Diffusion Tensor Imaging Based Tractography of Human Brain Fiber Bundles

Tractography is a non-invasive process for reconstruction, modeling and visualization of neural fibers in the white matter (WM) of human brain. It has emerged as a major breakthrough for neuroscience research due to its usefulness in clinical applications. Two types of tractography approaches: deterministic and probabilistic have been investigated to evaluate their performances on tracking fiber bundles using diffusion tensor imaging (DTI). The images are taken by applying pulsed magnetic fields in multiple gradient directions. After removing the non-brain areas from the images, the diffusion tensor indices for each image voxel are calculated. White matter connectivity of the brain, i.e. tractography, is primarily based upon streamline algorithms where the local tract direction is defined by the principle direction of the diffusion tensor. Simulations are performed using three approaches: fiber assignment by continuous tracking (FACT), probability index of connectivity (PICo) and Gibbs tracking (GT). Simulation results show that probabilistic tractography i.e. PICo and GT can reconstruct longer length of fibers compared to the deterministic approach-FACT but with a cost of high computation time. Moreover, GT handles the more complex fiber configurations of crossing and kissing fibers, more effectively and provides the best reconstruction of fibers. In addition, diffusion tensor indices: fractional anisotropy (FA) and mean diffusivity (MD) for a region of interest can be quantified and used to assess several brain diseases. Prospective investigation of DTI based tractography can reveal useful information on WM architecture in normal and diseased brain which will speed up the detection and treatment of various brain diseases

Bayesian Dynamic DAG Learning: Application in Discovering Dynamic Effective Connectome of Brain

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization \textbf{(BDyMA)} method to address the challenges in discovering DEC. The presented dynamic causal model enables us to discover bidirected edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and baseline methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process

