sensitivites) • SMASH (SiMultaneous Acquisition of Spatial Harmonics) • GRAPPA (GeneRalized Auto-calibrating Partially Parallel Acquisitions) • SPACE RIP (Sensitivity Profiles from an Array of Coils for Encoding and Reconstruction In Parallel) Parallel MRI: Characterization and Comparison - Swati Rane

  17. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  18. SENSE: SENSitivity Encoding ≈0 ≈0 i1 x S1(i1) + i1 x S2(i1) i2 x S1(i2) + i2 x S2(i2) i1 i2 S1 S2 • For a reduced scan i1 x S1(i1) + i2 x S1(i2) and i2 x S2(i2) + i1 x S2(i1) • For full scan • Uses matrix form of equations to solve for unaliased pixels S x I = A, S = sensitivity encoding matrix, I= un-aliased image pixel matrix, A =aliased image pixels Parallel MRI: Characterization and Comparison - Swati Rane

  19. SENSE: Reconstruction Issues = • Coil sensitivities change with object imaged. • Accurate sensitivity maps required. • Reference scans for estimation add to imaging time. Parallel MRI: Characterization and Comparison - Swati Rane Pruessman K., Weiger M., et al., “ SENSE: Sensitivity Encoding for fast,” Magnetic Resonance in Medicine, vol. 42, pp. 952-962, November 1999.

  20. SENSE: Reconstruction Issues • Self calibration with few extra lines possible. • Reconstruction depends on ability of the coil sensitivity to unfold aliased pixels. Determined by coil geometry factor ‘g’. Pruessman K., Weiger M., et al., “ SENSE: Sensitivity Encoding for fast,” Magnetic Resonance in Medicine, vol. 42, pp. 952-962, November 1999. Parallel MRI: Characterization and Comparison - Swati Rane

  21. PILS: Parallel Imaging with Localized Sensitivities S2 Estimate centers and CUT PASTE S2 S1 S1 S2 S1 • Cut and paste method • Coil FOV << Image FOV …No true aliasing! Parallel MRI: Characterization and Comparison - Swati Rane

  22. PILS: Reconstruction Issues • Coil sensitivities must be extremely localized…practically not always possible • No true aliasing must occur. May be a problem for non- linear arrays even for small reduction factors Grisworld M., Jakob P., et al., “Partially Parallel Imaging with Localized Sensitivities (PILS),” Magnetic Resonance in Medicine, vol. 42, pp. 952-962, November 1999. Parallel MRI: Characterization and Comparison - Swati Rane

  23. SMASH: SiMultaneous Acquisition of Spatial Harmonics . . . • Missed line is shifted in frequency from the acquired line • Frequency shifting in Fourier Theory: = If F( ω) FFT[f(x)], w - j x 0 = w - w e f ( x ) F ( ) 0 • Requires generation of complex spatial harmonics from the coil sensitivities Parallel MRI: Characterization and Comparison - Swati Rane

  24. SMASH: Reconstruction Issues • Coil profiles must be conducive for generating smooth spatial harmonics • Underlying coil phase affects harmonic generation Sodickson D., Manning W., et al., “SiMultaneous Acquisition of Spatial Harmonics (SMASH): Fast imaging with radio-frequency coil arrays, Magnetic Resonance in Medicine, vol. 38, pp. 591-603, 1997 Parallel MRI: Characterization and Comparison - Swati Rane

  25. GRAPPA: GeneRalized Auto-calibrating Partially Parallel Acquisition Repeat Use reconstruction coefficients Find reconstruction coefficients • Does not require sensitivity map calculation • Uses extra lines acquired directly for reconstruction Acquired Line ACS Unacquired Line • Depends on the placement of coils in a non-linear array and on the background phase Parallel MRI: Characterization and Comparison - Swati Rane

  26. GRAPPA: Reconstruction Issues • Flexibility in choosing blocks, multiple reconstructions possible Reconstruction 1 Reconstruction 2 • Computationally complex • Can take advantage of averaging and improve SNR • Reconstruction depends on where ACS data is collected from • in turn on coil geometry and underlying phase Grisworld M., Jakob P., et al., “Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA),” Magnetic Resonance in Medicine, vol. 47, pp. 1202-1210, June 2002. Parallel MRI: Characterization and Comparison - Swati Rane

