Multiscale Modularity in brain systemsiamis/bassett.pdf · MULTISCALEMODULARITY IN BRAIN SYSTEMS Danielle S. Bassett . University of California Santa Barbara . Department of Physics

MULTISCALE MODULARITY IN BRAIN SYSTEMS Danielle S. Bassett University of California Santa Barbara Department of Physics

The Brain: A Multiscale System

Danielle S. Bassett, Ph. D.

Spatial Hierarchy: Temporal-Spatial Hierarchy:

http://www.colorado.edu/intphys/Class/IPHY3730/image/figure7-12.jpg http://www.idac.tohoku.ac.jp/en/frontiers/column_070327/FigI-I.gif

NETWORK MODELS


Complex Systems & Network Theory


• Network Theory: Provides a set of representational rules to describe a system in terms of its components and their interactions. Particularly useful to study systems for which continuum models, mean-field theory, and

nearest neighbor interactions fail to adequately describe system dynamics

And in systems in which long-range, non-homogeneous interactions are thought to play a critical role.

System to Graph


nodes

edges

Graph

Network Diagnostics Hierarchy

Rentian Scaling

Path-length

Weight

Edge Diversity

Nodal Strength

Assortativity

Density


Network Diagnostics Synchronizability

Betweenness Centrality

Clustering

Local Efficiency

Communicability

Subgraph Centrality

Closeness Centrality


Modularity

Local to Global

Neighbor-Scale Community-Scale Network-Scale

Clustering Modularity Path-length


Topological to Physical

Topological Space Network Embedding Euclidean Space

Topological Dimension Rentian Scaling Connection Distance


THE HUMAN BRAIN AS A MULTISCALE NETWORK


Systems Biology: Complex interactions in biological systems


Neuroscience

Applied Mathematics

Statistical Physics

Brain Networks

The Human Brain

• Experiment (Large-Scale): Focus has been on system components rather than their interactions.

• Theory (Small-Scale): Cognitive processes stem from coherent

oscillatory activity between brain regions.

• Benefits as a Model System: strong statistical power (ensembles of humans), complex dynamics, meaningful perturbations (cognitive effort, disease), and sophisticated function.

Fries 2005 TICS


Noninvasive Neuroimaging M

RI

EE

G

ME

G

Wiring Blood Flow


Electrical Activity

Magnetic Flux

Imaging Modality Measures: Structure Function

Temporal R

esolution

Spatial R

esolution

Example Brain Network Construction Diffusion Tractography Whole-Brain Parcellation

Hagmann et al. 2008 PLoS Biology


BRAIN NETWORKS ARCHITECTURES


Network Architectures for Function


What do we know about the brain that can inform our hypotheses about what network architectures would be important for cognitive function? The brain is a dynamical system that requires flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior.

Izhekevich 2006

Architectures for Flexibility & Selectivity


What architectures are consistent with both flexibility and selectivity?

Modularity is a phenomenon that is

studied widely in evolution and development

because it provides selective

adaptability.

Modularity in Complex Systems


An important characteristic of many complex networks is that their subcomponents (nodes) are organized into communities (or “modules”).

Modules are groups of nodes that have more connections to one another than otherwise would be expected in a randomly sampled group of nodes. We can find

modules in complex systems using community detection algorithms.

Modularity in the Brain


Modularity in the brain system indicates that there are groups of brain regions that show coherent behavior and may therefore facilitate specific functions.

Nelson et al. 2010 Neuron

Network Statistics: Organizational Principles


Optimize the modularity value, Q. Supposing that node i is assigned to community gi and node j is assigned to community gj, the modularity index is defined as:

where Aij is the connectivity matrix of the system, δ(gi;gj) = 1 if gi = gj and it equals 0 otherwise, and Pij is the expected weight of the edge connecting node i and node j under a specified random network null model.

