Phase distribution graphs for fast, differentiable, and spatially encoded Bloch simulations of arbitrary MRI sequences.

PURPOSE: An analytical approach to Bloch simulations for MRI sequences is introduced that enables time efficient calculations of signals free of Monte-Carlo noise, while providing full flexibility and differentiability in RF flip angles, RF phases, magnetic field gradients and time, as well as insights into image formation. THEORY AND METHODS: We present an implementation of the extended phase graph (EPG) concept implemented in PyTorch, including an efficient state selection algorithm. This simulation is compared with an isochromat-based Bloch simulation with random isochromat distribution as well as with in vivo measurements using the Pulseq standard. Additionally, different sequences are tested and analyzed using this novel simulation approach. RESULTS: Our simulation outperforms isochromat-based simulations in terms of computation time as well as signal quality, without exhibiting any kind of Monte-Carlo noise. The novel approach allows extracting useful information about the magnetization evolution not available otherwise. Our approach extends the common state-tensor-based EPG simulation approach for the contribution of dephased states including spatial encoding and T 2 ' $$ {T}_2^{\prime } $$ effects, and arbitrary timing. This allows calculation of echo shapes in addition to echo amplitudes only. Our implementation provides full differentiability in all input parameters allowing gradient descent optimization. Simulation of non-instantaneous pulses via hard-pulse approximation is left for future work, as the performance and accuracy characteristics are not yet analyzed. CONCLUSIONS: Phase distribution graphs provide fast, differentiable, and spatially encoded Bloch simulations for most MRI sequences. It allows efficient simulation and optimization of arbitrary MRI sequences, which was previously only possible via high isochromat counts.

MR-zero meets RARE MRI: Joint optimization of refocusing flip angles and neural networks to minimize T2 -induced blurring in spin echo sequences.

PURPOSE: An end-to-end differentiable 2D Bloch simulation is used to reduce T2 induced blurring in single-shot turbo spin echo sequences, also called rapid imaging with refocused echoes (RARE) sequences, by using a joint optimization of refocusing flip angles and a convolutional neural network. METHODS: Simulation and optimization were performed in the MR-zero framework. Variable flip angle train and DenseNet parameters were optimized jointly using the instantaneous transverse magnetization, available in our simulation, at a certain echo time, which serves as ideal blurring-free target. Final optimized sequences were exported for in vivo measurements at a real system (3 T Siemens, PRISMA) using the Pulseq standard. RESULTS: The optimized RARE was able to successfully lower T2 -induced blurring for single-shot RARE sequences in proton density-weighted and T2 -weighted images. In addition to an increased sharpness, the neural network allowed correction of the contrast changes to match the theoretical transversal magnetization. The optimization found flip angle design strategies similar to existing literature, however, visual inspection of the images and evaluation of the respective point spread function demonstrated an improved performance. CONCLUSIONS: This work demonstrates that when variable flip angles and a convolutional neural network are optimized jointly in an end-to-end approach, sequences with more efficient minimization of T2 -induced blurring can be found. This allows faster single- or multi-shot RARE MRI with longer echo trains.