Diffusion MRI analysis:robust and efficient microstructure modeling

Diffusion MRI (dMRI) allows for investigating the structure of the human brain. This is useful for both scientific brain research as well as medical diagnosis. Since the raw dMRI data is not directly interpretable by humans, we use mathematical models to convert the raw dMRI data into something interpretable. These models can be computed using multiple different computational methods, each having a different trade-off in accuracy, robustness and efficiency. In this thesis we studied multiple different computational models for their usability and efficiency for dMRI modeling. In the end we provide the reader with methodological recommendations for dMRI modeling and provide a high performance GPU enabled dMRI computing platform containing all recommendations

Bayesian uncertainty quantification in linear models for diffusion MRI

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.Comment: Added results from a group analysis and a comparison with residual bootstra

Multimodality characterization of microstructure by the combination of diffusion NMR and time-domain diffuse optical data

Combining datasets with a model of the underlying physics prior to mapping of tissue provides a novel approach improving the estimation of parameters. We demonstrate this approach by merging near infrared diffuse optical signal data with diffusion NMR data to inform a model describing the microstructure of a sample. The study is conducted on a homogeneous emulsion of oil in a dispersion medium of water and proteins. The use of a protein based background, rich in collagen, introduces a similarity to real tissues compared to other models such as intralipids. The sample is investigated with the two modalities separately. Then, the two datasets are used to inform a combined model, and to estimate the size of the microstructural elements and the volume fraction. The combined model fits the microstructural properties by minimizing the difference between experimental and modelled data. The experimental results are validated with confocal laser scanning microscopy. The final results demonstrate that the combined model provides improved estimates of microstructural parameters compared to either individual model alone

Robust Biophysical Parameter Estimation with a Neural Network Enhanced Hamiltonian Markov Chain Monte Carlo Sampler

Probabilistic parameter estimation in model fitting runs the gamut from maximum likelihood or maximum a posteriori point estimates from optimization to Markov Chain Monte Carlo (MCMC) sampling. The latter, while more computationally intensive, generally provides a better characterization of the underlying parameter distribution than that of point estimates. However, in order to efficiently explore distributions, MCMC methods ideally require generating uncorrelated samples while also preserving reasonable acceptance probabilities; this becomes particularly important in problematic regions of parameter space. In this paper, we extend a recently proposed Hamiltonian MCMC sampler parametrized by neural networks (L2HMC) by modifying the loss function to jointly optimize the distance between samples and the acceptance probability such that it is stable and efficient. We apply this enhanced sampler to parameter estimation in a recently proposed MRI model, the multi-echo spherical mean technique. We show that it generally outperforms the state of the art Hamiltonian No-U-Turn (NUTS) sampler, L2HMC, and a least squares fitting in terms of accuracy and precision, also enabling the generation of more informative parameter posterior distributions. This illustrates the potential of machine learning enhanced samplers for improving probabilistic parameter estimation for medical imaging applications

Generalized Wishart processes for interpolation over diffusion tensor fields

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used in clinical applications: tissue segmentation, fiber tractography, brain atlas construction, brain conductivity models, among others. Due to hardware limitations of MRI scanners, DTI has the difficult compromise between spatial resolution and signal noise ratio (SNR) during acquisition. For this reason, the data are often acquired with very low resolution. To enhance DTI data resolution, interpolation provides an interesting software solution. The aim of this work is to develop a methodology for DTI interpolation that enhance the spatial resolution of DTI fields. We assume that a DTI field follows a recently introduced stochastic process known as a generalized Wishart process (GWP), which we use as a prior over the diffusion tensor field. For posterior inference, we use Markov Chain Monte Carlo methods. We perform experiments in toy and real data. Results of GWP outperform other methods in the literature, when compared in different validation protocols

Contributions to MCMC Methods in Constrained Domains with Applications to Neuroimaging

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented. The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is first formulated as a model selection and estimation problem. Using the framework of reversible jump MCMC, a novel Bayesian scheme that performs both the above tasks simultaneously using customizable priors and proposal distributions is proposed. The proposed method allows users to set a prior level of spatial separation between the nerve fibers, allowing more crossing paths to be detected when desired or a lower number to potentially only detect robust nerve tracts. Hence, estimation that is specific to a given region of interest within the brain can be performed. In simulated examples, the method has been shown to resolve up to four fibers even in instances of highly noisy data. Comparative analysis with other state-of-the-art methods on in-vivo data showed the method\u27s ability to detect more crossing nerve fibers. The second work involves the construction of an MCMC algorithm that efficiently performs (Bayesian) sampling of parameters with support constraints. The method works by embedding a transformation called inversion in a sphere within the Metropolis-Hastings sampler. This creates an image of the constrained support that is amenable to sampling using standard proposals such as Gaussian. The proposed strategy is tested on three domains: the standard simplex, a sector of an n-sphere, and hypercubes. In each domain, a comparison is made with existing sampling techniques

Regional variation models of white matter microstructure

Diffusion-weighted MRI (DW-MRI) is a powerful in vivo imaging technique that is particularly sensitive to the underlying microstructure of white matter tissue in the brain. Many models of the DW-MRI signal exist that allow us to relate the signals we measure to various aspects of the tissue structure, including measures of diffusivity, cellularity and even axon size. From histology, we know that many of these microstructure measures display distinct patterns of variation on length scales greater than the average voxel size. However very few methods exist that use this spatial coherence to inform and guide parameter estimation. Instead, most techniques treat each voxel of data independently. This is particularly problematic when estimating parameters such as axon radius which only weakly influence the signal, as the resulting estimates are noisy. Several methods have been proposed that spatially smooth parameter estimates after fitting the model in each voxel. However if the parameter estimates are very noisy, the underlying trend is likely to be obscured. These methods are also unable to account for spatial coupling that may exist between the various parameters. This thesis introduces a novel framework, the Regional Variation Model (RVM), which exploits the underlying spatial coherence within white matter tracts to estimate trends of microstructure variation across large regions of interest. We fit curves describing parameter variation directly to the diffusion-weighted signals which should capture spatial changes in a more natural way as well as reducing the effects of noise. This allows for more precise estimates of a range of microstructure indices, including axon radius. The resulting curves, which show how microstructure parameters vary spatially through white matter regions, can also be used to detect groupwise differences with potentially greater power than traditional methods

Adaptive microstructure-informed tractography for accurate brain connectivity analyses

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 orientation 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 acquisition 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

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