mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds

Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fr\'echet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.Comment: Accepted into IPMI 202

From Connectivity Models to Region Labels: Identifying Foci of a Neurological Disorder

We propose a novel approach to identify the foci of a neurological disorder based on anatomical and functional connectivity information. Specifically, we formulate a generative model that characterizes the network of abnormal functional connectivity emanating from the affected foci. This allows us to aggregate pairwise connectivity changes into a region-based representation of the disease. We employ the variational expectation-maximization algorithm to fit the model and subsequently identify both the afflicted regions and the differences in connectivity induced by the disorder. We demonstrate our method on a population study of schizophrenia.National Alliance for Medical Image Computing (U.S.) (Grant NIH NIBIB NAMIC U54-EB005149)Neuroimaging Analysis Center (U.S.) (Grant NIH NCRR NAC P41-RR13218)Neuroimaging Analysis Center (U.S.) (Grant NIH NCRR NAC P41-EB015902)National Science Foundation (U.S.) (CAREER Grant 0642971)National Institutes of Health (U.S.) (R01MH074794)National Institutes of Health (U.S.). Advanced Multimodal Neuroimaging Training Progra

Whole brain resting state functional connectivity abnormalities in schizophrenia

Background Schizophrenia has been associated with disturbances in brain connectivity; however the exact nature of these disturbances is not fully understood. Measuring temporal correlations between the functional MRI time courses of spatially disparate brain regions obtained during rest has recently emerged as a popular paradigm for estimating brain connectivity. Previous resting state studies in schizophrenia explored connections related to particular clinical or cognitive symptoms (connectivity within a-priori selected networks), or connections restricted to functional networks obtained from resting state analysis. Relatively little has been done to understand global brain connectivity in schizophrenia. Methods Eighteen patients with chronic schizophrenia and 18 healthy volunteers underwent a resting state fMRI scan on a 3 T magnet. Whole brain temporal correlations have been estimated using resting-state fMRI data and free surfer cortical parcellations. A multivariate classification method was then used to indentify brain connections that distinguish schizophrenia patients from healthy controls. Results The classification procedure achieved a prediction accuracy of 75% in differentiating between groups on the basis of their functional connectivity. Relative to controls, schizophrenia patients exhibited co-existing patterns of increased connectivity between parietal and frontal regions, and decreased connectivity between parietal and temporal regions, and between the temporal cortices bilaterally. The decreased parieto-temporal connectivity was associated with the severity of patients' positive symptoms, while increased fronto-parietal connectivity was associated with patients' negative and general symptoms. Discussion Our analysis revealed two co-existing patterns of functional connectivity abnormalities in schizophrenia, each related to different clinical profiles. Such results provide further evidence that abnormalities in brain connectivity, characteristic of schizophrenia, are directly related to the clinical features of the disorder.National Alliance for Medical Image Computing (U.S.) (Grant U54 EB005149)National Institutes of Health (U.S.) (R01 M074794)Medical Research Council of Australia (Overseas-Based Biomedical Traning Fellowship 520627

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

Detecting Epileptic Regions Based on Global Brain Connectivity Patterns

We present a method to detect epileptic regions based on functional connectivity differences between individual epilepsy patients and a healthy population. Our model assumes that the global functional characteristics of these differences are shared across patients, but it allows for the epileptic regions to vary between individuals. We evaluate the detection performance against intracranial EEG observations and compare our approach with two baseline methods that use standard statistics. The baseline techniques are sensitive to the choice of thresholds, whereas our algorithm automatically estimates the appropriate model parameters and compares favorably with the best baseline results. This suggests the promise of our approach for pre-surgical planning in epilepsy.MIT/Lincoln Laboratory CollaborationNational Alliance for Medical Image Computing (U.S.) (grant (NIH NIBIB NAMIC U54-EB005149))Neuroimaging Analysis Center (U.S.) (NIH NCRR NAC P41-RR13218)Neuroimaging Analysis Center (U.S.) (NIH NIBIB NAC P41-EB-015902)National Science Foundation (U.S.) (NSF CAREER Grant 0642971