Emergence of canonical functional networks from the structural connectome

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

[1]  Rachid Deriche,et al.  A unified framework for multimodal structure-function mapping based on eigenmodes , 2020, Medical Image Anal..

[2]  Maurizio Corbetta,et al.  The human brain is intrinsically organized into dynamic, anticorrelated functional networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Julia P. Owen,et al.  Spectral graph theory of brain oscillations , 2019, bioRxiv.

[4]  Danielle S Bassett,et al.  Spectral mapping of brain functional connectivity from diffusion imaging , 2018, Scientific Reports.

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

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

[7]  C. Yasuda,et al.  Frequent Seizures Are Associated with a Network of Gray Matter Atrophy in Temporal Lobe Epilepsy with or without Hippocampal Sclerosis , 2014, PloS one.

[8]  Li Qiu,et al.  Complex Laplacians and Applications in Multi-Agent Systems , 2014 .

[9]  Laura E. Suárez,et al.  Gradients of structure–function tethering across neocortex , 2019, Proceedings of the National Academy of Sciences.

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

[11]  M. Breakspear,et al.  The connectomics of brain disorders , 2015, Nature Reviews Neuroscience.

[12]  Olaf Sporns,et al.  Network structure of cerebral cortex shapes functional connectivity on multiple time scales , 2007, Proceedings of the National Academy of Sciences.

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

[14]  Elizabeth Jefferies,et al.  Situating the default-mode network along a principal gradient of macroscale cortical organization , 2016, Proceedings of the National Academy of Sciences.

[15]  M. Paluš,et al.  The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks. , 2011, Chaos.

[16]  G. Glover,et al.  Dissociable Intrinsic Connectivity Networks for Salience Processing and Executive Control , 2007, The Journal of Neuroscience.

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

[18]  Maria Giulia Preti,et al.  Decoupling of brain function from structure reveals regional behavioral specialization in humans , 2019, Nature Communications.

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

[20]  Jean M. Vettel,et al.  Controllability of structural brain networks , 2014, Nature Communications.

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

[22]  Tianzi Jiang,et al.  Brainnetome: A new -ome to understand the brain and its disorders , 2013, NeuroImage.

[23]  J. Rapoport,et al.  The anatomical distance of functional connections predicts brain network topology in health and schizophrenia. , 2013, Cerebral cortex.

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

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

[26]  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.

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

[28]  R Cameron Craddock,et al.  A whole brain fMRI atlas generated via spatially constrained spectral clustering , 2012, Human brain mapping.

[29]  D. Attwell,et al.  Node of Ranvier length as a potential regulator of myelinated axon conduction speed , 2017, eLife.

[30]  Benjamin J. Shannon,et al.  Molecular, Structural, and Functional Characterization of Alzheimer's Disease: Evidence for a Relationship between Default Activity, Amyloid, and Memory , 2005, The Journal of Neuroscience.

[31]  J. Zimmermann,et al.  Differentiation of Alzheimer's disease based on local and global parameters in personalized Virtual Brain models , 2018, NeuroImage: Clinical.

[32]  A. Schnitzler,et al.  Normal and pathological oscillatory communication in the brain , 2005, Nature Reviews Neuroscience.

[33]  Karl J. Friston,et al.  Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri , 2022 .

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

[35]  G. R. Noakes,et al.  Vibrations and Waves , 1962, Nature.

[36]  O. Sporns,et al.  Towards the virtual brain: network modeling of the intact and the damaged brain. , 2010, Archives italiennes de biologie.

[37]  H. U. Voss,et al.  The application of a mathematical model linking structural and functional connectomes in severe brain injury , 2016, NeuroImage: Clinical.

[38]  Anders M. Dale,et al.  An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest , 2006, NeuroImage.

[39]  Matthew J. Brookes,et al.  How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes , 2019, NeuroImage.

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

[41]  Viktor K. Jirsa,et al.  Noise during Rest Enables the Exploration of the Brain's Dynamic Repertoire , 2008, PLoS Comput. Biol..

[42]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[43]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

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

[45]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[46]  Julien Cohen-Adad,et al.  The Human Connectome Project and beyond: Initial applications of 300mT/m gradients , 2013, NeuroImage.

[47]  Maurizio Corbetta,et al.  Functional connectivity in resting-state fMRI: Is linear correlation sufficient? , 2011, NeuroImage.

[48]  R. Douglas Fields,et al.  A new mechanism of nervous system plasticity: activity-dependent myelination , 2015, Nature Reviews Neuroscience.

[49]  Juan C. Jiménez,et al.  Nonlinear EEG analysis based on a neural mass model , 1999, Biological Cybernetics.

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

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

[52]  Christian Grefkes,et al.  Cerebral network disorders after stroke: evidence from imaging‐based connectivity analyses of active and resting brain states in humans , 2013, The Journal of physiology.

[53]  P. Nunez The brain wave equation: a model for the EEG , 1974 .

[54]  N. Chatterjee,et al.  Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. , 2008, Progress in brain research.

[55]  Piet Van Mieghem,et al.  Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches , 2020, NeuroImage.

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

[57]  Somwrita Sarkar,et al.  Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment , 2016, NeuroImage.

[58]  Yong He,et al.  Topological organization of the human brain functional connectome across the lifespan , 2013, Developmental Cognitive Neuroscience.

[59]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

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

[61]  H. Haken,et al.  A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics , 1997 .

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

[63]  P. Fries A mechanism for cognitive dynamics: neuronal communication through neuronal coherence , 2005, Trends in Cognitive Sciences.

[64]  Bruce Fischl,et al.  FreeSurfer , 2012, NeuroImage.

[65]  Daniel S. Margulies,et al.  Macroscale cortical organization and a default-like apex transmodal network in the marmoset monkey , 2019, Nature Communications.

[66]  Richard F. Betzel,et al.  Linking Structure and Function in Macroscale Brain Networks , 2020, Trends in Cognitive Sciences.

[67]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

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

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

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

[71]  Piet Van Mieghem,et al.  A Mapping Between Structural and Functional Brain Networks , 2016, Brain Connect..

[72]  Marisa O. Hollinshead,et al.  The organization of the human cerebral cortex estimated by intrinsic functional connectivity. , 2011, Journal of neurophysiology.

[73]  E. Bullmore,et al.  Human brain networks in health and disease , 2009, Current opinion in neurology.

[74]  Boris C. Bernhardt,et al.  Gradients of structure–function tethering across neocortex , 2019, Proceedings of the National Academy of Sciences.

[75]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[76]  Keith A. Johnson,et al.  Stepwise Connectivity of the Modal Cortex Reveals the Multimodal Organization of the Human Brain , 2012, The Journal of Neuroscience.

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

[78]  O. Sporns,et al.  Key role of coupling, delay, and noise in resting brain fluctuations , 2009, Proceedings of the National Academy of Sciences.

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

[80]  Morten L. Kringelbach,et al.  Modeling the outcome of structural disconnection on resting-state functional connectivity , 2012, NeuroImage.

[81]  P Tewarie,et al.  The relation between structural and functional connectivity patterns in complex brain networks. , 2016, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[82]  Julia M. Huntenburg,et al.  Large-Scale Gradients in Human Cortical Organization , 2018, Trends in Cognitive Sciences.