  27. SPACE RIP: Sensitivity Profiles from an Array of Coils for Encoding and Reconstruction in Parallel Sensitivities Sensitivities Sensitivities SPACE RIP reconstruction coefficients ? X = DFT coefficients • Hybrid technique: Image reconstruction in partial k-space • Uses special inverse fourier transform technique. • Each DFT coefficient at every pixel modulated by coil sensitivity • Reconstruction is columnwise, huge matrix inversions required per column Kyriakos W., Panych L., et al., “Sensitivity profiles from an array of coils for Encoding and Reconstruction in parallel (SPACE RIP),” Magnetic Resonance in Medicine,” vol. 44, pp. 301-308, February 2000. Parallel MRI: Characterization and Comparison - Swati Rane

  28. Factors affecting Image Quality • Image quality therefore, depends on • Coil array - type - localization - background phase • Reduction factor • k-space coverage • Method of parallel image reconstruction selected Parallel MRI: Characterization and Comparison - Swati Rane

  29. Evaluation of Parallel MR Image Reconstruction • Need to evaluate the performance of parallel imaging methods • to find the method giving optimum performance for a particular imaging setup. • Evaluation is done on the basis of • SNR (2 region method) • SNR (pixel wise method) • SNR (2 acquisitions method) • Artifact Power • Resolution • Computational Complexity Parallel MRI: Characterization and Comparison - Swati Rane

  30. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  31. MATLAB Toolbox • Improved Reconstruction • Iterative SOS • Reconstruction • Regularized SENSE • AUTO-SMASH Sensitivity Estimation • Data Input • -Simulated data • Acquired data Filtering GRAPPA SENSE • Performance Analysis • - SNR • Artifact Power • ‘g’ factor calculation • - Resolution Harmonics- fitting Gaussian fitting SMASH PILS PILS PILS SPACE RIP • A MATLAB toolbox • to implement different parallel imaging methods of image reconstruction • to evaluate these methods on the basis of different parameters Reconstruction Parallel MRI: Characterization and Comparison - Swati Rane

  32. Data input • Simulated data • takes an image, generates coil sensitvities and simulates reduced k-space data • Coil sensitivities - Linear array with 1D Gaussian profiles - Non-linear array with 2D Gaussian profiles • Real/ Acquired full data • retrospectively decimates data to obtain a reduced data-set • Real/ Acquired reduced data • ACS/ Calibration lines may have to be entered separately Parallel MRI: Characterization and Comparison - Swati Rane

  33. Sensitivity Estimation • Self calibration using extra calibration lines Divide each unaliased image by the SOS image Obtain unaliased Image per coil Get extra calibration lines per coil Calculate sum-of squares (SOS) image • Self calibration using singular value decomposition (SVD) Obtain unaliased image per coil Calculate correlation of every coil with the other coil for every pixel and filter correlation matrix Get extra Calibration lines per coil Perform eigen analysis to estimate the noise and signal correlation between coils Reorganize eigen data to get an estimate of the coil sensitivity • Use ofreference scans divided by a body coil image. Walsh D., Gmitro A., et al., “ Adaptive Reconstruction of phased array imagery,” Magnetic Resonance in Medicine, vol. 43, pp. 683-690, November 2000 Parallel MRI: Characterization and Comparison - Swati Rane

  34. Image Reconstruction • Basic Methods • SENSE • PILS • SMASH • GRAPPA • SPACERIP • Improved Methods • Iterative SOS Reconstruction • Regularized SENSE • AUTO-SMASH • Tight harmonic fitting Jakob P., Grisworld M., et al., “AUTO-SMASH: A self calibrating technique for SMASH imaging: SiMultaneous Acquisition of Spatial Harmonics,” Magnetic Materials in, vol. 7, pp. 42-54, November 1998. Hsuan-Lin Fa, Kwong K., et al., “ Parallel Imaging Reconstruction using Automatic Regularization,” Magnetic Resonance in Medicine, vol. 51, pp. 559-567, March 2004. Parallel MRI: Characterization and Comparison - Swati Rane

  35. Image Reconstruction (contd. ) • Improved Methods • Iterative SOS Method Extra calibration lines FFT IFFT Reconstructed image Coil images Coil kspace data Coil kspace data Sum of squares Wang J., “ Using the Reference Lines to Improve the SNR in mSENSE,” 10th Proc. International Society for Magnetic Resonance in Medicine, May 2000 Parallel MRI: Characterization and Comparison - Swati Rane

