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      Brain Entropy Mapping Using fMRI

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          Abstract

          Entropy is an important trait for life as well as the human brain. Characterizing brain entropy (BEN) may provide an informative tool to assess brain states and brain functions. Yet little is known about the distribution and regional organization of BEN in normal brain. The purpose of this study was to examine the whole brain entropy patterns using a large cohort of normal subjects. A series of experiments were first performed to validate an approximate entropy measure regarding its sensitivity, specificity, and reliability using synthetic data and fMRI data. Resting state fMRI data from a large cohort of normal subjects (n = 1049) from multi-sites were then used to derive a 3-dimensional BEN map, showing a sharp low-high entropy contrast between the neocortex and the rest of brain. The spatial heterogeneity of resting BEN was further studied using a data-driven clustering method, and the entire brain was found to be organized into 7 hierarchical regional BEN networks that are consistent with known structural and functional brain parcellations. These findings suggest BEN mapping as a physiologically and functionally meaningful measure for studying brain functions.

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          Most cited references21

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          Approximate entropy as a measure of system complexity.

          Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
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            A whole brain fMRI atlas generated via spatially constrained spectral clustering.

            Connectivity analyses and computational modeling of human brain function from fMRI data frequently require the specification of regions of interests (ROIs). Several analyses have relied on atlases derived from anatomical or cyto-architectonic boundaries to specify these ROIs, yet the suitability of atlases for resting state functional connectivity (FC) studies has yet to be established. This article introduces a data-driven method for generating an ROI atlas by parcellating whole brain resting-state fMRI data into spatially coherent regions of homogeneous FC. Several clustering statistics are used to compare methodological trade-offs as well as determine an adequate number of clusters. Additionally, we evaluate the suitability of the parcellation atlas against four ROI atlases (Talairach and Tournoux, Harvard-Oxford, Eickoff-Zilles, and Automatic Anatomical Labeling) and a random parcellation approach. The evaluated anatomical atlases exhibit poor ROI homogeneity and do not accurately reproduce FC patterns present at the voxel scale. In general, the proposed functional and random parcellations perform equivalently for most of the metrics evaluated. ROI size and hence the number of ROIs in a parcellation had the greatest impact on their suitability for FC analysis. With 200 or fewer ROIs, the resulting parcellations consist of ROIs with anatomic homology, and thus offer increased interpretability. Parcellation results containing higher numbers of ROIs (600 or 1,000) most accurately represent FC patterns present at the voxel scale and are preferable when interpretability can be sacrificed for accuracy. The resulting atlases and clustering software have been made publicly available at: http://www.nitrc.org/projects/cluster_roi/. Copyright © 2011 Wiley Periodicals, Inc.
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              A measure for brain complexity: relating functional segregation and integration in the nervous system.

              In brains of higher vertebrates, the functional segregation of local areas that differ in their anatomy and physiology contrasts sharply with their global integration during perception and behavior. In this paper, we introduce a measure, called neural complexity (CN), that captures the interplay between these two fundamental aspects of brain organization. We express functional segregation within a neural system in terms of the relative statistical independence of small subsets of the system and functional integration in terms of significant deviations from independence of large subsets. CN is then obtained from estimates of the average deviation from statistical independence for subsets of increasing size. CN is shown to be high when functional segregation coexists with integration and to be low when the components of a system are either completely independent (segregated) or completely dependent (integrated). We apply this complexity measure in computer simulations of cortical areas to examine how some basic principles of neuroanatomical organization constrain brain dynamics. We show that the connectivity patterns of the cerebral cortex, such as a high density of connections, strong local connectivity organizing cells into neuronal groups, patchiness in the connectivity among neuronal groups, and prevalent reciprocal connections, are associated with high values of CN. The approach outlined here may prove useful in analyzing complexity in other biological domains such as gene regulation and embryogenesis.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2014
                21 March 2014
                : 9
                : 3
                : e89948
                Affiliations
                [1 ]Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
                [2 ]Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
                [3 ]Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
                Wake Forest School of Medicine, United States of America
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: ZW. Performed the experiments: ZW YL. Analyzed the data: ZW YL. Wrote the paper: ZW ARC JAD.

                Article
                PONE-D-13-44242
                10.1371/journal.pone.0089948
                3962327
                24657999
                68eb0863-a10e-4a56-b904-bac63bfcff94
                Copyright @ 2014

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 29 October 2013
                : 23 January 2014
                Page count
                Pages: 8
                Funding
                This work was supported by National Institutes of Health grants: R21DC011074, and 8P41-EB015893, and 5R33DA026114-04. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Neuroscience
                Neuroimaging
                Functional Magnetic Resonance Imaging
                Sensory Perception
                Medicine and Health Sciences
                Neurology
                Radiology and Imaging
                Physical Sciences
                Mathematics
                Statistics (Mathematics)
                Statistical Methods
                Physics
                Physical Laws and Principles
                Thermodynamics
                Research and Analysis Methods
                Research Design
                Clinical Research Design
                Cohort Studies

                Uncategorized
                Uncategorized

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