Energy landscape analysis of neuroimaging data

Computational neuroscience models have been used for understanding neural dynamics in the brain and how they may be altered when physiological or other conditions change. We review and develop a data-driven approach to neuroimaging data called the energy landscape analysis. The methods are rooted in statistical physics theory, in particular the Ising model, also known as the (pairwise) maximum entropy model and Boltzmann machine. The methods have been applied to fitting electrophysiological data in neuroscience for a decade, but their use in neuroimaging data is still in its infancy. We first review the methods and discuss some algorithms and technical aspects. Then, we apply the methods to functional magnetic resonance imaging data recorded from healthy individuals to inspect the relationship between the accuracy of fitting, the size of the brain system to be analysed and the data length. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

[1]  西森 秀稔.  Statistical physics of spin glasses and information processing : an introduction , 2001 .

[2]  Anthony G. Hudetz,et al.  Spin-glass model predicts metastable brain states that diminish in anesthesia , 2014, Front. Syst. Neurosci..

[3]  J. Besag.  Statistical Analysis of Non-Lattice Data , 1975 .

[4]  M. Karplus,et al.  The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics , 1997 .

[5]  Steen Moeller,et al.  The Human Connectome Project: A data acquisition perspective , 2012, NeuroImage.

[6]  Naoki Masuda,et al.  Network-dependent modulation of brain activity during sleep , 2014, NeuroImage.

[7]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[8]  Jascha Sohl-Dickstein,et al.  A new method for parameter estimation in probabilistic models: Minimum probability flow , 2011, Physical review letters.

[9]  Peter E. Latham,et al.  Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't , 2008, PLoS Comput. Biol..

[10]  W. Singer,et al.  Neuronal Dynamics and Neuropsychiatric Disorders: Toward a Translational Paradigm for Dysfunctional Large-Scale Networks , 2012, Neuron.

[11]  Jonathon Shlens,et al.  The Structure of Multi-Neuron Firing Patterns in Primate Retina , 2006, The Journal of Neuroscience.

[12]  Y. Miyashita,et al.  Effects of rTMS of Pre-Supplementary Motor Area on Fronto Basal Ganglia Network Activity during Stop-Signal Task , 2015, The Journal of Neuroscience.

[13]  Aonan Tang,et al.  Maximum Entropy Approaches to Living Neural Networks , 2010, Entropy.

[14]  Daniele Marinazzo,et al.  Information Transfer and Criticality in the Ising Model on the Human Connectome , 2014, PloS one.

[15]  M. Kramer,et al.  Beyond the Connectome: The Dynome , 2014, Neuron.

[16]  H. Nishimori.  Statistical Physics of Spin Glasses and Information Processing , 2001 .

[17]  Elad Schneidman,et al.  Towards the design principles of neural population codes , 2016, Current Opinion in Neurobiology.

[18]  Gustavo Deco,et al.  computational neuroscience approach to schizophrenia and its onset , 2011 .

[19]  Shan Yu,et al.  A Small World of Neuronal Synchrony , 2008, Cerebral cortex.

[20]  D. Chialvo.  Emergent complex neural dynamics , 2010, 1010.2530.

[21]  Naoki Masuda,et al.  Energy landscapes of resting-state brain networks , 2014, Front. Neuroinform..

[22]  Jonathan D. Power,et al.  Functional Brain Networks Develop from a “Local to Distributed” Organization , 2009, PLoS Comput. Biol..

[23]  Michael J. Berry,et al.  Network information and connected correlations. , 2003, Physical review letters.

[24]  S. Laureys,et al.  Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory , 2014, BioMed research international.

[25]  John M. Beggs,et al.  A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro , 2008, The Journal of Neuroscience.

[26]  H. Yamasue,et al.  Clinical and neural effects of six-week administration of oxytocin on core symptoms of autism. , 2015, Brain : a journal of neurology.

[27]  J. Hertz,et al.  Ising model for neural data: model quality and approximate methods for extracting functional connectivity. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Yutaka Sakai,et al.  Synchronous Firing and Higher-Order Interactions in Neuron Pool , 2003, Neural Computation.

[29]  Geraint Rees,et al.  Energy landscape and dynamics of brain activity during human bistable perception , 2014, Nature Communications.

[30]  D. Chialvo,et al.  Ising-like dynamics in large-scale functional brain networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Karl J. Friston,et al.  Computational psychiatry , 2012, Trends in Cognitive Sciences.

[32]  R. Segev,et al.  The Architecture of Functional Interaction Networks in the Retina , 2011, The Journal of Neuroscience.

[33]  J. Darroch,et al.  Generalized Iterative Scaling for Log-Linear Models , 1972 .

[34]  Naoki Masuda,et al.  A pairwise maximum entropy model accurately describes resting-state human brain networks , 2013, Nature Communications.