Probabilistic Ordinary Differential Equation Solvers - Theory and Applications

Ordinary differential equations are ubiquitous in science and engineering, as they provide mathematical models for many physical processes. However, most practical purposes require the temporal evolution of a particular solution. Many relevant ordinary differential equations are known to lack closed-form solutions in terms of simple analytic functions. Thus, users rely on numerical algorithms to compute discrete approximations. Numerical methods replace the intractable, and thus inaccessible, solution by an approximating model with known computational strategies. This is akin to a process in statistics where an unknown true relationship is modeled with access to instances of said relationship. One branch of statistics, Bayesian modeling, expresses degrees of uncertainty with probability distributions. In recent years, this idea has gained traction for the design and study of numerical algorithms which established probabilistic numerics as a research field in its own right. The theory part of this thesis is concerned with bridging the gap between classical numerical methods for ordinary differential equations and probabilistic numerics. To this end, an algorithm is presented based on Gaussian processes, a general and versatile model for Bayesian regression. This algorithm is compared to two standard frameworks for the solution of initial value problems. It is shown that the maximum a-posteriori estimator of certain Gaussian process regressors coincide with certain multistep formulae. Furthermore, a particular initialization scheme based on an improper prior model coincides with a Runge-Kutta method for the first discretization step. This analysis provides a higher-order probabilistic numerical algorithm for initial value problems. Based on the probabilistic description, an estimator of the local integration error is presented, which is used in a step size adaptation scheme. The completed algorithm is evaluated on a benchmark on initial value problems, confirming empirically the theoretically predicted error rates and displaying particularly efficient performance on domains with low accuracy requirements. To establish the practical benefit of the probabilistic solution, a probabilistic boundary value problem solver is applied to a medical imaging problem. In tractography, diffusion-weighted magnetic resonance imaging data is used to infer connectivity of neural fibers. The first application of the probabilistic solver shows how the quantification of the discretization error can be used in subsequent estimation of fiber density. The second application additionally incorporates the measurement noise of the imaging data into the tract estimation model. These two extensions of the shortest-path tractography method give more faithful data, modeling and algorithmic uncertainty representations in neural connectivity studies.Gewöhnliche Differentialgleichungen sind allgegenwärtig in Wissenschaft und Technik, da sie die mathematische Beschreibung vieler physikalischen Vorgänge sind. Jedoch benötigt ein Großteil der praktischen Anwendungen die zeitliche Entwicklung einer bestimmten Lösung. Es ist bekannt, dass viele relevante gewöhnliche Differentialgleichungen keine geschlossene Lösung als Ausdrücke einfacher analytischer Funktion besitzen. Daher verlassen sich Anwender auf numerische Algorithmen, um diskrete Annäherungen zu berechnen. Numerische Methoden ersetzen die unauswertbare, und daher unzugängliche, Lösung durch eine Annäherung mit bekannten Rechenverfahren. Dies ähnelt einem Vorgang in der Statistik, wobei ein unbekanntes wahres Verhältnis mittels Zugang zu Beispielen modeliert wird. Eine Unterdisziplin der Statistik, Bayes’sche Modellierung, stellt graduelle Unsicherheit mittels Wahrscheinlichkeitsverteilungen dar. In den letzten Jahren hat diese Idee an Zugkraft für die Konstruktion und Analyse von numerischen Algorithmen gewonnen, was zur Etablierung von probabilistischer Numerik als eigenständiges Forschungsgebiet führte. Der Theorieteil dieser Dissertation schlägt eine Brücke zwischen herkömmlichen numerischen Verfahren zur Lösung gewöhnlicher Differentialgleichungen und probabilistischer Numerik. Ein auf Gauß’schen Prozessen basierender Algorithmus wird vorgestellt, welche ein generelles und vielseitiges Modell der Bayesschen Regression sind. Dieser Algorithmus wird verglichen mit zwei Standardansätzen für die Lösung von Anfangswertproblemen. Es wird gezeigt, dass der Maximum-a-posteriori-Schätzer bestimmter Gaußprozess-Regressoren übereinstimmt mit bestimmten Mehrschrittverfahren. Weiterhin stimmt ein besonderes Initialisierungsverfahren basierend auf einer uneigentlichen A-priori-Wahrscheinlichkeit überein mit einer Runge-Kutta Methode im ersten Rechenschritt. Diese Analyse führt zu einer probabilistisch-numerischen Methode höherer Ordnung zur Lösung von Anfangswertproblemen. Basierend auf der probabilistischen Beschreibung wird ein Schätzer des lokalen Integrationfehlers präsentiert, welcher in einem Schrittweitensteuerungsverfahren verwendet wird. Der vollständige Algorithmus wird auf einem Satz standardisierter Anfangswertprobleme ausgewertet, um empirisch den von der Theorie vorhergesagten Fehler zu bestätigen. Der Test weist dem Verfahren einen besonders effizienten Rechenaufwand im Bereich der niedrigen Genauigkeitsanforderungen aus. Um den praktischen Nutzen der probabilistischen Lösung nachzuweisen, wird ein probabilistischer Löser für Randwertprobleme auf eine Fragestellung der medizinischen Bildgebung angewandt. In der Traktografie werden die Daten der diffusionsgewichteten Magnetresonanzbildgebung verwendet, um die Konnektivität neuronaler Fasern zu bestimmen. Die erste Anwendung des probabilistische Lösers demonstriert, wie die Quantifizierung des Diskretisierungsfehlers in einer nachgeschalteten Schätzung der Faserdichte verwendet werden kann. Die zweite Anwendung integriert zusätzlich das Messrauschen der Bildgebungsdaten in das Strangschätzungsmodell. Diese beiden Erweiterungen der Kürzesten-Pfad-Traktografie repräsentieren die Daten-, Modellierungs- und algorithmische Unsicherheit abbildungstreuer in neuronalen Konnektivitätsstudien

Identification of proprioceptive thalamocortical tracts in children : comparison of fMRI, MEG, and manual seeding of probabilistic tractography

Studying white matter connections with tractography is a promising approach to understand the development of different brain processes, such as proprioception. An emerging method is to use functional brain imaging to select the cortical seed points for tractography, which is considered to improve the functional relevance and validity of the studied connections. However, it is unknown whether different functional seeding methods affect the spatial and microstructural properties of the given white matter connection. Here, we compared functional magnetic resonance imaging, magnetoencephalography, and manual seeding of thalamocortical proprioceptive tracts for finger and ankle joints separately. We showed that all three seeding approaches resulted in robust thalamocortical tracts, even though there were significant differences in localization of the respective proprioceptive seed areas in the sensorimotor cortex, and in the microstructural properties of the obtained tracts. Our study shows that the selected functional or manual seeding approach might cause systematic biases to the studied thalamocortical tracts. This result may indicate that the obtained tracts represent different portions and features of the somatosensory system. Our findings highlight the challenges of studying proprioception in the developing brain and illustrate the need for using multimodal imaging to obtain a comprehensive view of the studied brain process.Peer reviewe

Probabilistic modeling of tensorial data for enhancing spatial resolution in magnetic resonance imaging.

