Spectral graph theory of brain oscillations

The relationship between the brain’s structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We propose a linear, hierarchical graph spectral model of brain activity at mesoscopic and macroscopic scales that accurately predicts spatial and spectral features of neural oscillations across the brain. This novel model yields an elegant closed-form solution of the structure-function problem specified by the graph Laplacian spectrum of the structural connectome with simple, universal rules of dynamics specified by few unknown parameters. This parsimony stands in contrast to conventional complex numerical simulations of coupled non-linear lumped neural mass models (NMM). The model was highly successful in reproducing empirical spatial and spectral patterns of activity measured by scalp magneto-encephalography (MEG) after source localization, in contrast to NMM. The model may represent an important step towards understanding the fundamental relationship between network topology and the macroscopic whole-brain dynamics.

[1]  H. Voss,et al.  Network diffusion accurately models the relationship between structural and functional brain connectivity networks , 2014, NeuroImage.

[2]  Joachim M. Buhmann,et al.  Regression DCM for fMRI , 2017, NeuroImage.

[3]  P. Nunez,et al.  A theoretical basis for standing and traveling brain waves measured with human EEG with implications for an integrated consciousness , 2006, Clinical Neurophysiology.

[4]  M. Weiner,et al.  A Network Diffusion Model of Disease Progression in Dementia , 2012, Neuron.

[5]  F. Haiss,et al.  Spatiotemporal Dynamics of Cortical Sensorimotor Integration in Behaving Mice , 2007, Neuron.

[6]  Adeel Razi,et al.  Construct validation of a DCM for resting state fMRI , 2015, NeuroImage.

[7]  Farras Abdelnour,et al.  Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure , 2018, NeuroImage.

[8]  L. F. Abbott,et al.  A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks , 2013, PLoS Comput. Biol..

[9]  Tim Head,et al.  Binder 2.0 - Reproducible, interactive, sharable environments for science at scale , 2018, SciPy.

[10]  Terrence J. Sejnowski,et al.  The Wilson–Cowan model, 36 years later , 2009, Biological Cybernetics.

[11]  Farras Abdelnour,et al.  Estimating brain's functional graph from the structural graph's Laplacian , 2015, SPIE Optical Engineering + Applications.

[12]  Sarah Feldt Muldoon,et al.  Stimulation-Based Control of Dynamic Brain Networks , 2016, PLoS Comput. Biol..

[13]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[14]  H Haken,et al.  Co-operative dynamics in organelles. , 1983, Journal of theoretical biology.

[15]  Richard F. Betzel,et al.  Resting-brain functional connectivity predicted by analytic measures of network communication , 2013, Proceedings of the National Academy of Sciences.

[16]  H. Markram.  The Blue Brain Project , 2006, Nature Reviews Neuroscience.

[17]  O Sporns,et al.  Predicting human resting-state functional connectivity from structural connectivity , 2009, Proceedings of the National Academy of Sciences.

[18]  Risi Kondor,et al.  Diffusion kernels on graphs and other discrete structures , 2002, ICML 2002.

[19]  Biyu J. He,et al.  The Temporal Structures and Functional Significance of Scale-free Brain Activity , 2010, Neuron.

[20]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[21]  G. Edelman,et al.  Large-scale model of mammalian thalamocortical systems , 2008, Proceedings of the National Academy of Sciences.

[22]  Eric J. Friedman,et al.  The structural connectome of the human brain in agenesis of the corpus callosum , 2013, NeuroImage.

[23]  Dimitri Van De Ville,et al.  The dynamic functional connectome: State-of-the-art and perspectives , 2017, NeuroImage.

[24]  James G. King,et al.  Reconstruction and Simulation of Neocortical Microcircuitry , 2015, Cell.

[25]  Alain Destexhe,et al.  A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States , 2009, Neural Computation.

[26]  A. J. Hermans,et al.  A model of the spatial-temporal characteristics of the alpha rhythm. , 1982, Bulletin of mathematical biology.

