Accelerated acquisition in MRI

MRI is a widely used neuroimaging technique used to probe brain tissues, their structure and provide diagnostic insights on the functional organization as well as the layout of brain vessels. However, MRI relies on an inherently slow imaging process. Reducing acquisition time has been a major challenge in high-resolution MRI and has been successfully addressed by Compressed Sensing (CS) theory. However, most of the Fourier encoding schemes under-sample existing k-space trajectories which unfortunately will never adequately encode all the information necessary. Recently, the Mind team has addressed this crucial issue by proposing the Spreading Projection Algorithm for Rapid K-space sampLING (SPARKLING) for 2D/3D non-Cartesian T2* and susceptibility weighted imaging (SWI) at 3 and 7 Tesla (T) 123, 124, 107. These advancements have interesting applications in cognitive and clinical neuroscience as we already have adapted this approach to address high-resolution functional and metabolic (Sodium 23Na) MR imaging at 7T – a very challenging feat  1. However, the original SPARKLING trajectories are prone to off-resonance effects due to susceptibility artifacts. Therefore, we have extended the original SPARKLING methodology and developed the MORE-SPARKLING (Minimized Off-Resonance Effects) approach to correct for these artifacts. The fondamental idea implemented in MORE-SPARKLING is to make different k-space trajectories more homogeneous in time, in the sense that samples supported by different trajectories that are close in k-space must be collected at approximately the same time point. This allows us to mitigate the issue of off-resonance effects (signal void, geometric distortions) without increasing the scan time, as MORE-SPARKLING trajectories have exactly the same duration as their SPARKLING ancestor. This approach has been published  2 and is illustrated in Fig. 1. A patent application has been filed by the CEA for MORE-SPARKLING.

Complementary to that, we have also extended SPARKLING in another direction, namely the way we sample the center of k-space and proposed the GoLF-SPARKLING version in the same paper  2. The core idea here is to reduce the over-sampling of the center of k-space and grid it to collect Cartesian data and make notably the estimation of sensitivity maps in multicoil acquisition easier. Similarly to MORE-SPARKLING, a patent application has been filed for GoLF-SPARKLING.

Additionally, we have shown that 3D-SPARKLING is a viable imaging technique and good alternative to Echo Planar Imaging for resting-state and task-based fMRI  4. This is illustrated in Fig. 2 during a retinotopic mapping experiment which consists in mapping the retina to the primary visual cortex. These results have been obtained at a 1mm isotropic resolution both for EPI and SPARKLING acquisitions.

Deep learning for MR image reconstruction and artifact correction

Although CS is used extensively, this approach suffers from a very slow image reconstruction process, which is detrimental to both patients and rapid diagnosis. To counteract this delay and improve image quality, as explained in Sec. 3.1 deep learning is used. In 2020 we secured the second spot in the 2020 brain fastMRI challenge (1.5 and 3T data)  139 with the XPDNet (Primal Dual Network where X plays the role of a magic card) deep learning architecture. Additionally, we assessed XPDNet’s transfer learning capacity on 7T NeuroSpin T2 images. However this DL reconstruction process was limited to Cartesian encoding, thus incompatible with our SPARKLING related technological push. In 2022, we went therefore further by proposing the NCPD-Net deep learning architecture for non-Cartesian imaging. NCPD-Net stands for Non-Cartesian Primal Dual Network and is able to handle both 2D and 3D non-Cartesian k-space data such as those collected with the full 3D SPARKLING encoding scheme  154. This progress allowed us to make a significant leap in image quality when implementing high resolution imaging while maintaining a high acceleration rate.

In 2023, we published novel significant results based on the original NC-PDNet archiecture. We actually combined with physics-driven model to speed up the correction of off-resonance effects induced by the inhomogeneities of the static magnetic field $B_0$  6. Fig. 3[left column] shows the signal void in the frontal region of the brain when not applying any correction. The CS correction yields a limited improvement when constraining its processing time to a little portion (actually 1/70) of the brute force correction shown in the top right column (Reference). Next, we show that the best correction of off-resonance artifacts is achieved by combining the NC-PDNet architecture (Network, 4th column in Fig. 3) with non Fourier encoding model in a 70-fold faster process compared to the reference correction (left column). In contrast, using a standard NC-PDNet architecture that is not physically informed by the degradation process causing these off-resonance artifacts leads to oversmoothed correction (cf. middle column in Fig. 3). Overall, this work has demonstrated how investigating into the combination of physics-informed deep learning architectures was instrumental in obtaining high image quality in clinically viable processing time.

