Network properties of healthy and Alzheimer brains

Abstract The application of graph theory in diffusion weighted resonance magnetic images have allowed the description of the brain as a complex network, often called structural network. For many years, the small-world properties of brain networks have been studied and reported. However, few studies have gone beyond of clustering and characteristic path length. In this work, we compare the structural connection network of a healthy brain and a brain affected by Alzheimer’s disease with artificial small-world networks. Based on statistical analysis, we demonstrate how artificial networks can be constructed using Newman–Watts procedure. The network quantifiers of both structural matrices are identified inside a probabilistic valley. Despite of similarities between structural connection matrices and artificial small-world networks, increased assortativity can be found in the Alzheimer brain. Due to limited experimental data, we cannot define a direct link between Alzheimer’s disease and assortativity. Nevertheless, we intend to call attention for an important network quantifier that has been neglected. Our results indicate that network quantifiers can be helpful to identify abnormalities in real structural connections, for instance Alzheimer’s disease that disrupts the communication among neurons. One of our main results is to show that the network indicators of the Alzheimer brain are almost identical with the small-world network, except the assortativity.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  Diana D. Suhr The Basics of Structural Equation Modeling , 2006 .

[3]  C. Stam,et al.  The organization of physiological brain networks , 2012, Clinical Neurophysiology.

[4]  Sang Won Seo,et al.  Non-monotonic reorganization of brain networks with Alzheimer's disease progression , 2015, Front. Aging Neurosci..

[5]  Alan C. Evans,et al.  Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. , 2009, Cerebral cortex.

[6]  Jürgen Kurths,et al.  Suppression of phase synchronisation in network based on cat's brain. , 2016, Chaos.

[7]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[8]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Karl J. Friston,et al.  Schizophrenia: a disconnection syndrome? , 1995, Clinical neuroscience.

[10]  Yong He,et al.  Diffusion Tensor Tractography Reveals Abnormal Topological Organization in Structural Cortical Networks in Alzheimer's Disease , 2010, The Journal of Neuroscience.

[11]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[12]  John Skvoretz,et al.  Node centrality in weighted networks: Generalizing degree and shortest paths , 2010, Soc. Networks.

[13]  O. Sporns Structure and function of complex brain networks , 2013, Dialogues in clinical neuroscience.

[14]  Massimo Filippi,et al.  Structural Brain Connectome and Cognitive Impairment in Parkinson Disease. , 2017, Radiology.

[15]  Edwin R. Hancock,et al.  Eigenspaces for Graphs , 2002, Int. J. Image Graph..

[16]  Jürgen Kurths,et al.  Synchronization in small-world networks. , 2008, Chaos.

[17]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[18]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[19]  James B. Grace,et al.  Structural Equation Modeling and Natural Systems , 2006 .

[20]  H. Kaiser An index of factorial simplicity , 1974 .

[21]  Danielle Smith Bassett,et al.  Small-World Brain Networks , 2006, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[22]  S. Bressler Large-scale cortical networks and cognition , 1995, Brain Research Reviews.

[23]  Edward Bullmore,et al.  Neural networks in psychiatry , 2013, European Neuropsychopharmacology.

[24]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[25]  Danielle S Bassett,et al.  Brain graphs: graphical models of the human brain connectome. , 2011, Annual review of clinical psychology.

[26]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[27]  A. Winsor Sampling techniques. , 2000, Nursing times.

[28]  Lester Melie-García,et al.  Characterizing brain anatomical connections using diffusion weighted MRI and graph theory , 2007, NeuroImage.

[29]  Marcus Kaiser,et al.  A tutorial in connectome analysis: Topological and spatial features of brain networks , 2011, NeuroImage.

[30]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[31]  Lester Melie-García,et al.  Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory , 2008, NeuroImage.

[32]  Cornelis J Stam,et al.  Graph theoretical analysis of complex networks in the brain , 2007, Nonlinear biomedical physics.

[33]  Dorothea Wagner,et al.  Approximating Clustering Coefficient and Transitivity , 2005, J. Graph Algorithms Appl..

[34]  Antonio M. Batista,et al.  A network of networks model to study phase synchronization using structural connection matrix of human brain , 2018 .

[35]  Michael I. Ham,et al.  Functional structure of cortical neuronal networks grown in vitro. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  P. V. van Zijl,et al.  Three‐dimensional tracking of axonal projections in the brain by magnetic resonance imaging , 1999, Annals of neurology.

[37]  H. Berendse,et al.  The application of graph theoretical analysis to complex networks in the brain , 2007, Clinical Neurophysiology.

[38]  C. Stam,et al.  Small-world networks and functional connectivity in Alzheimer's disease. , 2006, Cerebral cortex.

[39]  K. Gurney,et al.  Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence , 2008, PloS one.

[40]  Ruedi Stoop,et al.  Beyond scale-free small-world networks: cortical columns for quick brains. , 2013, Physical review letters.

[41]  M P Young,et al.  Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[42]  Olaf Sporns,et al.  Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network , 2019, Scientific Reports.

[43]  N. Tzourio-Mazoyer,et al.  Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain , 2002, NeuroImage.

[44]  Alan C. Evans,et al.  Revealing modular architecture of human brain structural networks by using cortical thickness from MRI. , 2008, Cerebral cortex.

[45]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.

[46]  K. Worsley,et al.  Impaired small-world efficiency in structural cortical networks in multiple sclerosis associated with white matter lesion load. , 2009, Brain : a journal of neurology.

[47]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[48]  C. Stam Modern network science of neurological disorders , 2014, Nature Reviews Neuroscience.

[49]  Mark Newman,et al.  Models of the Small World , 2000 .

[50]  O. Sporns,et al.  The economy of brain network organization , 2012, Nature Reviews Neuroscience.

[51]  L. Cronbach Coefficient alpha and the internal structure of tests , 1951 .

[52]  Alan C. Evans,et al.  Structural Insights into Aberrant Topological Patterns of Large-Scale Cortical Networks in Alzheimer's Disease , 2008, The Journal of Neuroscience.

[53]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Yuan Zhou,et al.  Abnormal Cortical Networks in Mild Cognitive Impairment and Alzheimer's Disease , 2010, PLoS Comput. Biol..

[55]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[56]  E. Courchesne,et al.  Why the frontal cortex in autism might be talking only to itself: local over-connectivity but long-distance disconnection , 2005, Current Opinion in Neurobiology.

[57]  B. T. Thomas Yeo,et al.  A Spotlight on Bridging Microscale and Macroscale Human Brain Architecture , 2017, Neuron.

[58]  E. Bullmore,et al.  Disrupted Axonal Fiber Connectivity in Schizophrenia , 2011, Biological Psychiatry.

[59]  Jacob G Foster,et al.  Edge direction and the structure of networks , 2009, Proceedings of the National Academy of Sciences.

[60]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.