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Diffusion imaging is a critical component in the pursuit of developing a better understanding of the human brain. Recent technical advances promise enabling the advancement in the quality of data that can be obtained. In this review the context for different approaches relative to the Human Connectome Project are compared. Significant new gains are anticipated from the use of high-performance head gradients. These gains can be particularly large when the high-performance gradients are employed together with ultrahigh magnetic fields. Transmit array designs are critical in realizing high accelerations in diffusion-weighted (d)MRI acquisitions, while maintaining large field of view (FOV) coverage, and several techniques for optimal signal-encoding are now available. Reconstruction and processing pipelines that precisely disentangle the acquired neuroanatomical information are established and provide the foundation for the application of deep learning in the advancement of dMRI for complex tissues. Level of Evidence: 3 Technical Efficacy Stage: Stage 3.

Purpose In this study, we sought to develop a self-navigation strategy for improving the reconstruction of diffusion weighted 3D multishot echo planar imaging (EPI). We propose a method for extracting the phase correction information from the acquisition itself, eliminating the need for a 2D navigator, further accelerating the acquisition. Methods In-vivo acquisitions at 3T with 0.9 mm and 1.5 mm isotropic resolutions were used to evaluate the performance of the self-navigation strategy. Sensitivity to motion was tested using a large difference in pitch position of the head. Using a multishell diffusion weighted acquisition, tractography results were obtained at (0.9 mm)3 to validate the quality with conventional acquisition. Results The use of 3D multislab EPI with self-navigation enables 3D diffusion-weighted spin echo EPI acquisitions that have the same efficiency as 2D single-shot acquisition. For matched acquisition time the image signal-to-noise ratio (SNR) between 3D and 2D acquisition is shown to be comparable for whole-brain coverage with (1.5 mm)3 resolution and for (0.9 mm)3 resolution the 3D acquisition has higher SNR than what can be obtained with 2D acquisitions using current state-of-art multiband techniques. The self-navigation technique was shown to be stable under inter-volume motion. In tractography analysis, the higher resolution afforded by our technique enabled clear delineation of the tapetum and posterior corona radiata. Conclusion The proposed self-navigation approach utilized a self-consistent phase in 3D diffusion weighted acquisitions. Its efficiency and stability were demonstrated for a plurality of common acquisitions. The proposed self-navigation approach allows for faster acquisition of 3D multishot EPI desirable for large field of view and/or higher resolution.

PURPOSE: To develop a fast and automated volume-of-interest (VOI) prescription pipeline (AutoVOI) for single-voxel MR spectroscopy (MRS) that removes the need for manual VOI placement, allows flexible VOI planning in any brain region, and enables high inter- and intra-subject consistency of VOI prescription. METHODS: AutoVOI was designed to transfer pre-defined VOIs from an atlas to the 3D anatomical data of the subject during the scan. The AutoVOI pipeline was optimized for consistency in VOI placement (precision), enhanced coverage of the targeted tissue (accuracy) and fast computation speed. The tool was evaluated against manual VOI placement using existing T(1)-weighted datasets and corresponding VOI prescriptions. Finally, it was implemented on two scanner platforms to acquire MRS data from clinically-relevant VOIs that span the cerebrum, cerebellum and the brainstem. RESULTS: The AutoVOI pipeline includes skull stripping, non-linear registration of the atlas to the subject’s brain, and computation of the VOI coordinates and angulations using a minimum oriented bounding box algorithm. When compared against manual prescription, AutoVOI showed higher intra- and inter-subject spatial consistency, as quantified by generalized Dice coefficients (GDC), lower intra- and inter-subject variability in tissue composition (gray matter, white matter and cerebrospinal fluid) and higher or equal accuracy, as quantified by GDC of prescribed VOI with targeted tissues. High quality spectra were obtained on Siemens and Philips 3T systems from 6 automatically prescribed VOIs by the tool. CONCLUSION: Robust automatic VOI prescription is feasible and can help facilitate clinical adoption of MRS by avoiding operator dependence of manual selection.

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates.

International audience; Computational methods are crucial for the analysis of diffusion magnetic resonance imaging (MRI) of the brain. Computational diffusion MRI can provide rich information at many size scales, including local microstructure measures such as diffusion anisotropies or apparent axon diameters, whole‐brain connectivity information that describes the brain's wiring diagram and population‐based studies in health and disease. Many of the diffusion MRI analyses performed today were not possible five, ten or twenty years ago, due to the requirements for large amounts of computer memory or processor time. In addition, mathematical frameworks had to be developed or adapted from other fields to create new ways to analyze diffusion MRI data. The purpose of this review is to highlight recent computational and statistical advances in diffusion MRI and to put these advances into context by comparison with the more traditional computational methods that are in popular clinical and scientific use. We aim to provide a high‐level overview of interest to diffusion MRI researchers, with a more in‐depth treatment to illustrate selected computational advances.

