1. 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 , osporns@indiana.edu
Outline
Brain Connectivity
Network Science Approaches
Brain Dynamics
Structure, Function, Information, Complexity
The Human Brain
Building a Map of the Human Brain

2. Outline
Brain Connectivity
Brain Dynamics
The Human Brain

3. Brain Connectivity
The Brain is a Complex Network Organized on Multiple Scales
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

4. Brain Connectivity
Structure and Function of the Brain are Intricately Linked
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.

5. Brain Connectivity
Brain Networks Form a Small World
In highly evolved brains, structural brain
connectivity 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 of
brain regions. These functional relations may be
a 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.

6. Outline
Brain Connectivity
Brain Dynamics
The Human Brain

7. Brain Dynamics
The 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.

8. Brain Dynamics
Segregation + Integration = Complexity
complexity:
coexistence of
complexity
segregation and
integration (local and
global 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

9. Outline
Brain Connectivity
Brain Dynamics
The Human Brain

10. 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-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)

11. 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

12. 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

13. The Human Brain
Functional Brain Networks form a Variable Repertoire
static pattern (anatomy)
variable pattern (functional
relations)

14. The Human Brain
The Connectome is Necessary for Understanding Brain Function
The human connectome represents a comprehensive structural description of the
network of elements and connections forming the human brain.
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.

15. The Human Brain
Fiber Pathways of the Cerebral Cortex can be Mapped with MRI
Diffusion Spectrum Imaging (DSI) and Computational Tractography
Hagmann, Cammoun, Gigandet, Meuli, Honey, Wedeen, Sporns (2008) PLoS Biology

17. A B
C
RH
LH

18. The Human Brain
Human Brain Networks have a Structural Core
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.

19. The Human Brain
A
scan 1 scan 2
subject A subject B subject C subject D subject E
B
subject A-E
C

20. The Human Brain
Human Brain Networks Have Numerous Hubs
connector hub distribution centrality distribution

21. The Human Brain
Human Brain Networks Show Individual Variations

22. The Human Brain
Structural and Functional Connections are Highly Correlated
A
B C
all subjects, PCUN + PC all subjects, all areas
r2 = 0.53 r2 = 0.62
C

23. RH LH

24. RH LH

25. 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 rsFC
SC (empirical) (nonlinear model)
empirical nonlinear model
SC
rsFC

26. Summary
The Brain is a Complex Network Organized on Multiple Scales
Structure-function relationship, plasticity, turnover, redundancy
Brain Networks Form a Small World
Allows 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 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 disturbances
Computational 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

27. Summary
The 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 plasticity
Brain Networks Form a Small World
High clustering, short path length
Reflects volume and processing constraints
The Brain is Organized to Efficiently Extract and Coordinate Information
A dual challenge addressed in a common architecture
Small-world attributes map onto information processing requirements
Segregation + Integration = Complexity
Complexity is a mixture of randomness and regularity
Complexity emerges from structural small-world networks

28. Summary
The Brain is Always Active – Even “at Rest”
Endogenous processes vs. exogenous perturbations
Connectivity + Dynamics = Endogenous Brain Activity
Coupled dynamic models
Metastability, itinerancy
Neural Dynamics Unfold on Multiple Time Scales
Milliseconds to seconds
Fractal (self-similar) functional connectivity
Long-term averages more stable than short-term averages
Functional Brain Networks form a Variable Repertoire
Cognitive microstates?
Robustness versus flexibility

29. Summary
Fiber Pathways of the Cerebral Cortex can be Mapped with MRI
Noninvasive methodology
Rapid technological development
Increasingly refined maps
Human 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
Human Brain Networks Show Individual Variations
Relation to cognitive/behavioral variation unknown
Network disturbances can help to diagnose brain disease
Structural and Functional Connections are Highly Correlated
Topological principles shared between anatomical and functional
networks
Endogenous brain activity – an expression of structural linkages
Computational 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

30. The Human Brain
1) 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
LH
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.

31. Macaque Brain Imaging
DSI acquisition from a single fixed m. fascicularis cortical hemisphere

32. Macaque Brain Imaging
A Comparison of DSI
tractography data with
classical tract tracing
neuroanatomical data
B B
DSI Cocomac
fiber data
density (symmetrized)
known present
unknown
known absent