Doctor of Philosophy

dissertationDiffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance imaging: where and how much are the uncertainties? How do we reduce these uncertainties? How can we possibly validate our algorithms

Development of High Angular Resolution Diffusion Imaging Analysis Paradigms for the Investigation of Neuropathology

Diffusion weighted magnetic resonance imaging (DW-MRI), provides unique insight into the microstructure of neural white matter tissue, allowing researchers to more fully investigate white matter disorders. The abundance of clinical research projects incorporating DW-MRI into their acquisition protocols speaks to the value this information lends to the study of neurological disease. However, the most widespread DW-MRI technique, diffusion tensor imaging (DTI), possesses serious limitations which restrict its utility in regions of complex white matter. Fueled by advances in DW-MRI acquisition protocols and technologies, a group of exciting new DW-MRI models, developed to address these concerns, are now becoming available to clinical researchers. The emergence of these new imaging techniques, categorized as high angular resolution diffusion imaging (HARDI), has generated the need for sophisticated computational neuroanatomic techniques able to account for the high dimensionality and structure of HARDI data. The goal of this thesis is the development of such techniques utilizing prominent HARDI data models. Specifically, methodologies for spatial normalization, population atlas building and structural connectivity have been developed and validated. These methods form the core of a comprehensive analysis paradigm allowing the investigation of local white matter microarcitecture, as well as, systemic properties of neuronal connectivity. The application of this framework to the study of schizophrenia and the autism spectrum disorders demonstrate its sensitivity sublte differences in white matter organization, as well as, its applicability to large population DW-MRI studies

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

International audienceDiffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-of- the-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI

Hitting the right target : noninvasive localization of the subthalamic nucleus motor part for specific deep brain stimulation

Deep brain stimulation of the subthalamic nucleus (STN) has gained momentum as a therapy for advanced Parkinson’s disease. The stimulation effectively alleviates the patients’ typical motor symptoms on a long term, but can give rise to cognitive and psychiatric adverse effects as well. Based on primate studies, the STN has been divided into three functionally different parts, which were distinguished by their afferent and efferent connections. The largest part is the motor area, followed by an associative and a limbic area. The serious adverse effects on cognition and behavior occurring after deep brain stimulation are assumed to be caused by electrical current spread to the associative and limbic areas of the STN. Therefore, selective stimulation of the motor part of the STN seems crucial, both to obtain the best possible therapeutic effect on the motor symptoms and to minimize the debilitating effects on cognition and behavior. However, current medical imaging techniques do not yet facilitate the required accurate identification of the STN itself, let alone its different functional areas. The final target for DBS is still often adjusted using intraoperative electrophysiology. Therefore, in this thesis we aimed to improve imaging for deep brain stimulation using noninvasive MRI protocols, in order to identify the STN and its motor part. We studied the advantages and drawbacks of already available noninvasive methods to target the STN. This review did not lead to a straightforward conclusion; identification of the STN motor part remained an open question. In follow-up on this question, we investigated the possibility to distinguish the different functional STN parts based on their connectivity information. Three types of information were carefully analyzed in this thesis. First, we looked into the clustering of local diffusion information within the STN region. We visually inspected the complex diffusion profiles, derived from postmortem rat brain data with high angular resolution, and augmented this manual segmentation method using k-means and graph cuts clustering. Because the weighing of different orders of diffusion information in the traditionally used L2 norm on the orientation distribution functions (ODFs) remained an open issue, we developed a specialized distance measure, the so-called Sobolev norm. This norm does not only take into account the amplitudes of the diffusion profiles, but also their extrema. We showed it to perform better than the L2 norm on synthetic phantom data and real brain (thalamus) data. The research done on this topic facilitates better classification by clustering of gray matter structures in the (deep) brain. Secondly, we were the first to analyze the STN’s full structural connectivity, based on probabilistic fiber tracking in diffusion MRI data of healthy volunteers. The results correspond well to topical literature on STN projections. Furthermore, we assessed the structural connectivity per voxel of the STN seed region and discovered a gradient in connectivity to the premotor cortex within the STN. While going from the medial to the lateral part of the STN, the connectivity increases, confirming the expected lateral location of the STN motor part. Finally, the connectivity analysis produced evidence for the existence of a "hyperdirect" pathway between the motor cortex and the STN in humans, which is very useful for future research into stimulation targets. The results of these experiments indicate that it is possible to find the motor part of the STN as specific target for deep brain stimulation using structural connectivity information acquired in a noninvasive way. Third and last, we studied functional connectivity using resting state functional MRI data of healthy volunteers. The resulting significant clusters provided us with the first complete description of the STN’s resting state functional connectivity, which corresponds with the expectations based on available literature. Moreover, we performed a reverse regression procedure with the average time series signals in motor and limbic areas as principal regressors. The results were analyzed for each STN voxel separately and also showed mediolateral gradients in functional connectivity within the STN. The lateral STN part exhibited more motor connectivity, while the medial part seemed to be more functionally connected to limbic brain areas, as described in neuronal tracer studies. These results show that functional connectivity analysis also is a viable noninvasive method to find the motor part of the STN. The work on noninvasive MRI methods for identification of the STN and its functional parts, as presented in this thesis, thus contributes to future specific stimulation of the motor part of the STN for deep brain stimulation in patients with Parkinson’s disease. This may help to maximize the motor effects and minimize severe cognitive and psychiatric side effects

