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.
--
Gary Green
York Neuroimaging Centre
The Biocentre
York Science Park
Innovation Way
Heslington
York
YO10 5DG
http://www.ynic.york.ac.uk
tel. 01904 435349
fax 01904 435356
mobile 07986 778954