Brain Networks for Efficient ComputationOlaf Sporns

Department of Psychological and Brain SciencesIndiana University, Bloomington, IN 47405

http://www.indiana.edu/~cortex , osporns@indiana.edu

Kavli Institute 2008

OutlineBrain Connectivity

Network Science ApproachesBrain Dynamics

Structure, Function, Information, ComplexityThe Human Brain

Building a Map of the Human Brain

Outline

Brain Connectivity

Brain Dynamics

The Human Brain

Brain Connectivity

Microscopic: Single neurons and their synaptic connections.

Mesoscopic: Connections within and between microcolumns (minicolumns) or other types of local cell assemblies

Macroscopic: Anatomically segregated brain regions and inter-regional pathways.

Sporns (2007) Brain Connectivity. www.scholarpedia.org

The Brain is a Complex Network Organized on Multiple Scales

Anatomical (Structural) Connectivity: Pattern of structural connections between neurons, neuronal populations, or brain regions.

Functional Connectivity: Pattern of statistical dependencies (e.g. temporal correlations) between distinct (often remote) neuronal elements.

Effective Connectivity: Network of causal effects, combination of functional connectivity and structural model.

Brain Connectivity

Structure and Function of the Brain are Intricately Linked

In highly evolved brains, structural brain connectivity forms a small-world (high clustering, short path length, low wiring cost, modules, hubs)

Highly clustered connection patterns at the large-scale reflect functional relations between sets of brain regions. These functional relations may be a result of clustered connectivity.

Short path lengths indicate that all cortical areas can be linked in very few processing steps.

Hilgetag et al., 2000

Kaiser and Hilgetag, 2006

Sporns and Zwi (2004)

Brain Connectivity

Brain Networks Form a Small World

Outline

Brain Connectivity

Brain Dynamics

The Human Brain

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.

Two major organizational principles of cortex:

Segregation (anatomical/functional)

Integration (anatomical/functional)

These principles are complementary and interdependent.

clustering

path length

The Brain is Organized to Efficiently Extract and Coordinate Information

Brain Dynamics

complexity:coexistence of segregation and integration (local and global structure)

complexity

Brain Dynamics

Segregation + Integration = Complexity

∑ −−=i ii xxHHC ).()()( XXX

Movie courtesy of Vincent, Raichle, Snyder et al (Washington University)

spontaneous activity in a neural model spontaneous activity in a human brainsmall-world structural network

Outline

Brain Connectivity

Brain Dynamics

The Human Brain

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-world attributes. Small-world networks (in wavelet space) may be fractal across multiple frequency ranges.

Achard et al., J Neurosci. (2006), Bassett et al., PNAS (2006)

The Human Brain

The Brain is Always Active – Even “at Rest”

The Human Brain

Connectivity + 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 Scales

Fast fluctuations in neural synchrony drive slower fluctuations in neural population activity.

Functional brain networks reflect the small-world architecture of their underlying structural substrate (structural/functional modularity).

simulated fMRI cross-correlations

Functional Brain Networks form a Variable Repertoire

The Human Brain

static pattern (anatomy)

variable pattern (functional relations)

Proposed initial focus: thalamocortical system

Possible 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 the mesoscale.

Sporns, O., Tononi, G., and Kötter, R. (2005) The human connectome: A structural description of the human brain. PLoS Comp. Biol.

The human connectome represents a comprehensive structural description of the network of elements and connections forming the human brain.

The Human Brain

The Connectome is Necessary for Understanding Brain Function

Hagmann, Cammoun, Gigandet, Meuli, Honey, Wedeen, Sporns (2008) PLoS Biology

The Human Brain

Fiber Pathways of the Cerebral Cortex can be Mapped with MRI

Diffusion Spectrum Imaging (DSI) and Computational Tractography

A B

C

LH RH

We analyzed weighted human brain connection matrices from 5 individual subjects for a broad range of measures, including degrees/strength, small-world attributes, assortativity, motifs, centrality, efficiency.

Network modularity was assessed with k-core decomposition, spectral community detection and nodal participation indices.

All network analyses point to the existence of a structural core in human cortex, centered on posterior medial cortex, and comprised of cuneus/precuneus, superior parietal cortex and portions of cingulate cortex.