Adolescence is a period of rapid brain maturation and a critical period for the onset of Major Depressive Disorder (MDD) that usually leads to serious outcomes such as suicide. Although changes in anatomical connectivity in MDD have been reported, changes in network topology for MDD remain unclear. Additionally, whether the changes are the same for adolescent MDD and adult MDD remains unclear as well. This paper explores anatomical features including: a) anatomical connectivity defined by diffusion tensor imaging measurements between a pair of brain regions, and b) topological measurements from anatomical networks, and apply machine learning approaches to identify responsive biomarkers distinguishing MDD patients from healthy subjects. In addition to statistical tests, univariate classifiers are designed to evaluate the discriminating power of features. Furthermore, multivariate classifiers are trained for distinguishing healthy subjects from MDD patients. The best classifier achieves an accuracy of 76.56%, 81.08% sensitivity, 70.37% specificity and 78.95% precision for 64 subjects (37 MDD and 27 matched healthy control). The selected features include: 1) betweenness centrality of the right lingual gyrus of the ADC network at 12% sparsity, 2) participation coefficient of the right pars opercularis of the AD network at 16% sparsity, 3) participation coefficient of the left insular cortex of the MD network at 21% sparsity, and 4) participation coefficient of the right lateral orbitofrontal cortex in the ADC network at 10% sparsity. These features reflect changes in the topological structure of the brain anatomical network in MDD.

Adolescent Major Depressive Disorder (MDD) is a common and serious mental illness that could lead to tragic outcomes including chronic adult disability and suicide. In this paper, we explore anatomical features and apply machine learning approaches to identify responsive biomarkers distinguishing MDD patients from healthy subjects. The features of interest include metrics in two categories: a) anatomical connectivity defined by diffusion tensor imaging measurements between a pair of brain regions, and b) topological measurements from anatomical networks. A combination of p-value based filtering and minimum redundancy maximum relevance method is performed to select features for optimal classification accuracy. A leave-one-out cross-validation method is used for the classification performance evaluation. The proposed methodology achieves an improved accuracy of 78%, 90.39% sensitivity, and 79.66% precision for 79 subjects. The most distinguishing features are the betweenness centrality of the right lingual gyrus of the ADC network at 12% sparsity, the participation coefficient of the right lateral occipital sulcus of the ADC network at 22% sparsity, the participation coefficient of the right pars opercularis of the AD network at 16% sparsity, and the participation coefficient of the right lateral orbitofrontal cortex in the ADC network at 10% sparsity. Those network measures reflect the change of connectivity between the regions and their associated anatomical subnetworks.

Identification of the treatment-related responders for adolescent Major Depressive Disorder (MDD) is urgently needed to develop effective treatments. In this paper, machine learning based classifiers are used to reveal anatomical features as responders for distinguishing MDD patients who have received treatment from those who never received any treatment. The features are drawn from two sets of measurements: 1) anatomical connectivity defined by diffusion tensor imaging measurements between a pair of brain regions, and 2) topological measurements from anatomical networks. Feature selection was performed based on p-value and minimum redundancy maximum relevance (mRMR) method to achieve improved classification accuracy. The classification performance is evaluated with a leave-one-out cross-validation method using 37 treated and 15 untreated subjects. The proposed methodology achieves 73% accuracy, 100% specificity, and 100% precision for 52 subjects. The most distinguishing features are the strength of the right hippocampus of the mean diffusivity (MD) network at 18% density and of the track-count (TR) network, the participation coefficient of the left middle temporal gyrus of the radial diffusivity (RD) network at 20% density, the axial diffusivity (AD) connectivity between right middle temporal gyrus and right supramarginal gyrus, the betweenness centrality of the right hippocampus of the TR network at 11% density, the apparent diffusion coefficient (ADC) connectivity between the left pars opercularis and the left rostral anterior cingulate cortex, the clustering coefficient of the middle anterior corpus callosum of the TR network at 11% density, and the AD connectivity between the left pars opercularis and the left rostral anterior cingulate cortex.

Mapping structural connectivity in healthy adults for the Human Connectome Project (HCP) benefits from high quality, high resolution, multiband (MB)-accelerated whole brain diffusion MRI (dMRI). Acquiring such data at ultrahigh fields (7 T and above) can improve intrinsic signal-to-noise ratio (SNR), but suffers from shorter T2 and T2* relaxation times, increased B1+ inhomogeneity (resulting in signal loss in cerebellar and temporal lobe regions), and increased power deposition (i.e. Specific Absorption Rate (SAR)), thereby limiting our ability to reduce the repetition time (TR). Here, we present recent developments and optimizations in 7 T image acquisitions for the HCP that allow us to efficiently obtain high-quality, high-resolution whole brain in-vivo dMRI data at 7 T. These data show spatial details typically seen only in ex-vivo studies and complement already very high quality 3 T HCP data in the same subjects. The advances are the result of intensive pilot studies aimed at mitigating the limitations of dMRI at 7 T. The data quality and methods described here are representative of the datasets that will be made freely available to the community in 2015.

We propose a sparse Bayesian learning algorithm for improved estimation of white matter fiber parameters from compressed (under-sampled q-space) multi-shell diffusion MRI data. The multi-shell data is represented in a dictionary form using a non-monoexponential decay model of diffusion, based on continuous gamma distribution of diffusivities. The fiber volume fractions with predefined orientations, which are the unknown parameters, form the dictionary weights. These unknown parameters are estimated with a linear un-mixing framework, using a sparse Bayesian learning algorithm. A localized learning of hyperparameters at each voxel and for each possible fiber orientations improves the parameter estimation. Our experiments using synthetic data from the ISBI 2012 HARDI reconstruction challenge and in-vivo data from the Human Connectome Project demonstrate the improvements.

Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies., The brain can often continue to function despite lesions in many areas, but damage to particular locations may have serious effects. Here, the authors use the concept of Ollivier-Ricci curvature to investigate the robustness of brain networks.

Purpose Diffusion MRI provides important information about the brain white matter structures and has opened new avenues for neuroscience and translational research. However, acquisition time needed for advanced applications can still be a challenge in clinical settings. There is consequently a need to accelerate diffusion MRI acquisitions. Methods A multi-task Bayesian compressive sensing (MT-BCS) framework is proposed to directly estimate the constant solid angle orientation distribution function (CSA-ODF) from under-sampled (i.e., accelerated image acquisition) multi-shell high angular resolution diffusion imaging (HARDI) datasets, and accurately recover HARDI data at higher resolution in q-space. The proposed MT-BCS approach exploits the spatial redundancy of the data by modeling the statistical relationships within groups (clusters) of diffusion signal. This framework also provides uncertainty estimates of the computed CSA-ODF and diffusion signal, directly computed from the compressive measurements. Experiments validating the proposed framework are performed using realistic multi-shell synthetic images and in vivo multi-shell high angular resolution HARDI datasets. Results Results indicate a practical reduction in the number of required diffusion volumes (q-space samples) by at least a factor of four to estimate the CSA-ODF from multi-shell data. Conclusion This work presents, for the first time, a multi-task Bayesian compressive sensing approach to simultaneously estimate the full posterior of the CSA-ODF and diffusion-weighted volumes from multi-shell HARDI acquisitions. It demonstrates improvement of the quality of acquired datasets by means of CS de-noising, and accurate estimation of the CSA-ODF, as well as enables a reduction in the acquisition time by a factor of two to four, especially when “staggered” q-space sampling schemes are used. The proposed MT-BCS framework can naturally be combined with parallel MR imaging to further accelerate HARDI acquisitions. Magn Reson Med 72:1471–1485, 2014. © 2013 Wiley Periodicals, Inc.

Purpose: To examine the effects of the reconstruction algorithm of magnitude images from multi-channel diffusion MRI on fibre orientation estimation. Theory and Methods: It is well established that the method used to combine signals from different coil elements in multi-channel MRI can have an impact on the properties of the reconstructed magnitude image. Utilising a root-sum-of-squares (RSoS) approach results in a magnitude signal that follows an effective non-central-distribution. As a result, the noise floor, the minimum measurable in the absence of any true signal, is elevated. This is particularly relevant for diffusion-weighted MRI, where the signal attenuation is of interest. Results: In this study, we illustrate problems that such image reconstruction characteristics may cause in the estimation of fibre orientations, both for model-based and model-free approaches, when modern 32-channel coils are employed. We further propose an alternative image reconstruction method that is based on sensitivity encoding (SENSE) and preserves the Rician nature of the single-channel, magnitude MR signal. We show that for the same k-space data, RSoS can cause excessive overfitting and reduced precision in orientation estimation compared to the SENSE-based approach. Conclusion: These results highlight the importance of choosing the appropriate image reconstruction method for tractography studies that use multi-channel receiver coils for diffusion MRI acquisition.

The acquisition of high angular resolution diffusion MRI is particularly long and subject motion can become an issue. The orientation distribution function (ODF) can be reconstructed online incrementally from diffusion-weighted MRI with a Kalman filtering framework. This online reconstruction provides real-time feedback throughout the acquisition process. In this article, the Kalman filter is first adapted to the reconstruction of the ODF in constant solid angle. Then, a method called STAR (STatistical Analysis of Residuals) is presented and applied to the online detection of motion in high angular resolution diffusion images. Compared to existing techniques, this method is image based and is built on top of a Kalman filter. Therefore, it introduces no additional scan time and does not require additional hardware. The performance of STAR is tested on simulated and real data and compared to the classical generalized likelihood ratio test. Successful detection of small motion is reported (rotation under 2°) with no delay and robustness to noise., National Institutes of Health (U.S.) (NIH grant Grant P41 RR008079), National Institutes of Health (U.S.) (NIH grant P41 EB015894), National Institutes of Health (U.S.) (NIH grant P30 NS057091), National Institutes of Health (U.S.) (Human Connectome Project U54 MH091657), United States. Air Force Office of Scientific Research (NSSEFF), National Science Foundation (U.S.), United States. Army Research Office, United States. Defense Advanced Research Projects Agency, United States. National Geospatial-Intelligence Agency, France. Agence nationale de la recherche (ANR NucleiPark), Institut national de recherche en informatique et en automatique (France), National Institutes of Health (U.S.) (Human Connectome Project, Grant R01 EB008432)

Hardware constraints, scanning time limitations, patient movement, and signal-to-noise ratio (SNR) considerations, restrict the slice-selection and the in-plane resolutions of MRI differently, generally resulting in anisotropic voxels. This nonuniform sampling can be problematic, especially in image segmentation and clinical examination. To alleviate this, the acquisition is divided into (two or) three separate scans, with higher in-plane resolutions and thick slices, yet orthogonal slice-selection directions. In this work, a noniterative wavelet-based approach for combining the three orthogonal scans is adopted, and its advantages compared with other existing methods, such as Fourier techniques, are discussed, including the consideration of the actual pulse response of the MRI scanner, and its lower computational complexity. Experimental results are shown on simulated and real 7 T MRI data.

