Ying Chen^{1}, Lisha Yuan^{1}, Yi Sun^{2}, and Jianhui Zhong^{1}

Single-shot spatiotemporally encoded (SPEN) MRI is a novel fast imaging scheme with remarkably reduced geometric distortions at high field compared to conventional single-shot EPI. The k-space along SPEN dimension is undersampled, resulting in aliases at regions of rapid profile variation. The feasibility of utilizing sensitivity profiles of array receiver coils to unravel the undersampling aliases is investigated. High resolution relative sensitivity profiles can be obtained from multicoil 2D polynomial fitting of the SPEN reconstructed images without additional reference scans. The effectiveness of the SPEN SENSE strategy is validated by healthy human brain scans at 3T.

Healthy
human brain data were acquired with informed consent on a SIEMENS 3T Prisma
scanner using a 20-channel head coil (16 channels were activated for data
collection), with the following parameters: field-of-view = 220x220mm^{2},
slice thickness = 5mm, acquisition matrix size = 64x64, bandwidth and
duration of the excitation chirp pulse = 50kHz and 5.12ms respectively (corresponding
to fully-sampled points of 256 and acceleration factor of 4 along SPEN
dimension), flip angle = 30°, acquisition bandwidth = 1502Hz/voxel,
and TE = 66ms. Single-shot accelerated EPI data were also acquired with
similar parameters and with 48 additional autocalibration data lines for
comparison. The postprocessing procedures of the SPEN SENSE scheme are listed
in **Fig.1**. Firstly, SPEN reconstructions were performed on each channel. Then high
resolution relative sensitivity profiles ^{4} were obtained from
multicoil SPEN reconstructed images directly, similar to the strategy
implemented in multi-shot phase scrambling MRI ^{5}. One coil was
chosen as reference to remove the influence of rapid phase variations on
sensitivity fitting. Next, SENSE unfolding was performed on multicoil SPEN
reconstructed data of each voxel. Each voxel along SPEN dimension can be
regarded as superposition of *N*_{full}/*N* aliased voxels, each separated by *N*^{2}/*N*_{full} voxels, where *N*
is the number of k-space points acquired and *N*_{full} is the number of fully-sampled points. The SENSE equation
set can be represented by

$$\bf {S}\bf{X}_\rm{unfold}=\bf{X}_\rm{pFT},\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{(1)}$$

where
$$$\bf{S}$$$ is the complex
sensitivity profile matrix,
$$$\bf{X}_\rm{pFT}$$$ is the vector of
multicoil voxel data obtained from partial Fourier reconstruction ^{2} and
$$$\bf{X}_\rm{unfold}$$$ is the unfolded
vector. This equation set can be easily solved by linear least squares
estimation using

$$\bf{X}_\rm{unfold}=(\bf{S^H}\bf{\Psi}\rm^{-1}\bf{S}\rm)^{-1}\bf{S^H}\bf{\Psi}\rm^{-1}\bf{X}_\rm{pFT},\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{(2)}$$

where $$$\bf{^H}$$$ represents transpose conjugate and $$$\bf{\Psi}$$$ is the noise covariance matrix. The aliased components are of large noise and discarded in this study. The unfolding calculations were performed voxel by voxel, instead of on each aliased group by conventional SENSE.

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2. Chen Y, Li J, Qu X, et al. Partial Fourier transform reconstruction for single-shot MRI with linear frequency-swept excitation. Magn Reson Med 2013; 69:1326-1336.

3. Pruessmann K P, Weiger M, Scheidegger M B, et al. SENSE: Sensitivity Encoding for Fast MRI. Magn Reson Med 1999; 42:952–962.

4. Bydder M, Larkman D J, Hajnal J V. Combination of Signals From Array Coils Using Image-Based Estimation of Coil Sensitivity Pro?les. Magn Reson Med 2002; 47:539–548

5. Zaitsev M, Schultz G, Hennig J, et al. Parallel Imaging with Phase Scrambling. Magn Reson Med 2015; 73:1407–1419.