MRI magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. In 2023, the MIND has made major contribution  9 to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel PROjection for Jointly lEarning non-Cartesian Trajectories while Optimizing Reconstructor (PROJeCTOR) trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92–0.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3–4 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes in Fig. 4, we show that data-driven joint learning-based PROJeCTOR trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM.

Large Scale Bayesian Network Resolution with Applications to Neuroimaging

Bayesian networks (BNs) have emerged as a powerful tool for modeling complex relationships among variables in neuroimaging data generatively. Their ability to capture causal and probabilistic dependencies makes them well-suited for representing the intricate and multifaceted nature of brain activity. However, the large scale of neuroimaging data presents a significant challenge for BNs. This data in a large database can scale to millions of random variables, if we consider 1,000 subjects with at least 32,000 measurements on the brain cortex per subject. As the number of variables increases, the complexity of the BN grows exponentially, making it computationally intractable to fit these models using existing generic algorithms. This computational bottleneck impedes the widespread application of BNs in neuroimaging research and hinders our ability to fully understand the intricate workings of the brain.

To address this problem we have porposed the PAVI method (Plate Amortized Variational Inference)  158 as a follow up of our previously proposed Automatic Dual Amortized Variational Inference (ADAVI)  159. These methods harness the symmetry of large neuroimaging models, specifically considering each cortical measurement and each subject as independent identically distributed realizations of the same random variables. In complement with stochastic optimization techniques, the PAVI algorithm is able to produce individualized parcellations of 1,000 of subjects at a time. Thus, we are now able to harness the descriptive and interpretable power of BNs to produce individualized cortical parcellations which we then test through the prediction of cognitive abilities.

Generalized parametric models for temporal point processes

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are illsuited for applications where latencies need to be estimated, such as in neuroscience. We developed an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ${\ell }_2$ gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach has been demonstrated through various numerical experiments. Finally, the method’s effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG), as reported in Fig. 6. This result was presented in Staerman et al.  34. These results are prerequisites to scale the resolution of bi-level optimization problems to larger applications such as the one in neurosciences.

Statistically Valid Variable Importance Assessment through Conditional Permutations

Variable importance assessment has become a crucial step in machine-learning applications when using complex learners, such as deep neural networks, on large-scale data. Removal-based importance assessment is currently the reference approach, particularly when statistical guarantees are sought to justify variable inclusion. It is often implemented with variable permutation schemes. On the flip side, these approaches risk misidentifying unimportant variables as important in the presence of correlations among covariates. Here we develop a systematic approach for studying Conditional Permutation Importance (CPI) that is model agnostic and computationally lean, as well as reusable benchmarks of state-of-the-art variable importance estimators. We show theoretically and empirically that CPI overcomes the limitations of standard permutation importance by providing accurate type-I error control. When used with a deep neural network, CPI consistently showed top accuracy across benchmarks. An experiment on real-world data analysis in a largescale medical dataset showed that CPI provides a more parsimonious selection of statistically significant variables. Our results suggest that CPI can be readily used as drop-in replacement for permutation-based methods.

False Discovery Proportion control for aggregated Knockoffs

Controlled variable selection is an important analytical step in various scientific fields, such as brain imaging or genomics. In these high-dimensional data settings, considering too many variables leads to poor models and high costs, hence the need for statistical guarantees on false positives. Knockoffs are a popular statistical tool for conditional variable selection in high dimension. However, they control for the expected proportion of false discoveries (FDR) and not their actual proportion (FDP). We present a new method, KOPI, that controls the proportion of false discoveries for Knockoff-based inference. The proposed method also relies on a new type of aggregation to address the undesirable randomness associated with classical Knockoff inference. We demonstrate FDP control and substantial power gains over existing Knockoff-based methods in various simulation settings and achieve good sensitivity/specificity tradeoffs on brain imaging and genomic data.