Introduction

Deep learning based MRI-reconstruction is showing a great promise in speeding up both acquisition time by sparse sampling as well as reconstruction time thanks to fast inference times using pre-trained networks on fast GPU-cards. In clinical practice, a wide variety of protocols is used, with a range of sequence parameters and designs that will be challenging to include in a training set. Most work to date is experimenting within the close measurement conditions of the training data, including acceleration level and MR-contrast. Here, promising results are reported, e.g. in detecting subtle pathologies in the knee joint$$$^1$$$. Our aim is to explore the unseen landscape of sequence parameters and pathologies, in a case study on reconstructing brain lesions in FLAIR data novel to a trained network.

Methods

The experimental overview and network architecture are depicted in Figs.1&2. Instead of learning a direct mapping from the sparsely sampled image to the full signal, Recurrent Inference Machines$$$^2$$$ (RIM) learn to reconstruct the signal in an iterative procedure similar to compressed sensing, where the goal is to optimize the maximum a posteriori estimate. To this aim it employs a recurrent architecture, where each step improves on the previous step’s reconstruction estimate by using as input the gradient of the log-likelihood distribution, as given under the assumption of normally distributed noise, along with the model’s current reconstruction state, which should enable it to estimate the gradient of the log-prior distribution. Due to their recurrent architecture, RIMs swap model parameters for internal states, moving dependency away from the training data and onto the input data instead. This prevents overfitting and enables the reconstruction of features that are not necessarily present in the training set, i.e. lesions after only being exposed to healthy volunteers.We trained a model of approximately 100k parameters, using the mean square error averaged over the model’s 8 reconstruction estimates as a loss function. Raw data of 12 participants was acquired on a Philips 3T scanner (Philips, The Netherlands) with a 32-channel head coil. For training, fully sampled 3D T1-weighted MPRAGE data at 1mm was acquired in 10 healthy volunteers (scanning time 10 minutes). For testing purposes, an accelerated 3D FLAIR scan of a single healthy volunteer was obtained at 1.1mm, with a sparse sampling pattern 6x as implemented by the vendor (scanning time 5 minutes). For validation, an identical 3D FLAIR was used to scan one patient with a mild white matter lesion load. Coil sensitivity maps were computed from the fully sampled center in all scans with calibration size 15 with ESPIRiT auto calibration$$$^3$$$.Two lesions were simulated in one slice of the healthy volunteer 3D-FLAIR testing dataset, initially reconstructed using compressed sensing (CS) for this purpose. Using manual annotation, the signal magnitude was augmented to create local hyperintensities (Fig. 1).The signal phase was not adjusted, assuming negligible phase shift. The resulting image was multiplied by coil sensitivity maps, Fourier transformed and subsampled with factors 4-10x. CS reconstruction was performed using the Berkeley Advanced Reconstruction toolbox, with an l1-norm sparsity term using the wavelet transform, and optimized regularization (r=0.005). RIM-reconstructions were performed using the network trained on T1-weighted data. In the reconstructed images, lesion contrast was computed as $$$(I_{peak}-I_{ref})/I_{ref}$$$, with $$$I_{peak}$$$ the peak intensity within the lesion and $$$I_{ref}$$$ the mean intensity in an adjacent reference intensity region.

Results

The RIM was trained until convergence in 1 day on a single GPU-card. T1-weighted images could be reconstructed at high acceleration levels (Fig.1). Inference times for single slices were approximately 0.1s. Figure 3 shows that at 30% intensity, the lesion is slightly more apparent in the RIM-reconstruction than in the CS-reconstruction. Figure 4 quantifies lesion contrast, showing that at 4x- and 6x-acceleration the RIM maintains contrast while at 8x- and 10x-acceleration more variable contrast for the two lesions is seen. CS underperforms at all acceleration levels. Figure 5 illustrates that in prospectively undersampled patient data, the T1w-trained RIM does not underperform on reconstructing WM lesions compared to CS.

Discussion and Conclusion

The RIM can reconstruct FLAIR images with small lesions that were not presented during training. Our lesion model of multiplying by small Gaussians corresponds to convolutions with large Gaussians in Fourier domain. Thus, a large extent of k-space, far beyond the sub-sampling range, contributes to the lesion signal. Future work is needed to assess how other deep learning methods that operate solely in image domain perform compared to the RIM.

Acknowledgements

No acknowledgement found.