Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex fiber configurations, albeit at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a kq-space under-sampling scheme to enable accelerated acquisitions. The inverse problem for reconstruction of the fiber orientation distribution (FOD) is regularized by a structured sparsity prior promoting simultaneously voxelwise sparsity and spatial smoothness of fiber orientation. Prior knowledge of the spatial distribution of white matter, gray matter and cerebrospinal fluid is also assumed. A minimization problem is formulated and solved via a forward-backward convex optimization algorithmic structure. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes, potentially enabling high spatio-angular dMRI in the clinical setting.Comment: 10 pages, 5 figures, Supplementary Material

Ball and rackets: inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions

Quantitative Susceptibility Mapping: Contrast Mechanisms and Clinical Applications.

Quantitative susceptibility mapping (QSM) is a recently developed MRI technique for quantifying the spatial distribution of magnetic susceptibility within biological tissues. It first uses the frequency shift in the MRI signal to map the magnetic field profile within the tissue. The resulting field map is then used to determine the spatial distribution of the underlying magnetic susceptibility by solving an inverse problem. The solution is achieved by deconvolving the field map with a dipole field, under the assumption that the magnetic field is a result of the superposition of the dipole fields generated by all voxels and that each voxel has its unique magnetic susceptibility. QSM provides improved contrast to noise ratio for certain tissues and structures compared to its magnitude counterpart. More importantly, magnetic susceptibility is a direct reflection of the molecular composition and cellular architecture of the tissue. Consequently, by quantifying magnetic susceptibility, QSM is becoming a quantitative imaging approach for characterizing normal and pathological tissue properties. This article reviews the mechanism generating susceptibility contrast within tissues and some associated applications

Homogeneity based segmentation and enhancement of Diffusion Tensor Images : a white matter processing framework

In diffusion magnetic resonance imaging (DMRI) the Brownian motion of the water molecules, within biological tissue, is measured through a series of images. In diffusion tensor imaging (DTI) this diffusion is represented using tensors. DTI describes, in a non-invasive way, the local anisotropy pattern enabling the reconstruction of the nervous fibers - dubbed tractography. DMRI constitutes a powerful tool to analyse the structure of the white matter within a voxel, but also to investigate the anatomy of the brain and its connectivity. DMRI has been proved useful to characterize brain disorders, to analyse the differences on white matter and consequences in brain function. These procedures usually involve the virtual dissection of white matters tracts of interest. The manual isolation of these bundles requires a great deal of neuroanatomical knowledge and can take up to several hours of work. This thesis focuses on the development of techniques able to automatically perform the identification of white matter structures. To segment such structures in a tensor field, the similarity of diffusion tensors must be assessed for partitioning data into regions, which are homogeneous in terms of tensor characteristics. This concept of tensor homogeneity is explored in order to achieve new methods for segmenting, filtering and enhancing diffusion images. First, this thesis presents a novel approach to semi-automatically define the similarity measures that better suit the data. Following, a multi-resolution watershed framework is presented, where the tensor field’s homogeneity is used to automatically achieve a hierarchical representation of white matter structures in the brain, allowing the simultaneous segmentation of different structures with different sizes. The stochastic process of water diffusion within tissues can be modeled, inferring the homogeneity characteristics of the diffusion field. This thesis presents an accelerated convolution method of diffusion images, where these models enable the contextual processing of diffusion images for noise reduction, regularization and enhancement of structures. These new methods are analysed and compared on the basis of their accuracy, robustness, speed and usability - key points for their application in a clinical setting. The described methods enrich the visualization and exploration of white matter structures, fostering the understanding of the human brain

Axonal T₂ estimation using the spherical variance of the strongly diffusion-weighted MRI signal.

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T <sub>2</sub> that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T <sub>2</sub> , as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T <sub>2</sub> based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T <sub>2</sub> estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system

Tractographie adaptative basée sur la microstructure pour des analyses précises de la connectivité cérébrale