[27]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[28]  W. Freeman,et al.  Simulated power spectral density (PSD) of background electrocorticogram (ECoG) , 2008, Cognitive Neurodynamics.

[29]  E. Brown,et al.  Thalamocortical Mechanisms for the Anteriorization of Alpha Rhythms during Propofol-Induced Unconsciousness , 2013, The Journal of Neuroscience.

[30]  Selen Atasoy,et al.  Human brain networks function in connectome-specific harmonic waves , 2016, Nature Communications.

[31]  Ashish Raj,et al.  Spectral graph theory of brain oscillations , 2020, Human brain mapping.

[32]  Gustavo Deco,et al.  How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model , 2012, Front. Comput. Neurosci..

[33]  L. J. van Vliet,et al.  Detection of protrusions in curved folded surfaces applied to automated polyp detection in CT colonography , 2006 .

[34]  Tobias C. Potjans,et al.  The Cell-Type Specific Cortical Microcircuit: Relating Structure and Activity in a Full-Scale Spiking Network Model , 2012, Cerebral cortex.

[35]  Farras Abdelnour,et al.  Relating Cortical Atrophy in Temporal Lobe Epilepsy with Graph Diffusion-Based Network Models , 2015, PLoS Comput. Biol..

[36]  Karl J. Friston,et al.  Linking canonical microcircuits and neuronal activity: Dynamic causal modelling of laminar recordings , 2017, NeuroImage.

[37]  Rasmus Larsen,et al.  Medical Image Computing and Computer-Assisted Intervention - MICCAI 2006, 9th International Conference, Copenhagen, Denmark, October 1-6, 2006, Proceedings, Part I , 2006, MICCAI.

[38]  Mark W. Woolrich,et al.  FSL , 2012, NeuroImage.

[39]  Christian Igel,et al.  A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging , 2010, PLoS Comput. Biol..

[40]  Karl J. Friston,et al.  Anatomical connectivity and the resting state activity of large cortical networks , 2013, NeuroImage.

[41]  Ninon Burgos,et al.  New advances in the Clinica software platform for clinical neuroimaging studies , 2019 .

[42]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[43]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[44]  Joachim M. Buhmann,et al.  A generative model of whole-brain effective connectivity , 2018, NeuroImage.

[45]  Diego Contreras,et al.  Long-Range Parallel Processing and Local Recurrent Activity in the Visual Cortex of the Mouse , 2012, The Journal of Neuroscience.

[46]  R. Kahn,et al.  Functionally linked resting‐state networks reflect the underlying structural connectivity architecture of the human brain , 2009, Human brain mapping.

[47]  Olaf Sporns,et al.  Communication Efficiency and Congestion of Signal Traffic in Large-Scale Brain Networks , 2014, PLoS Comput. Biol..

[48]  Gustavo Deco,et al.  Tracing evolution of spatio-temporal dynamics of the cerebral cortex: cortico-cortical communication dynamics , 2014, Front. Syst. Neurosci..

[49]  Scott T. Grafton,et al.  Structural foundations of resting-state and task-based functional connectivity in the human brain , 2013, Proceedings of the National Academy of Sciences.

[50]  Julia P. Owen,et al.  Brain network eigenmodes provide a robust and compact representation of the structural connectome in health and disease , 2017, PLoS Comput. Biol..

[51]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[52]  Hamid Reza Mohseni,et al.  How delays matter in an oscillatory whole-brain spiking-neuron network model for MEG alpha-rhythms at rest , 2014, NeuroImage.

[53]  Benjamin Auffarth.  Spectral Graph Clustering , 2007 .

[54]  Adeel Razi,et al.  Dynamic causal modelling revisited , 2017, NeuroImage.

[55]  Terry M. Peters,et al.  Medical Image Computing and Computer Assisted Intervention – MICCAI 2019: 22nd International Conference, Shenzhen, China, October 13–17, 2019, Proceedings, Part IV , 2019, MICCAI.

