Comparative Analysis of Connection and Disconnection in the Human Brain Using Diffusion MRI: New Methods and Applications

Institute for Adaptive and Neural ComputationDiffusion magnetic resonance imaging (dmri) is a technique that can be used to examine the diffusion characteristics of water in the living brain. A recently developed application of this technique is tractography, in which information from brain images obtained using dmri is used to reconstruct the pathways which connect regions of the brain together. Proxy measures for the integrity, or coherence, of these pathways have also been defined using dmri-derived information. The disconnection hypothesis suggests that specific neurological impairments can arise from damage to these pathways as a consequence of the resulting interruption of information flow between relevant areas of cortex. The development of dmri and tractography have generated a considerable amount of renewed interest in the disconnectionist thesis, since they promise a means for testing the hypothesis in vivo in any number of pathological scenarios. However, in order to investigate the effects of pathology on particular pathways, it is necessary to be able to reliably locate them in three-dimensional dmri images. The aim of the work described in this thesis is to improve upon the robustness of existing methods for segmenting specific white matter tracts from image data, using tractography, and to demonstrate the utility of the novel methods for the comparative analysis of white matter integrity in groups of subjects. The thesis begins with an overview of probability theory, which will be a recurring theme throughout what follows, and its application to machine learning. After reviewing the principles of magnetic resonance in general, and dmri and tractography in particular, we then describe existing methods for segmenting particular tracts from group data, and introduce a novel approach. Our innovation is to use a reference tract to define the topological characteristics of the tract of interest, and then search a group of candidate tracts in the target brain volume for the best match to this reference. In order to assess how well two tracts match we define a heuristic but quantitative tract similarity measure. In later chapters we demonstrate that this method is capable of successfully segmenting tracts of interest in both young and old, healthy and unhealthy brains; and then describe a formalised version of the approach which uses machine learning methods to match tracts from different subjects. In this case the similarity between tracts is represented as a matching probability under an explicit model of topological variability between equivalent tracts in different brains. Finally, we examine the possibility of comparing the integrity of groups of white matter structures at a level more fine-grained than a whole tract

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described