# Beamformer time course

Robert Oostenveld r.oostenveld at FCDONDERS.RU.NL
Wed May 24 20:52:26 CEST 2006

```On 24 May 2006, at 19:27, Marie Smith wrote:

> Thanks for the pointer to the earlier discussion, unfortunately it
> does not answer my question.
> I had assumed that the dics filters were output for a fixed dipole
> orientation (that which maximizes filter output) - hence i was
> expecting to have a 1 dimensional set of filter weights with which
> to compute a time series (cf. a virtual channel).
> I am unsure how to interpret the three time series resulting from
> multiplying the 3D filter with the time series. Does this mean the
> orientation could change trial per trial and time point per time
> point?

yes, for each trial you could estimate a different maximal
orientation from the 3xNtime matrix. See beow.

> Does this mean that for calculations involving the time course
> (e.g. synchrony) that you only use the amplitude, disregarding the
> orientation?

The CTF-SAM algorithm internally optimizes the orientation with a non-
linear fit, while in the LCMV algorithm you can optimize the
orientation afterwards using the linear PCA approach described below.
The results will be slighly different. The published DICS algorithm
does not specify how to operate in single trial mode, but basically
the DICS corresponds to a complex version of LCMV without timecourses
(since frequency domain).

If you are only interested in the dipole moment along the most
dominant direction (i.e the direction with the largest power, you can
do a PCA with
[u,s,v] = svd(source2.trial(1).mom{source2.inside(1)});
and use the first column of v multiplied by s(1,1), which gives the
timecourse of the orthogonal component with the most variance, i.e.
power. The orientation itself is in u(:,1). If you want to determine
the orientation with the maximal power over all trials, you would
have to concatenate all single trial dipole moments into one large 3x
(Ntrials*Ntime) matrix and do the pca/svd on that.

Regarding dipole orientations: note that we typically find better
results if we restrict the MEG forward model to contain only the two
tangential dipole components, which is achieved by precomputing the
dipole model is still represented in three carthesian directions, but
the leadfield (and the filter and projected data) have rank 2, i.e.
there is one orientation in which the dipole is silent. Reducing the
rank of the forward model to two removes the most silent dipole
orientation (i.e. the radial orientation), which is also the
orientation along which the beamformer is most sensitive for picking
up noise. Note that if you use a single-sphere mode, the radial
component is already completely zero, for a multisphere model it is
not zero, but small (there will always be a sphere in which the