[56]  Hagai Attias,et al.  Probabilistic algorithms for MEG/EEG source reconstruction using temporal basis functions learned from data , 2008, NeuroImage.

[57]  Mathew P. Dafilis,et al.  A spatially continuous mean field theory of electrocortical activity , 2002, Network.

[58]  Olaf Sporns,et al.  Symbiotic relationship between brain structure and dynamics , 2009, BMC Neuroscience.

[59]  Yasser Iturria-Medina,et al.  Anatomical Brain Networks on the Prediction of Abnormal Brain States , 2013, Brain Connect..

[60]  P. Robinson,et al.  Multiscale brain modelling , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[61]  William M. Wells,et al.  Medical Image Computing and Computer-Assisted Intervention — MICCAI’98 , 1998, Lecture Notes in Computer Science.

[62]  Julia P. Owen,et al.  Robust Bayesian estimation of the location, orientation, and time course of multiple correlated neural sources using MEG , 2010, NeuroImage.

[63]  Adeel Razi,et al.  Dynamic effective connectivity in resting state fMRI , 2017, NeuroImage.

[64]  Srikantan S. Nagarajan,et al.  Parameter Identifiability and Non-Uniqueness In Connectome Based Neural Mass Models , 2018 .

[65]  S. Baillet,et al.  Localization of realistic cortical activity in MEG using current multipoles , 2004, NeuroImage.

[66]  K Sekihara,et al.  NUTMEG: a neuromagnetic source reconstruction toolbox. , 2004, Neurology & clinical neurophysiology : NCN.

[67]  Viktor K. Jirsa,et al.  Systematic approximations of neural fields through networks of neural masses in the virtual brain , 2013, NeuroImage.

[68]  R. Kötter,et al.  Cortical network dynamics with time delays reveals functional connectivity in the resting brain , 2008, Cognitive Neurodynamics.

[69]  Farras Abdelnour,et al.  Network Analysis on Predicting Mean Diffusivity Change at Group Level in Temporal Lobe Epilepsy , 2016, Brain Connect..

[70]  Karl J. Friston,et al.  Dynamic causal modelling of distributed electromagnetic responses , 2009, NeuroImage.

[71]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[72]  D. Liley,et al.  Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons. , 1999, Network.

[73]  Karl J. Friston,et al.  Large-scale DCMs for resting-state fMRI , 2017, Network Neuroscience.

[74]  Karl J. Friston,et al.  Structural and Functional Brain Networks: From Connections to Cognition , 2013, Science.

[75]  Viktor K. Jirsa,et al.  Spatiotemporal forward solution of the EEG and MEG using network modeling , 2002, IEEE Transactions on Medical Imaging.

[76]  Adeel Razi,et al.  Dynamic causal modelling of fluctuating connectivity in resting-state EEG , 2018, NeuroImage.

[77]  R. F. Galán,et al.  On How Network Architecture Determines the Dominant Patterns of Spontaneous Neural Activity , 2008, PLoS ONE.

[78]  Ashish Raj,et al.  Identifiability In Connectome Based Neural Mass Models , 2018 .

[79]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[80]  Klaas E. Stephan,et al.  Dynamic causal modelling: A critical review of the biophysical and statistical foundations , 2011, NeuroImage.

[81]  Paul L. Nunez,et al.  A Study of Origins of the Time Dependencies of Scalp EEG: I - Theoretical Basis , 1981, IEEE Transactions on Biomedical Engineering.

[82]  A. Dale,et al.  Whole Brain Segmentation Automated Labeling of Neuroanatomical Structures in the Human Brain , 2002, Neuron.

[83]  Richard F. Betzel,et al.  Cooperative and Competitive Spreading Dynamics on the Human Connectome , 2015, Neuron.

[84]  Farras Abdelnour,et al.  Estimating function from structure in epileptics using graph diffusion model , 2015, 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI).