Improving the Tractography Pipeline: on Evaluation, Segmentation, and Visualization

Recent advances in tractography allow for connectomes to be constructed in vivo. These have applications for example in brain tumor surgery and understanding of brain development and diseases. The large size of the data produced by these methods lead to a variety problems, including how to evaluate tractography outputs, development of faster processing algorithms for tractography and clustering, and the development of advanced visualization methods for verification and exploration. This thesis presents several advances in these fields. First, an evaluation is presented for the robustness to noise of multiple commonly used tractography algorithms. It employs a Monte–Carlo simulation of measurement noise on a constructed ground truth dataset. As a result of this evaluation, evidence for obustness of global tractography is found, and algorithmic sources of uncertainty are identified. The second contribution is a fast clustering algorithm for tractography data based on k–means and vector fields for representing the flow of each cluster. It is demonstrated that this algorithm can handle large tractography datasets due to its linear time and memory complexity, and that it can effectively integrate interrupted fibers that would be rejected as outliers by other algorithms. Furthermore, a visualization for the exploration of structural connectomes is presented. It uses illustrative rendering techniques for efficient presentation of connecting fiber bundles in context in anatomical space. Visual hints are employed to improve the perception of spatial relations. Finally, a visualization method with application to exploration and verification of probabilistic tractography is presented, which improves on the previously presented Fiber Stippling technique. It is demonstrated that the method is able to show multiple overlapping tracts in context, and correctly present crossing fiber configurations

Integrated navigation and visualisation for skull base surgery

Skull base surgery involves the management of tumours located on the underside of the brain and the base of the skull. Skull base tumours are intricately associated with several critical neurovascular structures making surgery challenging and high risk. Vestibular schwannoma (VS) is a benign nerve sheath tumour arising from one of the vestibular nerves and is the commonest pathology encountered in skull base surgery. The goal of modern VS surgery is maximal tumour removal whilst preserving neurological function and maintaining quality of life but despite advanced neurosurgical techniques, facial nerve paralysis remains a potentially devastating complication of this surgery. This thesis describes the development and integration of various advanced navigation and visualisation techniques to increase the precision and accuracy of skull base surgery. A novel Diffusion Magnetic Resonance Imaging (dMRI) acquisition and processing protocol for imaging the facial nerve in patients with VS was developed to improve delineation of facial nerve preoperatively. An automated Artificial Intelligence (AI)-based framework was developed to segment VS from MRI scans. A user-friendly navigation system capable of integrating dMRI and tractography of the facial nerve, 3D tumour segmentation and intraoperative 3D ultrasound was developed and validated using an anatomically-realistic acoustic phantom model of a head including the skull, brain and VS. The optical properties of five types of human brain tumour (meningioma, pituitary adenoma, schwannoma, low- and high-grade glioma) and nine different types of healthy brain tissue were examined across a wavelength spectrum of 400 nm to 800 nm in order to inform the development of an Intraoperative Hypserpectral Imaging (iHSI) system. Finally, functional and technical requirements of an iHSI were established and a prototype system was developed and tested in a first-in-patient study

Non-negative data-driven mapping of structural connections with application to the neonatal brain

© 2020 Mapping connections in the neonatal brain can provide insight into the crucial early stages of neurodevelopment that shape brain organisation and lay the foundations for cognition and behaviour. Diffusion MRI and tractography provide unique opportunities for such explorations, through estimation of white matter bundles and brain connectivity. Atlas-based tractography protocols, i.e. a priori defined sets of masks and logical operations in a template space, have been commonly used in the adult brain to drive such explorations. However, rapid growth and maturation of the brain during early development make it challenging to ensure correspondence and validity of such atlas-based tractography approaches in the developing brain. An alternative can be provided by data-driven methods, which do not depend on predefined regions of interest. Here, we develop a novel data-driven framework to extract white matter bundles and their associated grey matter networks from neonatal tractography data, based on non-negative matrix factorisation that is inherently suited to the non-negative nature of structural connectivity data. We also develop a non-negative dual regression framework to map group-level components to individual subjects. Using in-silico simulations, we evaluate the accuracy of our approach in extracting connectivity components and compare with an alternative data-driven method, independent component analysis. We apply non-negative matrix factorisation to whole-brain connectivity obtained from publicly available datasets from the Developing Human Connectome Project, yielding grey matter components and their corresponding white matter bundles. We assess the validity and interpretability of these components against traditional tractography results and grey matter networks obtained from resting-state fMRI in the same subjects. We subsequently use them to generate a parcellation of the neonatal cortex using data from 323 new-born babies and we assess the robustness and reproducibility of this connectivity-driven parcellation

