hide
Free keywords:
-
Abstract:
Introduction: The slow acquisition speed of MRI has led to the development of a variety of acceleration methods. One approach to accelerating MRI acquisition, called Parallel Imaging, utilizes multiple receiver coils to simultaneously acquire multiple views of the object. Conventional reconstruction methods, GRAPPA 1 synthesizes missing data points directly in k-space. Another step towards the current state-of-the-art image reconstruction is by using advanced deep-learning-based reconstruction models. Variational networks 2 (VN) represent an unrolled network, which turns an iterative reconstruction algorithm into a deep neural network. Training of such networks uses large datasets of raw MRI data, such as the fastMRI 3 database. For the training fully sampled raw data is retrospectively under-sampled. However, for non-steady-state sequences, like TSE with long echo trains, this procedure is inconsistent with actual acquired under-sampled data, as it does not take the change of the signal dynamic into account. In this work, we demonstrate the benefits of simulated training data, using MRzero 4, as this can be generated with the correct signal decay, yielding correct targets for VN training. Furthermore, we extend our previous work5 on solving T2-induced blurring in TSE sequences by including a VN as reconstruction model in the optimization pipeline to yield a fully joint reconstruction and sequence optimization.
Methods: All simulations and optimizations were performed in the MRzero framework using a fully differentiable Phase Distribution Graph6 (PDG) algorithm for signal generation. To demonstrate the differences between correct simulated and retrospective under-sampled data a single-shot PDw-TSE sequence (matrix: 128 9 128 9 1, FoV = 200 9 200 9 8 mm2, FA = 180°, TE = 14.5 ms, centric reordered phase-encoding) was simulated. The sequence uses a uniform cartesian under-sampling of factor 2. As reference a two-shot TSE with full relaxation between each shot is being used to yield an ideal fully sampled target. The training data uses synthetic brain samples based on the BrainWeb 7 database consisting of 20 subject volumes with 70 slices each. The VN is implemented in PyTorch and uses T = 10 cascades. For the joint optimization, the forward simulation outputs the decaying TSE signal, which is reconstructed by the VN, and in addition the corresponding transversal magnetization as ideal sharp target. Fig. 1 visualizes the optimization process in MRzero. The gradient update propagates back through the whole chain of differentiable operators. As loss function MSE is being employed and Adam is used as optimizer. The complete FA train and VN parameters are updated at each iteration step simultaneously. Results The difference between images generated from the correctly simulated signals and retrospective under-sampled signals reveal that the T2 decay in TSE sequences leads to considerable changes in contrast and sharpness (Fig. 2). As shown in Fig. 3 the inconsistent training data of a VN trained with retrospective under-sampled signals leads to low performance when applied on the test dataset, when compared to a VN trained with correctly simulated signals. Identical optimizations were performed for transient GRE MRI (data not shown). The simultaneous reconstruction and sequence optimization to reduce T2-induced blurring is shown in Fig. 4. The optimization discovers a suitable FA train and a matching VN resulting in a reconstructed image with strong correlation to the target transverse magnetization. Compared to the single-shot TSE sequence with constant 180° FA train, the output yields strongly improved sharpness especially in white and gray matter structures due to their low T2 relaxation time.
Discussion and Conclusion: Retrospective under-sampling of data leads to inconsistencies with actually acquired data, as the signal decay is altered. We demonstrated the importance of VN training of correctly simulated under-sampled data of non-steady-state sequences. MRzero provides such simulation framework that also makes possible to train networks for novel sequences and contrasts of which no datasets are available. By using variational networks more flexiility in the reconstruction could allow a completely new degree of freedom in the sequence optimization. We showed that that the VN could be incorporated in the existing optimization pipeline of our previous work by replacing the conventional reconstruction and leading to a fully joint optimization. This is not only limited to the task of deblurring, but it also suitable to supersede any reconstruction or image processing task, as well as joint optimization of under-sampling factor and pattern, refocusing FA and the matching optimal variational network.
