Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates

Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

Reconstruction algorithms for Magnetic Resonance Imaging

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 135-142).This dissertation presents image reconstruction algorithms for Magnetic Resonance Imaging (MRI) that aims to increase the imaging efficiency. Algorithms that reduce imaging time without sacrificing the image quality and mitigate image artifacts are proposed. The goal of increasing the MR efficiency is investigated across multiple imaging techniques: structural imaging with multiple contrasts preparations, Diffusion Spectrum Imaging (DSI), Chemical Shift Imaging (CSI), and Quantitative Susceptibility Mapping (QSM). The main theme connecting the proposed methods is the utilization of prior knowledge on the reconstructed signal. This prior often presents itself in the form of sparsity with respect to either a prespecified or learned signal transformation.by Berkin Bilgic.Ph.D

Advances in diffusion MRI acquisition and processing in the Human Connectome Project

The Human Connectome Project (HCP) is a collaborative 5-year effort to map human brain connections and their variability in healthy adults. A consortium of HCP investigators will study a population of 1200 healthy adults using multiple imaging modalities, along with extensive behavioral and genetic data. In this overview, we focus on diffusion MRI (dMRI) and the structural connectivity aspect of the project. We present recent advances in acquisition and processing that allow us to obtain very high-quality in-vivo MRI data, whilst enabling scanning of a very large number of subjects. These advances result from 2 years of intensive efforts in optimising many aspects of data acquisition and processing during the piloting phase of the project. The data quality and methods described here are representative of the datasets and processing pipelines that will be made freely available to the community at quarterly intervals, beginning in 2013

Fast diffusion MRI based on sparse acquisition and reconstruction for long-term population imaging