RECOVERING LOCAL NEURAL TRACT DIRECTIONS AND RECONSTRUCTING NEURAL PATHWAYS IN HIGH ANGULAR RESOLUTION DIFFUSION MRI

Magnetic resonance imaging (MRI) is an imaging technique to visualize internal structures of the body. Diffusion MRI is an MRI modality that measures overall diffusion effect of molecules in vivo and non-invasively. Diffusion tensor imaging (DTI) is an extended technique of diffusion MRI. The major application of DTI is to measure the location, orientation and anisotropy of fiber tracts in white matter. It enables non-invasive investigation of major neural pathways of human brain, namely tractography. As spatial resolution of MRI is limited, it is possible that there are multiple fiber bundles within the same voxel. However, diffusion tensor model is only capable of resolving a single direction. The goal of this dissertation is to investigate complex anatomical structures using high angular resolution diffusion imaging (HARDI) data without any assumption on the parameters. The dissertation starts with a study of the noise distribution of truncated MRI data. The noise is often not an issue in diffusion tensor model. However, in HARDI studies, with many more gradient directions being scanned, the number of repetitions of each gradient direction is often small to restrict total acquisition time, making signal-to-noise ratio (SNR) lower. Fitting complex diffusion models to data with reduced SNR is a major interest of this study. We focus on fitting diffusion models to data using maximum likelihood estimation (MLE) method, in which the noise distribution is used to maximize the likelihood. In addition to the parameters being estimated, we use likelihood values for model selection when multiple models are fit to the same data. The advantage of carrying out model selection after fitting the models is that both the quality of data and the quality of fitting results are taken into account. When it comes to tractography, we extend streamline method by using covariance of the estimated parameters to generate probabilistic tracts according to the uncertainty of local tract orientations

Characterising population variability in brain structure through models of whole-brain structural connectivity

Models of whole-brain connectivity are valuable for understanding neurological function. This thesis seeks to develop an optimal framework for extracting models of whole-brain connectivity from clinically acquired diffusion data. We propose new approaches for studying these models. The aim is to develop techniques which can take models of brain connectivity and use them to identify biomarkers or phenotypes of disease. The models of connectivity are extracted using a standard probabilistic tractography algorithm, modified to assess the structural integrity of tracts, through estimates of white matter anisotropy. Connections are traced between 77 regions of interest, automatically extracted by label propagation from multiple brain atlases followed by classifier fusion. The estimates of tissue integrity for each tract are input as indices in 77x77 ”connectivity” matrices, extracted for large populations of clinical data. These are compared in subsequent studies. To date, most whole-brain connectivity studies have characterised population differences using graph theory techniques. However these can be limited in their ability to pinpoint the locations of differences in the underlying neural anatomy. Therefore, this thesis proposes new techniques. These include a spectral clustering approach for comparing population differences in the clustering properties of weighted brain networks. In addition, machine learning approaches are suggested for the first time. These are particularly advantageous as they allow classification of subjects and extraction of features which best represent the differences between groups. One limitation of the proposed approach is that errors propagate from segmentation and registration steps prior to tractography. This can cumulate in the assignment of false positive connections, where the contribution of these factors may vary across populations, causing the appearance of population differences where there are none. The final contribution of this thesis is therefore to develop a common co-ordinate space approach. This combines probabilistic models of voxel-wise diffusion for each subject into a single probabilistic model of diffusion for the population. This allows tractography to be performed only once, ensuring that there is one model of connectivity. Cross-subject differences can then be identified by mapping individual subjects’ anisotropy data to this model. The approach is used to compare populations separated by age and gender