Network Modularity

Bassett et al. 2010 PLoS Comp Biology Bassett et al. 2011 Neuroimage Meunior et al. 2009 Front Neuroinform

Multi-scale Organization


Nod

es

Nodes

Modules

Sub-Modules

Sub-Sub-Modules

Bassett et al. 2010 PLoS Comp Biology

0

1 Topological sim

ilarity

Multi-scale Structure & Function


Nod

es

Nodes

Modules

Sub-Modules

Sub-Sub-Modules

0

1 Topological sim

ilarity

Audition Vision Motor

Form Color Motion

CW Stable CCW

Physical Constraints: Wiring Efficiency The brain represents only 2% of the human body’s weight but demands up to 20% of the body’s energy.

• Energy is needed for neuronal communication • Development, maintenance, and use of wiring


p=0.77

Log(n) Lo

g(e)

101

102

103

104

100 101 102 103

Rentian scaling has been found in systems that have been cost-efficiently embedded into physical space, for example brains, neuronal networks, and computer circuits.

Bassett et al. 2010 PLoS Comp Biology

MODULARITY & ADAPTIVE FUNCTION


Functional Network Organization

Functional network organization changes with • behavioral /cognitive variables • genetic factors • experimental task • age & gender • drugs • disease such as Alzheimer’s, schizophrenia,

epilepsy, multiple sclerosis, acute depression, seizures, attention deficit hyperactivity disorder, stroke, spinal cord injury, fronto-temporal lobar degeneration, and early blindness.

M

agne

tic

Flux

B

lood

Flo

w

Ele

ctric

al

Act

ivity

Functional Imaging

Functional Networks: Nodes = Brain Regions Edges = Signals Similarities

MR

I E

EG

M

EG


Dynamic, Flexible Modules


Hypothesis: Flexible network structure facilitates adaptive function.

Flex

ible

R

igid

Approach: Multi-layer dynamic network models

Bassett et al. 2011 PNAS

Time

The brain as a dynamic system.

Modularity & Learning


Audition Vision Motor Form Color Motion

CW Stable CCW

The selective adaptability necessary for human learning could naturally be provided

by dynamic modular structure.

Model System: Simple Motor Learning Paradigm

Hypothesis: Modularity of human brain function changes dynamically during learning, and that characteristics of these dynamics are associated with learning success.

Functional Brain Network Construction


Multi-scale Temporal Analysis


Example Multilayer Network Structure:

Multilayer Modularity


Example Multilayer Network Structure:

Multilayer Modularity:

Quantifying Network Flexibility


Bassett et al. 2011, PNAS

1 2

3 4

Flexibility might be driven by physiological processes that facilitate the participation of cortical regions in multiple functional communities or by task-

dependent processes that require the capacity to balance learning across subtasks.

Flexibility & Learning


Bassett et al. 2011, PNAS

Lear

ning

Flexibility predicts learning in future experimental sessions.

Brain regions responsible included association processing areas.

Flexibility changes with learning.

SUMMARY


Concluding Remarks


• Modularity of functional connectivity may be an important organizational principle of the human brain.

• Facilitates adaptive function, flexibility, and selectivity

• Network flexiblility predicts learning on a simple motor task • Can we use this for identifying who and when to train? • Monitoring of treatment and neurorehabilitation

• Multiscale modularity is consistent with efficient use of wiring. • Can we use this to understand network development and its

alteration in disease states?

Acknowledgements University of Cambridge:

Prof. Ed Bullmore

Daniel Greenfield

Prof. Simon Moore

University of Oxford Prof. Mason A. Porter

Central Institute of Mental Health Andreas Meyer-Lindenberg

National Institute of Mental Health

Daniel Weinberger

Beth Verchinski

Venkata Mattay

University of California Santa Barbara Prof. Scott Grafton

Prof. Jean Carlson

Nick Wymbs

Siemens Medical Solutions Vibhas Deshpande

University of California Los Angeles Jesse Brown

University of North Carolina Chapel Hill Prof. Peter Mucha



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Multiscale Modularity in brain systemsiamis/bassett.pdf · MULTISCALEMODULARITY IN BRAIN SYSTEMS Danielle S. Bassett . University of California Santa Barbara . Department of Physics