Diffusion Tensor Magnetic Resonance Imaging : Brain Connectivity Mapping

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. We introduce a novel approach to the cerebral white matter connectivity mapping from diffusion tensor MRI. We address the problem of consistent neural fibers reconstruction in areas of complex diffusion profiles with potentially multiple fibers orientations. Our method relies on a global modelization of the acquired MRI volume as a Riemannian manifold M and proceeds in 4 majors steps:1. We establish the link between Brownian motion and diffusion MRI by using the Laplace-Beltrami operator on M.2. We then expose how the sole knowledge of the diffusion properties of water molecules on M is sufficient to infer its geometry. There exists a direct mapping between the diffusion tensor and the metric of M.3. Having access to that metric, we propose a novel level set formulation to approximate the distance function related to a radial Brownian motion on M.4. On that basis, a rigorous numerical scheme using the exponential map is derived to estimate the geodesics of M, seen as the diffusion paths of water molecules.Numerical experimentations conducted on synthetic and real diffusion MRI datasets illustrate the potentialities of this global approach

Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images

Diffusion magnetic resonance imaging probes and quantifies the anisotropic diffusion of water molecules in biological tissues, make it possible to non-invasively infer the architecture of the underlying structures. 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 technique and exhibit promising results

Statistics on Multivariate Normal Distributions: A Geometric Approach and its Application to Diffusion Tensor MRI

This report is dedicated to the statistical analysis of the space of multivariate normal probability density functions. It relies on the differential geometrical properties of the underlying parameter space, endowed with a Riemannian metric, as well as on recent works that led to the generalization of the normal law on non-linear spaces. We will first proceed to the state of the art in section 1, while expressing some quantities related to the structure of the manifold of interest, and then focus on the derivation of closed-form expressions for the mean, covariance matrix, modes of variation and normal law between multivariate normal distributions in section 2. We will also address the derivation of accurate and efficient numerical schemes to estimate the proposed quantities. A major application of the present work is the statistical analysis of diffusion tensor Magnetic Resonance Imaging. We show promising results on synthetic and real data in section

Toward Segmentation of 3D Probability Density Fields by Surface Evolution: Application to Diffusion MRI

We propose three original approaches for the segmentation of three-dimensional fields of probability density functions. This presents a wide range of applications in medical image 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 first approach involves the use of a multivariate Gaussian law to approximate the distribution of the components of diffusion tensors for each sub-region of a DTI volume. The second technique 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 third technique considers the 6-dimensional statistical manifold defined by the parameters of the diffusion tensors and proposes a segmentation algorithm by rigorously defining the geodesic distance and the intrinsic mean on this Riemannian manifold. The variational formulations of the problems yield three differents level-set evolutions converging towards the respective optimal segmentation. We validate these approaches on synthetical data and show promising results on the extraction of the corpus callosum and of the lateral brain ventricles from a real dataset

Non Rigid Registration of Diffusion Tensor Images

We propose a novel variational framework for the dense non-rigid registration of Diffusion Tensor Images (DTI). Our approach relies on the differential geometrical properties of the Riemannian manifold of multivariate normal distributions endowed with the metric derived from the Fisher information matrix. The availability of closed form expressions for the geodesics and the Christoffel symbols allows us to define statistical quantities and to perform the parallel transport of tangent vectors in this space. We propose a matching energy that aims to minimize the difference in the local statistical content (means and covariance matrices) of two DT images through a gradient descent procedure. The result of the algorithm is a dense vector field that can be used to wrap the source image into the target image. This article is essentially a mathematical study of the registration problem. Some numerical experiments are provided as a proof of concept

Anatomical connections in the human visual cortex: validation and new insights using a DTI Geodesic Connectivity Mapping method

Various approaches have been introduced to infer the organization of white matter connectivity using Diffusion Tensor Imaging (DTI). In this study, we validate a recently introduced geometric tractography technique, Geodesic Connectivity Mapping (GCM), able to overcome the main limitations of geometrical approaches. Using the GCM technique, we could successfully characterize anatomical connections in the human low-level visual cortex. We reproduce previous findings regarding the topology of optic radiations linking the LGN to V1 and the regular organization of splenium fibers with respect to their origin in the visual cortex. Moreover, our study brings further insights regarding the connectivity of the human MT complex (hMT+) and the retinotopic areas

A Hough transform global approach to diffusion MRI tractography

International audienceTractography in Diffusion-Weighted MRI provides a unique quantitative measurement of the brain's anatomical connectivity using information not available from other imaging techniques. Many tractography algorithms are based on local fiber orientation estimates, such as streamline methods, and are vulnerable to noise and partial volume effects; fiber crossing and kissing are also difficult to distinguish. This led to the development of probabilistic techniques [1] and global approaches relying on front propagation [2, 3] or simulation of the diffusion process [4]. In this work, we present a global approach based on the voting process provided by the Hough transform [5]. Our proposed tractography algorithm essentially tests all possible 3D curves in the volume, assigning a score to each of them, then selecting the curves with the highest scores, and returning them as the potential anatomical connections. We present experimental results on both artificial and real diffusion tensor images (DTI) and high-angular resolution diffusion images (HARDI)

Design of multishell sampling schemes with uniform coverage in diffusion MRI

International audiencePURPOSE: In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques. METHODS: The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell. RESULTS: We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination. DISCUSSION: We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning

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

Incremental gradient table for multiple Q-shells diffusion MRI

International audienceMost studies on sampling optimality for diffusion MRI deal with single Q-shell acquisition. For single Q-shell acquisition, incremental gradient table has proved useful in clinical setup, where the subject is likely to move, or for online reconstruction. In this article, we propose a generalization of the electrostatic repulsion to generate gradient tables for multiple Q-shells acquisitions, designed for incremental reconstruction or processing of data prematurely aborted