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A tutorial in Connectome Analysis (2) - Marcus Kaiser

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COMPLEX NETWORKS: THEORY, METHODS, AND APPLICATIONS (2ND EDITION)
May 16-20, 2016

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A tutorial in Connectome Analysis (2) - Marcus Kaiser

  1. 1. http://www.dynamic-connectome.org http://neuroinformatics.ncl.ac.uk/ @ConnectomeLab Dr Marcus Kaiser A Tutorial in Connectome Analysis (II): Topological and Spatial Features of Brain Networks Professor of Neuroinformatics School of Computing Science / Institute of Neuroscience Newcastle University United Kingdom
  2. 2. 2 Outline • Spatial neural networks • Connection length distributions • Component placement optimization • Role of long-distance connections • Deficits due to changes in long-distance connectivity (Alzheimer’s disease and IQ)
  3. 3. 3 Macaque (rhesus monkey) cortical network
  4. 4. 4 C. elegans neural network Global level (277 neurons) Local level (131 neurons)
  5. 5. 5 Most projections connect adjacent neurons (Gamma function for connection length distribution) 0 20 40 0.05 0.1 0.15 0.2 Connection length[mm] Frequency 0 0.5 1 0 0.1 0.2 0.3 Connection length[mm] Frequency 0 0.02 0.04 0.06 0.08 0.05 0.1 0.15 0.2 0.25 Connection length[mm] Frequency 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 Connection length[mm] Frequency Macaque cortical Rat neuronal C. elegans neuronal (local) C. elegans neuronal (global) Kaiser et al. (2009) Cerebral Cortex
  6. 6. 0 10 20 30 40 50 0 0.05 0.1 0.15 0.2 0.25 Connection length [mm] Relativefrequency C 0 0.2 0.4 0.6 0.8 1 1.2 0 0.05 0.1 0.15 0.2 0.25 0.3 Connection length [mm] Relativefrequency D 0 20 40 60 80 100 120 0 0.05 0.1 0.15 0.2 0.25 0.3 Connection length [mm] Relativefrequency A 20 40 60 80 100 0.05 0.1 0.15 0.2 0.25 Connection length [mm] Relativefrequency B Macaque cortical Rat neuronal Human DTI Human rsMRI Also true for human structural and functional connectivity Kaiser (2011) Neuroimage
  7. 7. 7 Why is there an exponential tail? 100 0 0 50 100 0 100 200 300 w2d1000001 0 50 100 0 100 200 300 w2d1000010 0 50 1 0 100 200 300 w2d1000011 0 300 w2d1000101 300 w2d1000110 300 w2d1000111 Connection length (units) Occurrences X: number of steps until another neuron is in the range of the axonal growth cone p: probability that unit space contains a neuron q = 1 - p t=1 t=2 t=3 P(X = n) = p * qn-1 -> exponential distribution Kaiser et al. (2009) Cerebral Cortex
  8. 8. 8 Reducing neural wiring costs • Minimizing total wire length reduces metabolic costs for connection establishment and signal propagation • Component Placement Optimization, CPO Every alternative arrangement of network nodes will lead to a higher total wiring length • Not the case! Reductions by 30-50% possible A B C D A B C D rearranging nodes A and D Kaiser & Hilgetag (2006) PLoS Computational Biology, 7:e95
  9. 9. 9 More long-distance projections than expected Arrangement with reduced total wiring length Original arrangement
  10. 10. 10 When long-distance fibers are missing (minimal): original minimal ASP Long-distance connections are short-cuts that help to reduce the characteristic path length (or average shortets path, ASP): Less long-distance connections -> longer path lengths
  11. 11. 11 Low path lengths = few intermediate processing steps are beneficial - Synchrony of near and distant regions - Reduced transmission delays - Less (cross-modal) interference - Higher reliability of transmission
  12. 12. 12 Linking structure and function
  13. 13. 13 Small-world properties Stam et al. Cerebral Cortex (2007) EEG synchronization Network (functional connectivity) in Alzheimer’s patients and control group
  14. 14. 14 Alzheimer: Path length vs. task performance Mini Mental State Examination (attention, memory, language) Diamonds: Alzheimer patients Empty squares: Control
  15. 15. 15 Cognition: Path length vs. IQ Van den Heuvel (2009) J. Neurosci. 29: 7619 Correlations between local path length lambda (shortest path length from one node to any other node) and IQ (Intelligence Quotient) for medial prefrontal cortex, bilateral inferior parietal cortex and precuneus / posterior cingulate regions (p < 0.05, corrected for age). Resting state fMRI in 19 subjects (functional connectivity based on coherence)
  16. 16. 16 Summary 5. Linking structure and function: - Alzheimer’s disease: path lengths - IQ: path lengths 4. Spatial properties: - Preference for connections to neighbours - Fast processing due to long-distance connections

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