Modeling diffusion directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

Beyond Crossing Fibers: Tractography Exploiting Sub-voxel Fibre Dispersion and Neighbourhood Structure

In this paper we propose a novel algorithm which leverages models of white matter fibre dispersion to improve tractography. Tractography methods exploit directional information from diffusion weighted magnetic resonance (DW-MR) imaging to infer connectivity between different brain regions. Most tractography methods use a single direction (e.g. the principal eigenvector of the diffusion tensor) or a small set of discrete directions (e.g. from the peaks of an orientation distribution function) to guide streamline propagation. This strategy ignores the effects of within-bundle orientation dispersion, which arises from fanning or bending at the sub-voxel scale, and can lead to missing connections. Various recent DW-MR imaging techniques estimate the fibre dispersion in each bundle directly and model it as a continuous distribution. Here we introduce an algorithm to exploit this information to improve tractography. The algorithm further uses a particle filter to probe local neighbourhood structure during streamline propagation. Using information gathered from neighbourhood structure enables the algorithm to resolve ambiguities between converging and diverging fanning structures, which cannot be distinguished from isolated orientation distribution functions. We demonstrate the advantages of the new approach in synthetic experiments and in vivo data. Synthetic experiments demonstrate the effectiveness of the particle filter in gathering and exploiting neighbourhood information in recovering various canonical fibre configurations and experiments with in vivo brain data demonstrate the advantages of utilising dispersion in tractography, providing benefits in practical situations. © 2013 Springer-Verlag

Multichannel source separation and tracking with phase differences by random sample consensus

Blind audio source separation (BASS) is a fascinating problem that has been tackled from many different angles. The use case of interest in this thesis is that of multiple moving and simultaneously-active speakers in a reverberant room. This is a common situation, for example, in social gatherings. We human beings have the remarkable ability to focus attention on a particular speaker while effectively ignoring the rest. This is referred to as the ``cocktail party effect'' and has been the holy grail of source separation for many decades. Replicating this feat in real-time with a machine is the goal of BASS. Single-channel methods attempt to identify the individual speakers from a single recording. However, with the advent of hand-held consumer electronics, techniques based on microphone array processing are becoming increasingly popular. Multichannel methods record a sound field from various locations to incorporate spatial information. If the speakers move over time, we need an algorithm capable of tracking their positions in the room. For compact arrays with 1-10 cm of separation between the microphones, this can be accomplished by applying a temporal filter on estimates of the directions-of-arrival (DOA) of the speakers. In this thesis, we review recent work on BSS with inter-channel phase difference (IPD) features and provide extensions to the case of moving speakers. It is shown that IPD features compose a noisy circular-linear dataset. This data is clustered with the RANdom SAmple Consensus (RANSAC) algorithm in the presence of strong reverberation to simultaneously localize and separate speakers. The remarkable performance of RANSAC is due to its natural tendency to reject outliers. To handle the case of non-stationary speakers, a factorial wrapped Kalman filter (FWKF) and a factorial von Mises-Fisher particle filter (FvMFPF) are proposed that track source DOAs directly on the unit circle and unit sphere, respectively. These algorithms combine directional statistics, Bayesian filtering theory, and probabilistic data association techniques to track the speakers with mixtures of directional distributions

Modeling Diffusion Directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

Filtered Multitensor Tractography

We describe a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by those previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Using two- and three-fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

Tractographie de la matière blanche par réseaux de neurones récurrents

La matière blanche du cerveau fait encore l'objet de nombreuses études. Grâce à l'IRM de diffusion, on peut étudier de façon non invasive la connectivité du cerveau avec une précision sans précédent. La reconstruction de la matière blanche --- la tractographie --- n'est pas parfaite cependant. En effet, la tractographie tend à reconstruire tous les chemins possibles au sein de la matière blanche; l'expertise des neuroanatomistes est donc requise pour distinguer les chemins qui sont possibles anatomiquement de ceux qui résultent d'une mauvaise reconstruction. Cette connaissance est difficile à exprimer et à codifier sous forme de règles logiques. L'intelligence artificielle a refait surface dans les années 1990 --- suite à une amélioration remarquable de la vitesse des processeurs --- en tant que solution viable à plusieurs problèmes qui étaient considérés comme fondamentalement > et quasi impossibles à résoudre pour une machine. Celle-ci représente un outil unique pour intégrer l'expertise des neuroanatomistes dans le processus de reconstruction de la matière blanche, sans avoir à fournir de règles explicitement. Un modèle peut ainsi apprendre la définition d'un chemin valide à partir d'exemples valides, pour ensuite reproduire ce qu'il a appris, sans répéter les erreurs classiques. Plus particulièrement, les réseaux de neurones récurrents sont une famille de modèles créés spécifiquement pour le traitement de séquences de données. Comme une fibre de matière blanche est représentée par une séquence de points, le lien se fait naturellement. Malgré leur potentiel énorme, l'application des réseaux récurrents à la tractographie fait face à plusieurs problèmes techniques. Cette thèse se veut très exploratoire, et détaille donc les débuts de l'utilisation des réseaux de neurones récurrents pour la tractographie par apprentissage, des problèmes qui sont apparus suite à la création d'une multitude d'algorithmes basés sur l'intelligence artificielle, ainsi que des solutions développées pour répondre à ces problèmes. Les résultats de cette thèse ont démontré le potentiel des réseaux de neurones récurrents pour la reconstruction de la matière blanche, en plus de contribuer à l’avancement du domaine grâce à la création d’une base de données publique pour la tractographie par apprentissage

A filtered approach to neural tractography using the Watson directional function

We propose a technique to simultaneously estimate the local fiber orientations and perform multifiber tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. Further, to overcome noise, many algorithms use a filter as a post-processing step to obtain a smooth trajectory. We formulate fiber tracking as causal estimation: at each step of tracing the fiber, the current estimate of the signal is guided by the previous. To do this, we model the signal as a discrete mixture of Watson directional functions and perform tractography within a filtering framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides an accurate estimate of the local structure at each point along the fiber. We choose the Watson function since it provides a compact representation of the signal parameterized by the principal diffusion direction and a scaling parameter describing anisotropy, and also allows analytic reconstruction of the oriented diffusion function from those parameters. Using a mixture of two and three components (corresponding to two-fiber and three-fiber models) we demonstrate in synthetic experiments that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments examine the corpus callosum and internal capsule and confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization