Download - STATISTICAL ANALYSIS AND SOURCE LOCALISATION
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STATISTICAL ANALYSIS AND SOURCE LOCALISATION
METHODS FOR DUMMIES2012-2013ANADUAKA, CHISOMKRISHNA, LILA
UNIVERSITY COLLEGE LONDON
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M/EEG SO FARSource of SignalDipolesPreprocessing and Experimental design
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E/MEG SIGNAL
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Statistical Analysis
Source Reconstruction
E/MEG SIGNAL
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How does it work?
Statistical analysis1. Sensor level analysis in SPM
2. Scalp vs. Time Images
3. Time-frequency analysis
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Neuroimaging produces continuous data e.g. EEG/MEG data.
Time varying modulation of EEG/MEG signal at each electrode or sensor.
Statistical significance of condition specific effects.
Effective correction of number of tests required- FWER.
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Steps in SPMData transformed to image files (NifTI)
Between subject analysis as in “2nd level for fMRI”
Within subject possible
Generate scalp map/time frame using 2D sensor layout and linear interpolation btw sensors (64 pixels each spatial direction suggested)
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Sensor level analysis
Space-space-time maps
SPM
In
a
EVOKED SCALP RESPONSE
SLOW EVOLUTION IN TIME
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Sensor Level AnalysisThis is used to identify pre-stimulus time or
frequency windows.
Using standard SPM procedures(topological inference) applied to electromagnetic data; features are organised into images.
SPM
Raw contrast time frequency maps Smoothin
g Kernel
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Topological inferenceDone when location of evoked/induced responses is
unknown
Increased sensitivity provided smoothed data
Vs Bonferroni: acknowledges non-independent neighbours
ASSUMPTION Irrespective of underlying geometry or data support, topological behaviour is invariant.
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Time vs. Frequency dataTime-frequency data: Decrease from 4D
to 3D or 2D time-frequency (better for SPM).
Data features: Frequency-Power or Energy(Amplitudes) of signal.
Reduces multiple comparison problems by averaging the data over pre-specified sensors and time bins of interest.
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AveragingAveraging over time/frequencyImportant: requires prior knowledge of
time window of interest
Well characterised ERP→2D image + spatial dimensions
E.g. Scalp vs. time or Scalp vs. Frequency
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Smoothing step Smoothing: prior to 2nd level/group analysis -multi
dimensional convolution with Gaussian kernel.
Important to accommodate spatial/temporal variability over subjects and ensure images conform to assumptions.
Multi-dimensional convolution with Gaussian kernel
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Source localisationSource of signal difficult to obtain
Ill-posed inverse problem (infers brain activity from scalp data): Any field potential vector can be explained with an infinite number of possible dipole combinations.
Absence of constraints No UNIQUE solution
Need for Source Localisation/Reconstruction/Analysis
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NO CORRECT ANSWER; AIM IS TO GET A CLOSE ENOUGH APPROXIMATION….
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Forward/Inverse problemsForward model: Gives information about Physical and Geometric head properties.
Important for modeling propagation of electromagnetic field sources.
Approximation of data from Brain to Scalp.
Backward model/Inverse Problem: Scalp data to Brain Source localization in SPM solves the Inverse problem.
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Forward/Inverse problemsFORWARD PROBLEM
INVERSE PROBLEM
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Forward/Inverse problems
Head model: conductivity layoutSource model: current dipolesSolutions are mathematically derived.
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Source reconstructionSource space modelingData co-registrationForward computationInverse reconstructionSummarise reconstructed response as
image
FORWARD MODEL
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Source space modelling
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Data co-registrationa) Rigid-body transformation matrices
Fiducial matched to MRI applied to sensor positions
b) Surface matching: between head shape in MEEG and MRI-derived scalp tessellations. It is important to specify MRI points corresponding to fiducials whilst ensuring no shift
RotationTransformation
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Data Co-registration “Normal” cortical template mesh (8196 vertices), left view
Example of co-registration display (appears after the co-registration step has been completed)
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Compute effects on sensors for each dipole
N x M matrix
Single shell model recommended for MEG, BEM(Boundary Element Model) for EEG.
Forward computation
No of mesh vertices
No of sensors
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Distributed source reconstruction 3DUsing Cortical mesh Forward model
parameterisationAllows consideration of multiple
sources simultaneously.Individual meshes created based on
subject’s structural MR scan–apply inverse of spatial deformation
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Y = kJ + E
Data gain matrix noise/error
Estimate J (dipole amplitudes/strength)Solve linear optimisation problem to determine YReconstructs later ERP components
ProblemFewer sensors than sources needs constraints
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Constraints Every constraint can provide different
solutionsBayesian model tries to provide optimal
solution given all available constraints
POSSIBILITIES1) IID- Summation of power across all sources2) COH- adjacent sources should be added3) MSP- data is a combination of different
patchesSometimes MSP may not work.
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Bayesian principleUse probabilities to formalize complex
models to incorporate prior knowledge and deal with randomness, uncertainty or incomplete observations.
Global strategy for multiple prior-based regularization of M/EEG source reconstruction.
Can reproduce a variety of standard constraints of the sort associated with minimum norm or LORETA algorithms.
Test hypothesis on both parameters and models
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Summarise Reconstructed DataSummarise reconstructed data as an
imageSummary statistics image created in
terms of measures of parameter/activity estimated over time and frequency(CONTRASTS)
Images normalised to reduce subject variance
The resulting images can enter standard SPM statistical pipeline (via ‘Specify 2nd level’ button).
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Summarise inverse reconstruction as an image
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Equivalent Current Dipole (ECD)Small number of parameters compared to
amount of dataPrior information requiredMEG data Y=f(a)+e1) Reconstructs Subcortical data 2) Reconstructs early components ERPs (Event
related potentials)3) Requires estimate of dipole directionProblemNon-linear optimisation
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Dipole Fitting
-6
-4
-2
0
2
4
6x 10
-13
-6-4-20246x 10
-13
-6
-4
-2
0
2
4
6x 10
-13
Measured data
Estimated Positions
Estimated data
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Variational bayesian- ECDPriors for source locations can be
specified.Estimates expected source location
and its conditional variance.Model comparison can be used to
compare models with different number of sources and different source locations.
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VB-ECDASSUMPTIONS1) Only few sources are simultaneously active2) Sources are focal3) Independent and identical normal distribution
for errors4) Iterative scheme which estimates posterior
distribution of parameters◦ Number of ECDs must not exceed no of channels÷6◦ Non-linear form- optimise dipole parameters given
observed potentials ◦ takes into account model complexity◦ Prepare head model as for 3D
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ExtrasRendering interface: extra features
e.g. videosGroup inversion: for multiple datasetsBatching source reconstruction:
different contrasts for the same inversion
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IN SPMActivate SPM for M/EEG: type
spm eeg on MATLAB command line enter
GUI INTERFACE BETTER FOR NEW USERS LIKE ME!!!!! Instructions are clearly outlined.
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SPM Buttons 1
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2Forward computation inversion
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3
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REFERENCESSPM Course – May 2012 – LondonSPM-M/EEG Course Lyon, April 2012Tolga Esat Ozkurt-High Temporal Resolution
brain Imaging with EEG/MEG Lecture 10: Statistics for M/EEG data
James Kilner and Karl Friston. 2010.Topological Inference for EEG and MEG. Annals of Applied Statistics Vol 4:3 pp 1272-1290
Vladimir Litvak et al. 2011. EEG and MEG data analysis in SPM 8. Computational Intelligence and Neuroscience Vol 2011
MFD 2011/12