Introduction

State-of-the-art MRSI acquisitions generate raw data of up to ~100 GB per 15 minutes. The size of the raw data increases proportionally with the number of receive coil elements(1,2).Within post-processing pipelines, the coil combination step is the most critical reconstruction step with respect to reducing the amount of data. Currently, the coil combination of MRSI is performed in the image domain.To lower the hardware demands the proposed coil combination is performed in native sensor space (i.e., ungridded k-space).This should (i) dramatically reduce the RAM requirements (ii) make repetition of reconstruction steps obsolete (iii) allow performing the major workload "on the fly"(in parallel to data acquisition).However, especially for non-Cartesian k-space sampling,this poses a significant challenge with respect to finding the right k-space convolution kernel(3).In this study we propose a k-Space-based coil combination method for non-Cartesian data via geometric deep learning.

Methods

Experimental Data
Ten volunteers (5 males and 5 females) were measured on a 3T Prisma MR scanner with a 20 channel receive head/neck coil array (both Siemens Healthineers).Internal review board approval and written informed consent were obtained for all volunteers.For each volunteer, rapid water-unsuppressed MRSI scans were performed with the head placed in 10 different positions inside of the coil with a short-TR FID-MRSI sequence(4,5):FOV 220×220×200mm³, VOI 220×220×100mm³, TR:60ms, TE:1.3ms, FA:16°, vector size 16 points, SBW 1030Hz, and TA:20 s. In-plane (kx,ky)-encoding was performed by 16 concentric ring readouts. Through plane (kz)-encoding was achieved via 25 phase encoding gradients, resulting in a 32×32×25 matrix size.Water-suppressed long-TR FID-MRSI was measured with another head position with TR 470ms, FA 50°, vector size 360 points, and TA:3:11 min:s. All other scan parameters were identical. Additionally MPRAGE data(6) was scanned within 2:38 min:s.
Training and testing data
Training data were derived from the short-TR MRSI data. The data were reconstructed to the image space, and used to calculate sensitivity maps using ESPIRiT. Pairs of non-Cartesian kSpace data were generated:(i) the input to the network, which was corrected for FOV shifts and (ii) the desired output of the network, which was additionally corrected by the sensitivity maps. Additionally a Hamming filter and the annhiliation filter used in reference(7) were applied in kx and ky dimension. Training data were obtained only from 7 volunteers. The long-TR data of the remaining three volunteers were pre-processed in the same way and used for testing.
Neural network architecture
A shallow graph neural network was designed in Graph Deep Library(9) consisting only of two Gaussian Mixture Model Convolution layers(8) with 10 Gaussian kernels, no bias terms and a tanh activation after the first layer. The pseudo coordinates of the nodes in the neighborhood were defined in Euclidean coordinates. The number of input and output features was the same, while the output of the first convolutional layer had only half of the input features.
Network training
The training and the following inference of the network with the data was done on an Nvidia DGX-station using one GPU card (Nvidia Tesla V100 32 Gb). The Deep graph library(9) was used on top of the PyTorch(10) DL framework.At first, the network was trained without introducing any noise (50 epochs, batch size 10, ADAM optimizer with LR of 1e-4, loss: mean squared error). Then, the network was fine-tuned by adding white noise to the input data to stabilize the network against noise within 30 epochs. White Gaussian noise was simulated for each instance and epoch with standard deviations increasing progressively with the epochs.
Evaluation
The analysis was carried out on two volunteers:(i) the first volunteer whose water unsuppressed MRSI data were included in the training dataset, but not the water suppressed MRSI,(ii) the second volunteer for who no data were ever shown to the network. Directly after prediction, the annihilation filter was removed from the output data.The data were then summed up across the channels and Hamming filtered in the partition direction. The data were then Fourier transformed to the image space(5) and spectra were fitted using LCModel(11).Metabolic ratio maps CRLBs of three main metabolite groups(tCr, tNAA, tCho), SNRs of NAA and tCr, and FWHMs of tCr were obtained from the LCModel results. The results of the kSpace coil combination (kspCC) were compared against a conventional image based coil combination (cCC) termed iMUSICAL(12,13).

Results

The spatial distribution of the SNR and the FWHM (Figure 2) are very similar. Quantitative results suggest underperformance of the kspCC compared to the cCC in terms of the SNR, which is driven mainly by the high SNR region (Figure 3a,b).There is no difference in the FWHM between both methods (Figure 3e,f).The agreement is valid across the whole range of values (Figure 3g,h).Qualitatively, the spatial distribution of CRLBs for both methods follow the same pattern. However, the CRLBs are higher for kspCC compared to cCC in accordance with the lower SNRs (Figure 4).The metabolic ratio maps are similar in all three projections as well as the example spectra (Figure 5).

Discussion and Conclusion

The results of the non-Cartesian kspace coil combination were presented utilizing geometric deep learning and compared with conventional coil combination. Promising results with a minimalistic neuronal network architecture were achieved, which opens possibilities for the rapid online reconstruction of MRSI data.

Acknowledgements

This study was supported by the Austrian Science Fund (FWF) grant P 34198.