Transcript arnaud2 - The Department of Mathematics and Statistics

Connectivity between MS lesion
density and cortical thickness
Keith Worsley
Arnaud Charil
Jason Lerch
Department of Mathematics and Statistics,
McConnell Brain Imaging Centre,
Montreal Neurological Institute,
McGill University
Connectivity
• Measured by the correlation between data at pairs
of voxels:
Activation only
Voxel 2
++
+ +++
Correlation only
Voxel 2
+
++
Voxel 1
+ +
Voxel 1
+
Method 1: ‘Seed’
Friston et al. (19??): Pick one voxel, then find all
others that are correlated with it:
Problem: how to pick the ‘seed’ voxel?
Method 2: Iterated ‘seed’
• Problem: how to find the rest of the connectivity
network?
• Hampson et al., (2002): Find significant correlations,
use them as new seeds, iterate.
Method 3: All correlations
• Problem: how to find isolated parts of the connectivity
network?
• Cao & Worsley (1998): find all correlations (!)
Practical details
• Find threshold first, using random field theory
• Keep only correlations > threshold
• Then keep only local maxima i.e.
cor(voxel1, voxel2)
> cor(voxel1, neighbours of voxel2),
> cor(neighbours of voxel1, voxel2),
MS lesions and cortical thickness
(Arnaud et al., 2004)
•
•
•
•
N = 425 mild MS patients
Lesion density, smoothed 10mm
Cortical thickness, smoothed 20mm
Hypothesis: increased lesion density in white
matter -> thinner cortex in connected grey matter
• Find connectivity i.e. find voxels in 3D, nodes in
2D with high
cor(lesion density, cortical thickness)
n=425 subjects, correlation = -0.56826
Average cortical thickness
5.5
5
4.5
4
3.5
3
2.5
2
1.5
0
10
20
30
40
50
60
Average lesion volume
70
80
Same hemisphere
0.1
1
-0.3
threshold
-0.4
-0.5
0
50
100
150
distance (mm)
Correlation = 0.091943
0.1
correlation
0
correlation
1.5
-0.2
-0.1
-0.2
1.5
-0.3
1
0
-0.5
1
0.1
-0.2
0.4
threshold
2
-0.4
0.6
-0.3
-0.1
0.5
threshold
0
50
100
150
distance (mm)
Correlation = -0.1257
0.5
0
1
0
0.8
5
x 10
2.5
0
2
-0.1
Different hemisphere
0.1
correlation
correlation
0
5
x 10
2.5
0.8
-0.1
0.6
-0.2
0.4
-0.3
threshold
-0.4
0.2
-0.4
0.2
-0.5
0
-0.5
0
0
50
100
150
distance (mm)
0
50
100
150
distance (mm)
What would be really nice:
• Use DTI fibre tracking data to get a measure of
probability of connection between each point in
WM and each point on the cortical surface
• Huge fibre tracking problem:
– Seeds at every voxel!
– Repeat over subjects?
– How to combine subjects?
• Plot correlation vs. probability of connection should be a positive relationship …
Dinner: meet in Hilton Coffee Shop, 6 p.m.