Probabilistic Ordinary Differential Equation Solvers - Theory and Applications

Ordinary differential equations are ubiquitous in science and engineering, as they provide mathematical models for many physical processes. However, most practical purposes require the temporal evolution of a particular solution. Many relevant ordinary differential equations are known to lack closed-form solutions in terms of simple analytic functions. Thus, users rely on numerical algorithms to compute discrete approximations. Numerical methods replace the intractable, and thus inaccessible, solution by an approximating model with known computational strategies. This is akin to a process in statistics where an unknown true relationship is modeled with access to instances of said relationship. One branch of statistics, Bayesian modeling, expresses degrees of uncertainty with probability distributions. In recent years, this idea has gained traction for the design and study of numerical algorithms which established probabilistic numerics as a research field in its own right. The theory part of this thesis is concerned with bridging the gap between classical numerical methods for ordinary differential equations and probabilistic numerics. To this end, an algorithm is presented based on Gaussian processes, a general and versatile model for Bayesian regression. This algorithm is compared to two standard frameworks for the solution of initial value problems. It is shown that the maximum a-posteriori estimator of certain Gaussian process regressors coincide with certain multistep formulae. Furthermore, a particular initialization scheme based on an improper prior model coincides with a Runge-Kutta method for the first discretization step. This analysis provides a higher-order probabilistic numerical algorithm for initial value problems. Based on the probabilistic description, an estimator of the local integration error is presented, which is used in a step size adaptation scheme. The completed algorithm is evaluated on a benchmark on initial value problems, confirming empirically the theoretically predicted error rates and displaying particularly efficient performance on domains with low accuracy requirements. To establish the practical benefit of the probabilistic solution, a probabilistic boundary value problem solver is applied to a medical imaging problem. In tractography, diffusion-weighted magnetic resonance imaging data is used to infer connectivity of neural fibers. The first application of the probabilistic solver shows how the quantification of the discretization error can be used in subsequent estimation of fiber density. The second application additionally incorporates the measurement noise of the imaging data into the tract estimation model. These two extensions of the shortest-path tractography method give more faithful data, modeling and algorithmic uncertainty representations in neural connectivity studies.Gewöhnliche Differentialgleichungen sind allgegenwärtig in Wissenschaft und Technik, da sie die mathematische Beschreibung vieler physikalischen Vorgänge sind. Jedoch benötigt ein Großteil der praktischen Anwendungen die zeitliche Entwicklung einer bestimmten Lösung. Es ist bekannt, dass viele relevante gewöhnliche Differentialgleichungen keine geschlossene Lösung als Ausdrücke einfacher analytischer Funktion besitzen. Daher verlassen sich Anwender auf numerische Algorithmen, um diskrete Annäherungen zu berechnen. Numerische Methoden ersetzen die unauswertbare, und daher unzugängliche, Lösung durch eine Annäherung mit bekannten Rechenverfahren. Dies ähnelt einem Vorgang in der Statistik, wobei ein unbekanntes wahres Verhältnis mittels Zugang zu Beispielen modeliert wird. Eine Unterdisziplin der Statistik, Bayes’sche Modellierung, stellt graduelle Unsicherheit mittels Wahrscheinlichkeitsverteilungen dar. In den letzten Jahren hat diese Idee an Zugkraft für die Konstruktion und Analyse von numerischen Algorithmen gewonnen, was zur Etablierung von probabilistischer Numerik als eigenständiges Forschungsgebiet führte. Der Theorieteil dieser Dissertation schlägt eine Brücke zwischen herkömmlichen numerischen Verfahren zur Lösung gewöhnlicher Differentialgleichungen und probabilistischer Numerik. Ein auf Gauß’schen Prozessen basierender Algorithmus wird vorgestellt, welche ein generelles und vielseitiges Modell der Bayesschen Regression sind. Dieser Algorithmus wird verglichen mit zwei Standardansätzen für die Lösung von Anfangswertproblemen. Es wird gezeigt, dass der Maximum-a-posteriori-Schätzer bestimmter Gaußprozess-Regressoren übereinstimmt mit bestimmten Mehrschrittverfahren. Weiterhin stimmt ein besonderes Initialisierungsverfahren basierend auf einer uneigentlichen A-priori-Wahrscheinlichkeit überein mit einer Runge-Kutta Methode im ersten Rechenschritt. Diese Analyse führt zu einer probabilistisch-numerischen Methode höherer Ordnung zur Lösung von Anfangswertproblemen. Basierend auf der probabilistischen Beschreibung wird ein Schätzer des lokalen Integrationfehlers präsentiert, welcher in einem Schrittweitensteuerungsverfahren verwendet wird. Der vollständige Algorithmus wird auf einem Satz standardisierter Anfangswertprobleme ausgewertet, um empirisch den von der Theorie vorhergesagten Fehler zu bestätigen. Der Test weist dem Verfahren einen besonders effizienten Rechenaufwand im Bereich der niedrigen Genauigkeitsanforderungen aus. Um den praktischen Nutzen der probabilistischen Lösung nachzuweisen, wird ein probabilistischer Löser für Randwertprobleme auf eine Fragestellung der medizinischen Bildgebung angewandt. In der Traktografie werden die Daten der diffusionsgewichteten Magnetresonanzbildgebung verwendet, um die Konnektivität neuronaler Fasern zu bestimmen. Die erste Anwendung des probabilistische Lösers demonstriert, wie die Quantifizierung des Diskretisierungsfehlers in einer nachgeschalteten Schätzung der Faserdichte verwendet werden kann. Die zweite Anwendung integriert zusätzlich das Messrauschen der Bildgebungsdaten in das Strangschätzungsmodell. Diese beiden Erweiterungen der Kürzesten-Pfad-Traktografie repräsentieren die Daten-, Modellierungs- und algorithmische Unsicherheit abbildungstreuer in neuronalen Konnektivitätsstudien