High angular resolution diffusion imaging (HARDI) has become an important technique for imaging complex oriented structures in the brain and other anatomical tissues. This has motivated the recent development of several methods for computing the orientation probability density function (PDF) at each voxel. However, much less work has been done on developing techniques for filtering, interpolation, averaging and principal geodesic analysis of orientation PDF fields. In this paper, we present a Riemannian framework for performing such operations. The proposed framework does not require that the orientation PDFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a nonparametric representation of the orientation PDF. We exploit the fact that under the square-root re-parameterization, the space of orientation PDFs forms a Riemannian manifold: the positive orthant of the unit Hilbert sphere. We show that various orientation PDF processing operations, such as filtering, interpolation, averaging and principal geodesic analysis, may be posed as optimization problems on the Hilbert sphere, and can be solved using Riemannian gradient descent. We illustrate these concepts with numerous experiments on synthetic, phantom and real datasets. We show their application to studying left/right brain asymmetries.

Estimating brain wiring patterns is critical to better understand the brain organization and function. Anatomical brain connectivity models axonal pathways, while the functional brain connectivity characterizes the statistical dependencies and correlation between the activities of various brain regions. The synchronization of brain activity can be inferred through the variation of blood-oxygen-level dependent (BOLD) signal from functional MRI (fMRI) and the neural connections can be estimated using tractography from diffusion MRI (dMRI). Functional connections between brain regions are supported by anatomical connections, and the synchronization of brain activities arises through sharing of information in the form of electro-chemical signals on axon pathways. Jointly modeling fMRI and dMRI data may improve the accuracy in constructing anatomical connectivity as well as functional connectivity. Such an approach may lead to novel multimodal biomarkers potentially able to better capture functional and anatomical connectivity variations. We present a novel brain network model which jointly models the dMRI and fMRI data to improve the anatomical connectivity estimation and extract the anatomical subnetworks associated with specific functional modes by constraining the anatomical connections as structural supports to the functional connections. The key idea is similar to a multi-commodity flow optimization problem that minimizes the cost or maximizes the efficiency for flow configuration and simultaneously fulfills the supply-demand constraint for each commodity. In the proposed network, the nodes represent the grey matter (GM) regions providing brain functionality, and the links represent white matter (WM) fiber bundles connecting those regions and delivering information. The commodities can be thought of as the information corresponding to brain activity patterns as obtained for instance by independent component analysis (ICA) of fMRI data. The concept of information flow is introduced and used to model the propagation of information between GM areas through WM fiber bundles. The link capacity , i.e., ability to transfer information, is characterized by the relative strength of fiber bundles, e.g., fiber count gathered from the tractography of dMRI data. The node information demand is considered to be proportional to the correlation between neural activity at various cortical areas involved in a particular functional mode (e.g. visual, motor, etc.). These two properties lead to the link capacity and node demand constraints in the proposed model. Moreover, the information flow of a link cannot exceed the demand from either end node. This is captured by the feasibility constraints . Two different cost functions are considered in the optimization formulation in this paper. The first cost function, the reciprocal of fiber strength represents the unit cost for information passing through the link. In the second cost function, a min-max (minimizing the maximal link load) approach is used to balance the usage of each link. Optimizing the first cost function selects the pathway with strongest fiber strength for information propagation. In the second case, the optimization procedure finds all the possible propagation pathways and allocates the flow proportionally to their strength. Additionally, a penalty term is incorporated with both the cost functions to capture the possible missing and weak anatomical connections. With this set of constraints and the proposed cost functions, solving the network optimization problem recovers missing and weak anatomical connections supported by the functional information and provides the functional-associated anatomical subnetworks. Feasibility is demonstrated using realistic diffusion and functional MRI phantom data. It is shown that the proposed model recovers the maximum number of true connections, with fewest number of false connections when compared with the connectivity derived from a joint probabilistic model using the expectation-maximization (EM) algorithm presented in a prior work. We also apply the proposed method to data provided by the Human Connectome Project (HCP).

The RubiX [1] algorithm combines high SNR characteristics of low resolution data with high spacial specificity of high resolution data, to extract microstructural tissue parameters from diffusion MRI. In this paper we focus on estimating crossing fiber orientations and introduce sparsity to the RubiX algorithm, making it suitable for reconstruction from compressed (under-sampled) data. We propose a sparse Bayesian algorithm for estimation of fiber orientations and volume fractions from compressed diffusion MRI. The data at high resolution is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible directions. Volume fractions of fibers along these orientations define the dictionary weights. The data at low resolution is modeled using a spatial partial volume representation. The proposed dictionary representation and sparsity priors consider the dependence between fiber orientations and the spatial redundancy in data representation. Our method exploits the sparsity of fiber orientations, therefore facilitating inference from under-sampled data. Experimental results show improved accuracy and decreased uncertainty in fiber orientation estimates. For under-sampled data, the proposed method is also shown to produce more robust estimates of fiber orientations.

