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Modern tractography algorithms such as anatomically-constrained tractography (ACT) are based on segmentation maps of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). These maps are generally estimated from a T1-weighted (T1w) image and then registered in diffusion weighted images (DWI) space. Registration of T1w to diffusion space and partial volume estimation are challenging and rarely voxel-perfect. Diffusion-based segmentation would, thus, potentially allow not to have higher quality anatomical priors injected in the tractography process. On the other hand, even if FA-based tractography is possible without T1 registration, the literature shows that this technique suffers from multiple issues such as holes in the tracking mask and a high proportion of generated broken and anatomically implausible streamlines. Therefore, there is an important need for a tissue segmentation algorithm that works directly in the native diffusion space. We propose DORIS, a DWI-based deep learning segmentation algorithm. DORIS outputs 10 different tissue classes including WM, GM, CSF, ventricles, and 6 other subcortical structures (putamen, pallidum, hippocampus, caudate, amygdala, and thalamus). DORIS was trained and validated on a wide range of subjects, including 1,000 individuals from 22 to 90 years old from clinical and research DWI acquisitions, from 5 public databases. In the absence of a “true” ground truth in diffusion space, DORIS used a silver standard strategy from Freesurfer output registered onto the DWI. This strategy is extensively evaluated and discussed in the current study. Segmentation maps provided by DORIS are quantitatively compared to Freesurfer and FSL-fast and the impacts on tractography are evaluated. Overall, we show that DORIS is fast, accurate, and reproducible and that DORIS-based tractograms produce bundles with a longer mean length and fewer anatomically implausible streamlines.

International audience; Understanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure–function mapping. Specifically, we revisit previously proposed structure–function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so–called glass ceiling on the performance of mappings based on eigenmodes.

Diffusion MRI (dMRI) has become an invaluable tool to assess the microstructural organization of brain tissue. Depending on the specific acquisition settings, the dMRI signal encodes specific properties of the underlying diffusion process. In the last two decades, several signal representations have been proposed to fit the dMRI signal and decode such properties. Most methods, however, are tested and developed on a limited amount of data, and their applicability to other acquisition schemes remains unknown. With this work, we aimed to shed light on the generalizability of existing dMRI signal representations to different diffusion encoding parameters and brain tissue types. To this end, we organized a community challenge - named MEMENTO, making available the same datasets for fair comparisons across algorithms and techniques. We considered two state-of-the-art diffusion datasets, including single-diffusion-encoding (SDE) spin-echo data from a human brain with over 3820 unique diffusion weightings (the MASSIVE dataset), and double (oscillating) diffusion encoding data (DDE/DODE) of a mouse brain including over 2520 unique data points. A subset of the data sampled in 5 different voxels was openly distributed, and the challenge participants were asked to predict the remaining part of the data. After one year, eight participant teams submitted a total of 80 signal fits. For each submission, we evaluated the mean squared error, the variance of the prediction error and the Bayesian information criteria. The received submissions predicted either multi-shell SDE data (37%) or DODE data (22%), followed by cartesian SDE data (19%) and DDE (18%). Most submissions predicted the signals measured with SDE remarkably well, with the exception of low and very strong diffusion weightings. The prediction of DDE and DODE data seemed more challenging, likely because none of the submissions explicitly accounted for diffusion time and frequency. Next to the choice of the model, decisions on fit procedure and hyperparameters play a major role in the prediction performance, highlighting the importance of optimizing and reporting such choices. This work is a community effort to highlight strength and limitations of the field at representing dMRI acquired with trending encoding schemes, gaining insights into how different models generalize to different tissue types and fiber configurations over a large range of diffusion encodings. Funding Agencies|European Research Council (ERC) under the European UnionEuropean Research Council (ERC) [694665]; French government, through the 3IA Cote DAzur Investments in the Future project [ANR-19-P3IA-0002]; EPSRCUK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) [EP/N018702/1, MR/T020296/1, ISLRA-2009]; European Space AgencyEuropean Space AgencyEuropean Commission; Belgian Science Policy Office-ProdexBelgian Federal Science Policy Office; Research Foundation Flanders (FWO Vlaanderen)FWO [12M3119N, G0D7216N]; Wellcome Trust Investigator AwardWellcome Trust [096646/Z/11/Z]; Wellcome Trust Strategic AwardWellcome Trust [104943/Z/14/Z]; Polish National Agency for Academic ExchangePolish National Agency for Academic Exchange (NAWA) [PN/BEK/2019/1/00421]; Ministry of Science and Higher Education (Poland)Ministry of Science and Higher Education, Poland [692/STYP/13/2018]; AGH Science and Technology, Poland [16.16.120.773]; Linkoping University (LiU) Center for Industrial Information Technology (CENIIT); LiU Cancer [VINNOVA/ITEA3 17021 IMPACT]; Swedish Foundation for Strategic ResearchSwedish Foundation for Strategic Research [RMX18-0056]; "la Caixa" FoundationLa Caixa Foundation [100010434]; European UnionEuropean Commission [847648, LCF/BQ/PI20/11760029]; Ministerio de Ciencia e Innovacion" of SpainSpanish Government [RTI2018-094569-B-I00]; National Institute for Biomedical Imaging [5R01EB027585-02]