Las imágenes médicas usan los principios de la Resonancia Magnética (IRM) para medir de forma no invasiva las propiedades de este movimiento. Cuando se aplica al cerebro humano, proporciona información única sobre la conectividad del tejido, lo que hace que la resonancia magnética sea una de las tecnologías clave en un esfuerzo científico continuo a gran escala para mapear el conector del cerebro humano. En consecuencia, es un tema de investigación oportuno e importante para crear modelos matemáticos que infieren parámetros biológicamente significativos a partir de dichos datos. La MRI y la difusión-MRI (dMRI) se han utilizado en aplicaciones que abarcan desde el procesamiento de señales, la visión por computadora y las neurociencias. Aunque los protocolos clínicos actuales permiten adquisiciones rápidas en un número diferente de cortes en varios planos, la resolución espacial no es lo suficientemente alta en muchos casos para el diagnóstico clínico. El principal problema ocurre debido a las limitaciones de hardware en los escáneres de adquisición. Por lo tanto, MRI y dMRI tienen un compromiso difícil entre una buena resolución espacial y una relación de ruido de señal (SNR). Esto conduce a adquisiciones de datos con baja resolución espacial. Se convierte en un problema serio para el análisis clínico por dos razones principales. Primero, una baja resolución espacial en datos visuales reduce la calidad en procesos médicos importantes tales como: diagnóstico de enfermedades, segmentación (tejido, nervios y hueso), construcción anatómica de atlas, reconstrucción detallada de fibras (tractografía), modelos de conductividad cerebral, etc. Segundo, para obtener imágenes de alta resolución se requiere una adquisición a largo plazo. Sin embargo, los protocolos clínicos actuales no permiten una exposición prolongada de la radiación (MRI y dMRI) en sujetos humanos

Probabilistic modeling of tensorial data for enhancing spatial resolution in magnetic resonance imaging.

Las imágenes médicas usan los principios de la Resonancia Magnética (IRM) para medir de forma no invasiva las propiedades de este movimiento. Cuando se aplica al cerebro humano, proporciona información única sobre la conectividad del tejido, lo que hace que la resonancia magnética sea una de las tecnologías clave en un esfuerzo científico continuo a gran escala para mapear el conector del cerebro humano. En consecuencia, es un tema de investigación oportuno e importante para crear modelos matemáticos que infieren parámetros biológicamente significativos a partir de dichos datos. La MRI y la difusión-MRI (dMRI) se han utilizado en aplicaciones que abarcan desde el procesamiento de señales, la visión por computadora y las neurociencias. Aunque los protocolos clínicos actuales permiten adquisiciones rápidas en un número diferente de cortes en varios planos, la resolución espacial no es lo suficientemente alta en muchos casos para el diagnóstico clínico. El principal problema ocurre debido a las limitaciones de hardware en los escáneres de adquisición. Por lo tanto, MRI y dMRI tienen un compromiso difícil entre una buena resolución espacial y una relación de ruido de señal (SNR). Esto conduce a adquisiciones de datos con baja resolución espacial. Se convierte en un problema serio para el análisis clínico por dos razones principales. Primero, una baja resolución espacial en datos visuales reduce la calidad en procesos médicos importantes tales como: diagnóstico de enfermedades, segmentación (tejido, nervios y hueso), construcción anatómica de atlas, reconstrucción detallada de fibras (tractografía), modelos de conductividad cerebral, etc. Segundo, para obtener imágenes de alta resolución se requiere una adquisición a largo plazo. Sin embargo, los protocolos clínicos actuales no permiten una exposición prolongada de la radiación (MRI y dMRI) en sujetos humanos

Imagerie de diffusion en temps-réel (correction du bruit et inférence de la connectivité cérébrale)

