## Ex 3: MEG source modeling

This exercise is about source modelling. The task is to construct and apply a cortically constrained L2 minimum norm estimator to two averaged data sets, visualize the estimate on the cortical surface and interpret the results.

The Matlab data file given below contains all the ingredients:

 data1, data2, timeaxis, n_trial two evoked-response data matrices, the latencies of each sample in those matrices, and the number of trials averaged. The datasets are baseline corrected and filtered to 0-40 Hz. Note that the data are rank deficient due to the application of interference suppression methods; the effective number of channels (degrees of freedom) is 64. L the lead field / gain matrix Cn noise covariance matrix, computed from pre-stimulus baseline periods in unaveraged data Cd data covariance matrix, computed from the window 0 - 0.5 s about each unaveraged trial (needed only for a beamformer) anat_decim low-resolution cortical surface mesh for visualizations

The regularization coefficient in the L2 MNE inverse operator can set to lambda = tr(L*L') / (tr(Cn) * snr^2) where tr is the trace of a matrix and snr refers to the estimated signal-to-noise ratio of the data. In unaveraged data, this can be assumed to be 1. Recall how trial averaging improves signal-to-noise ratio and use that as the snr above.

Source covariance is unknown and thus you may use an identity matrix for that.

Matrix inversions that involve noise or data covariance need to be regularized. SVD truncation with tolerance about 1.0e-24 is appropriate. On MatLab, the pseudoinversion function pinv() can do this; check its help page.

For visualization, you can use the provided Matlab function

vis_surface_data(source_estimate, threshold, anatomy)

which displays 'source_estimate' vector on the cortical surface found in 'anatomy'. The function creates separate views to the left and right hemispheres, which you can zoom and rotate using the normal Matlab plot window controls.

In the report:

• explain how you constructed the L2 MNE operator (you may also include the Matlab code snippet)
• include figures of the source estimates of the two data sets
• discuss the differences of the estimates: what can you say about the laterality of the stimuli presented in data1 vs. those in data2?
• discuss how the spatial extent of the estimated activity reflects extent of the underlying neural current distribution

Bonus tasks (one extra point from each):

• Construct a beamformer operator and apply it to the data sets
• Include depth weighting in the L2 MNE operator by modifying the source covariance matrix appropriately