International audience; In this work, we evaluate the performance of three different diffusion MRI (dMRI) signal representations in the estimation of brain microstructural indices in combination with fully connected neural networks (FC-NN). The considered signal representations are the raw samples on the sphere, the spherical harmonics coefficients, and a novel set of recently presented rotation invariant features (RIF). To train FC-NN and validate our results, we create a synthetic dMRI dataset that mimics the signal properties of brain tissues and provides us a real ground truth for our experiments. We test 8 different network configurations changing both the depth of the networks and the number of perceptrons. Results show that our new RIF are able to estimate the brain microstructural indices more precisely than the diffusion signal samples or its spherical harmonics coefficients in all the tested network configurations. Finally, we apply the best-performing FC-NN in-vivo on a healthy human brain.

Diffusion MRI (dMRI) has become an invaluable tool to assess the microstructural organization of brain tissue. Depending on the specific acquisition settings, the dMRI signal encodes specific properties of the underlying diffusion process. In the last two decades, several signal representations have been proposed to fit the dMRI signal and decode such properties. Most methods, however, are tested and developed on a limited amount of data, and their applicability to other acquisition schemes remains unknown. With this work, we aimed to shed light on the generalizability of existing dMRI signal representations to different diffusion encoding parameters and brain tissue types. To this end, we organized a community challenge - named MEMENTO, making available the same datasets for fair comparisons across algorithms and techniques. We considered two state-of-the-art diffusion datasets, including single-diffusion-encoding (SDE) spin-echo data from a human brain with over 3820 unique diffusion weightings (the MASSIVE dataset), and double (oscillating) diffusion encoding data (DDE/DODE) of a mouse brain including over 2520 unique data points. A subset of the data sampled in 5 different voxels was openly distributed, and the challenge participants were asked to predict the remaining part of the data. After one year, eight participant teams submitted a total of 80 signal fits. For each submission, we evaluated the mean squared error, the variance of the prediction error and the Bayesian information criteria. Most predictions predicted either multi-shell SDE data (37%) or DODE data (22%), followed by cartesian SDE data (19%) and DDE (18%). Most submissions predicted the signals measured with SDE remarkably well, with the exception of low and very strong diffusion weightings. The prediction of DDE and DODE data seemed more challenging, likely because none of the submissions explicitly accounted for diffusion time and frequency. Next to the choice of the model, decisions on fit procedure and hyperparameters play a major role in the prediction performance, highlighting the importance of optimizing and reporting such choices. This work is a community effort to highlight strength and limitations of the field at representing dMRI acquired with trending encoding schemes, gaining insights into how different models generalize to different tissue types and fiber configurations over a large range of diffusion encodings.

State-of-the-art multi-compartment microstructural models of diffusion MRI (dMRI) in the human brain have limited capability to model multiple tissues at the same time. In particular, the available techniques that allow this multi-tissue modelling are based on multi-TE acquisitions. In this work we propose a novel multi-tissue formulation of classical multi-compartment models that relies on more common single-TE acquisitions and can be employed in the analysis of previously acquired datasets. We show how modelling multiple tissues provides a new interpretation of the concepts of signal fraction and volume fraction in the context of multi-compartment modelling. The software that allows to inspect single-TE diffusion MRI data with multi-tissue multi-compartment models is included in the publicly available Dmipy Python package.

International audience; The growing availability of novel interpretation techniques opened the way to the application of deep learning models in the clinical field, including neuroimaging, where their use is still largely underexploited. In this framework, we focus the stratification of Multiple Sclerosis (MS) patients in the Primary Progressive versus the Relapsing-Remitting state of the disease using a 3D Convolutional Neural Network trained on structural MRI data. Within this task, the application of Layer-wise Relevance Propagation visualization allowed detecting the voxels of the input data mostly involved in the classification decision, potentially bringing to light brain regions which might reveal disease state.

