Ricardo Otazo, PhD ricardo.otazo@nyumc.org

G16.4428 – Practical Magnetic Resonance Imaging II Sackler Institute of Biomedical Sciences New York University School of Medicine

Parallel Imaging II

SMASH: Fitting spatial harmonics

constant

cos∆kyy sin∆kyy

cos2∆kyy sin2∆kyy

R = 3

k-space

Coil array

Sodickson DK, Manning WJ. Magn Reson Med. 1997; 38: 591-603

krjmN

ll erCw

c∆−

=

=∑ )(1

• Solve to get the weights

)()(1

kDwkmkDcN

ll∑

=

=∆+• Compute the missing points:

GRAPPA: More general k-space fitting • Coil-by-coil k-space reconstruction • Linear combination of k-space neighbors from all coils

Coil 1

ky

kx

Coil 2

Sampled Non-sampled

2x3 kernel

Griswold MA et al. Magn Reson Med 2002; 47: 1202-10

)()()(kernel

0 kDkwkDk

l ∑∈

=

GRAPPA: More general k-space fitting

Griswold MA et al. Magn Reson Med 2002; 47: 1202-10

kx

ky Autocalibration signal (ACS)

• Reconstruction weights (GRAPPA kernel) – Fully-sampled k-space region (calibration)

• Within the accelerated data (autocalibration) • Separate acquisition

– Least-square fit using examples of target and source points

GRAPPA: More general k-space fitting • Reconstruction weights (GRAPPA kernel)

Griswold MA et al. Magn Reson Med 2002; 47: 1202-10

ACS: 4x4 matrix Kernel size: 2x3 Ry=2

S: source matrix (Nb × KsizeNc) T: target matrix (Nb×Nc)

=T Sw

H 1 H( )−=w S S S T (Nb × KsizeNc)

4 examples

Calibration model:

Invert to get the weights:

• No need to compute explicit coil sensitivities

GRAPPA: More general k-space fitting • GRAPPA algorithm

– Compute GRAPPA weights from calibration data – Compute missing k-space data using GRAPPA weights – Reconstruct individual coil images – Combine coil images

Calibration region

Zero-pad at the border

Reconstruction examples • Simulation of brain imaging acceleration • 8-channel circular array coil

SENSE

GRAPPA

R=2 R=3 R=4

GRAPPA: More general k-space fitting • Advantages

– No need to estimate coil sensitivities – More robust than SENSE to inconsistencies between

calibration and imaging data

• Issues

– Calibration region size – GRAPPA kernel size – Sampling geometry dependence

GRAPPA: More general k-space fitting • Sampling geometry dependence

– Simple for 1D acceleration (same weights work everywhere)

– Harder for 2D acceleration (each geometry has its own weights)

– Unmanageable for irregular undersampling (non-Cartesian)

Does not work!

Needs a different

kernel

2D-GRAPPA using multiple 1D-GRAPPA reconstructions

• Solve 1D-GRAPPA for each set of Rz aliased partitions

Blaimer M et al. J Magn Reson Imaging. 2006;24(2):444-50.

z

z+Wz/Rz

1D-GRAPPA R=RyRz

GRAPPA weights

GRAPPA weights

SPIRiT • Generalization of GRAPPA to arbitrary undersampling

– Same kernel for arbitrary geometries – Kernel includes all neighbors (known and unknown)

• Iterative algorithm (POCS-type) – Data consistency – Kernel consistency

Lustig M, Pauly JM. Magn Reson Med. 2010;64(2):457-71.

Gxx = x: k-space data G: GRAPPA kernel

SPIRiT • Basic idea

– Calibrate on entire neighborhood (e.g. 5x5 kernel) – Initial solution: zero-filled k-space data – For each iteration

• Apply the kernel to estimate all data (kernel consistency) • Restore know data (data consistency)

Lustig M, Pauly JM. Magn Reson Med. 2010;64(2):457-71.

R=2x2

Summary • Parallel MRI reconstruction in k-space

– Coil-by-coil reconstruction – No need to estimate coil sensitivity maps

• GRAPPA algorithm

– Unknown k-space points reconstructed as a linear combination of known k-space points

– GRAPPA weights computed from calibration data

• SPIRiT

– Extension of GRAPPA to arbitrary sampling geometries – Iterative algorithm exploiting data and kernel consistency