La plupart des constructeurs de systèmes d'imagerie par résonance magnétique (IRM) proposent un large choix d'applications de post-traitement sur les données IRM reconstruites a posteriori, mais très peu de ces applications peuvent être exécutées en temps réel pendant l'examen. Mises à part certaines solutions dédiées à l'IRM fonctionnelle permettant des expériences relativement simples ainsi que d'autres solutions pour l'IRM interventionnelle produisant des scans anatomiques pendant un acte de chirurgie, aucun outil n'a été développé pour l'IRM pondérée en diffusion (IRMd). Cependant, comme les examens d'IRMd sont extrêmement sensibles à des perturbations du système hardware ou à des perturbations provoquées par le sujet et qui induisent des données corrompues, il peut être intéressant d'investiguer la possibilité de reconstruire les données d'IRMd directement lors de l'examen. Cette thèse est dédiée à ce projet innovant. La contribution majeure de cette thèse a consisté en des solutions de débruitage des données d'IRMd en temps réel. En effet, le signal pondéré en diffusion peut être corrompu par un niveau élevé de bruit qui n'est plus gaussien, mais ricien ou chi non centré. Après avoir réalisé un état de l'art détaillé de la littérature sur le bruit en IRM, nous avons étendu l'estimateur linéaire qui minimise l'erreur quadratique moyenne (LMMSE) et nous l'avons adapté à notre cadre de temps réel réalisé avec un filtre de Kalman. Nous avons comparé les performances de cette solution à celles d'un filtrage gaussien standard, difficile à implémenter car il nécessite une modification de la chaîne de reconstruction pour y être inséré immédiatement après la démodulation du signal acquis dans l'espace de Fourier. Nous avons aussi développé un filtre de Kalman parallèle qui permet d'appréhender toute distribution de bruit et nous avons montré que ses performances étaient comparables à celles de notre méthode précédente utilisant un filtre de Kalman non parallèle. Enfin, nous avons investigué la faisabilité de réaliser une tractographie en temps-réel pour déterminer la connectivité structurelle en direct, pendant l'examen. Nous espérons que ce panel de développements méthodologiques permettra d'améliorer et d'accélérer le diagnostic en cas d'urgence pour vérifier l'état des faisceaux de fibres de la substance blanche.Most magnetic resonance imaging (MRI) system manufacturers propose a huge set of software applications to post-process the reconstructed MRI data a posteriori, but few of them can run in real-time during the ongoing scan. To our knowledge, apart from solutions dedicated to functional MRI allowing relatively simple experiments or for interventional MRI to perform anatomical scans during surgery, no tool has been developed in the field of diffusion-weighted MRI (dMRI). However, because dMRI scans are extremely sensitive to lots of hardware or subject-based perturbations inducing corrupted data, it can be interesting to investigate the possibility of processing dMRI data directly during the ongoing scan and this thesis is dedicated to this challenging topic. The major contribution of this thesis aimed at providing solutions to denoise dMRI data in real-time. Indeed, the diffusion-weighted signal may be corrupted by a significant level of noise which is not Gaussian anymore, but Rician or noncentral chi. After making a detailed review of the literature, we extended the linear minimum mean square error (LMMSE) estimator and adapted it to our real-time framework with a Kalman filter. We compared its efficiency to the standard Gaussian filtering, difficult to implement, as it requires a modification of the reconstruction pipeline to insert the filter immediately after the demodulation of the acquired signal in the Fourier space. We also developed a parallel Kalman filter to deal with any noise distribution and we showed that its efficiency was quite comparable to the non parallel Kalman filter approach. Last, we addressed the feasibility of performing tractography in real-time in order to infer the structural connectivity online. We hope that this set of methodological developments will help improving and accelerating a diagnosis in case of emergency to check the integrity of white matter fiber bundles.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Brain connectivity analysis: a short survey

This short survey the reviews recent literature on brain connectivity studies. It encompasses all forms of static and dynamic connectivity whether anatomical, functional, or effective. The last decade has seen an ever increasing number of studies devoted to deduce functional or effective connectivity, mostly from functional neuroimaging experiments. Resting state conditions have become a dominant experimental paradigm, and a number of resting state networks, among them the prominent default mode network, have been identified. Graphical models represent a convenient vehicle to formalize experimental findings and to closely and quantitatively characterize the various networks identified. Underlying these abstract concepts are anatomical networks, the so-called connectome, which can be investigated by functional imaging techniques as well. Future studies have to bridge the gap between anatomical neuronal connections and related functional or effective connectivities