Physics-based Reconstruction Methods for Magnetic Resonance Imaging

Conventional Magnetic Resonance Imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction -- addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report about our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code.Comment: 8 figures, review accepted to Philos. Trans. R. Soc.

Quantitative Magnetic Resonance Imaging by Nonlinear Inversion of the Bloch Equations

Purpose: Development of a generic model-based reconstruction framework for multi-parametric quantitative MRI that can be used with data from different pulse sequences. Methods: Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative $T_1$ and $T_2$ mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain. Results: The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ODE solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate $T_1$ and $T_2$ maps for the NIST phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects. Conclusion: By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.Comment: 30 pages, 7 Figures, 1 Table, Research Pape

Correction d'inhomogénéités de champs pour la SWI non-cartésienne par estimation des cartes de champs

International audiencePatient-induced inhomogeneities in the magnetic field cause distortions and blurring during acquisitions with long echo times, as in susceptibility-weighted imaging. Most correction methods require collecting an additional ΔB0 field map. To avoid that, we propose a method to approximate this field map using the single echo acquisition only. The main component of the observed phase is linearly related to ΔB0 and TE, and the relative impact of non-ΔB0 terms becomes insignificant with TE>20ms at 3T. The estimated 3D field maps, produced at 0.6 mm isotropic under 3 minutes, provide equivalent corrections to acquired ones.Les inhomogénéités de champs induites par les patients sont à l'origine de distorsions et de floutages durant les acquisitions à temps d'écho longs, comme pour l'imagerie pondérée en susceptibilité. La plupart des méthodes de correction nécessitent d'acquérir une carte de champ ΔB0 additionnelle. Pour éviter cela, nous proposons une méthode pour approximer cette carte de champs en utilisant seulement l'acquisition à écho unique. La composante principale de la phase observée est linéairement liée au ΔB0 et au TE, et l'impact relatif des termes indépendants du ΔB0 deviennent négligeables pour TE>20ms à 3T. Les cartes 3D estimées, produites à 0.6 mm isotrope en moins de 3 minutes, permettent d'obtenir une correction équivalente aux cartes acquises

Learning to sample in Cartesian MRI

Despite its exceptional soft tissue contrast, Magnetic Resonance Imaging (MRI) faces the challenge of long scanning times compared to other modalities like X-ray radiography. Shortening scanning times is crucial in clinical settings, as it increases patient comfort, decreases examination costs and improves throughput. Recent advances in compressed sensing (CS) and deep learning allow accelerated MRI acquisition by reconstructing high-quality images from undersampled data. While reconstruction algorithms have received most of the focus, designing acquisition trajectories to optimize reconstruction quality remains an open question. This thesis explores two approaches to address this gap in the context of Cartesian MRI. First, we propose two algorithms, lazy LBCS and stochastic LBCS, that significantly improve upon G\"ozc\"u et al.'s greedy learning-based CS (LBCS) approach. These algorithms scale to large, clinically relevant scenarios like multi-coil 3D MR and dynamic MRI, previously inaccessible to LBCS. Additionally, we demonstrate that generative adversarial networks (GANs) can serve as a natural criterion for adaptive sampling by leveraging variance in the measurement domain to guide acquisition. Second, we delve into the underlying structures or assumptions that enable mask design algorithms to perform well in practice. Our experiments reveal that state-of-the-art deep reinforcement learning (RL) approaches, while capable of adaptation and long-horizon planning, offer only marginal improvements over stochastic LBCS, which is neither adaptive nor does long-term planning. Altogether, our findings suggest that stochastic LBCS and similar methods represent promising alternatives to deep RL. They shine in particular by their scalability and computational efficiency and could be key in the deployment of optimized acquisition trajectories in Cartesian MRI.Comment: PhD Thesis; 198 page

Calibrationless oscar-based image reconstruction in compressed sensing parallel MRI

International audienceReducing acquisition time is a crucial issue in MRI especially in the high resolution context. Compressed sensing has faced this problem for a decade. However, to maintain a high signal-to-noise ratio (SNR), CS must be combined with parallel imaging. This leads to harder reconstruction problems that usually require the knowledge of coil sensitivity profiles. In this work, we introduce a calibra-tionless image reconstruction approach that no longer requires this knowledge. The originality of this work lies in using for reconstruction a group sparsity structure (called OSCAR) across channels that handles SNR inhomogeneities across receivers. We compare this reconstruction with other calibrationless approaches based on group-LASSO and its sparse variation as well as with the auto-calibrated method called 1-ESPIRiT. We demonstrate that OSCAR outper-forms its competitors and provides similar results to 1-ESPIRiT. This suggests that the sensitivity maps are no longer required to perform combined CS and parallel imaging reconstruction