Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Accurate Anisotropic Fast Marching for Diffusion-Based Geodesic Tractography

Using geodesics for inferring white matter fibre tracts from diffusion-weighted MR data is an attractive method for at least two reasons: (i) the method optimises a global criterion, and hence is less sensitive to local perturbations such as noise or partial volume effects, and (ii) the method is fast, allowing to infer on a large number of connexions in a reasonable computational time. Here, we propose an improved fast marching algorithm to infer on geodesic paths. Specifically, this procedure is designed to achieve accurate front propagation in an anisotropic elliptic medium, such as DTI data. We evaluate the numerical performance of this approach on simulated datasets, as well as its robustness to local perturbation induced by fiber crossing. On real data, we demonstrate the feasibility of extracting geodesics to connect an extended set of brain regions

An improvement to Global Tractography Using Anatomical Priors

Tractography is a visualization technique which reconstructs and models neural fibers in the white matter of the brain based on data from diffusion magnetic resonance imaging. It is already used locally to model parts of dominant fiber pathways but global methods are also emerging which aim to reconstruct all the brain fibers simultaneously. In this thesis we have attempted to improve the current state of the art of Global Tractography by introducing three principles: * Anatomical Priors * Introduction of fiber weights * Reduced complexity Our approach uses an optimization method based on Markov Chain Monte Carlo (MCMC) and Simulated annealing in order to fit a set of plausible initial fiber trajectories to a dataset acquired by diffusion MRI. Our method was compared to the state of the art global tractography method known as the Gibbs Tracker in a phantom study using conventional global tractography evaluation methods. In a second test, we also try the method on an in-vivo dataset of a human brain and derive the connectivity matrix with corresponding network parameters. Our approach showed considerable improvements in decreasing the amount of wrong fibers and reduced computational time. However the method still struggles to eliminate certain false but plausible connections. To remedy this, several improvements to the MCMC sampler are suggested for future work

Methods for improved mapping of brain lesion connectivity

Recent advances over the past two decades in neuroimaging methods have enabled us to map the connectivity of the brain. In parallel, pathophysiological models of brain disease have shifted from an emphasis on understanding pathology in specific brain regions to characterizing disruptions to interconnected neural networks. Nevertheless, these recent methods for mapping brain connectivity are still under development. Every step of the mapping process becomes a potential source for additional error due to noise or artifacts that could impact final analyses. Segmentation, parcellation, registration, and tractography are some of the steps where this occurs. Moreover, mapping the connectivity in a brain lesion is even more susceptible to errors in these steps. In this body of work, I describe multiple new methods for improving the accuracy of mapping lesion connectivity by reducing errors at the tractography stage which is the most error prone stage. First, we develop an approach for directly normalizing streamlines into a template space that avoids performing tractography in the normalized template space, reducing the error of connectomes constructed in the template space with respect to the ground truth native space connectome. Second, we develop a rapid approach for performing shortest path tractography and constructing shortest path probability weighted connectomes which increases the connection specificity relative to local streamline tracking approaches. We then demonstrate how our shortest path tractography approach can be used construct a disconnectome, a connectivity map of the proportion of connections lost due to intersecting a lesion. We then develop a fast, greedy graph-theoretic algorithm that extracts the maximally disconnected subgraph containing brain regions with the greatest shared loss of connectivity. Finally, we demonstrate how combining methods from diffusion based image inpainting and optimal estimation can be used to restore or inpaint corrupted fiber diffusion models in lesioned white matter tissue, enabling tractography and the study of lesion connectivity and modeling of microstructural measures in the patient’s native space

Global brain connectivity analysis by diffusion MR tractography:algorithms, validation and applications

The human cerebral cortex consists of approximately 1010 neurons that are organized into a complex network of local circuits and long-range connections. During the past years there has been an increasing interest from the neuro-scientific community towards the study of this network, referred to as the human connectome. Due to its ability to probe the tissue microstructure in vivo and non invasively, diffusion MRI has revealed to be a helpful tool for the analysis of brain axonal pathways at the millimeter scale. Whereas the neuronal level remains unreachable, diffusion MRI enables the mapping of a low-resolution estimate of the human connectome, which should give a new breath to the study of normal or pathologic neuroanatomy. After a short introduction on diffusion MRI and tractography, the process by which fiber tracts are reconstructed from the diffusion images, we present a methodology allowing the creation of normalized whole-brain structural connection matrices derived from tractography and representing the human connectome. Based on the developed framework we then investigate the potential of front propagation algorithms in tractography. We compare their performance with classical tractography approaches on several well-known associative fiber pathways, and we discuss their advantages and limitations. Several solutions are proposed in order to evaluate and validate the connectome-related methodology. We develop a method to estimate the respective contributions of diffusion contrast versus other effects to a tractography result. Using this methodology, we show that whereas we can have a strong confidence in mid- and long-range connections, short-range connectivity has to be interpreted with care. Next, we demonstrate the strong relationship between the structural connectivity obtained from diffusion MR tractography and the functional connectivity measured with functional MRI. Then, we compare the performance of several diffusion MRI techniques through connectome-based measurements. We find that diffusion spectrum imaging is more sensitive and therefore enhances the results of tractography. Finally, we present two network-oriented applications. We use the human connectome to reveal the small-world architecture of the brain, a very efficient network topology in terms of wiring and power supply. We identify the cortical areas that belong to the core of structural connectivity. We show that these regions also belong to the default mode network, a set of dynamically coupled brain regions that are found to be more highly activated at rest. As a conclusion, we emphasize the potential of human connectome mapping for clinical applications and pathological studies

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