Kavli Institute 2008 Brain Networks for Efficient Computation Olaf Sporns Department of Psychological and Brain Sciences Indiana University, Bloomington, IN 47405 http://www.indiana.edu/~cortex , firstname.lastname@example.orgOutlineBrain Connectivity Network Science ApproachesBrain Dynamics Structure, Function, Information, ComplexityThe Human Brain Building a Map of the Human Brain
OutlineBrain Connectivity Brain Dynamics The Human Brain
Brain Connectivity The Brain is a Complex Network Organized on Multiple ScalesMicroscopic: Single neurons and their synaptic connections.Mesoscopic: Connections within and between microcolumns (minicolumns) or othertypes of local cell assembliesMacroscopic: Anatomically segregated brain regions and inter-regional pathways. Sporns (2007) Brain Connectivity. www.scholarpedia.org
Brain Connectivity Structure and Function of the Brain are Intricately LinkedAnatomical (Structural) Connectivity: Pattern of structural connectionsbetween neurons, neuronal populations, or brain regions.Functional Connectivity: Pattern of statistical dependencies (e.g. temporalcorrelations) between distinct (often remote) neuronal elements.Effective Connectivity: Network of causal effects, combination of functionalconnectivity and structural model.
Brain Connectivity Brain Networks Form a Small WorldIn highly evolved brains, structural brainconnectivity forms a small-world (high clustering,short path length, low wiring cost, modules,hubs) Sporns and Zwi (2004)Highly clustered connection patterns at the large-scale reflect functional relations between sets ofbrain regions. These functional relations may bea result of clustered connectivity. Hilgetag et al., 2000 Kaiser and Hilgetag, 2006 Short path lengths indicate that all cortical areas can be linked in very few processing steps.
OutlineBrain ConnectivityBrain Dynamics The Human Brain
Brain DynamicsThe Brain is Organized to Efficiently Extract and Coordinate Information Two major organizational principles of cortex: Segregation (anatomical/functional) clustering Integration (anatomical/functional) path length These principles are complementary and interdependent. Two major challenges for information processing in the brain: Rapid extraction of information (elimination of redundant dimensions, efficient coding, maximum information transfer) Coordination of distributed resources to create coherent states Both challenges must be solved simultaneously, within a common neural architecture.
Brain Dynamics Segregation + Integration = Complexitycomplexity:coexistence of complexitysegregation andintegration (local andglobal structure)C ( X ) = H ( X ) − ∑i H ( xi X − xi ). Movie courtesy of Vincent, Raichle, Snyder et al (Washington University) small-world structural network spontaneous activity in a neural model spontaneous activity in a human brain
Outline Brain Connectivity Brain DynamicsThe Human Brain
The Human Brain The Brain is Always Active – Even “at Rest”Slow fluctuations in fMRI signal at rest may reflect neuronal baseline activity.Patterns of resting state BOLD signal change are consistent across subjects.Spontaneous fluctuations reveal the existence of two distributed and anti-correlated resting state networks. Damoiseaux et al., PNAS (2006) Fox et al., PNAS (2005)fMRI resting state functional networks of wavelet coefficients show small-worldattributes. Small-world networks (in wavelet space) may be fractal acrossmultiple frequency ranges. Achard et al., J Neurosci. (2006), Bassett et al., PNAS (2006)
The Human BrainConnectivity + Dynamics = Endogenous Brain Activity Connection matrix of macaque cortex + Dynamic equations describing the physiology of a neural population = Spontaneous (endogenous) neural dynamics (chaoticity, metastability) Honey, Breakspear, Kötter, Sporns (2007) PNAS
The Human Brain Neural Dynamics Unfold on Multiple Time ScalesFast fluctuations in neural synchrony drive slower fluctuations in neuralpopulation activity.Functional brain networks reflect the small-world architecture of theirunderlying structural substrate (structural/functional modularity). simulated fMRI cross-correlations
The Human BrainFunctional Brain Networks form a Variable Repertoire static pattern (anatomy) variable pattern (functional relations)
The Human Brain The Connectome is Necessary for Understanding Brain FunctionThe human connectome represents a comprehensive structural description of thenetwork of elements and connections forming the human brain.Proposed initial focus: thalamocortical systemPossible scales of the human connectome: Microscale (neurons, synapses) Macroscale (parcellated brain regions, voxels) Mesoscale (columns, minicolumns)Most feasible approach: macroscale (first draft), followed by “filling-in” at themesoscale. Sporns, O., Tononi, G., and Kötter, R. (2005) The human connectome: A structural description of the human brain. PLoS Comp. Biol.
