close

Enter

Log in using OpenID

08_MEEG_SourceLocalis

embedDownload
The M/EEG inverse problem and solutions
Gareth R. Barnes
Format
• The inverse problem
• Choice of prior knowledge in some popular
algorithms
• Why the solution is important.
Magnetic field
MEG pick-up coil
Electrical potential difference (EEG)
scalp
skull
cortex
Volume currents
MEG measurement
What we’ve got
Forward problem
Inverse problem
pick-up coils
1pT
Active
Passive
Local field potential (LFP)
1nAm
What we want
1s
Useful priors cinema audiences
• Things further from the camera appear
smaller
• People are about the same size
• Planes are much bigger than people
Where does the data come from ?
1pT
1s
Useful priors for MEG analysis
• At any given time only a small number of
sources are active. (dipole fitting)
• All sources are active but overall their energy
is minimized. (Minimum norm)
• As above but there are also no correlations
between distant sources (Beamformers)
Source number
The source covariance matrix
Source number
Measured data
-13
x 10
6
4
2
0
-2
-4
-6
?
-6
-4
-2
0
2
4
Estimated data
x 10
6
-13
Estimated position
Dipole Fitting
Prior source covariance
-13
x 10
6
4
2
0
-2
-4
-6
-4
-2
0
2
4
x 10
6
Measured data/
Channel covariance
True source covariance
Estimated data/
Channel covariance matrix
-13
Dipole fitting
Dipole fitting
Effective at modelling short (<200ms)
latency evoked responses
Clinically very useful: Pre-surgical
mapping of sensory /motor cortex (
Ganslandt et al 1999)
Need to specify number of dipoles
(but see Kiebel et al. 2007), nonlinear minimization becomes
unstable for more sources.
Fisher et al. 2004
-8-8
-10
-10
00
Minimum norm
100
100
200
200
300
400
300
400
time ms
ms
time
500
500
- allow all sources to be active, but keep energy to a minimum
PPMatat379
379ms
ms(79
(79percent
percentconfidence)
confidence)
PPM
512
dipoles
512 dipoles
Percentvariance
varianceexplained
explained99.91
99.91(93.65)
(93.65)
Percent
log-evidence==21694116.2
21694116.2
log-evidence
Solution
True
(Single
Dipole)
Prior
600
600
700
700
Problem is that superficial elements
have much larger lead fields
Basic Minimum norm solutions
Solutions are diffuse and have superficial bias
(where source power can be smallest).
But unlike dipole fit, no need to specify the
number of sources in advance.
Can we extend the assumption set ?
MEG sensitivity
1.0
0.5
8-13Hz band
0
“We have managed to check the
alpha band rhythm with intra-cerebral
electrodes in the occipital-parietal
cortex; in regions which are practically
adjacent and almost congruent one
finds a variety of alpha rhythms, some
are blocked by opening and closing
the eyes, some are not, some respond
in some way to mental activity, some
do not.” Grey Walter 1964
Coherence
Cortical oscillations have local domains
0
12
24
Distance
30mm
Bullock et al. 1989
Leopold et al. 2003.
-10
0
100
200
300
400
time ms
500
Beamformer: if you assume no correlations between
sources, can calculate a prior covariance matrix from the
PPM at 379 ms (79 percent confidence)
data
512 dipoles
Percent variance explained 99.91 (93.65)
log-evidence = 21694116.2
True
Prior,
Estimated
From data
600
700
fMRI
Oscillatory changes are co-located with haemodynamic changes
MEG composite
Beamformers
Robust localisation of induced changes,
not so good at evoked responses.
Excellent noise immunity.
Clincally also very useful
(Hirata et al. 2004; Gaetz et al. 2007)
But what happens if there are correlated
sources ?
Singh et al. 2002
-1.5
0
100
200
400
300
time ms
500
600
Beamformer for correlated sources
True Sources
Prior
(estimated
from data)
PPM at 229 ms (99 percent confidence)
512 dipoles
Percent variance explained 99.81 (65.46)
log-evidence = 8249519.0
70
Prior source covariance
-13
x 10
6
4
2
0
-2
-4
-6
?
-4
-2
0
2
4
x 10
6
Measured data/
Channel covariance
True source covariance
Estimated data/
Channel covariance matrix
-13
Dipole fitting
Multiple Sparse Priors (MSP)
True
P(l)
l
-4
el1
Priors
+
el2
eln
Estimated (based on data)
= sensitivity (lead field matrix)
(Covariance estimates are made in channel space)
-4
-1
-1
8
10
-6
-1.5
-1.5
-1.5
-2
-8
0
100
200
-2
300
0400
time ms
500
100
6
10
600
200
-2
700
300
4000
time ms
500
100
PPM at 229 ms (100 percent confidence) PPM at 229 ms (100 percent confidence)
512 dipoles
512 dipoles
Percent variance explained 99.15 (65.03)Percent variance explained 99.93 (65.54)
log-evidence = 8157380.8 4
log-evidence = 8361406.1
10
600
200
0
700
300
400
time ms
100
500
200
600
Free
energy
Accuracy
PPM at 229 ms
(100 percent confidence)
Accuracy
Free
Energy
512 dipoles
Percent variance
explained 99.87 (65.51)
Compexity
Complexity
0
50
log-evidence = 8388254.2
100
Iteration
500
PPM at 229 ms (100 percent confidence)
512 dipoles
Percent variance explained 99.90 (65.53)
log-evidence = 8389771.6
2
10
300
400
time ms
700
150
6
512 dipoles
Percent variance explained 99.81 (65.46)
log-evidence = 8249519.0
512 dipoles
Percent variance explained 99.90 (65.53)
log-evidence = 8389771.6
Can use model evidence to choose between solutions
8400000
8350000
8300000
Free energy
Model
Evidence
8250000
8200000
8150000
BMF
MSP
So it is possible,
but why bother ?
Correct inversion algorithm
Stimulus(3cpd,1.5º)
Single trial data
• Correct location information
• Correct unmixing of sensor
data = best estimate of source
level time series
• Higher SNR (~ sqrt (Nchans))
Duncan et al . 2010
Conclusion
• MEG inverse problem can be solved.. If you
have some prior knowledge.
• All prior knowledge encapsulated in a source
covariance matrix
• Can test between priors in a Bayesian
framework.
• Exciting part is the millisecond temporal
resolution we can now exploit.
Thanks to
•
•
•
•
•
•
Vladimir Litvak
Will Penny
Jeremie Mattout
Guillaume Flandin
Tim Behrens
Karl Friston and methods group
Author
52   documents Email
Document
Category
Uncategorized
Views
2
File Size
2 430 KB
Tags
1/--pages
Report inappropriate content