Generative models of brain connectivity for population studies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 131-139).Connectivity analysis focuses on the interaction between brain regions. Such relationships inform us about patterns of neural communication and may enhance our understanding of neurological disorders. This thesis proposes a generative framework that uses anatomical and functional connectivity information to find impairments within a clinical population. Anatomical connectivity is measured via Diffusion Weighted Imaging (DWI), and functional connectivity is assessed using resting-state functional Magnetic Resonance Imaging (fMRI). We first develop a probabilistic model to merge information from DWI tractography and resting-state fMRI correlations. Our formulation captures the interaction between hidden templates of anatomical and functional connectivity within the brain. We also present an intuitive extension to population studies and demonstrate that our model learns predictive differences between a control and a schizophrenia population. Furthermore, combining the two modalities yields better results than considering each one in isolation. Although our joint model identifies widespread connectivity patterns influenced by a neurological disorder, the results are difficult to interpret and integrate with our regioncentric knowledge of the brain. To alleviate this problem, we present a novel approach to identify regions associated with the disorder based on connectivity information. Specifically, we assume that impairments of the disorder localize to a small subset of brain regions, which we call disease foci, and affect neural communication to/from these regions. This allows us to aggregate pairwise connectivity changes into a region-based representation of the disease. Once again, we use a probabilistic formulation: latent variables specify a template organization of the brain, which we indirectly observe through resting-state fMRI correlations and DWI tractography. Our inference algorithm simultaneously identifies both the afflicted regions and the network of aberrant functional connectivity. Finally, we extend the region-based model to include multiple collections of foci, which we call disease clusters. Preliminary results suggest that as the number of clusters increases, the refined model explains progressively more of the functional differences between the populations.by Archana Venkataraman.Ph.D

Signal approximation using the bilinear transform

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 117-118).This thesis explores the approximation properties of a unique basis expansion. The expansion implements a nonlinear frequency warping between a continuous-time signal and its discrete-time representation according to the bilinear transform. Since there is a one-to-one mapping between the continuous-time and discrete-time frequency axes, the bilinear representation avoids any frequency aliasing distortions. We devote the first portion of this thesis to some theoretical properties of the bilinear representation, including the analysis and synthesis networks as well as bounds on the basis functions. These properties are crucial when we further analyze the bilinear approximation performance. We also consider a modified version of the bilinear representation in which the continuous-time signal is segmented using a short-duration window. This segmentation procedure affords greater time resolution and, in certain cases, improves the overall approximation quality. In the second portion of this thesis, we evaluate the approximation performance of the bilinear representation in two different applications. The first is approximating instrumental music. We compare the bilinear representation to a discrete cosine transform based approximation technique. The second application is computing the inner product of two continuous-time signals for a binary detection problem. In this case, we compare the bilinear representation with Nyquist sampling.by Archana Venkataraman.M.Eng