An Optimal Dimensionality Multi-shell Sampling Scheme with Accurate and Efficient Transforms for Diffusion MRI

This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an optimal number of samples, equal to the degrees of freedom of the band-limited diffusion signal in the SPF domain, and allows for computationally efficient reconstruction. We use synthetic data sets to demonstrate that the proposed scheme allows for greater reconstruction accuracy of the diffusion signal than the multi-shell sampling schemes obtained using the generalised electrostatic energy minimisation (gEEM) method used in the Human Connectome Project. We also demonstrate that the proposed sampling scheme allows for increased angular discrimination and improved rotational invariance of reconstruction accuracy than the gEEM schemes.Comment: 4 pages, 4 figures presented at ISBI 201

An Optimal Dimensionality Sampling Scheme on the Sphere for Antipodal Signals In Diffusion Magnetic Resonance Imaging

We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.Comment: Will be published in the proceedings of the International Conference Acoustics, Speech and Signal Processing 2015 (ICASSP'2015

Predictive Diagnosis of Alzheimer's Disease using Diffusion MRI

Age-related neurodegenerative diseases, including Alzheimer’s Disease (AD), are an increasing cause of concern for the world’s ageing population. The current consensus in the research community is that the main setbacks in the treatment of AD include the inability to diagnose it in its early stages and the lack of accurate stratification techniques for the prodromal stages of the disease and normal control (NC) subject groups. Numerous studies show that AD causes damage to the white matter microstructure in the brain. Commonly used techniques for diagnosing this disease include, neuropsychological assessments, genetics, proteomics, and image-based analysis. However, unlike these techniques, recent advances in Diffusion Magnetic Resonance Imaging (dMRI) analysis posits its sensitivity to the microstructural organization of cerebral white matter, and hence its applicability for early diagnosis of AD. Since tissue damage is reflected in the pattern of water diffusion in neural fibre structures, dMRI can be used to track disease-related changes in the brain. Contemporary dMRI approaches are broadly classified as being either region-based or tract-based. This thesis draws on the strengths of both these approaches by proposing an original extension of region-based methods to the simultaneous analysis of multiple brain regions. A predefined set of features is derived from dMRI data and used to compute the probabilistic distances between different brain regions. The resulting statistical associations can be modelled as an undirected and fully-connected graph encoding a unique brain connectivity pattern. Subsequently, the characteristics of this graph are used for the stratification of AD and NC subjects. Although the current work focuses on AD and NC subject populations, the perfect separability achieved between the two groups suggests the suitability of the technique for separating NC, AD, in addition to subjects in the prodromal stage of the disease, i.e., mild cognitive impairment (MCI)

Unsupervised deep learning of human brain diffusion magnetic resonance imaging tractography data

L'imagerie par résonance magnétique de diffusion est une technique non invasive permettant de connaître la microstructure organisationnelle des tissus biologiques. Les méthodes computationnelles qui exploitent la préférence orientationnelle de la diffusion dans des structures restreintes pour révéler les voies axonales de la matière blanche du cerveau sont appelées tractographie. Ces dernières années, diverses méthodes de tractographie ont été utilisées avec succès pour découvrir l'architecture de la matière blanche du cerveau. Pourtant, ces techniques de reconstruction souffrent d'un certain nombre de défauts dérivés d'ambiguïtés fondamentales liées à l'information orientationnelle. Cela a des conséquences dramatiques, puisque les cartes de connectivité de la matière blanche basées sur la tractographie sont dominées par des faux positifs. Ainsi, la grande proportion de voies invalides récupérées demeure un des principaux défis à résoudre par la tractographie pour obtenir une description anatomique fiable de la matière blanche. Des approches méthodologiques innovantes sont nécessaires pour aider à résoudre ces questions. Les progrès récents en termes de puissance de calcul et de disponibilité des données ont rendu possible l'application réussie des approches modernes d'apprentissage automatique à une variété de problèmes, y compris les tâches de vision par ordinateur et d'analyse d'images. Ces méthodes modélisent et trouvent les motifs sous-jacents dans les données, et permettent de faire des prédictions sur de nouvelles données. De même, elles peuvent permettre d'obtenir des représentations compactes des caractéristiques intrinsèques des données d'intérêt. Les approches modernes basées sur les données, regroupées sous la famille des méthodes d'apprentissage profond, sont adoptées pour résoudre des tâches d'analyse de données d'imagerie médicale, y compris la tractographie. Dans ce contexte, les méthodes deviennent moins dépendantes des contraintes imposées par les approches classiques utilisées en tractographie. Par conséquent, les méthodes inspirées de l'apprentissage profond conviennent au changement de paradigme requis, et peuvent ouvrir de nouvelles possibilités de modélisation, en améliorant ainsi l'état de l'art en tractographie. Dans cette thèse, un nouveau paradigme basé sur les techniques d'apprentissage de représentation est proposé pour générer et analyser des données de tractographie. En exploitant les architectures d'autoencodeurs, ce travail tente d'explorer leur capacité à trouver un code optimal pour représenter les caractéristiques des fibres de la matière blanche. Les contributions proposées exploitent ces représentations pour une variété de tâches liées à la tractographie, y compris (i) le filtrage et (ii) le regroupement efficace sur les résultats générés par d'autres méthodes, ainsi que (iii) la reconstruction proprement dite des fibres de la matière blanche en utilisant une méthode générative. Ainsi, les méthodes issues de cette thèse ont été nommées (i) FINTA (Filtering in Tractography using Autoencoders), (ii) CINTA (Clustering in Tractography using Autoencoders), et (iii) GESTA (Generative Sampling in Bundle Tractography using Autoencoders), respectivement. Les performances des méthodes proposées sont évaluées par rapport aux méthodes de l'état de l'art sur des données de diffusion synthétiques et des données de cerveaux humains chez l'adulte sain in vivo. Les résultats montrent que (i) la méthode de filtrage proposée offre une sensibilité et spécificité supérieures par rapport à d'autres méthodes de l'état de l'art; (ii) le regroupement des tractes dans des faisceaux est fait de manière consistante; et (iii) l'approche générative échantillonnant des tractes comble mieux l'espace de la matière blanche dans des régions difficiles à reconstruire. Enfin, cette thèse révèle les possibilités des autoencodeurs pour l'analyse des données des fibres de la matière blanche, et ouvre la voie à fournir des données de tractographie plus fiables.Abstract : Diffusion magnetic resonance imaging is a non-invasive technique providing insights into the organizational microstructure of biological tissues. The computational methods that exploit the orientational preference of the diffusion in restricted structures to reveal the brain's white matter axonal pathways are called tractography. In recent years, a variety of tractography methods have been successfully used to uncover the brain's white matter architecture. Yet, these reconstruction techniques suffer from a number of shortcomings derived from fundamental ambiguities inherent to the orientation information. This has dramatic consequences, since current tractography-based white matter connectivity maps are dominated by false positive connections. Thus, the large proportion of invalid pathways recovered remains one of the main challenges to be solved by tractography to obtain a reliable anatomical description of the white matter. Methodological innovative approaches are required to help solving these questions. Recent advances in computational power and data availability have made it possible to successfully apply modern machine learning approaches to a variety of problems, including computer vision and image analysis tasks. These methods model and learn the underlying patterns in the data, and allow making accurate predictions on new data. Similarly, they may enable to obtain compact representations of the intrinsic features of the data of interest. Modern data-driven approaches, grouped under the family of deep learning methods, are being adopted to solve medical imaging data analysis tasks, including tractography. In this context, the proposed methods are less dependent on the constraints imposed by current tractography approaches. Hence, deep learning-inspired methods are suit for the required paradigm shift, may open new modeling possibilities, and thus improve the state of the art in tractography. In this thesis, a new paradigm based on representation learning techniques is proposed to generate and to analyze tractography data. By harnessing autoencoder architectures, this work explores their ability to find an optimal code to represent the features of the white matter fiber pathways. The contributions exploit such representations for a variety of tractography-related tasks, including efficient (i) filtering and (ii) clustering on results generated by other methods, and (iii) the white matter pathway reconstruction itself using a generative method. The methods issued from this thesis have been named (i) FINTA (Filtering in Tractography using Autoencoders), (ii) CINTA (Clustering in Tractography using Autoencoders), and (iii) GESTA (Generative Sampling in Bundle Tractography using Autoencoders), respectively. The proposed methods' performance is assessed against current state-of-the-art methods on synthetic data and healthy adult human brain in vivo data. Results show that the (i) introduced filtering method has superior sensitivity and specificity over other state-of-the-art methods; (ii) the clustering method groups streamlines into anatomically coherent bundles with a high degree of consistency; and (iii) the generative streamline sampling technique successfully improves the white matter coverage in hard-to-track bundles. In summary, this thesis unlocks the potential of deep autoencoder-based models for white matter data analysis, and paves the way towards delivering more reliable tractography data

