MULTISCALE MODULARITY IN BRAIN SYSTEMS

Transcription

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

2 The Brain: A Multiscale System Spatial Hierarchy: Temporal-Spatial Hierarchy:

3 NETWORK MODELS

4 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.

5 System to Graph nodes Graph edges

6 Network Diagnostics Density Hierarchy Rentian Scaling Assortativity Path-length Nodal Strength Weight Edge Diversity

7 Network Diagnostics Synchronizability Closeness Centrality Betweenness Centrality Clustering Subgraph Centrality Communicability Local Efficiency Modularity

8 Local to Global Neighbor-Scale Community-Scale Network-Scale Clustering Modularity Path-length

9 Topological to Physical Topological Space Network Embedding Euclidean Space Topological Dimension Rentian Scaling Connection Distance

10 THE HUMAN BRAIN AS A MULTISCALE NETWORK

11 Systems Biology: Complex interactions in biological systems Applied Mathematics Brain Networks Statistical Physics Neuroscience

12 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

13 Noninvasive Neuroimaging Imaging Modality Measures: Structure Function MRI EEG Wiring Blood Flow Electrical Activity Temporal Resolution Spatial Resolution MEG Magnetic Flux

14 Example Brain Network Construction Diffusion Tractography Whole-Brain Parcellation Hagmann et al PLoS Biology

15 BRAIN NETWORKS ARCHITECTURES

16 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

17 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.

18 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.

19 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 Neuron

20 Network Statistics: Organizational Principles Network Modularity Optimize the modularity value, Q. Supposing that node i is assigned to community g i and node j is assigned to community g j, the modularity index is defined as: where A ij is the connectivity matrix of the system, δ(g i ;g j ) = 1 if g i = g j and it equals 0 otherwise, and P ij is the expected weight of the edge connecting node i and node j under a specified random network null model. Bassett et al PLoS Comp Biology Bassett et al Neuroimage Meunior et al Front Neuroinform

21 Multi-scale Organization Nodes Modules Nodes 1 0 Topological similarity Sub-Modules Sub-Sub-Modules Bassett et al PLoS Comp Biology

22 Multi-scale Structure & Function Modules Nodes Nodes 1 0 Topological similarity Audition Vision Motor Form Sub-Modules Color Motion CW Sub-Sub-Modules Stable CCW

23 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 Bassett et al PLoS Comp Biology Log(e) p= Log(n) Rentian scaling has been found in systems that have been cost-efficiently embedded into physical space, for example brains, neuronal networks, and computer circuits.

24 MODULARITY & ADAPTIVE FUNCTION

25 Functional Network Organization Functional Imaging 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. Magnetic Electrical Flux Activity Blood Flow MRI EEG MEG Functional Networks: Nodes = Brain Regions Edges = Signals Similarities

26 Dynamic, Flexible Modules The brain as a dynamic system. Hypothesis: Flexible network structure facilitates adaptive function. Approach: Multi-layer dynamic network models Rigid Flexible Time Bassett et al PNAS

27 Modularity & Learning Audition The selective adaptability necessary for human learning could naturally be provided by dynamic modular structure. Form Vision Model System: Simple Motor Learning Paradigm Motor CW Color Stable Hypothesis: Modularity of human brain function Motion changes dynamically during learning, and that characteristics of these dynamics are associated with learning success. CCW

28 Functional Brain Network Construction

29 Multi-scale Temporal Analysis Example Multilayer Network Structure:

30 Multilayer Modularity Example Multilayer Network Structure: Multilayer Modularity:

31 Quantifying Network Flexibility Flexibility might be driven by physiological processes that facilitate the participation of cortical regions in multiple functional communities or by taskdependent processes that require the capacity to balance learning across subtasks. Bassett et al. 2011, PNAS

32 Flexibility & Learning Flexibility changes with learning. Brain regions responsible included association processing areas. Flexibility predicts learning in future experimental sessions. Learning Bassett et al. 2011, PNAS

33 SUMMARY

34 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?

35 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

36 Questions?