Mapping neuronal fiber crossings in the human brain

International audienceNew magnetic resonance imaging processing tools allow white-matter fiber bundles to be segmented and tracked in regions of high complexity

Adaptive Design of Sampling Directions in Diffusion Tensor MRI and Validation on Human Brain Images

International audienceDiffusion tensor reconstruction is made possible through the acquisition of several diffusion weighted images, each corresponding to a given sampling direction in the Q-space. In this study, we address the question of sampling efficiency, and show that in case we have some prior knowledge on the diffusion characteristics, we may be able to adapt the sampling directions for better reconstruction of the diffusion tensor. The prior is a tensor distribution function, estimated over a given region of interest, possibly on several subjects. We formulate an energy related to error on tensor reconstruction, and calculate analytical gradient expression for efficient minimization. We validate our approach on a set of 5199 tensors taken within the corpus callosum of the human brain, and show improvement by an order of 10% on the MSE of the reconstructed tensor

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Recursively implementating the Gaussian and its derivatives

Gaussian filtering is one of the most successfully operation in computer vision in order to reduce noise, calculating the gradient intensity change or performing Laplacian or the second directional derivative of an image. However, it is well known that in a multi-resolution context, where the need for large filters is required, this technique suffers from the fact it is a computationally expensive since the number of operations per point in convolving an image with a Gaussian filter is directly proportional to the width of the operator. We propose in this paper a technique in order to use Gaussian filtering with a reduced and fixed number of operations per output independently of the size of the filter. The key of our approach is to approximate in a mean square sense the prototype Gaussian filters with an exponentially based filter family depending on the same scale factor than the Gaussian filters (i.e. s) and then to implement in an exact and recursive way the approximate filters. An important point of the design presented in this paper is that dealing with Gaussian filters having different scale factor (i.e. s) will not require a new design algorithm as. The coefficients looked for in the recursive realization are determined function of the scale factor of each considered prototype filter, namely the Gaussian filter, its first and second derivative. Some experimental results will be shown to illustrate the efficiency of the approximation process and some applications to edge detection problems and multi-resolution techniques will be considered and discussed

Optimal Real-Time QBI using Regularized Kalman Filtering with Incremental Orientation Sets

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI), Diffusion Spectrum Imaging (DSI) and Q-Ball Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition time (TR) of the acquisition sequence \cite{Miccai:2007,Med. Image Analysis -Vol 12, Issue 5, June 2008}. In this article, we first revisite and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard off-line processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. Our work allows to start an acquisition just with the minimum number of gradient directions and an initial estimate of the q-ball and then all the rest, including the next gradient directions and the q-ball estimates, are recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal q-ball estimate. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and, real-time fiber tracking and connectivity mapping

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

Computational Brain Connectivity Mapping: A Core Health and Scientific Challenge

International audienceOne third of the burden of all the diseases in Europe is due to problems caused by diseases affecting brain. Although exceptional progress have been obtained for exploring the brain during the past decades, it is still terra-incognita and calls for specific efforts in research to better understand its architecture and functioning. To take up this great challenge of modern science and to solve the limited view of the brain provided just by one imaging modality, this article advocates the idea developed in my research group of a global approach involving new generation of models for brain connectivity mapping and strong interactions between structural and functional connectivities. Capitalizing on the strengths of integrated and complementary non invasive imaging modalities such as diffusion Magnetic Resonance Imaging (dMRI) and Electro & Magneto-Encephalography (EEG & MEG) will contribute to achieve new frontiers for identifying and characterizing structural and functional brain connectivities and to provide a detailed mapping of the brain connectivity, both in space and time. Thus leading to an added clinical value for high impact diseases with new perspectives in computational neuro-imaging and cognitive neuroscience

4TH ORDER DIFFUSION TENSOR ESTIMATION AND APPLICATION

International audienceHistorically Diffusion MRI started with Diffusion Tensor Imaging (DTI), which boosted the development of schemes for estimating positive definite tensors but were limited by their inability to detect fiber-crossings. Recent HARDI techniques have overcome that shortcoming with a plethora of new reconstruction schemes such as radial basis functions, Spherical Harmonics (SH), Higher Order Tensors (HOT), etc. It is appropriate, therefore, to explore HOT while leveraging the extensive framework already established for classical DTI. In this work, we propose a review and a comparison of the existing methods and an extension to the Riemannian framework to the space of 4 th order diffusion tensors

TERNARY QUARTIC APPROACH FOR POSITIVE 4TH ORDER DIFFUSION TENSORS REVISITED

International audienceIn Diffusion Magnetic Resonance Imaging (D-MRI), the 2nd order diffusion tensor has given rise to a widely used tool – Diffusion Tensor Imaging (DTI). However, it is known that DTI is limited to a single prominent diffusion direction and is inaccurate in regions of complex fiber structures such as crossings. Various other approaches have been introduced to recover such complex tissue micro-geometries, one of which is Higher Order Cartesian Tensors. Estimating a positive diffusion function has also been emphasised mathematically, since diffusion is a physical quantity. Recently there have been efforts to estimate 4th order diffusion tensors from DiffusionWeighted Images (DWIs), which are capable of describing crossing configurations with the added property of a positive diffusion function. We take up one such, the Ternary Quartic approach, and reformulate the estimation equation to facilitate the estimation of the non-negative 4th order diffusion tensor. With our modified approach we test on synthetic, phantom and real data and confirm previous results

Le cerveau dans tous ses états. Des sciences cognitives au diagnostic : entretien avec Stéphane Lehéricy propos recueillis par Dominique Chouchan

Article suivi par un entretien "des sciences cognitives au diagnostic" avec Stéphane Lehéricy directeur du Centre de neuro-imagerie de recherche (CENIR) du CHU Pitié Salpêtrière et professeur dans le service de neuroradiologie de ce CHU. Propos recueillis par Dominique ChouchanNational audienceChacun de nos quelque 100 milliards de neurones peut communiquer avec des milliers d'autres : autant dire qu'à ce jour, le cerveau est pour l'essentiel terra incognita. On sait qu'il comporte des aires spécialisées (dans la vision, la marche, les émotions...) dites corticales, qui constituent la matière grise. Celles-ci s'échangent des messages, électriques notamment, au travers de fibres nerveuses, la substance blanche. La compréhension de l'anatomie du cerveau (structure spatiale) et de sa réponse à des stimuli (approche temporelle) vont donc de pair. Aujourd'hui, nous disposons de techniques de mesure et d'imagerie performantes. Mais encore faut-il interpréter les données obtenues. Un défi qui nécessite d'étroites collaborations entre mathématiciens, informaticiens, spécialistes des neurosciences et médecins