Partial Parallel imaging (PPI) in MR for faster imaging

1. Partial Parallel imaging (PPI) in MR for faster imaging IMA Compressed Sensing June, 2007 Acknowledgement: NIH Grants 5RO1CA092004 and 5P41RR008079, Pierre-Francois Van de Moortele, Gregor Adriany, Kamil Ugurbil

2. Our coils • Open face coil • 16 Channel “closed” coil

3. Intrinsically, surface coils offer a representation of signal as The sensitivities are complex valued Acquired k-space, How to INTERPOLATE most stably to the Non-acquired data. we will see why it makes completely sense to think about interpolation

4. Field of View Courtesy: Douglas Noll, University of Michigan

5. Undersampled images Undersampled individual images

6. The linear system The solution of the linear system gives rice to a spatially varying noise amplification. This is solely dependent on the sensitivities and is referred to as the geometry factor

7. The geometry factor α is the index of an aliased pixel, βn is the index of an unaliased pixel. Overall loss when using PPI is SNRred=SNRfull/(g sqrt(R)) The reduced FOV is the RSOS of all the channels with a reduced FOV, only for illu.

8. Back to the equation Image space S indv. Channels. E encoding. p un-aliased image K-space S indv. Channels. E encoding. p un-aliased image (all in k-space) Convolution operator

9. E is known, but we can make the formal separation of S, as follows: E”acq” includes all of k-space for the sensitivities Two matrix equations, two unknowns

10. SENSE/SMASH formalism (get one image) GRAPPA idea, get multiple images. The interpolation is essentially similar to Kriging

11. Courtesy: Yeh, et al, MRM Volume 53, Issue 6 , Pages 1383 - 1392

12. GRAPPA Reconstructing the data for EACH coil Courtesy: Griswold et al. MRM, 47(6):1202-1210 (2002)

13. Several reconstruction is found for EACH k-space point- due to the blocks. A weigthed average is used to compute just one

14. ACS (Auto-Calibration Signal) lines (no x) • GRAPPA formula to reconstruct signal in one channel ,l where A represents the acceleration factor. Nbis the number of blocks used in the reconstruction, where a block is defined as a single acquired line and A-1 missing lines. 4-8 blocks are needed

15. Temporal sampling Interleaved/segmented (2) PE ½ k-space ½ k-space time Interleaved (2) Works well for imaging of static objects. For dynamic imaging, each image is not only undersampled, but also captures a different part of the “motion”/”change”. The acquisition is assumed faster than the motion

16. PSF considerations (generally) • Let us start with imaging PE or t Standard PPI used to “unalias” the effects of the psf

17. UNFOLD (does not require multichannels) • Specifically, alternate the sampling by a factor 2, such that … ½ k-space Remove aliasing by Courtesy: Madore. MRM 48:493 (2002).

18. fMRI (UNFOLD) Remove aliased frequency by selective filtering FIG. 16. Results obtained for a single-trial fMRI experiment (4 spiral interleaves, 16 kz phase-encode values, axial images, matrix size 128 3 128, TR 5 250 msec, TE 5 40 msec, 5 mm resolution along z, 24 cm FOV). Bilateral finger tapping was performed while a 2 sec audio cue was on, and then stopped for 12 sec. The acquisition time for a time frame (16 sec) is longer than a paradigm cycle (14 sec). UNFOLD is used to reduce the acquisition time by a factor 8, providing 7 frames per paradigm cycle. a: The acquired frames are corrupted by an 8-fold aliasing in the through slice direction. b: Temporal frequency spectrum for the highlighted image point in a. UNFOLD interleaves 8 spectra into the same temporal bandwidth. Marks are placed on the axis at the locations of the DC, fundamental and harmonic frequencies for the non-aliased material. Selecting only these frequencies, the aliasing seen in a is removed in c. Courtesy: Madore. MRM 48:493 (2002).

19. Extend the concept of aliasing Line in image Unalias the support in x-f space, just like we unalias in x space with SENSE Tsao et al, MRM 50: 1031-1042 (2003)

20. DATA challenge • Where is the support in x-f space? Interleaved training set Used to define support in x-f space “Equivalent” to a reference scan Similar concepts hold for radial, where the center is the “prior”. This is used in speech imaging Tsao et al, MRM 50: 1031-1042 (2003)

21. How do the methods compare?k-t SENSE, vs. Sliding Window • Consensus (in cardiac imaging) of: Xu et al. MRM, 57:918-930 (2007)

22. What does the artifact mean Xu et al. MRM, 57:918-930 (2007)

23. Looking at the temporal variation (in speech [radial]) Sliding window K-t SENSE y t Comments/Conclusions Michael S. Hansen. Workshop on Non-catesian MRI. 2007

25. Formally The mising information can be determined from the acquired data, if the coeeficients a(i,j,k) are known With localized sensitivities (smooth in image space)

26. SMASH • Find weights nk(m)(x) [no x –readout dependence] such that we get a new synthetic sensitivity profile Cmcomp WE do parallel Imaging by finding ONE combined image (just like SENSE) m is selected depending on how FAR the data must be interpolated. Only one line is used to advance the data

27. Generalised SMASH • Find weights ak(m)(x) [with x –readout dependence] such that (x) Express • We use several phase-encoding lines to generate missing information. For each readout point a new set of weights are comp.

28. Two severe issues • The final image is that of a complex sum image of the individual images. Not optimal for SNR • Total cancellation can occur with such complex sums. • Coils where phase-aligned PRIOR to reconstruction

29. AUTO-SMASH • ACS (Auto-Calibration Signal) lines (no x), not fitting to a harmonic, but a “missing” PE-line