Dear Users

Yesterday we had an extremely useful brainstorming session.

The discussion brought to light some issues about using beamforming which have not been reported in the literature yet. As these observations might affect other users we thought it would be of interest to bring them to the attention of all users.

Uzma Urooj, supervised by Andy Ellis with Michael Simpson as SLO, had identified two particular puzzling issues when using the beamforming approach to (a) localise time locked activity and (b) create virtual electrodes.

(a) the first observation is that if one constructs a NAI map from a beamformer, the statistically significant blobs do not necessarily align with the largest amplitude averaged response seen with virtual electrodes. What the user has done was to perform a standard beamforming analysis of some data and localised the most significant blob. They then placed virtual electrodes at this point and around it. At each of these virtual electrode positions they calculated the average response across epochs. The largest amplitude evoked response was not at the location of the beamformer blob. This observation has also been replicated in simulation studies by Mark Hymers where he has placed dipoles at known locations in a model brain which had realistic background noise.

The reason this occurs is because of the way the beamformer works. The beamformer is a set of spatial filters which are designed to measure the brain activity (the NAI) from each brain location in turn. The filters are constructed to ensure that activity only comes from one location at a time. All other locations are suppressed. This is done by computing the power within the MEG signal and ensuring that this is measured with a gain of one from a specified location and that it is zero from all other positions. This is the key point - the beamformer is specified in terms of MEG power. The power in an MEG signal can come from two forms of oscillation, those that are time locked to the stimulus and those power changes that produced by a stimulus but are not time locked in terms of the oscillatory phase (often called the stimulus induced power). Thus the blobs created by the application of the beamformer programme are in terms of total power (time locked and induced). When the average virtual electrodes were computed, these measures were only of time locked activity. The user that brought this to our attention has made an important observation, within a specific region, brain responses that are time locked maybe at a different location to induced power changes. As we do not know the relationship between fMRI haemodynamic changes and MEG oscillations (time locked vs induced), it may be that beamformer results will not always align with fMRI results either. This does not mean that the beamformer is wrong in some way. In means that we have to be very careful in how we interpret beamformer output in terms of blobs and virtual electrodes. There clearly is a need to be able to distinguish between time locked and induced responses. To this end, Will Woods has been working on a 'evoked' beamformer.

implications for users of the beamformer NAI statistical maps reflect total power changes within a band and can contain both induced and time locked responses, just induced power changes or just time locked responses. In the latter case the virtual electrode averages will align with the NAI maps. In the other two cases, NAI maps may not align with VE maps. The issue for users is what form of response should be used to test a specific hypothesis. This will be down to the individual user who will have a specified model for their particular experiment in terms of how stimuli may be encoded. NAI maps are estimates of statistical changes in total power, these maps are related to the mean and variance of the power in the oscillations produced by both induced and time locked responses Averages of VEs provide estimates of the average time locked response, only.

(b) the second interesting observation made by Uzma related to the construction of time series of virtual electrode activity for every epoch.

Uzma has used a specific time window (say 200 milliseconds) to estimate weights for a beamformer. Uzma then used these weights to estimate the virtual electrode time series for a much longer time window beyond that of the original 200 milliseconds for every epoch. The virtual electrode output (three orthogonal components) was manipulated to create an estimate of power as a function of time. This was done by taking the squares of each VE component and summing them. This gives a measure of the power as a function of time for each epoch. Uzma then averaged these power time series, producing the average power changes as a function of time. Uzma made an observation that has not been reported before. Beyond the end of the original 200milliseconds, a large slow change in power was observed. If this was all repeated for a window that was 1000 milliseconds long, the slow change in power was now observed if the power was estimated for times greater than 1 second.

This is a very important observation. The current thoughts about this are that this is a property of the beamformer. It might arise as follows. The beamformer weights are estimated from the covariance matrix of the original MEG data within the specified window (say 200 milliseconds). Covariance is related to power within a signal, that is why it is stated that a set of beamformer weights is about detecting the power from a specific location and not any other. If a window is only 200 milliseconds long, a very poor estimate will be made of power below 5Hz (1/0.2). Thus this beamformer will not be able to correctly deal with slow changes in power and estimates beyond the original window may be inaccurate.

implications for users of the beamformer When using a beamformer to estimate changes in power (especially induced power) with time, observations are only reliable when made within the time contraints of the original window length that was used to construct the beamformer. The problem with this is that a beamformer works best if the window length matches the duration of the induced power change, especially if performing a statistical comparison between two conditions. If long windows are used and the induced power changes are fractional proportions of the length of the window, then statistical power will be lost. In this case it would be best to use moving windows as in the Pammer and Cornelissen paper.

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I believe this demonstrates that brainstorming sessions are quite important activities. Some people might be concerned about bringing problems to the attention of other users, but as the above demonstrates, it can be invaluable as it can highlight problems that are not fully appreciated.

Many thanks to the user who brought this to our attention.