Tobias Wech^{1,2}, Julius Heidenreich^{1,2}, Daniel Gensler^{2,3}, Tim Salinger^{2,3}, Peter Nordbeck^{2,3}, Daniel Stäb^{4}, Peter Speier^{5}, Thorsten Alexander Bley^{1}, and Herbert Köstler^{1,2}

The anatomical coverage in first-pass myocardial perfusion imaging was extended by applying undersampled radial MS-CAIPIRINHA and a model-based reconstruction exploiting low-rank plus sparse matrix decomposition. The technique was tested in a patient with acute left ventricular myocardial infarction, yielding six short-axis slices from base to apex with a temporal resolution of one heartbeat. The reconstructed images exhibited a quality which is comparable to the conventional approach of acquiring only three slices per RR interval.

The applied ECG-gated TurboFLASH prototype [5]
utilized a dual-band pulse to excite two slices simultaneously, while the RF phase
of the first slice was kept unmodulated and the phase of the second slice was
toggled between 0° and 180°. Radial readouts were implemented with a golden-angle
increment and no resets of the projection angle for each RR-interval. Three
saturation recovery (SR)-prepared acquisition blocks (one block per
dual-slice/slice-pair) consisting of 52 consecutive projections were acquired
per RR-interval (~60 RR-intervals in total).

The hereafter-proposed algorithm
was then used to obtain six images per RR-interval out of this data: To
reconstruct the highly undersampled radial MS-CAIPIRINHA dataset, a low-rank
plus sparse matrix decomposition of the temporal image series [4] was used (referred to as "LRS-CAIPIRINHA"):

$$ \min_{L_{sl},S_{sl}} \; \biggl\Vert \biggl(\sum_{sl=1}^2
\Phi_{sl} \, E_{sl} \, (L_{sl}+S_{sl}) \biggr)-y \, \biggr\Vert_2^2 +
\alpha \sum_{sl=1}^2 \Vert L_{sl} \Vert_* + \beta \sum_{sl=1}^2 \Vert
\mathcal{F} S_{sl} \Vert_1 $$

$$$y$$$ represents the measured k-t-space multi-coil data
for **one** of the three dual-slice acquisitions. $$$L_{sl}$$$ and $$$S_{sl}$$$ correspond to the low-rank and the sparse
component of the temporal image series for one of the two slices $$$sl$$$, in accordance to the single-slice
definition in [6]. $$$E_{sl}$$$ is the encoding operator, which incorporates an
inverse Fourier transform, the re-gridding back to the initial radial
projections and the superposition of the coil sensitivities to obtain
multi-coil data. The coil sensitivities for each slice were determined using an
oversampled temporal average, i.e. data were pooled from all RR-intervals and
gridded into one single k-space. $$$\Phi_{sl}$$$ performs the applied CAIPIRINHA phase
modulation, $$$\Vert \; \Vert_*$$$
represents the nuclear norm and $$$\alpha, \beta$$$ balance the weighting of the different
constraints. The latter parameters were chosen based on visual inspection of
the reconstructed images. $$$\mathcal{F}$$$
performs a 1D Fourier transform in the
temporal domain to additionally sparsify $$$S_{sl}$$$. Projection
onto convex sets (POCS) was used to perform the optimization. 50 iterations
were applied, and the reconstruction of the whole dataset took approximately
five hours on an Intel Core i7-3820 CPU @ 3.60 GHz without parallel
computation.

The imaging technique was tested on a 3T MR scanner (MAGNETOM Skyra, Siemens Healthcare, Erlangen, Germany) in a patient with known acute left ventricular myocardial infarction (BMI = 26.6). The study was approved by our local ethics committee, and the patient gave written informed consent prior to scanning. Imaging parameters were chosen as follows: Slice distance between adjacent slices =12.3mm, slice distance between simultaneously acquired slices = 37.0mm, saturation preparation & ECG triggering, TE = 1.5ms, TR = 2.6ms, slice thickness = 8mm, in-plane resolution = 1.9mm x 1.9mm, 52 radial projections per image pair, image matrix = 160 x 160. A compact bolus of gadoterate meglumine (Dotarem, Guerbet, Aulnay-sous-Bois, France) was injected, and imaging was performed over 60 RR-intervals with 3x2 short-axis slices, acquired within each interval. The measurement was started with an initial breath-hold of the patient, which lasted for approximately 20-25 of the 60 heartbeats of the entire investigation. To provide a reference for the size and the shape of the myocardial scar, the reconstructed perfusion series were analyzed in conjunction with the phase-sensitive inversion recovery late-enhancement (PSIR-LE) images acquired during the clinical MR investigation.