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). A DTI produces, from a set of diffusion-weighted MR images, tensor-valued images where each voxel is assigned with a 3 times 3 symmetric, positive-definite matrix. This second order tensor is simply the covariance matrix of a local Gaussian process, with zero-mean, modeling the average motion of water molecules. As we will show in this paper, the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully. We claim and demonstrate that, by using the theoretically well-founded differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. The main goal of this paper is to prove that the choice of the probability metric, i.e., the dissimilarity measure, has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation, in the level-set framework, to estimate the optimal segmentation of a DTI according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. We must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the DTI. We show how to express all the statistical quantities for the different probability metrics. We validate and compare the results obtained on various synthetic data-sets, a biological rat spinal cord phantom and human brain DTIs

Quantitative investigations of fiber orientation and structural connectivity at microscopic resolution have led to great challenges for current neuroimaging techniques. Here, we present a structure tensor (ST) analysis of ex vivo rat brain images acquired by a multicontrast (MC) serial optical coherence scanner. The ST considers the gradients of images in local neighbors to generate a matrix whose eigen-decomposition can estimate the local features such as the edges, anisotropy, and orientation of tissue constituents. This computational analysis is applied on the conventional- and polarization-based contrasts of optical coherence tomography. The three-dimensional (3-D) fiber orientation maps are computed from the image stacks of sequential scans both at mesoresolution for a global view and at high-resolution for the details. The computational orientation maps demonstrate a good agreement with the optic axis orientation contrast which measures the in-plane fiber orientation. Moreover, tractography is implemented using the directional information extracted from the 3-D ST. The study provides a unique opportunity to leverage MC high-resolution information to map structural connectivity of the whole brain.

Volumetric segmentation of subcortical structures, such as the basal ganglia and thalamus, is necessary for noninvasive diagnosis and neurosurgery planning. This is a challenging problem due in part to limited boundary information between structures, similar intensity profiles across the different structures, and low contrast data. This paper presents a semiautomatic segmentation system exploiting the superior image quality of ultrahigh field (7 T) MRI. The proposed approach utilizes the complementary edge information in the multiple structural MRI modalities. It combines optimally selected two modalities from susceptibility-weighted, T2-weighted, and diffusion MRI, and introduces a tailored new edge indicator function. In addition to this, we employ prior shape and configuration knowledge of the subcortical structures in order to guide the evolution of geometric active surfaces. Neighboring structures are segmented iteratively, constraining oversegmentation at their borders with a nonoverlapping penalty. Several experiments with data acquired on a 7 T MRI scanner demonstrate the feasibility and power of the approach for the segmentation of basal ganglia components critical for neurosurgery applications such as deep brain stimulation surgery.

We introduce a framework for population analysis of white matter tracts based on diffusion-weighted images of the brain. The framework enables extraction of fibers from high angular resolution diffusion images (HARDI); clustering of the fibers based partly on prior knowledge from an atlas; representation of the fiber bundles compactly using a path following points of highest density (maximum density path; MDP); and registration of these paths together using geodesic curve matching to find local correspondences across a population. We demonstrate our method on 4-Tesla HARDI scans from 565 young adults to compute localized statistics across 50 white matter tracts based on fractional anisotropy (FA). Experimental results show increased sensitivity in the determination of genetic influences on principal fiber tracts compared to the tract-based spatial statistics (TBSS) method. Our results show that the MDP representation reveals important parts of the white matter structure and considerably reduces the dimensionality over comparable fiber matching approaches.

We consider the problem of improving the accuracy and reliability of probabilistic white matter tractography methods by improving the built-in sampling scheme, which randomly draws, from a diffusion model such as the orientation distribution function (ODF), a direction of propagation. Existing methods employing inverse transform sampling require an ad hoc thresholding step to prevent the less likely directions from being sampled. We herein propose to perform importance sampling of spherical harmonics, which redistributes an input point set on the sphere to match the ODF using hierarchical sample warping. This produces a point set that is more concentrated around the modes, allowing the subsequent inverse transform sampling to generate orientations that are in better accordance with the local fiber configuration. Integrated into a Kalman filter-based framework, our approach is evaluated through experiments on synthetic, phantom, and real datasets.

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

We consider the problem of tracking white matter fibers in high angular resolution diffusion imaging (HARDI) data while simultaneously estimating the local fiber orientation profile. Prior work showed that an unscented Kalman filter (UKF) can be used for this problem, yet existing algorithms employ parametric mixture models to represent water diffusion and to define the state space. To address this restrictive model dependency, we propose to extend the UKF to HARDI data modeled by orientation distribution functions (ODFs), a more generic diffusion model. We consider the spherical harmonic representation of the HARDI signal as the state, enforce nonnegativity of the ODFs, and perform tractography using the directions at which the ODFs attain their peaks. In simulations, our method outperforms filtered two-tensor tractography at different levels of noise by achieving a reduction in mean Chamfer error of 0.05 to 0.27 voxels; it also produced in vivo fiber tracking that is consistent with the neuroanatomy.

