a tutorial in connectome analysis (ii): topological and ... · dr marcus kaiser a tutorial in...
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http://www.biological-networks.org
Dr Marcus Kaiser
A Tutorial in Connectome Analysis (II): Topological and Spatial Features of Brain Networks
School of Computing Science /
Institute of Neuroscience Newcastle University
United Kingdom
WCU Dept of Brain & Cognitive Sciences Seoul National University South Korea http://bcs.snu.ac.kr/
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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)
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Macaque (rhesus monkey) cortical network
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C. elegans neural network
Global level (277 neurons)
Local level (131 neurons)
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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]
Freq
uenc
y
0 0.5 1 0
0.1 0.2 0.3
Connection length [mm]
Freq
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0 0.02 0.04 0.06 0.08 0.05
0.1 0.15
0.2 0.25
Connection length [mm]
Freq
uenc
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0.2 0.4 0.6 0.8 1
0.2
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Connection length [mm]
Freq
uenc
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Macaque cortical
Rat neuronal
C. elegans neuronal (local)
C. elegans neuronal (global)
Kaiser et al. (2009) Cerebral Cortex
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Macaque cortical
Rat neuronal
Human DTI Human rsMRI
Also true for human structural and functional connectivity
Kaiser (2011) Neuroimage
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Why is there an exponential tail?
0 50 1000
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w2d1000000
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w2d1000001
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w2d1000010
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w2d1000011
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w2d1000100
Num
ber o
f occ
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Connection length0 50 100
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Connection length (units)
Occ
urre
nces
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
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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
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More long-distance projections than expected
Arrangement with reduced total wiring length
Original arrangement
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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
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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
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Linking structure and function
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Small-world properties
Stam et al. Cerebral Cortex (2007)
EEG synchronization Network (functional connectivity) in Alzheimer’s patients and control group
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Alzheimer: Path length vs. task performance
Mini Mental State Examination (attention, memory, language)
Diamonds: Alzheimer patients Empty squares: Control
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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)
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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