International audience; Objective.The mechanisms driving multiple sclerosis (MS) are still largely unknown, calling for new methods allowing to detect and characterize tissue degeneration since the early stages of the disease. Our aim is to decrypt the microstructural signatures of the Primary Progressive versus the Relapsing-Remitting state of disease based on diffusion and structural magnetic resonance imaging data.Approach.A selection of microstructural descriptors, based on the 3D-Simple Harmonics Oscillator Based Reconstruction and Estimation and the set of new algebraically independent Rotation Invariant spherical harmonics Features, was considered and used to feed convolutional neural networks (CNNs) models. Classical measures derived from diffusion tensor imaging, that are fractional anisotropy and mean diffusivity, were used as benchmark for diffusion MRI (dMRI). Finally, T1-weighted images were also considered for the sake of comparison with the state-of-the-art. A CNN model was fit to each feature map and layerwise relevance propagation (LRP) heatmaps were generated for each model, target class and subject in the test set. Average heatmaps were calculated across correctly classified patients and size-corrected metrics were derived on a set of regions of interest to assess the LRP contrast between the two classes.Main results.Our results demonstrated that dMRI features extracted in grey matter tissues can help in disambiguating primary progressive multiple sclerosis from relapsing-remitting multiple sclerosis patients and, moreover, that LRP heatmaps highlight areas of high relevance which relate well with what is known from literature for MS disease.Significance.Within a patient stratification task, LRP allows detecting the input voxels that mostly contribute to the classification of the patients in either of the two classes for each feature, potentially bringing to light hidden data properties which might reveal peculiar disease-state factors.

International audience; This paper highlights a systematic bias in white matter tissue microstructure modelling via diffusion MRI that is due to the common, yet inaccurate, assumption that all brain tissues have a similar T2 response. We show that the concept of "signal fraction" is more appropriate to describe what have always been referred to as "volume fraction". This dichotomy is described from the theoretical point of view by analysing the mathematical formulation of the diffusion MRI signal. We propose a generalized multi tissue modelling framework that allows to compute the actual volume fractions. The Dmipy implementation of this framework is then used to verify the presence of this bias in four classical tissue microstructure models computed on two subjects from the Human Connectome Project database. The proposed paradigm shift exposes the research field of brain tissue microstructure estimation to the necessity of a systematic review of the results obtained in the past that takes into account the difference between the concept of volume fraction and tissue fraction.

In this work, we present a novel computational framework for analytically generating a complete set of algebraically independent Rotation Invariant Features (RIF) given the Laplace-series expansion of a spherical function. Our computational framework provides a closed-form solution for these new invariants, which are the natural expansion of the well known spherical mean, power-spectrum and bispectrum invariants. We highlight the maximal number of algebraically independent invariants which can be obtained from a truncated Spherical Harmonic (SH) representation of a spherical function and show that most of these new invariants can be linked to statistical and geometrical measures of spherical functions, such as the mean, the variance and the volume of the spherical signal. Moreover, we demonstrate their application to dMRI signal modeling including the Apparent Diffusion Coefficient (ADC), the diffusion signal and the fiber Orientation Distribution Function (fODF). In addition, using both synthetic and real data, we test the ability of our invariants to estimate brain tissue microstructure in healthy subjects and show that our framework provides more flexibility and open up new opportunities for innovative development in the domain of microstructure recovery from diffusion MRI.

The development of noninvasive techniques to image the human brain has enabled the demonstration of structural plasticity in response to motor learning. In the last years evidence has emerged on the potential of some measures derived from diffusion Magnetic Resonance Imaging (DMRI) as numerical biomarkers of tissue changes in regions involved in the motor network. In these works, the descriptors were extensively analysed in contralateral white matter (WM) along both single connections and networks relying on tract-based analyses and statistical evaluation. Though, their ability to detect changes in gray matter (GM) has been scarcely investigated. This work aims at the assessment of propagator-based microstructural indices in capturing GM changes and the relation of such changes to functional recovery at six months from the injury focusing on the Diffusion Tensor Imaging (DTI) and the three dimensional Simple Harmonics Oscillator based Reconstruction and Estimation (3D-SHORE) models.

International audience; Characterizing the connection between brain structure and brain function is essential for understanding how behaviour emerges from the underlying anatomy. A number of studies have shown that the network structure of the white matter shapes functional connectivity. Therefore, it should be possible to predict, at least partially, functional connectivity given the structural network. Many structure-function mappings have been proposed in the literature, including several direct mappings between the structural and functional connectivity matrices. However, the current literature is fragmented and does not provide a uniform treatment of current methods based on eigendecompositions. In particular, existing methods have never been compared to each other and their relationship explicitly derived in the context of brain structure-function mapping. In this work, we propose a unified computational framework that generalizes recently proposed structure-function mappings based on eigenmodes. Using this unified framework, we highlight the link between existing models and show how they can be obtained by specific choices of the parameters of our framework. By applying our framework to 50 subjects of the Human Connectome Project, we reproduce 6 recently published results, devise two new models and provide a direct comparison between all mappings. Finally, we show that a glass ceiling on the performance of mappings based on eigenmodes seems to be reached and conclude with possible approaches to break this performance limit.

