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/

1

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

Macaque (rhesus monkey) cortical network

4

C. elegans neural network

Global level (277 neurons)

Local level (131 neurons)

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]

Freq

uenc

y

0 0.5 1 0

0.1 0.2 0.3

Connection length [mm]

Freq

uenc

y

0 0.02 0.04 0.06 0.08 0.05

0.1 0.15

0.2 0.25

Connection length [mm]

Freq

uenc

y

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

Connection length [mm]

Freq

uenc

y

Macaque cortical

Rat neuronal

C. elegans neuronal (local)

C. elegans neuronal (global)

Kaiser et al. (2009) Cerebral Cortex

! "! #! $! %! &!!

!'!&

!'"

!'"&

!'#

!'#&

()**+,-.)*/0+*1-2/3445

6+07-.8+/9:+;<+*,=

!

! !'# !'% !'> !'? " "'#!

!'!&

!'"

!'"&

!'#

!'#&

!'$

()**+,-.)*/0+*1-2/3445

6+07-.8+/9:+;<+*,=

"

! #! %! >! ?! "!! "#!!

!'!&

!'"

!'"&

!'#

!'#&

!'$

()**+,-.)*/0+*1-2/3445

6+07-.8+/9:+;<+*,=

#

#! %! >! ?! "!!

!'!&

!'"

!'"&

!'#

!'#&

()**+,-.)*/0+*1-2/3445

6+07-.8+/9:+;<+*,=

$

Macaque cortical

Rat neuronal

Human DTI Human rsMRI

Also true for human structural and functional connectivity

Kaiser (2011) Neuroimage

7

Why is there an exponential tail?

0 50 1000

100

200

300

w2d1000000

0 50 1000

100

200

300

w2d1000001

0 50 1000

100

200

300

w2d1000010

0 50 1000

100

200

300

w2d1000011

0 50 1000

100

200

300

w2d1000100

Num

ber o

f occ

urre

nces

0 50 1000

100

200

300

w2d1000101

0 50 1000

100

200

300

w2d1000110

0 50 1000

100

200

300

w2d1000111

0 50 1000

20

40

60

w2d400100

0 50 1000

20

40

60

w2d400101

Connection length0 50 100

0

20

40

60

w2d400110

0 50 1000

20

40

60

w2d400111

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

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

More long-distance projections than expected

Arrangement with reduced total wiring length

Original arrangement

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

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

Linking structure and function

13

Small-world properties

Stam et al. Cerebral Cortex (2007)

EEG synchronization Network (functional connectivity) in Alzheimer’s patients and control group

14

Alzheimer: Path length vs. task performance

Mini Mental State Examination (attention, memory, language)

Diamonds: Alzheimer patients Empty squares: Control

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

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