Diffusion weighted magnetic resonance imaging (dMRI) is a unique MRI modality to probe the diffusive molecular transport in biological tissue. Due to its noninvasiveness and its ability to investigate the living human brain at submillimeter scale, dMRI is frequently performed in clinical and biomedical research to study the brain’s complex microstructural architecture. Over the last decades large prospective cohort studies have been set up with the aim to gain new insights into the development and progression of brain diseases across the life span and to discover biomarkers for disease prediction and potentially prevention. To allow for diverse brain imaging using different MRI modalities, stringent scan time limits are typically imposed in population imaging. Nevertheless, population studies aim to apply advanced and thereby time consuming dMRI protocols that deliver high quality data with great potential for future analysis. To allow for time-efficient but also versatile diffusion imaging, this thesis contributes to the investigation of accelerating diffusion spectrum imaging (DSI), an advanced dMRI technique that acquires imaging data with high intra-voxel resolution of tissue microstructure. Combining state-of-the-art parallel imaging and the theory of compressed sensing (CS) enables the acceleration of spatial encoding and diffusion encoding in dMRI. In this way, the otherwise long acquisition times in DSI can be reduced significantly. In this thesis, first, suitable q-space sampling strategies and basis functions are explored that fulfill the requirements of CS theory for accurate sparse DSI reconstruction. Novel 3D q-space sample distributions are investigated for CS-DSI. Moreover, conventional CS-DSI based on the discrete Fourier transform is compared for the first time to CS-DSI based on the continuous SHORE (simple harmonic oscillator based reconstruction and estimation) basis functions. Based on these findings, a CS-DSI protocol is proposed for application in a prospective cohort study, the Rhineland Study. A pilot study was designed and conducted to evaluate the CS-DSI protocol in comparison with state-of-the-art 3-shell dMRI and dedicated protocols for diffusion tensor imaging (DTI) and for the combined hindered and restricted model of diffusion (CHARMED). Population imaging requires processing techniques preferably with low computational cost to process and analyze the acquired big data within a reasonable time frame. Therefore, a pipeline for automated processing of CS-DSI acquisitions was implemented including both in-house developed and existing state-of-the-art processing tools. The last contribution of this thesis is a novel method for automatic detection and imputation of signal dropout due to fast bulk motion during the diffusion encoding in dMRI. Subject motion is a common source of artifacts, especially when conducting clinical or population studies with children, the elderly or patients. Related artifacts degrade image quality and adversely affect data analysis. It is, thus, highly desired to detect and then exclude or potentially impute defective measurements prior to dMRI analysis. Our proposed method applies dMRI signal modeling in the SHORE basis and determines outliers based on the weighted model residuals. Signal imputation reconstructs corrupted and therefore discarded measurements from the sparse set of inliers. This approach allows for fast and robust correction of imaging artifacts in dMRI which is essential to estimate accurate and precise model parameters that reflect the diffusive transport of water molecules and the underlying microstructural environment in brain tissue.Die diffusionsgewichtete Magnetresonanztomographie (dMRT) ist ein einzigartiges MRTBildgebungsverfahren, um die Diffusionsbewegung von Wassermolekülen in biologischem Gewebe zu messen. Aufgrund der Möglichkeit Schichtbilder nicht invasiv aufzunehmen und das lebende menschliche Gehirn im Submillimeter-Bereich zu untersuchen, ist die dMRT ein häufig verwendetes Bildgebungsverfahren in klinischen und biomedizinischen Studien zur Erforschung der komplexen mikrostrukturellen Architektur des Gehirns. In den letzten Jahrzehnten wurden große prospektive Kohortenstudien angelegt, um neue Einblicke in die Entwicklung und den Verlauf von Gehirnkrankheiten über die Lebenspanne zu erhalten und um Biomarker zur Krankheitserkennung und -vorbeugung zu bestimmen. Um durch die Verwendung unterschiedlicher MRT-Verfahren verschiedenartige Schichtbildaufnahmen des Gehirns zu ermöglich, müssen Scanzeiten typischerweise stark begrenzt werden. Dennoch streben Populationsstudien die Anwendung von fortschrittlichen und daher zeitintensiven dMRT-Protokollen an, um Bilddaten in hoher Qualität und mit großem Potential für zukünftige Analysen zu akquirieren. Um eine zeiteffizente und gleichzeitig vielseitige Diffusionsbildgebung zu ermöglichen, leistet diese Dissertation Beiträge zur Untersuchung von Beschleunigungsverfahren für die Bildgebung mittels diffusion spectrum imaging (DSI). DSI ist ein fortschrittliches dMRT-Verfahren, das Bilddaten mit hoher intra-voxel Auflösung der Gewebestruktur erhebt. Werden modernste Verfahren zur parallelen MRT-Bildgebung mit der compressed sensing (CS) Theorie kombiniert, ermöglicht dies eine Beschleunigung der räumliche Kodierung und der Diffusionskodierung in der dMRT. Dadurch können die ansonsten langen Aufnahmezeiten für DSI erheblich reduziert werden. In dieser Arbeit werden zuerst geeigenete Strategien zur Abtastung des q-space sowie Basisfunktionen untersucht, welche die Anforderungen der CS-Theorie für eine korrekte Signalrekonstruktion der dünnbesetzten DSI-Daten erfüllen. Neue 3D-Verteilungen von Messpunkten im q-space werden für die Verwendung in CS-DSI untersucht. Außerdem wird konventionell auf der diskreten Fourier-Transformation basierendes CS-DSI zum ersten Mal mit einem CS-DSI Verfahren verglichen, welches kontinuierliche SHORE (simple harmonic oscillator based reconstruction and estimation) Basisfunktionen verwendet. Aufbauend auf diesen Ergebnissen wird ein CS-DSI-Protokoll zur Anwendung in einer prospektiven Kohortenstudie, der Rheinland Studie, vorgestellt. Eine Pilotstudie wurde entworfen und durchgeführt, um das CS-DSI-Protokoll im Vergleich mit modernster 3-shell-dMRT und mit dedizierten Protokollen für diffusion tensor imaging (DTI) und für das combined hindered and restricted model of diffusion (CHARMED) zu evaluieren. Populationsbildgebung erfordert Prozessierungsverfahren mit möglichst geringem Rechenaufwand, um große akquirierte Datenmengen in einem angemessenen Zeitrahmen zu verarbeiten und zu analysieren. Dafür wurde eine Pipeline zur automatisierten Verarbeitung von CS-DSI-Daten implementiert, welche sowohl eigenentwickelte als auch bereits existierende moderene Verarbeitungsprogramme enthält. Der letzte Beitrag dieser Arbeit ist eine neue Methode zur automatischen Detektion und Imputation von Signalabfall, welcher durch schnelle Bewegungen während der Diffusionskodierung in der dMRT entsteht. Bewegungen der Probanden während der dMRT-Aufnahme sind eine häufige Ursache für Bildfehler, vor allem in klinischen oder Populationsstudien mit Kindern, alten Menschen oder Patienten. Diese Artefakte vermindern die Datenqualität und haben einen negativen Einfluss auf die Datenanalyse. Daher ist es das Ziel, fehlerhafte Messungen vor der dMRI-Analyse zu erkennen und dann auszuschließen oder wenn möglich zu ersetzen. Die vorgestellte Methode verwendet die SHORE-Basis zur dMRT-Signalmodellierung und bestimmt Ausreißer mit Hilfe von gewichteten Modellresidualen. Die Datenimputation rekonstruiert die unbrauchbaren und daher verworfenen Messungen mit Hilfe der verbleibenden, dünnbesetzten Menge an Messungen. Dieser Ansatz ermöglicht eine schnelle und robuste Korrektur von Bildartefakten in der dMRT, welche erforderlich ist, um korrekte und präzise Modellparameter zu schätzen, die die Diffusionsbewegung von Wassermolekülen und die zugrundeliegende Mikrostruktur des Gehirngewebes reflektieren