Le cerveau est un sujet de recherche depuis plusieurs décennies, puisque son rôle est central dans la compréhension du genre humain. Le cerveau est composé de neurones, où leurs dendrites et synapses se retrouvent dans la matière grise alors que les axones en constituent la matière blanche. L’information traitée dans les différentes régions de la matière grise est ensuite transmise par l’intermédiaire des axones afin d’accomplir différentes fonctions cognitives. La matière blanche forme une structure d’interconnections complexe encore dif- ficile à comprendre et à étudier. La relation entre l’architecture et la fonction du cerveau a été étudiée chez les humains ainsi que pour d’autres espèces, croyant que l’architecture des axones déterminait la dynamique du réseau fonctionnel. Dans ce même objectif, l’Imagerie par résonance (IRM) est un outil formidable qui nous permet de visualiser les tissus cérébraux de façon non-invasive. Plus partic- ulièrement, l’IRM de diffusion permet d’estimer et de séparer la diffusion libre de celle restreinte par la structure des tissus. Cette mesure de restriction peut être utilisée afin d’inférer l’orientation locale des faisceaux de matière blanche. L’algorithme de tractographie exploite cette carte d’orientation pour reconstruire plusieurs connexions de la matière blanche (nommées “streamlines”). Cette modélisation de la matière blanche permet d’estimer la connectivité cérébrale dite structurelle entre les différentes régions du cerveau. Ces résultats peuvent être employés directement pour la planification chirurgicale ou indirectement pour l’analyse ou une évaluation clinique. Malgré plusieurs de ses limitations, telles que sa variabilité et son imprécision, la tractographie reste l’unique moyen d’étudier l’architecture de la matière blanche ainsi que la connectivité cérébrale de façon non invasive. L’objectif de ce projet de doctorat est de répondre spécifiquement à ces limitations et d’améliorer la précision anatomique des estimations de connectivité structurelle. Dans ce but, nous avons développé un algorithme d’optimisation globale qui exploite les informations de micro et macrostructure, en introduisant une procédure itéra- tive qui utilise les propriétés sous-jacentes des tissus pour piloter la reconstruction en utilisant une approche semi-globale. Ensuite, nous avons étudié la possibilité d’adapter dynamiquement la position d’un ensemble de lignes de courant candidates tout en intégrant le préalable anatomique de la douceur des trajectoires et en adap- tant la configuration en fonction des données observées. Enfin, nous avons introduit le concept de bundle-o-graphy en mettant en œuvre une méthode pour modéliser des groupes de lignes de courant basées sur le concept que les axones sont organisés en fascicules, en adaptant leur forme et leur étendue en fonction de la microstructure sous-jacente.Abstract : Human brain has been subject of deep interest for centuries, given it’s central role in controlling and directing the actions and functions of the body as response to external stimuli. The neural tissue is primarily constituted of neurons and, together with dendrites and the nerve synapses, constitute the gray matter (GM) which plays a major role in cognitive functions. The information processed in the GM travel from one region to the other of the brain along nerve cell projections, called axons. All together they constitute the white matter (WM) whose wiring organization still remains challenging to uncover. The relationship between structure organization of the brain and function has been deeply investigated on humans and animals based on the assumption that the anatomic architecture determine the network dynamics. In response to that, many different imaging techniques raised, among which diffusion-weighted magnetic resonance imaging (DW-MRI) has triggered tremendous hopes and expectations. Diffusion-weighted imaging measures both restricted and unrestricted diffusion, i.e. the degree of movement freedom of the water molecules, allowing to map the tissue fiber architecture in vivo and non-invasively. Based on DW-MRI data, tractography is able to exploit information of the local fiber orien- tation to recover global fiber pathways, called streamlines, that represent groups of axons. This, in turn, allows to infer the WM structural connectivity, becoming widely used in many different clinical applications as for diagnoses, virtual dissections and surgical planning. However, despite this unique and compelling ability, data acqui- sition still suffers from technical limitations and recent studies have highlighted the poor anatomical accuracy of the reconstructions obtained with this technique and challenged its effectiveness for studying brain connectivity. The focus of this Ph.D. project is to specifically address these limitations and to improve the anatomical accuracy of the structural connectivity estimates. To this aim, we developed a global optimization algorithm that exploits micro and macro- structure information, introducing an iterative procedure that uses the underlying tissue properties to drive the reconstruction using a semi-global approach. Then, we investigated the possibility to dynamically adapt the position of a set of candidate streamlines while embedding the anatomical prior of trajectories smoothness and adapting the configuration based on the observed data. Finally, we introduced the concept of bundle-o-graphy by implementing a method to model groups of streamlines based on the concept that axons are organized into fascicles, adapting their shape and extent based on the underlying microstructure.Sommario : Il cervello umano è oggetto di profondo interesse da secoli, dato il suo ruolo centrale nel controllare e dirigere le azioni e le funzioni del corpo in risposta a stimoli esterno. Il tessuto neurale è costituito principalmente da neuroni che, insieme ai dendriti e alle sinapsi nervose, costituiscono la materia grigia (GM), la quale riveste un ruolo centrale nelle funzioni cognitive. Le informazioni processate nella GM viaggiano da una regione all’altra del cervello lungo estensioni delle cellule nervose, chiamate assoni. Tutti insieme costituiscono la materia bianca (WM) la cui organizzazione strutturale rimane tuttora sconosciuta. Il legame tra struttura e funzione del cervello sono stati studiati a fondo su esseri umani e animali partendo dal presupposto che l’architettura anatomica determini la dinamica della rete funzionale. In risposta a ciò, sono emerse diverse tecniche di imaging, tra cui la risonanza magnetica pesata per diffusione (DW-MRI) ha suscitato enormi speranze e aspettative. Questa tecnica misura la diffusione sia libera che ristretta, ovvero il grado di libertà di movimento delle molecole d’acqua, consentendo di mappare l’architettura delle fibre neuronali in vivo e in maniera non invasiva. Basata su dati DW-MRI, la trattografia è in grado di sfruttare le informazioni sull’orientamento locale delle fibre per ricostruirne i percorsi a livello globale. Questo, a sua volta, consente di estrarre la connettività strutturale della WM, utilizzata in diverse applicazioni cliniche come per diagnosi, dissezioni virtuali e pianificazione chirurgica. Tuttavia, nonostante questa capacità unica e promettente, l’acquisizione dei dati soffre ancora di limitazioni tecniche e recenti studi hanno messo in evidenza la scarsa accuratezza anatomica delle ricostruzioni ottenute con questa tecnica, mettendone in dubbio l’efficacia per lo studio della connettività cerebrale. Il focus di questo progetto di dottorato è quello di affrontare in modo specifico queste limitazioni e di migliorare l’accuratezza anatomica delle stime di connettività strutturale. A tal fine, abbiamo sviluppato un algoritmo di ottimizzazione globale che sfrutta le informazioni sia micro che macrostrutturali, introducendo una procedura iterativa che utilizza le proprietà del tessuto neuronale per guidare la ricostruzione utilizzando un approccio semi-globale. Successivamente, abbiamo studiato la possibilità di adattare dinamicamente la posizione di un insieme di streamline candidate incorporando il prior anatomico per cui devono seguire traiettorie regolari e adattando la configurazione in base ai dati osservati. Infine, abbiamo introdotto il concetto di bundle-o-graphy implementando un metodo per modellare gruppi di streamline basato sul concetto che gli assoni sono organizzati in fasci, adattando la loro forma ed estensione in base alla microstruttura sottostante