Methods and models for brain connectivity assessment across levels of consciousness

The human brain is one of the most complex and fascinating systems in nature. In the last decades, two events have boosted the investigation of its functional and structural properties. Firstly, the emergence of novel noninvasive neuroimaging modalities, which helped improving the spatial and temporal resolution of the data collected from in vivo human brains. Secondly, the development of advanced mathematical tools in network science and graph theory, which has recently translated into modeling the human brain as a network, giving rise to the area of research so called Brain Connectivity or Connectomics. In brain network models, nodes correspond to gray-matter regions (based on functional or structural, atlas-based parcellations that constitute a partition), while links or edges correspond either to structural connections as modeled based on white matter fiber-tracts or to the functional coupling between brain regions by computing statistical dependencies between measured brain activity from different nodes. Indeed, the network approach for studying the brain has several advantages: 1) it eases the study of collective behaviors and interactions between regions; 2) allows to map and study quantitative properties of its anatomical pathways; 3) gives measures to quantify integration and segregation of information processes in the brain, and the flow (i.e. the interacting dynamics) between different cortical and sub-cortical regions. The main contribution of my PhD work was indeed to develop and implement new models and methods for brain connectivity assessment in the human brain, having as primary application the analysis of neuroimaging data coming from subjects at different levels of consciousness. I have here applied these methods to investigate changes in levels of consciousness, from normal wakefulness (healthy human brains) or drug-induced unconsciousness (i.e. anesthesia) to pathological (i.e. patients with disorders of consciousness)