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

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum, respectively) with respect to this new data-driven connection and corresponding Riemannian manifold. Then we use these shortest curves for geodesic tracking of complex vasculature in multi-orientation image representations defined on $\mathbb{M}_{2}$. The data-driven Cartan connection characterizes the Hamiltonian flow of all geodesics. It also allows for improved adaptation to curvature and misalignment of the (lifted) vessel structure that we track via globally optimal geodesics. We compute these geodesics numerically via steepest descent on distance maps on $\mathbb{M}_2$ that we compute by a new modified anisotropic fast-marching method. Our experiments range from tracking single blood vessels with fixed endpoints to tracking complete vascular trees in retinal images. Single vessel tracking is performed in a single run in the multi-orientation image representation, where we project the resulting geodesics back onto the underlying image. The complete vascular tree tracking requires only two runs and avoids prior segmentation, placement of extra anchor points, and dynamic switching between geodesic models. Altogether we provide a geodesic tracking method using a single, flexible, transparent, data-driven geodesic model providing globally optimal curves which correctly follow highly complex vascular structures in retinal images. All experiments in this article can be reproduced via documented Mathematica notebooks available at GitHub (https://github.com/NickyvdBerg/DataDrivenTracking)

Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)

Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the retina allows for noninvasive diagnosis of several diseases as these vessels and their behavior are representative of the behavior of vessels throughout the human body. For early diagnosis and analysis of diseases, it is important to compare and analyze the complex vasculature in retinal images automatically. In previous work, PDE-based geometric tracking and PDE-based enhancements in the homogeneous space of positions and orientations have been studied and turned out to be useful when dealing with complex structures (crossing of blood vessels in particular). In this article, we propose a single new, more effective, Finsler function that integrates the strength of these two PDE-based approaches and additionally accounts for a number of optical effects (dehazing and illumination in particular). The results greatly improve both the previous left-invariant models and a recent data-driven model, when applied to real clinical and highly challenging images. Moreover, we show clear advantages of each module in our new single Finsler geometrical method

Geodesic tractography segmentation for directional medical image analysis

Acknowledgements page removed per author's request, 01/06/2014.Geodesic Tractography Segmentation is the two component approach presented in this thesis for the analysis of imagery in oriented domains, with emphasis on the application to diffusion-weighted magnetic resonance imagery (DW-MRI). The computeraided analysis of DW-MRI data presents a new set of problems and opportunities for the application of mathematical and computer vision techniques. The goal is to develop a set of tools that enable clinicians to better understand DW-MRI data and ultimately shed new light on biological processes. This thesis presents a few techniques and tools which may be used to automatically find and segment major neural fiber bundles from DW-MRI data. For each technique, we provide a brief overview of the advantages and limitations of our approach relative to other available approaches.Ph.D.Committee Chair: Tannenbaum, Allen; Committee Member: Barnes, Christopher F.; Committee Member: Niethammer, Marc; Committee Member: Shamma, Jeff; Committee Member: Vela, Patrici

Blood Vessel Segmentation and shape analysis for quantification of Coronary Artery Stenosis in CT Angiography

This thesis presents an automated framework for quantitative vascular shape analysis of the coronary arteries, which constitutes an important and fundamental component of an automated image-based diagnostic system. Firstly, an automated vessel segmentation algorithm is developed to extract the coronary arteries based on the framework of active contours. Both global and local intensity statistics are utilised in the energy functional calculation, which allows for dealing with non-uniform brightness conditions, while evolving the contour towards to the desired boundaries without being trapped in local minima. To suppress kissing vessel artifacts, a slice-by-slice correction scheme, based on multiple regions competition, is proposed to identify and track the kissing vessels throughout the transaxial images of the CTA data. Based on the resulting segmentation, we then present a dedicated algorithm to estimate the geometric parameters of the extracted arteries, with focus on vessel bifurcations. In particular, the centreline and associated reference surface of the coronary arteries, in the vicinity of arterial bifurcations, are determined by registering an elliptical cross sectional tube to the desired constituent branch. The registration problem is solved by a hybrid optimisation method, combining local greedy search and dynamic programming, which ensures the global optimality of the solution and permits the incorporation of any hard constraints posed to the tube model within a natural and direct framework. In contrast with conventional volume domain methods, this technique works directly on the mesh domain, thus alleviating the need for image upsampling. The performance of the proposed framework, in terms of efficiency and accuracy, is demonstrated on both synthetic and clinical image data. Experimental results have shown that our techniques are capable of extracting the major branches of the coronary arteries and estimating the related geometric parameters (i.e., the centreline and the reference surface) with a high degree of agreement to those obtained through manual delineation. Particularly, all of the major branches of coronary arteries are successfully detected by the proposed technique, with a voxel-wise error at 0.73 voxels to the manually delineated ground truth data. Through the application of the slice-by-slice correction scheme, the false positive metric, for those coronary segments affected by kissing vessel artifacts, reduces from 294% to 22.5%. In terms of the capability of the presented framework in defining the location of centrelines across vessel bifurcations, the mean square errors (MSE) of the resulting centreline, with respect to the ground truth data, is reduced by an average of 62.3%, when compared with initial estimation obtained using a topological thinning based algorithm