The Human BrainFiber Pathways of the Cerebral Cortex can be Mapped with MRIDiffusion Spectrum Imaging (DSI) and Computational Tractography Hagmann, Cammoun, Gigandet, Meuli, Honey, Wedeen, Sporns (2008) PLoS Biology
The Human Brain Human Brain Networks have a Structural CoreWe analyzed weighted human brain connection matrices from 5 individualsubjects for a broad range of measures, including degrees/strength, small-world attributes, assortativity, motifs, centrality, efficiency.Network modularity was assessed with k-core decomposition, spectralcommunity detection and nodal participation indices.All network analyses point to the existence of a structural core in humancortex, centered on posterior medial cortex, and comprised ofcuneus/precuneus, superior parietal cortex and portions of cingulate cortex.Brain regions within the structural core share high degree, strength andbetweenness centrality, and they constitute connector hubs that link all majorstructural modules. The structural core contains brain regions that form theposterior components of the human default network.
The Human BrainA scan 1 scan 2 subject A subject B subject C subject D subject EB subject A-E C
The Human Brain Human Brain Networks Have Numerous Hubsconnector hub distribution centrality distribution
The Human BrainHuman Brain Networks Show Individual Variations
The Human Brain Structural and Functional Connections are Highly CorrelatedAB C all subjects, PCUN + PC all subjects, all areas r2 = 0.53 r2 = 0.62 C
The Human Brain Computational Models Capture Large-Scale Human Brain Activity Structural connections of the human brain shape functional activations and dynamic states. r = 0.85 rPC r = 0.76 r = 0.87 Honey et al. (PNAS, in revision) rsFC rsFCSC (empirical) (nonlinear model) empirical nonlinear model SC rsFC
SummaryThe Brain is a Complex Network Organized on Multiple Scales Structure-function relationship, plasticity, turnover, redundancyBrain Networks Form a Small World Allows the brain to efficiently process information, promotes complexityThe Brain is Always Active – Even “at Rest” Endogenous processes vs. exogenous perturbations, multiple time scalesHuman Brain Networks have a Structural Core and Hubs Core located in medial parietal cortex – a region central to self and consciousness Hubs may serve as integrators of cortico-cortical signal traffic Individual variations – clinical disturbancesComputational Models Capture Large-Scale Human Brain Activity Possibility of a global brain simulator Models as tools for exploring mechanistic substrates of human cognition Funded by the JS McDonnell Foundation
SummaryThe Brain is a Complex Network Organized on Multiple Scales Cells to systems Scalable architecture – common principles?Structure and Function of the Brain are Intricately Linked Structure shapes function shapes structure … Reorganization and plasticityBrain Networks Form a Small World High clustering, short path length Reflects volume and processing constraintsThe Brain is Organized to Efficiently Extract and Coordinate Information A dual challenge addressed in a common architecture Small-world attributes map onto information processing requirementsSegregation + Integration = Complexity Complexity is a mixture of randomness and regularity Complexity emerges from structural small-world networks
SummaryThe Brain is Always Active – Even “at Rest” Endogenous processes vs. exogenous perturbationsConnectivity + Dynamics = Endogenous Brain Activity Coupled dynamic models Metastability, itinerancyNeural Dynamics Unfold on Multiple Time Scales Milliseconds to seconds Fractal (self-similar) functional connectivity Long-term averages more stable than short-term averagesFunctional Brain Networks form a Variable Repertoire Cognitive microstates? Robustness versus flexibility
SummaryFiber Pathways of the Cerebral Cortex can be Mapped with MRI Noninvasive methodology Rapid technological development Increasingly refined mapsHuman Brain Networks have a Structural Core and Hubs Core located in medial parietal cortex – a region central to self and consciousness Hubs may serve as integrators of cortico-cortical signal trafficHuman Brain Networks Show Individual Variations Relation to cognitive/behavioral variation unknown Network disturbances can help to diagnose brain diseaseStructural and Functional Connections are Highly Correlated Topological principles shared between anatomical and functional networks Endogenous brain activity – an expression of structural linkagesComputational Models Capture Large-Scale Human Brain Activity Possibility of a global brain simulator Models as tools for exploring mechanistic substrates of human cognition Funded by the JS McDonnell Foundation
The Human Brain1) High consistency of DSI tractography between hemispheres.2) High consistency of DSI tractography in repeat scans. r2 = 0.78 scan 1 scan 2 RH r2 = 0.94 LH3) Connection patterns are robust to degradation (simulation scanning and tractography noise).4) Comparison between macaque DSI tractography and connection patterns derived by anatomical tract tracing shows significant overlap.5) Comparison between structural and functional connections in human brain shows significant correlation.
Macaque Brain ImagingDSI acquisition from a single fixed m. fascicularis cortical hemisphere
Macaque Brain ImagingA Comparison of DSI tractography data with classical tract tracing neuroanatomical data B BDSI Cocomacfiber datadensity (symmetrized) known present unknown known absent