Brain regions within the structural core share high degree, strength and betweenness centrality, and they constitute connector hubs that link all major structural modules. The structural core contains brain regions that form the posterior components of the human default network.

The Human Brain

Human Brain Networks have a Structural Core

subject A subject B subject C subject D subject Escan 1 scan 2

A

Bsubject A-E C

The Human Brain

connector hub distribution centrality distribution

The Human Brain

Human Brain Networks Have Numerous Hubs

The Human Brain

Human Brain Networks Show Individual Variations

C

A

r2 = 0.53

all subjects, PCUN + PCB

all subjects, all areasC

r2 = 0.62

Structural and Functional Connections are Highly Correlated

The Human Brain

RH LH

RH LH

r = 0.76 r = 0.87r = 0.85rPC

empirical nonlinear modelSC rsFC

SCrsFC(empirical)

rsFC(nonlinear model)

The Human Brain

Computational Models Capture Large-Scale Human Brain Activity

Honey et al. (PNAS, in revision)

Structural connections of the human brain shape functional activations and dynamic states.

Summary

The Brain is a Complex Network Organized on Multiple ScalesStructure-function relationship, plasticity, turnover, redundancy

Brain Networks Form a Small WorldAllows the brain to efficiently process information, promotes complexity

The Brain is Always Active – Even “at Rest”Endogenous processes vs. exogenous perturbations, multiple time scales

Human Brain Networks have a Structural Core and HubsCore located in medial parietal cortex – a region central to self and consciousnessHubs may serve as integrators of cortico-cortical signal trafficIndividual variations – clinical disturbances

Computational Models Capture Large-Scale Human Brain ActivityPossibility of a global brain simulatorModels as tools for exploring mechanistic substrates of human cognition

Funded by the JS McDonnell Foundation

Summary

The Brain is a Complex Network Organized on Multiple ScalesCells to systemsScalable architecture – common principles?

Structure and Function of the Brain are Intricately LinkedStructure shapes function shapes structure …Reorganization and plasticity

Brain Networks Form a Small WorldHigh clustering, short path lengthReflects volume and processing constraints

The Brain is Organized to Efficiently Extract and Coordinate InformationA dual challenge addressed in a common architectureSmall-world attributes map onto information processing requirements

Segregation + Integration = ComplexityComplexity is a mixture of randomness and regularityComplexity emerges from structural small-world networks

Summary

The Brain is Always Active – Even “at Rest”Endogenous processes vs. exogenous perturbations

Connectivity + Dynamics = Endogenous Brain ActivityCoupled dynamic modelsMetastability, itinerancy

Neural Dynamics Unfold on Multiple Time ScalesMilliseconds to secondsFractal (self-similar) functional connectivityLong-term averages more stable than short-term averages

Functional Brain Networks form a Variable RepertoireCognitive microstates?Robustness versus flexibility

Summary

Fiber Pathways of the Cerebral Cortex can be Mapped with MRINoninvasive methodologyRapid technological developmentIncreasingly refined maps

Human Brain Networks have a Structural Core and HubsCore located in medial parietal cortex – a region central to self and consciousnessHubs may serve as integrators of cortico-cortical signal traffic

Human Brain Networks Show Individual VariationsRelation to cognitive/behavioral variation unknownNetwork disturbances can help to diagnose brain disease

Structural and Functional Connections are Highly CorrelatedTopological principles shared between anatomical and functional networksEndogenous brain activity – an expression of structural linkages

Computational Models Capture Large-Scale Human Brain ActivityPossibility of a global brain simulatorModels as tools for exploring mechanistic substrates of human cognition

Funded by the JS McDonnell Foundation

1) High consistency of DSI tractography between hemispheres.

2) High consistency of DSI tractography in repeat scans.

3) 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.

RH

LH

scan 1 scan 2

r2 = 0.94

r2 = 0.78

The Human Brain

Macaque Brain Imaging

DSI acquisition from a single fixed m. fascicularis cortical hemisphere

B

A

unkn

own

know

n ab

sent

know

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esen

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BDSI fiber density

Cocomacdata(symmetrized)

Macaque Brain Imaging

Comparison of DSI tractography data with classical tract tracing neuroanatomical data