BRONCO: Automated modelling of the bronchovascular bundle using the Computed Tomography Images

Segmentation of the bronchovascular bundle within the lung parenchyma is a key step for the proper analysis and planning of many pulmonary diseases. It might also be considered the preprocessing step when the goal is to segment the nodules from the lung parenchyma. We propose a segmentation pipeline for the bronchovascular bundle based on the Computed Tomography images, returning either binary or labelled masks of vessels and bronchi situated in the lung parenchyma. The method consists of two modules, modeling of the bronchial tree and vessels. The core revolves around a similar pipeline, the determination of the initial perimeter by the GMM method, skeletonization, and hierarchical analysis of the created graph. We tested our method on both low-dose CT and standard-dose CT, with various pathologies, reconstructed with various slice thicknesses, and acquired from various machines. We conclude that the method is invariant with respect to the origin and parameters of the CT series. Our pipeline is best suited for studies with healthy patients, patients with lung nodules, and patients with emphysema

Blood vessel segmentation and shape analysis for quantification of coronary artery stenosis in CT angiography

This thesis presents an automated framework for quantitative vascular shape analysis of the coronary arteries, which constitutes an important and fundamental component of an automated image-based diagnostic system. Firstly, an automated vessel segmentation algorithm is developed to extract the coronary arteries based on the framework of active contours. Both global and local intensity statistics are utilised in the energy functional calculation, which allows for dealing with non-uniform brightness conditions, while evolving the contour towards to the desired boundaries without being trapped in local minima. To suppress kissing vessel artifacts, a slice-by-slice correction scheme, based on multiple regions competition, is proposed to identify and track the kissing vessels throughout the transaxial images of the CTA data. Based on the resulting segmentation, we then present a dedicated algorithm to estimate the geometric parameters of the extracted arteries, with focus on vessel bifurcations. In particular, the centreline and associated reference surface of the coronary arteries, in the vicinity of arterial bifurcations, are determined by registering an elliptical cross sectional tube to the desired constituent branch. The registration problem is solved by a hybrid optimisation method, combining local greedy search and dynamic programming, which ensures the global optimality of the solution and permits the incorporation of any hard constraints posed to the tube model within a natural and direct framework. In contrast with conventional volume domain methods, this technique works directly on the mesh domain, thus alleviating the need for image upsampling. The performance of the proposed framework, in terms of efficiency and accuracy, is demonstrated on both synthetic and clinical image data. Experimental results have shown that our techniques are capable of extracting the major branches of the coronary arteries and estimating the related geometric parameters (i.e., the centreline and the reference surface) with a high degree of agreement to those obtained through manual delineation. Particularly, all of the major branches of coronary arteries are successfully detected by the proposed technique, with a voxel-wise error at 0.73 voxels to the manually delineated ground truth data. Through the application of the slice-by-slice correction scheme, the false positive metric, for those coronary segments affected by kissing vessel artifacts, reduces from 294% to 22.5%. In terms of the capability of the presented framework in defining the location of centrelines across vessel bifurcations, the mean square errors (MSE) of the resulting centreline, with respect to the ground truth data, is reduced by an average of 62.3%, when compared with initial estimation obtained using a topological thinning based algorithm.EThOS - Electronic Theses Online ServiceGBUnited Kingdo