The presence of noise in High Angular Resolution Diffusion Imaging (HARDI) data of the brain can limit the accuracy with which fiber pathways of the brain can be extracted. In this work, we present a variational model to denoise HARDI data corrupted by Rician noise. Numerical experiments are performed on three types of data: 2D synthetic data, 3D diffusion-weighted Magnetic Resonance Imaging (DW-MRI) data of a hardware phantom containing synthetic fibers, and 3D real HARDI brain data. Experiments show that our model is effective for denoising HARDI-type data while preserving important aspects of the fiber pathways such as fractional anisotropy and the orientation distribution functions.

Cortical connectivity is associated with cognitive and behavioral traits that are thought to vary between sexes. Using high-angular resolution diffusion imaging at 4 Tesla, we scanned 234 young adult twins and siblings (mean age: 23.4 ± 2.0 SD years) with 94 diffusion-encoding directions. We applied a novel Hough transform method to extract fiber tracts throughout the entire brain, based on fields of constant solid angle orientation distribution functions (ODFs). Cortical surfaces were generated from each subject's 3D T1-weighted structural MRI scan, and tracts were aligned to the anatomy. Network analysis revealed the proportions of fibers interconnecting 5 key subregions of the frontal cortex, including connections between hemispheres. We found significant sex differences (147 women/87 men) in the proportions of fibers connecting contralateral superior frontal cortices. Interhemispheric connectivity was greater in women, in line with long-standing theories of hemispheric specialization. These findings may be relevant for ongoing studies of the human connectome.

International audience; The orientation distribution function (ODF) can be reconstructed online incrementally from diffusion-weighted MRI with a Kalman filtering framework. This online reconstruction can provide real-time feedback to the practitioner, especially appreciated for long acquisition protocols typical in Q-ball imaging. On top of the Kalman filter, we propose a method to evaluate online the reconstruction accuracy of the estimated ODF in constant solid angle. In addition, monitoring the residuals of the Kalman filter, we design, based on statistical tests, two algorithms for online detection of subject motion. The proposed techniques, tested on real and synthetic data under various experimental conditions, can detect rotation by angle less than 3°.

High angular resolution diffusion imaging (HARDI) allows in vivo analysis of the white matter structure and connectivity. Based on orientation distribution functions (ODFs) that represent the directionality of water diffusion at each point in the brain, tractography methods can recover major axonal pathways. This enables tract-based analysis of fiber integrity and connectivity. For multi-subject comparisons, fibers may be clustered into bundles that are consistently found across subjects. To do this, we scanned 20 young adults with HARDI at 4 T. From the reconstructed ODFs, we performed whole-brain tractography with a novel Hough transform method. We then used measures of agreement between the extracted 3D curves and a co-registered probabilistic DTI atlas to select key pathways. Using median filtering and a shortest path graph search, we derived the maximum density path to compactly represent each tract in the population. With this tract-based method, we performed tract-based analysis of fractional anisotropy, and assessed how the chosen tractography algorithm influenced the results. The resulting method may expedite population-based statistical analysis of HARDI and DTI.

International audience; The diffusion orientation distribution function (ODF) can be reconstructed from q-ball imaging (QBI) to map the complex intravoxel structure of water diffusion. As acquisition time is particularly large for high angular resolution diffusion imaging (HARDI), fast estimation algorithms have recently been proposed, as an on-line feedback on the reconstruction accuracy. Thus the acquisition could be stopped or continued on demand. We adapt these real-time algorithms to the mathematically correct definition of ODF in constant solid angle (CSA), and develop a motion detection algorithm upon this reconstruction. Results of improved fiber crossing detection by CSA ODF are shown, and motion detection was implemented and tested in vivo.

Localizing brain structures and pathways associated with intellectual performance and cognition may clarify the networks involved, their development, and their dysfunction in disease. Here we introduce a measure of fiber crossing computed from high angular resolution diffusion images (HARDI), with the goal of better characterizing complex white matter microstructure. We aimed to detect white matter features associated with intellectual performance, previously missed due to limitations of the single tensor diffusion model.

In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI).

Q-ball imaging (QBI) is a high angular resolution diffusion imaging (HARDI) technique which has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (ODF, the probability of diffusion in a given direction) from q-ball uses linear radial projection, neglecting the change in the volume element along the ray, thereby resulting in distributions different from the true ODFs. A new technique has been recently proposed that, by considering the solid angle factor, uses the mathematically correct definition of the ODF and results in a dimensionless and normalized ODF expression from a single q-shell. In this paper, we extend this technique in order to exploit HARDI data from multiple q-shells. We consider the more flexible multi-exponential model for the diffusion signal, and show how to efficiently compute the ODFs in constant solid angle. We describe our method and demonstrate its improved performance on both artificial and real HARDI data.

A stratification and manifold learning approach for analyzing High Angular Resolution Diffusion Imaging (HARDI) data is introduced in this paper. HARDI data provides high- dimensional signals measuring the complex microstructure of biological tissues, such as the cerebral white matter. We show that these high-dimensional spaces may be understood as unions of manifolds of varying dimensions/complexity and densities. With such analysis, we use clustering to characterize the structural complexity of the white matter. We briefly present the underlying framework and numerical experiments illustrating this original and promising approach.

