Finding New Communities: A Principle of Neuronal Network Reorganization in Alzheimer's Disease.

Background: Graph-theoretical analyses have been previously used to investigate changes in the functional connectome in patients with Alzheimer's disease (AD). However, these analyses generally assume static organizational principles, thereby neglecting a fundamental reconfiguration of functional connections in the face of neurodegeneration. Methods: Here, we focus on differences in the community structure of the functional connectome in young and old individuals and patients with AD. Patients with AD, moreover, underwent molecular imaging positron emission tomography by using [18F]AV1451 to measure tau burden, a major hallmark of AD. Results: Although the overall organizational principles of the community structure of the human functional connectome were preserved even in advanced healthy aging, they were considerably changed in AD. We discovered that the communities in AD are re-organized, with nodes changing their allegiance to communities, thus resulting in an overall less efficient re-organized community structure. We further discovered that nodes with a tendency to leave the communities displayed a relatively higher tau pathology burden. Discussion: Together, this study suggests that local tau pathology in AD is associated to fundamental changes in basic organizational principles of the human connectome. Our results shed new light on previous findings obtained by using the graph theory in AD and imply a general principle of the brain in response to neurodegeneration.

Towards non-invasive EIT imaging of domains with deformable boundaries.

We investigate on the use of the Domain Embedding Method (DEM) for the forward modelling in EIT. This approach is suitably configured to overcome the model meshing bottleneck since it does not require that the mesh on the domain is adapted to the boundary surface. This is of crucial importance for, e.g., clinical applications of EIT, as it avoids tedious and time-consuming (re-)meshing procedures. The suggested DEM approach can accommodate arbitrary yet Lipschitz smooth boundary surfaces and is not limited to polygonal domains. For the discretisation purposes, we employ B-splines as they allow for arbitrary accuracy by raising the polynomial degree and are easy to implement due to their inherent piecewise polynomial structure. Numerical experiments confirm that a B-spline discretization yields, similarly to conventional Finite Difference discretizations, increasing condition numbers of the system matrix with respect to the discretisation levels. Fortunately, multiresolution ideas based on B-splines allow for optimal wavelet preconditioning.

Robust regression of scattered data with adaptive spline-wavelets.

A coarse-to-fine data fitting algorithm for irregularly spaced data based on boundary-adapted adaptive tensor-product semi-orthogonal spline-wavelets has been proposed in Castaño and Kunoth, 2003. This method has been extended in Castaño and Kunoth, 2005 to include regularization in terms of Sobolev and Besov norms. In this paper, we develop within this least-squares approach some statistical robust estimators to handle outliers in the data. Our wavelet scheme yields a numerically fast and reliable way to detect outliers.