Partial Parallel imaging (PPI) in MR for faster imaging IMA Compressed Sensing June, 2007 Acknowledgement: NIH Grants 5RO1CA and 5P41RR008079, Pierre-Francois Van de Moortele, Gregor Adriany, Kamil Ugurbil

Our coils  Open face coil  16 Channel “closed” coil

Intrinsically, surface coils offer a representation of signal as 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 The sensitivities are complex valued

Field of View Courtesy: Douglas Noll, University of Michigan

Undersampled images Undersampled individual images

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

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

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

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

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

Courtesy: Yeh, et al, MRM Volume 53, Issue 6, Pages

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

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

 GRAPPA formula to reconstruct signal in one channel  ACS (Auto-Calibration Signal) lines (no x) where A represents the acceleration factor. N b is 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,l,l

Temporal sampling PE Interleaved/segmented (2) 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 time ½ k- space

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

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

fMRI (UNFOLD) FIG. 16. Results obtained for a single-trial fMRI experiment (4 spiral interleaves, 16 kz phase-encode values, axial images, matrix size , TR 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. Remove aliased frequency by selective filtering Courtesy: Madore. MRM 48:493 (2002).

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: (2003)

DATA challenge 1. Where is the support in x-f space? Used to define support in x-f space “Equivalent” to a reference scan Interleaved training set Similar concepts hold for radial, where the center is the “prior”. This is used in speech imaging Tsao et al, MRM 50: (2003)

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

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

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

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

SMASH  Find weights n k (m) (x) [no x –readout dependence] such that we get a new synthetic sensitivity profile C m comp 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

Generalised SMASH  Find weights a k (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.

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

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