Spatially Regularized Reconstruction of Fibre Orientation Distributions in the Presence of Isotropic Diffusion

The connectivity and structural integrity of the white matter of the brain is known to be implicated in a wide range of brain-related diseases and injuries. However, it is only since the advent of diffusion magnetic resonance imaging (dMRI) that researchers have been able to probe the miscrostructure of white matter in vivo. Presently, among a range of methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). It preserves the high angular resolution property of diffusion spectrum imaging (DSI) but requires less measurements. Meanwhile, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel. Unfortunately, the ability of HARDI to discriminate neural fibres that cross each other at acute angles is always limited. The limitation becomes the motivation to develop numerous post-processing tools, aiming at the improvement of the angular resolution of HARDI. Among such methods, spherical deconvolution (SD) is the one which attracts the most attentions. Due to its ill-posed nature, however, standard SD relies on a number of a priori assumptions needed to render its results unique and stable. In the present thesis, we introduce a novel approach to the problem of non-blind SD of HARDI signals, which does not only consider the existence of anisotropic diffusion component of HARDI signal but also explicitly take the isotropic diffusion component into account. As a result of that, in addition to reconstruction of fODFs, our algorithm can also yield a useful estimation of its related IDM, which quantifies a relative contribution of the isotropic diffusion component as well as its spatial pattern. Moreover, one of the principal contributions is to demonstrate the effectiveness of exploiting different prior models for regularization of the spatial-domain behaviours of the reconstructed fODFs and IDMs. Specifically, the fibre continuity model has been used to force the local maxima of the fODFs to vary consistently throughout the brain, whereas the bounded variation model has helped us to achieve piecewise smooth reconstruction of the IDMs. The proposed algorithm is formulated as a convex minimization problem, which admits a unique and stable minimizer. Moreover, using ADMM, we have been able to find the optimal solution via a sequence of simpler optimization problems, which are both computationally efficient and amenable to parallel computations. In a series of both in silico and in vivo experiments, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatial coherency of cerebral diffusion at moderate to severe noise levels. The performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach. Moreover, the results illustrate the power of applied spatial regularization terms

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

On noise, uncertainty and inference for computational diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) has revolutionised the way brain microstructure and connectivity can be studied. Despite its unique potential in mapping the whole brain, biophysical properties are inferred from measurements rather than being directly observed. This indirect mapping from noisy data creates challenges and introduces uncertainty in the estimated properties. Hence, dMRI frameworks capable to deal with noise and uncertainty quantification are of great importance and are the topic of this thesis. First, we look into approaches for reducing uncertainty, by de-noising the dMRI signal. Thermal noise can have detrimental effects for modalities where the information resides in the signal attenuation, such as dMRI, that has inherently low-SNR data. We highlight the dual effect of noise, both in increasing variance, but also introducing bias. We then design a framework for evaluating denoising approaches in a principled manner. By setting objective criteria based on what a well-behaved denoising algorithm should offer, we provide a bespoke dataset and a set of evaluations. We demonstrate that common magnitude-based denoising approaches usually reduce noise-related variance from the signal, but do not address the bias effects introduced by the noise floor. Our framework also allows to better characterise scenarios where denoising can be beneficial (e.g. when done in complex domain) and can open new opportunities, such as pushing spatio-temporal resolution boundaries. Subsequently, we look into approaches for mapping uncertainty and design two inference frameworks for dMRI models, one using classical Bayesian methods and another using more recent data-driven algorithms. In the first approach, we build upon the univariate random-walk Metropolis-Hastings MCMC, an extensively used sampling method to sample from the posterior distribution of model parameters given the data. We devise an efficient adaptive multivariate MCMC scheme, relying upon the assumption that groups of model parameters can be jointly estimated if a proper covariance matrix is defined. In doing so, our algorithm increases the sampling efficiency, while preserving accuracy and precision of estimates. We show results using both synthetic and in-vivo dMRI data. In the second approach, we resort to Simulation-Based Inference (SBI), a data-driven approach that avoids the need for iterative model inversions. This is achieved by using neural density estimators to learn the inverse mapping from the forward generative process (simulations) to the parameters of interest that have generated those simulations. By addressing the problem via learning approaches offers the opportunity to achieve inference amortisation, boosting efficiency by avoiding the necessity of repeating the inference process for each new unseen dataset. It also allows inversion of forward processes (i.e. a series of processing steps) rather than only models. We explore different neural network architectures to perform conditional density estimation of the posterior distribution of parameters. Results and comparisons obtained against MCMC suggest speed-ups of 2-3 orders of magnitude in the inference process while keeping the accuracy in the estimates