Diffusion weighted magnetic resonance signals convey information about tissue microstructure and cytoarchitecture. In the last years, many models have been proposed for recovering the diffusion signal and extracting information to constitute new families of numerical indices. Two main categories of reconstruction models can be identified in diffusion magnetic resonance imaging (DMRI): ensemble average propagator (EAP) models and compartmental models. From both, descriptors can be derived for elucidating the underlying microstructural architecture. While compartmental models indices directly quantify the fraction of different cell compartments in each voxel, EAP-derived indices are only a derivative measure and the effect of the different microstructural configurations on the indices is still unclear. In this paper, we analyze three EAP indices calculated using the 3D Simple Harmonic Oscillator based Reconstruction and Estimation (3D-SHORE) model and estimate their changes with respect to the principal microstructural configurations. We take advantage of the state of the art simulations to quantify the variations of the indices with the simulation parameters. Analysis of in-vivo data correlates the EAP indices with the microstructural parameters obtained from the Neurite Orientation Dispersion and Density Imaging (NODDI) model as a pseudo ground truth for brain data. Results show that the EAP derived indices convey information on the tissue microstructure and that their combined values directly reflect the configuration of the different compartments in each voxel.

International audience; Rotation invariant features are an indispensable tool for characterizing diffusion Magnetic Resonance Imaging (MRI) and in particular for brain tissue microstructure estimation. In this work, we propose a new mathematical framework for efficiently calculating a complete set of such invariants from any spherical function. Specifically, our method is based on the spherical harmonics series expansion of a given function of any order and can be applied directly to the resulting coefficients by performing a simple integral operation analytically. This enable us to derive a general closed-form equation for the invariants. We test our invariants on the diffusion MRI fiber orientation distribution function obtained from the diffusion signal both in-vivo and in synthetic data. Results show how it is possible to use these invariants for characterizing the white matter using a small but complete set of features.

International audience

Recent tract-based analyses provided evidence for the exploitability of 3D-SHORE microstructural descriptors derived from diffusion MRI (dMRI) in revealing white matter (WM) plasticity. In this work, we focused on the main open issues left: (1) the comparative analysis with respect to classical tensor-derived indices, i.e., Fractional Anisotropy (FA) and Mean Diffusivity (MD); and (2) the ability to detect plasticity processes in gray matter (GM). Although signal modeling in GM is still largely unexplored, we investigated their sensibility to stroke-induced microstructural modifications occurring in the contralateral hemisphere. A more complete picture could provide hints for investigating the interplay of GM and WM modulations. Ten stroke patients and ten age/gender-matched healthy controls were enrolled in the study and underwent diffusion spectrum imaging (DSI). Acquisitions at three and two time points (tp) were performed on patients and controls, respectively. For all subjects and acquisitions, FA and MD were computed along with 3D-SHORE-based indices [Generalized Fractional Anisotropy (GFA), Propagator Anisotropy (PA), Return To the Axis Probability (RTAP), Return To the Plane Probability (RTPP), and Mean Square Displacement (MSD)]. Tract-based analysis involving the cortical, subcortical and transcallosal motor networks and region-based analysis in GM were successively performed, focusing on the contralateral hemisphere to the stroke. Reproducibility of all the indices on both WM and GM was quantitatively proved on controls. For tract-based, longitudinal group analyses revealed the highest significant differences across the subcortical and transcallosal networks for all the indices. The optimal regression model for predicting the clinical motor outcome at tp3 included GFA, PA, RTPP, and MSD in the subcortical network in combination with the main clinical information at baseline. Region-based analysis in the contralateral GM highlighted the ability of anisotropy indices in discriminating between groups mainly at tp1, while diffusivity indices appeared to be altered at tp2. 3D-SHORE indices proved to be suitable in probing plasticity in both WM and GM, further confirming their viability as a novel family of biomarkers in ischemic stroke in WM and revealing their potential exploitability in GM. Their combination with tensor-derived indices can provide more detailed insights of the different tissue modulations related to stroke pathology.

Diffusion Magnetic Resonance Imaging (DMRI) has been widely used to characterize the principal directions of white matter fibers, also known as fiber Orientation Distribution Function (fODF), and axonal density in brain tissues.