  36. Improved Reconstruction Object FOV PE • AUTO-SMASH (Auto- calibratingSMASH): - Does not require sensitivity estimation process - Uses ACS lines to obtain coefficients for harmonic fitting • Tight Harmonic Fitting: - Fit harmonics over object FOV only to reduce erroneous results due to noise in the background Image before and after harmonic fitting Parallel MRI: Characterization and Comparison - Swati Rane

  37. Image Reconstruction • Improved Methods • Regularized SENSE - Uses tikhnov regularization Uses least squares solution by Tikhnov Regularization given by where S= coil sensitivity matrix Irec= reconstructed unregularized image Iprior= low resolution full FOV images λ=regularization parameters Ireg=regularized image Image before and after regularization Hsuan-Lin Fa, Kwong K., et al., “ Parallel Imaging Reconstruction using Automatic Regularization, Magnetic Resonance in Medicine, vol. 51, pp. 559-567, March 2004. Parallel MRI: Characterization and Comparison - Swati Rane

  38. The GUI Parallel MRI: Characterization and Comparison - Swati Rane

  39. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  40. Performance Evaluation: SNR • Two-region method: ROI RON • Convenient method for comparison • Highly erroneousin value Madore B. and Pelc N., “SMASH and SENSE: Experimental and Numerical Comparisons,” Magnetic Resonance in Medicine, vol. 45, pp. 1103-1111, June 2001 Parallel MRI: Characterization and Comparison - Swati Rane

  41. Performance Analysis: SNR (contd.) • Pixel wise method: SENSE GRAPPA • Gives a map of SNR values at every pixel • Very accurate • Requires atleast 50 iterations for correct values Parallel MRI: Characterization and Comparison - Swati Rane

  42. Performance Analysis: (contd.) • Two-acquisitions method • Very accurate • Artifact power • Squared error evaluation • Useful to determine accuracy of reconstruction Grisworld M., Jakob P., et al., “Partially Parallel Imaging with Localized Sensitivities (PILS),” Magnetic Resonance in Medicine, vol. 42, pp. 952-962, November 1999. Parallel MRI: Characterization and Comparison - Swati Rane

  43. Performance Analysis: Resolution • Resolution • Parallel MRI is not a linear shift invariant system – point spread function (psf) varies spatially • Cannot use convolution to characterize the psf Resolution phantom for measurement of resolution degradation Parallel MRI: Characterization and Comparison - Swati Rane

  44. Performance Analysis: ‘g’ factor for SENSE • ‘g’ factor: determines ability of coil to separate the folded pixels • A value of 1 indicates separation possible, any value > 1 indicates inability of coil to separate pixels S = sensitivity encoding matrix Ψ = noise correlation matrix Parallel MRI: Characterization and Comparison - Swati Rane

  45. Performance Analysis: Computational complexity • Computational complexity defined by • Matrix inversions • Inverse Fourier transforms • Complex multiplications • Complex additions • Also measured in terms of time taken by the software to reconstruct an image • Depends on the optimality of the software codes • Depends on processor used Parallel MRI: Characterization and Comparison - Swati Rane

  46. Computational complexity: Comparison For image size N X N, Coils = C, Reduction factor = R, ACS: n Parallel MRI: Characterization and Comparison - Swati Rane

  47. Comparison results for computations • For Image size 128 X 128, 8 coils, R=2 1: SENSE, 2: PILS, 3: SMASH, 4: GRAPPA - 4 ACS, 5: GRAPPA -8 ACS, 6: SPACE RIP Parallel MRI: Characterization and Comparison - Swati Rane

  48. Outline • Introduction to Magnetic Resonance Imaging • Generation of MR Signal • Signal Acquisition time and need for fast acquisition • Rapid Imaging • Fast scans with pulse sequences • Parallel Imaging: Basic concept • Parallel Imaging • Characterization of different parallel MRI techniques • Software for evaluation of techniques • Performance Analysis • Analysis of real/acquired data and synthetic data • Conclusion Parallel MRI: Characterization and Comparison - Swati Rane

  49. Results: 8 channel data (linear Array) • Size: 256 x 256, R=2, 16 center lines self calibration SENSE PILS GRAPPA SPACE RIP Parallel MRI: Characterization and Comparison - Swati Rane

  50. Results: 8 channel data (Non-Linear Array) • Size: 256 x 256, R=2, 16 center lines, self calibration SENSE GRAPPA SPACE RIP Parallel MRI: Characterization and Comparison - Swati Rane

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