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images. Our approach is grounded on the theoretically well-founded differential geometrical properties of the space of multivariate normal distributions. We introduce a variational formulation, in the level set framework, to estimate the optimal segmentation according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. Moreover, we must respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the diffusion tensor image. We validate our algorithm on synthetic data and report interesting results on real datasets. We focus on two structures of the white matter with different properties and respectively known as the corpus callosum and the corticospinal tract.

Diffusion Tensor Imaging (DTI) is currently a widespread technique to infer white matter architecture in the human brain. An important application of DTI is to understand the anatomical coupling between functional cortical regions of the brain. To solve this problem, anisotropy maps are insufficient and fiber tracking methods are used to obtain the main fibers. While the diffusion tensor (DT) is important to obtain anisotropy maps and apparent diffusivity of the underlying tissue, fiber tractography using the full DT may result in diffusive tracking that leaks into unexpected regions. Sharpening is thus of utmost importance to obtain complete and accurate tracts. In the tracking literature, only heuristic methods have been proposed to deal with this problem. We propose a new tensor sharpening transform. Analogously to the general issue with the diffusion and fiberOrientation Distribution Function (ODF) encountered when working with High Angular Resolution Diffusion Imaging (HARDI), we show how to transform the diffusion tensors into so-called fiber tensors. We demonstrate that this tensor transform is a natural pre-processing task when one is interested in fiber tracking. It also leads to a dramatic improvement of the tractography results obtained by front propagation techniques on the full diffusion tensor. We compare and validate sharpening and tracking results on synthetic data and on known fiber bundles in the human brain.

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). DTI can be estimated from a set of diffusion weighted images and provides tensor-valued images where each voxel is assigned with a 3 /spl times/ 3 symmetric, positive-definite matrix. As we will show in this paper, the definition of a dissimilarity measure and statistics between tensors is a non trivial task which must be carefully tackled. We claim that, by using the differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. Our goal is to prove that the choice of this probability metric has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation to estimate the optimal segmentation of a diffusion tensor image. We show how to estimate diffusion tensors statistics for three different probability metrics and evaluate their respective performances. We validate and compare the results obtained on synthetic and real datasets.

Diffusion magnetic resonance imaging probes and quantifies the anisotropic diffusion of water molecules in biological tissues, making it possible to non-invasively infer the architecture of the underlying structure. In this chapter, we present a set of new techniques for the robust estimation and regularization of diffusion tensor images (DTI) as well as a novel statistical framework for the segmentation of cerebral white matter structures from this type of dataset. Numerical experiments conducted on real diffusion weighted MRI illustrate the techniques and exhibit promising results.

Diffusion tensor MRI probes and quantifies the anisotropic diffusion of water molecules in biological tissues, making it possible to non-invasively infer the architecture of the underlying structures. In this article, we present a set of new techniques for the estimation and regularization of diffusion tensors MRI datasets as well as a novel approach to the cerebral white matter connectivity mapping. Numerical experimentations conducted on real diffusion weighted MRI will exhibit promising results.

We survey the recent activities of the Odyssee Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.

Diffusion Tensor Imaging (DTI) is a relatively new modality for human brain imaging. During the last years, this modality has become widely used in medical studies. Tractography is currently the favorite technique to characterize and analyse the structure of the brain white matter. Only a few studies have been proposed to group data of particular interest. Rather than working on extracted fibers or on an estimated scalar value accounting for anisotropy as done in other approaches, we propose to extend classical segmentation techniques based on surface evolution by considering region statistics defined on the full diffusion tensor field itself. A multivariate Gaussian is used to approximate the density of the components of diffusion tensor for each sub-region of the volume. We validate our approach on synthetical data and we show promising results on the extraction of the corpus callosum from a real dataset.

We propose an original approach for the segmentation of three-dimensional fields of probability density functions. This presents a wide range of applications in medical images processing, in particular for diffusion magnetic resonance imaging where each voxel is assigned with a function describing the average motion of water molecules. Being able to automatically extract relevant anatomical structures of the white matter, such as the corpus callosum, would dramatically improve our current knowledge of the cerebral connectivity as well as allow for their statistical analysis. Our approach relies on the use of the symmetrized Kullback-Leibler distance and on the modelization of its distribution over the subsets of interest in the volume. The variational formulation of the problem yields a level-set evolution converging toward the optimal segmentation.

This paper describes a collision detection method for polygonal deformable objects using OpenGL, which is suitable for surgery simulations. The method relies on the OpenGL selection mode which can be used to find out which objects or geometrical primitives (such as polygons) in the scene are drawn inside a specified region, called the viewing volume. We achieve a significant reduction in the detection time by using a data structure based on an AABB tree. The strength of our method is that it doesn't require the AABB hierarchy tree to be updated from bottom to top. We are using only a limited set of bounding volumes, which is much smaller than the object's number of polygons. This enables us to perform a fast update of our structure when objects deform. Therefore, our approach appears to be a reasonable choice for collision detection of deformable objects.