To which extent connectivity measures are able to characterize subjective features? The pipeline leading from the signal acquisition to the connectivity matrix allows numerous degrees of freedom each having an impact on the final result. In this paper, we investigated the sensitivity and specificity of the connectivity models within a machine learning framework through the assessment of the detectability of repeated measures of the same subject versus other subjects. Two fiber Orientation Distribution Function (fODF) reconstruction methods, one of which firstly proposed in this paper, three tractography algorithms and four connectivity features were considered and performance was expressed in terms of Area Under the Curve of the test-retest recognition task. Results suggest that there is a trade-off between the selectivity of the fODF reconstruction methods and the conservativeness of the fiber tracking algorithms across all microstructural indices . The best solution was provided by using an high angular resolution fODF estimation method and the most restrictive deterministic tractography algorithm.

In this paper we present a new methodology, based on genetic algorithms and multiple linear regression, for discovering regulation mechanisms responsible for observed time series in biological networks. The modeling framework employed is called Metabolic P systems; they are deterministic and time-discrete dynamical systems proposed as an effective alternative to ordinary differential equations for modeling biochemical systems. Our methodology is here successfully applied to the mitotic oscillator in early amphibian embryos. Starting from the time series of substances involved in this system, we are able to reconstruct an MP system reproducing the observed dynamics, where the regulatory components were discovered by our evolutionary methodology. In particular, genetic algorithms are used as a variable selection technique to identify the best representation of any regulation function in terms of some given primitive functions.

Diffusion imaging with confinement tensor (DICT) is a new model that employs a tensorial representation of the geometry confining the movements of water molecules. The model differs substantially from the commonly employed diffusion tensor imaging (DTI) technique even at small diffusion weightings when the dependence of the signal on the timing parameters of the pulse sequence is concerned. In this work, we assess the accuracy of the two models on a data set acquired from an excised monkey brain. The publicly available data set features differing values for diffusion pulse duration and separation. Our results indicate that the normalized mean squared error is reduced in an overwhelming portion of the voxels when the DICT model is employed, suggesting the superiority of DICT in characterizing the temporal dependence of the diffusion process in nervous tissue.

New analytical reconstruction techniques of diffusion weighted signal have been proposed. A previous work evidenced the exploitability of some indices derived from the simple harmonic oscillator-based reconstruction and estimation (3D-SHORE) model as numerical biomarkers of neural plasticity after stroke. Here, the analysis is extended to two additional indices: return to the plane/origin (RTPP/RTOP) probabilities. Moreover, several motor networks were introduced and the results were analyzed at different time scales. Ten patients underwent three diffusion spectrum imaging (DSI) scans [1 week (tp1), 1 month (tp2) and 6 months (tp3) after stroke]. Ten matched controls underwent two DSI scans 1 month apart. 3D-SHORE was used for reconstructing the signal and the microstructural indices were derived. Tract-based analysis was performed along motor cortical, subcortical and transcallosal networks in the contralesional area. The optimal intra-class correlation coefficient (ICC) was obtained in the subcortical loop for propagator anisotropy (ICC $$=$$ 0.96), followed by generalized fractional anisotropy (ICC $$=$$ 0.94). The new indices reached the highest stability in the transcallosal network and performed well in the cortical and subcortical networks with the exception of RTOP in the cortical loop (ICC $$=$$ 0.59). They allowed discriminating patients from controls at the majority of the timescales. Finally, the regression model using indices calculated along the subcortical loop at tp1 resulted in the best prediction of clinical outcome. The whole set of microstructural indices provide measurements featuring high precision. The new indices allow discriminating patients from controls in all networks, except for RTPP in the cortical loop. Moreover, the 3D-SHORE indices in subcortical connections constitute a good regression model for predicting the clinical outcome at 6 months, supporting their suitability as numerical biomarkers for neuronal plasticity after stroke.

Diffusion Magnetic Resonance Imaging (dMRI) is able to detect the properties of tissue microstructure underneath the voxel through the imaging of water molecules diffusion. Many reconstruction methods have been proposed to calculate the Orientation Distribution Function (ODF) from the diffusion signal in order to distinguish between coherent fiber bundles and crossing fibers. The diffusion signal was also used to infer other microstructural information such as the axon diameter, but most often in areas with coherent fiber direction such as the corpus callosum. In this work, we developed a reconstruction model called Multi-Tensor MAPMRI (MT-MAPMRI) that is an extension of the MAPMRI model which improves the performance of MAPMRI for crossing fibers. In particular, it provides (a) enhanced signal fitting; (b) improved ODFs; (c) a more accurate diameter estimation. The model was tested and validated on both simulated and in-vivo data.