COMPARISON OF BRAIN NETWORKS WITH UNKNOWN CORRESPONDENCES SI - - PowerPoint PPT Presentation

COMPARISON OF BRAIN NETWORKS WITH UNKNOWN CORRESPONDENCES

SI Ktena, S Parisot, J Passerat-Palmbach and D Rueckert

The brain from a network perspective

• cognition is a network

phenomenon [Sporns, Dial.

• Clin. Neurosc. (2013)]
• no physical trace of certain

diseases, only changes in the physical wiring and strength of connections

• given two brain graphs

representing connectivity, how similar are they? (within/between subjects, between modalities etc.)

Timeseries data Imaging data Functional brain network Structural brain network Brain parcellation Network analysis

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Inference: Naive approach

Graph construction

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{ {

Graph embedding class class Model training and inference

Richiardi et al., IEEE Signal Processing Magazine (2013) Varoquaux and Craddock, Neuroimage (2013)

Why individual parcellations?

• Standard anatomical atlases subdivide the brain based on

cytoarchitecture (e.g. Brodmann) or anatomical landmarks (e.g. Desikan-Killiany)

• Individual variability in terms of anatomy or function due to

maturation or brain injury are not accounted for [Timofiyeva,

PLoS One (2014)]

• Data-driven single subject parcellations capture this variability

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Inexact graph matching

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Graph embedding Graph kernels

r e q u i r e s n

• d

e c

• r

r e s p

• n

d e n c e s d

• n
• t

p r

• v

i d e e l e m e n t c

• r

r e s p

• n

d e n c e s

• Evaluate how much two graphs share

Craddock et al., Nature Methods (2013) Jie et al. Human Brain Mapping (2014)

Graph edit distance

• Measure of dissimilarity between graphs, defined directly in

their domain as a nonnegative function this is a long lon. Able to model structural variation in a very intuitive and illustrative way.

G d : G × G → R+

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4 2 1 3

G

edge-delete (2,3)

4 2 1 3

G1

5 4 2 3

G2

label-change (1,5)

6 5 4 2 3

G3

node-add (6)

6 5 4 2 3

G4

edge-add(2,6)

7 6 5 4 2 3

G’

node-add(7)

• The Hungarian algorithm provides a fast approximate solution

to the GED computation [Riesen & Bunke, Img & Vis. Comp., (2009)]

• Given two labeled graphs , with and

his is a long l a square cost matrix C of order is defined, which encodes all the possible edit operation costs

GED computation

G1 G2 |V(G1)| = n

|V(G2)| = m

n + m

C =           c1,1 . . . c1,m c1,ε . . . ∞ . . . ... . . . . . . ... . . . cn,1 . . . cn,m ∞ . . . cn,ε cε,1 . . . ∞ . . . . . . ... . . . . . . ... . . . ∞ . . . cε,m . . .          

substitutions deletions insertions

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Node features

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• Spatial information (coordinates in standard brain space)
• Feature information (network measures, egonet based)

v4 v3 v1 v2

xv1 yv1 zv1

spatial coordinates egonet network features

dv4 sv4 cv4 dv3 sv3 cv3

mean standard deviation

f 1

v1 f 2 v1 f 3 v1 f 4 v1 f 5 v1 f 6 v1

Node distance

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• Spatial distance
• Feature distance

fv = ( ¯ du, ¯ su, ¯ cu)

lv = (x, y, z)

Egonet dl = deucl(v1, v2) = klv1 lv2k

df = dcanb(v1, v2) =

d

X

i=1

|fv1i − fv2i| |fv1i| + |fv2i|

d(v1, v2) = α ∗ deucl(v1, v2) + (1 − α) ∗ dcanb(v1, v2)

Tailoring GED for brain graphs

• In order to achieve better approximation of the true edit

distance, edge operations need to be involved.

• Constrain substitutions to the nearest N nodes - set cost to Inf

for the rest of the substitutions if then else

• Take into account node betweenness centrality g for the cost
• f node insertion/deletion

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uj ∈ neigh(vi) ci,j = ∞ c✏,j = α + (1 − α) ∗ g(uj) ci,✏ = α + (1 − α) ∗ g(vi)

ci,j = α ∗ deuclidean(vi, uj) + (1 − α) ∗ dcanberra(vi, uj) + dedge(vi, uj)

Summary

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Brain connectivity networks Labeled graphs

. . . . . .

Graph Edit Distance (Hungarian algorithm)

Evaluation

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• Diffusion and functional MRI data from the Human

Connectome Project

• 30 healthy unrelated subjects as well as 20 monozygotic and

20 dizygotic female twin pairs (MZ twins share 100% of genetic information, while DZ share only 50%)

• Connectivity driven single-subject parcellations [Parisot et al.,

MICCAI, (2016)]

• Structural networks derived with probabilistic tractography
• Functional networks estimated using partial correlation

Single-subject parcellations

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same subject different subjects GED(same subject) < GED(different subjects)

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Structural networks

* p<0.05 ** p<0.001 ns non-significant

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Functional networks

* p<0.05 ** p<0.001 ns non-significant

Monozygotic vs. unrelated pair

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Monozygotic vs. unrelated pair

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Conclusions

• Novel way of evaluating graph similarity between brain

networks based on graph edit distance

• Enforces spatial constraints and incorporates feature

information

• Applied on healthy unrelated subjects and twin pairs and was

able to reflect similarities between corresponding networks

• Future steps:
• Predicting phenotype using GED distance matrix
• Network dynamics (brain development, disease

progression, brain plasticity)

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Acknowledgements:

Daniel Rueckert Sarah Parisot Salim Arslan

• J. Passerat-Palmbach

Emma Robinson

Funding sources:

EPSRC Foundation for Education and European Culture