Available online 22 August 2021. White matter bundle segmentation using diffusion MRI fiber tractography has become the method of choice to identify white matter fiber pathways in vivo in human brains. However, like other analyses of complex data, there is considerable variability in segmentation protocols and techniques. This can result in different reconstructions of the same intended white matter pathways, which directly affects tractography results, quantification, and interpretation. In this study, we aim to evaluate and quantify the variability that arises from different protocols for bundle segmentation. Through an open call to users of fiber tractography, including anatomists, clinicians, and algorithm developers, 42 independent teams were given processed sets of human whole-brain streamlines and asked to segment 14 white matter fascicles on six subjects. In total, we received 57 different bundle segmentation protocols, which enabled detailed volume-based and streamline-based analyses of agreement and disagreement among protocols for each fiber pathway. Results show that even when given the exact same sets of underlying streamlines, the variability across protocols for bundle segmentation is greater than all other sources of variability in the virtual dissection process, including variability within protocols and variability across subjects. In order to foster the use of tractography bundle dissection in routine clinical settings, and as a fundamental analytical tool, future endeavors must aim to resolve and reduce this heterogeneity. Although external validation is needed to verify the anatomical accuracy of bundle dissections, reducing heterogeneity is a step towards reproducible research and may be achieved through the use of standard nomenclature and definitions of white matter bundles and well-chosen constraints and decisions in the dissection process. This work was conducted in part using the resources of the Ad- vanced Computing Center for Research and Education at Vanderbilt University, Nashville, TN. KS, BL, CH were supported by the Na- tional Institutes of Health under award numbers R01EB017230, and T32EB001628, and in part by ViSE/VICTR VR3029 and the National Center for Research Resources, Grant UL1 RR024975-01. This work was also possible thanks to the support of the Institutional Research Chair in NeuroInformatics of Universitéde Sherbrooke, NSERC and Compute Canada (MD, FR). MP received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk ł odowska-Curie grant agreement No 754462. The Wisconsin group acknowledges the support from a core grant to the Waisman Cen- ter from the National Institute of Child Health and Human Develop- ment (IDDRC U54 HD090256). NSF OAC-1916518, NSF IIS-1912270, NSF IIS-1636893, NSF BCS-1734853, NIH NIBIB 1R01EB029272-01, and a Microsoft Faculty Fellowship to F.P. LF acknowledges the sup- port of the Cluster of Excellence Matters of Activity. Image Space Mate- rial funded by the Deutsche Forschungsgemeinschaft (DFG, German Re- search Foundation) under Germany´s Excellence Strategy –EXC 2025. SW is supported by a Medical Research Council PhD Studentship UK [MR/N013913/1]. The Nottingham group’s processing was performed using the University of Nottingham’s Augusta HPC service and the Pre- cision Imaging Beacon Cluster. JPA, MA and SMS acknowledges the support of FCT - Fundação para a Ciência e a Tecnologia within CIN- TESIS, R&D Unit (reference UID/IC/4255/2013). MM was funded by the Wellcome Trust through a Sir Henry Wellcome Postdoctoral Fellow- ship [213722/Z/18/Z]. EJC-R is supported by the Swiss National Sci- ence Foundation (SNSF, Ambizione grant PZ00P2 185814/1). CMWT is supported by a Sir Henry Wellcome Fellowship (215944/Z/19/Z) and a Veni grant from the Dutch Research Council (NWO) (17331). FC acknowledges the support of the National Health and Medical Re- search Council of Australia (APP1091593 and APP1117724) and the Australian Research Council (DP170101815). NSF OAC-1916518, NSF IIS-1912270, NSF IIS-1636893, NSF BCS-1734853, Microsoft Faculty Fellowship to F.P. D.B. was partially supported by NIH NIMH T32- MH103213 to William Hetrick (Indiana University). CL is partly sup- ported by NIH grants P41 EB027061 and P30 NS076408 “Institutional Center Cores for Advanced Neuroimaging. JYMY received positional funding from the Royal Children’s Hospital Foundation (RCH 1000). JYMY, JC, and CEK acknowledge the support of the Royal Children’s Hospital Foundation, Murdoch Children’s Research Institute, The Uni- versity of Melbourne Department of Paediatrics, and the Victorian Gov- ernment’s Operational Infrastructure Support Program. C-HY is grateful to the Ministry of Science and Technology of Taiwan (MOST 109-2222- E-182-001-MY3) for the support. LC acknowledges support from CONA- CYT and UNAM. ARM acknowledges support from CONACYT. LJO, YR, and FZ were supported by NIH P41EB015902 and R01MH119222. AJG was supported by P41EB015898. NM was supported by R01MH119222, K24MH116366, and R01MH111917. This project has received funding from the European Union’s Horizon 2020 Research and Innovation Pro- gramme under Grant Agreement No. 785907 & 945539 (HBP SGA2 & SGA3), and from the ANR IFOPASUBA- 19-CE45-0022-01. PG, CR, NL and AV were partially supported by ANID-Basal FB0008 and ANID- FONDECYT 1190701 grants. We would like to acknowledge John C Gore, Hiromasa Takemura, Anastasia Yendiki, and Riccardo Galbusera for their helplful suggestions regarding the analysis, figures, and discussions.