Feature-Based Correspondences to Infer the Location of Anatomical Landmarks

A methodology has been developed for automatically determining inter-image correspondences between cliques of features extracted from a reference and a query image. Cliques consist of up to threefeatures and correspondences between them are determined via a hierarchy of similarity metrics based on the inherent properties of the features and geometric relationships between those features. As opposed to approaches that determine correspondences solely by voxel intensity, features that also include shape description are used. Specifically, medial-based features areemployed because they are sparse compared to the number of image voxels and can be automatically extracted from the image.The correspondence framework has been extended to automatically estimate the location of anatomical landmarks in the query image by adding landmarks to the cliques. Anatomical landmark locationsare then inferred from the reference image by maximizing landmark correspondences. The ability to infer landmark locations has provided a means to validate the correspondence framework in thepresence of structural variation between images. Moreover, automated landmark estimation imparts the user with anatomical information and can hypothetically be used to initialize andconstrain the search space of segmentation and registration methods.Methods developed in this dissertation were applied to simulated MRI brain images, synthetic images, and images constructed from several variations of a parametric model. Results indicate that the methods are invariant to global translation and rotation and can operate in the presence of structure variation between images.The automated landmark placement method was shown to be accurate as compared to ground-truth that was established both parametrically and manually. It is envisioned that these automated methods could prove useful for alleviating time-consuming and tedious tasks in applications that currently require manual input, and eliminate intra-user subjectivity

Spatially Regularized Spherical Reconstruction: A Cross-Domain Filtering Approach for HARDI Signals

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations

Predicting the Outcome of Cognitive Training in Parkinson’s Disease using Magnetic Resonance Imaging

Motivation: Cognitive impairment is an important symptom of Parkinson’s Disease (PD), usually having a substantial negative impact on the quality of life of patients, families, and caregivers. Cognitive Training (CT) have been proven effective in halting the process of cognitive decline in PD. However, the efficacy of CT is unpredictable from subject to subject. Objective: Investigate the possibility of predicting the outcome of CT in PD patients with Mild Cognitive Impairment using structural and functional Magnetic Resonance Imaging (MRI) data. Methods: Before CT, a sample of 42 PD patients underwent structural and functional MRI. Graph measures were then extracted from their structural and functional con nectomes and used as features for random forest (RFo) and decision tree (DT) machine learning (ML) regression algorithms with and without prior latent component analysis (LCA). CT response was evaluated by assessing the outcomes of the Tower of London task pre- and post-treatment. Finally, the 4 ML models were used to predict CT response and their performances were assessed. Post hoc analyses were conducted to investigate whether these algorithms could predict age using connectomic measures on a sample of 80 PD patients. Results: The performances of the aforementioned algorithms did not differ signifi cantly from the baseline performance predicting the subject-specific CT outcome. The performance of the RFo without LCA differed significantly from the baseline performance in the age prediction task for the sample of 80 patients. Conclusion: Notwithstanding the lack of statistical significance in predicting our xicognitive outcomes, the relative success of the age prediction task points towards the potential of this approach. We hypothesise that bigger sample sizes are needed in order to predict the outcome of CT using ML