Exploratory graphical models of functional and structural connectivity patterns for Alzheimer's Disease diagnosis

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people. Its development has been shown to be closely related to changes in the brain connectivity network and in the brain activation patterns along with structural changes caused by the neurodegenerative process. Methods to infer dependence between brain regions are usually derived from the analysis of covariance between activation levels in the different areas. However, these covariance-based methods are not able to estimate conditional independence between variables to factor out the influence of other regions. Conversely, models based on the inverse covariance, or precision matrix, such as Sparse Gaussian Graphical Models allow revealing conditional independence between regions by estimating the covariance between two variables given the rest as constant. This paper uses Sparse Inverse Covariance Estimation (SICE) methods to learn undirected graphs in order to derive functional and structural connectivity patterns from Fludeoxyglucose (18F-FDG) Position Emission Tomography (PET) data and segmented Magnetic Resonance images (MRI), drawn from the ADNI database, for Control, MCI (Mild Cognitive Impairment Subjects), and AD subjects. Sparse computation fits perfectly here as brain regions usually only interact with a few other areas. The models clearly show different metabolic covariation patters between subject groups, revealing the loss of strong connections in AD and MCI subjects when compared to Controls. Similarly, the variance between GM (Gray Matter) densities of different regions reveals different structural covariation patterns between the different groups. Thus, the different connectivity patterns for controls and AD are used in this paper to select regions of interest in PET and GM images with discriminative power for early AD diagnosis. Finally, functional an structural models are combined to leverage the classification accuracy. The results obtained in this work show the usefulness of the Sparse Gaussian Graphical models to reveal functional and structural connectivity patterns. This information provided by the sparse inverse covariance matrices is not only used in an exploratory way but we also propose a method to use it in a discriminative way. Regression coefficients are used to compute reconstruction errors for the different classes that are then introduced in a SVM for classification. Classification experiments performed using 68 Controls, 70 AD, and 111 MCI images and assessed by cross-validation show the effectiveness of the proposed method.This work was partly supported by the MICINN under the TEC2012-34306 project and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía, Spain) under the Excellence Projects P09-TIC-4530, P11-TIC-7103, and the Universidad de Málaga. Programa de fortalecimiento de las capacidades de I+D+I en las Universidades 2014–2015, de la Consejería de Economía, Innovación, Ciencia y Empleo, cofinanciado por el fondo europeo de desarrollo regional (FEDER) under the project FC14-SAF30.This research was also supported by NIH grants P30 AG010129, K01 AG030514, and the Dana Foundation

Efficient Algorithm for Distinction Mild Cognitive Impairment from Alzheimer’s Disease Based on Specific View FCM White Matter Segmentation and Ensemble Learning

Purpose: Alzheimer's Disease (AD) is in the dementia group and is one of the most prevalent neurodegenerative disorders. Between existing characteristics, White Matter (WM) is a known marker for AD tracking, and WM segmentation in MRI based on clustering can be used to decrease the volume of data. Many algorithms have been developed to predict AD, but most concentrate on the distinction of AD from Cognitive Normal (CN). In this study, we provided a new, simple, and efficient methodology for classifying patients into AD and MCI patients and evaluated the effect of the view dimension of Fuzzy C Means (FCM) in prediction with ensemble classifiers. Materials and Methods: We proposed our methodology in three steps; first, segmentation of WM from T1 MRI with FCM according to two specific viewpoints (3D and 2D). In the second, two groups of features are extracted: approximate coefficients of Discrete Wavelet Transform (DWT) and statistical (mean, variance, skewness) features. In the final step, an ensemble classifier that is constructed with three classifiers, K-Nearest Neighbor (KNN), Decision Tree (DT), and Linear Discriminant Analysis (LDA), was used. Results: The proposed method has been evaluated by using 1280 slices (samples) from 64 patients with MCI (32) and AD (32) of the ADNI dataset. The best performance is for the 3D viewpoint, and the accuracy, precision, and f1-score achieved from the methodology are 94.22%, 94.45%, and 94.21%, respectively, by using a ten-fold Cross-Validation (CV) strategy. Conclusion: The experimental evaluation shows that WM segmentation increases the performance of the ensemble classifier, and moreover the 3D view FCM is better than the 2D view. According to the results, the proposed methodology has comparable performance for the detection of MCI from AD. The low computational cost algorithm and the three classifiers for generalization can be used in practical application by physicians in pre-clinical

Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis