Signal Stability and Sensitivity of Referenceless Reconstructions by a Neural Network in Simultaneous Multi-Slice Imaging
Klaus Eickel1,2, Martin Blaimer3, and Matthias Günther1,2

1MR-Imaging & Spectroscopy, Faculty 01 (Physics/Electrical Engineering), University of Bremen, Bremen, Germany, 2MR Physics, Fraunhofer MEVIS, Bremen, Germany, 3Fraunhofer IIS, Würzburg, Germany


A deep neural network for reconstruction of SMS data without the need of additional reference data to calibrate for the spatial encoding information of the multi-coil receiver is presented. Noise-propagation through the reconstruction process is investigated in form of g-factors. Simulations with pseudo-multiple replicas showed robustness and stability of this new method. In addition, the sensitivity for physiological signal variations of this approach is considered in BOLD-signal dynamics. Results are compared to conventional methods like split slice-GRAPPA.


Simultaneous multi-slice (SMS) imaging1-3 has emerged as a promising acceleration technique for multi-coil systems4 in magnetic resonance imaging (MRI) where undersampled data are recovered by utilizing the spatial encoding information inherent in multi-coil receiver arrays. However, the prominent methods like (split) slice-GRAPPA5,6 require additional, scan-specific reference data, i.e. auto-calibration signal (ACS), to disentangle overlapping image content7. ACS-acquisition can be time-consuming and a source of reconstruction-errors, if ACS data are corrupted. Here, a deep neural network (DNN), named SMSnet, reconstructs the SMS data without the need of any reference-scans8. The predicted images by SMSnet are compared to conventional approaches, i.e. split slice-GRAPPA (SSG) in terms of image quality, noise propagation and sensitivity to physiological changes. The spatially varying noise amplification in SMS can be characterized by the g-factor delivered by the pseudo-multiple-replica method (PMRM)9,10 to investigate signal stability. SMSnet’s sensitivity to small signal variations is evaluated in a time-series of blood-oxygenation-level dependent (BOLD) signal11.


The architecture depicted in Figure 1 is similar to8. Raw-data of 38 GRE and MPRAGE scans measured with a 20-channel head-coil at 3T (MAGNETOM Skyra, Siemens Healthineers, Erlangen, Germany) were augmented by downsampling and different CAIPIRINHA-patterns12 into a pool of Ntrain=41939 (Nval=24660) source- and target-pairs for training (validation). SMSnet was set up in Keras13 and training of 7 epochs was performed on a GTX1080 graphics card (Nvidia, Santa Clara, United States). A combined loss-function E = MSE x TV of mean-squared (MSE) and total-variation (TV) error accounted for global errors as well as borders mismatches. Acquired test data simulated a whole head scan in 6 slices (25mm gap), the parameters of the MRI protocol were: α=30°, TE=5ms, TR=126ms with an acquisition matrix of 96x104 (zero-filled to 128x128). 5 measurements yielded a ‘noise-free’ ground-truth (REF). A visual comparison between the 4 reconstruction methods was done first. The reconstruction performance was then quantified with respect to REF using the structural similarity index (SSIM). SSIM assesses perceptual image quality by taking advantage of characteristics of the human visual system14. Thereafter, PMRM was run for 100 repetitions, SMS data were synthesized thereafter for a multi-band-factor (MB) of 2 and a CAIPIRINHA-pattern of FOV-shift=1/4. These SMS data were processed in 4 reconstructions: a) SMSnet, b) SSGstd with correct ACS, c) SSGavg,h&p with corrupted ACS (averaged from multiple phantom- and head scans) and d) SSGavg,h also with corrupted ACS (averaged from multiple head scans).
In a second experiment, an accelerated (MB=2, FOV-shift=1/2) multi-echo (TE=8.6s/19.1s/30s) mutli-shot EPI scan (EPI-factor=13) was run for 130s (120 measurements) while the volunteer (31 years, male) performed finger-tapping (paradigm: 20s [rest] / 20s [active]). BOLD-dynamics were calculated after signal-separation into S0 and T2* by a mono-exponential fit15 and compared for SSGstd and SMSnet reconstructions of identical data.


Visual inspection generally approves the quality of SMSnet reconstructions (Fig. 2). The 4 compared reconstruction methods reached mean SSIMs of 0.91 (SMSnet), 0.99 (SSGstd), 0.81 (SSGavg,h&p) and 0.87 (SSGavg,h) with respect to REF. Figure 3 shows the local, reconstruction-related noise-enhancement. While SMSnet and SSGstd perform almost equally in average (mean g-factors 1.71 and 1.72), higher local g-factors appear in SMSnet. Noise is clearly enhanced in SSGavg,h&p and SSGavg,h (mean g-factors 1.97 and 2.15) in accordance with the apparent leakage-artifacts. Signal-separation of the finger-tapping SMS-data displayed in Figure 4 gives reasonable T2*-curves corresponding to the paradigm. Both reconstructions lead to correlated results (r=0.97).


In general, the reconstructions by SMSnet show promising and robust results with an acceptable g-factor penalty, while ensuring sensitivity not only to anatomical structures, but also physiological variations. Structures in proximity to regions of high susceptibility suffer from higher SNR-reductions (Fig. 2) which is physically plausible as coil-sensitivities are expect to vary stronger near these perturbations in the B-field homogeneity.
Main limitations of this work are that the presented test data have relatively large slice-distances and minimal acceleration (MB=2). Smaller slice-distances with higher MBs will require suitable training data and extension of the DNN’s architecture which can be realized easily with the modular design of SMSnet. Furthermore, transfer to coil-systems other than the head-coil may be of interest, in particular for applications where ACS can not be acquired reliably.


It is shown, that SMSnet reconstructs data with minor g-factor penalties compared to conventional SSG. However, SMSnet outperforms SSG reconstructions where correct ACS is missing as it does not rely on any scan-specific ACS to disentangle overlapping slices. SMSnet’s sensitivity to relatively small signal changes is proved in BOLD-dynamics induced by controlled finger-tapping. Furthermore, the reconstruction itself is fast, as no heavy computations have to be done after training.


The authors gratefully thank Markus Wenzel and Hans Meine for valuable, interdisciplinary discussions on deep learning in image-processing.


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The 20-channel preprocessed complex input data are split into real and imaginary components which are concatenated along channel dimension resulting in 40 input-channels. In the left tree, named CS-path, features similar to coil sensitivities are derived from reduced k-space data (32x32x40). These are merged by multiplication with the input image data (128x128x40) after passing the right tree, named Im-path, similar to the unfolding process in SSG. The last section, called merge-path, reduces the number of channels. The combined channels yielding a single magnitude image per slice (128x128) at the output. SMSnet for MB=2 has about 9.9x106 trainable parameters.

Reconstructions of synthetic SMS data (MB=2, FOV-shift=1/4). REF represent the noise-free ground-truth. SMSnet and SSGstd recover the test data without obvious artifacts unlike SSG reconstructions with corrupted ACS (SSGavg,h&p,SSGavg,h). Images were slice-wise normalized before plotting.

Monte-Carlo generated g-factor maps show the reconstruction-related noise-enhancement for all 4 reconstruction methods. Masks were applied to remove irritating background and limit the calculation of the mean g-factor to voxels inside the object.

T2*-dynamics, i.e. BOLD-signal, of identical data, but reconstructed differently. Results of SMSnet and SSGstd correlate with r=0.97. Signal was averaged from 6 neighboring voxels.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)