A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data

Diffusion weighted ( DW ) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation ( with various well-documented limitations ), towards more complex high angular resolution diffusion imaging ( HARDI ) analysis techniques. Spherical deconvolution ( SD ) approaches assume that the fibre orientation density function ( fODF ) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: ( 1 ) constrained spherical harmonic deconvolution ( CSHD )—a technique that exploits spherical harmonic basis sets and ( 2 ) damped Richardson–Lucy ( dRL ) deconvolution—a technique based on the standard Richardson–Lucy deconvolution. Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed ( ‘Target’ ) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks ( consistent with well known ringing artefacts ) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration ( with a calibration response function for a highly anisotropic fibre being optimal ). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography

Segmentation of diffusion weighted MRI using the level set framework

Medical imaging is a rapidly growing field in which diffusion imaging is a recently developed modality. This novel imaging contrast permits in-vivo measurement of the diffusion of water molecules. This is particularly interesting in brain imaging where the diffusion reveals an amazing insight into the neuronal organization and cerebral cytoarchitecture. Diffusion images contain from six up to hundreds of values in each voxel and are represented as tensor fields (Diffusion Tensor Imaging (DTI)) or as fields of functions (High Angular Resolution Diffusion (HARD) imaging). To fully extract the large amount of data contained within these images new processing and analysis tools are needed. The aim of this thesis is the development of such tools. The method we have been mainly focusing on for this purpose is the level set method. The level set method is a numerical and theoretical tool for propagating interfaces. In image processing it is used for propagating curves in 2D or surfaces in 3D for delineation of objects or for regularization purposes. In this thesis we have explored some of the numerous aspects of the level set frame work to see how the diffusion properties can be used for segmentation. For segmentation of tensor fields we have considered similarity measures for comparison of tensors. From these similarity measures several applications of the level set method have been developed for the segmentation of different structures. Different measures of similarity have been used dependent on the application. When segmenting white matter regions in DTI, the similarity measure emphasizes anisotropic regions. The segmentation algorithm itself has a very local dependence since white matter, in general fiber tracts, experiences different diffusion in different parts of the structure. The presented results show segmentations of the major fiber tracts in the brain. Other structures, such as the deep cerebral nuclei, that are mainly composed of gray matter, have more homogenous diffusion properties than white matter structures. Therefore, in these structures we maximize the internal coherence within the entire structure by using a region based approach to the segmentation problem. Segmentations of the thalamus and its nuclei as well as on tensor fields from fluid mechanics are presented. For High Angular Resolution Diffusion (HARD) images, two methods for fiber tract segmentation are presented based on different types of coherence. The coherence is either measured as the similarity between fibers obtained from a tractography algorithm, or the similarity of scalar values in a five-dimensional non-Euclidean space. The similarity between two fibers is determined by a counting strategy and is equal to the number of voxels they have in common. A spectral clustering algorithm is then used for grouping fibers with a high inter-resemblance. When segmenting white matter with the level set method, we propose to expand the space we are working in from a three-dimensional space of Orientation Distribution Functions (ODF) to a five-dimensional space of position and orientation. By a careful definition of this space and an adaptation of the level set to five dimensions the fibers tracts can be segmented as separated structures. We show some preliminary results from segmentations in this 5D space. The approaches proposed in this thesis permit a consideration of the fiber tracts and gray matter structures as an entity, allowing quantitative measures of the diffusion without losing information by simplifying the images to scalar representations