The gray-white matter boundary defines the locations and directions of the primary currents in the cortex and can be used as an anatomical constraint for various kinds of beamforming algorithms [4]. Here we show results using an extension of the

1
Each pair (?,f) on the sphere corresponds to a
location in 3-d space described by its cartesian
coordinates (x,y,z). Color codes below are the
values of these coordinates as functions of the
angles in rectangular and polar plots. Contour
lines at constant values of x, y and z define the
boundary lines between the gray and white matter
in corresponding sagittal, coronal and axial
slices, respectively.
The sensitivity of EEG and MEG to sources on the
gray-white matter boundary is quite different.
For MEG the orientation is most important and
regions of high sensitivity (indicated in yellow
for MEG and EEG) are located in the walls of the
fissures where the current flow is tangential
with respect to the surface defined by the
sensors. For EEG distance from the electrodes is
more important than orientation. The plot on the
right shows the differences of normalized
sensitivities with red/yellow indicating regions
where MEG is more sensitive, plotted in blue
shades are areas of higher sensitivity for EEG.
Applying the beamformer allows us to estimate the
source power at locations posterior and anterior
of the central sulcus. Going top to bottom in the
plots below means moving left to right along the
sulcus. Each row exhibits the forward solution,
the beamformer pattern and two time series.
Dotted blues lines show the time course from a
single MEG sensor as a reference. The red curves
represent the time dependence of local activity
for a time span of 480ms with the vertical black
line at maximum finger flexion. From bottom to
top activation shifts from a time point prior to
peak flexion to a time thereafter, representing
traveling waves from right to left along both
walls of the central sulcus.
We show how a parameterization of the strongly
folded boundary between the gray and white matter
can be used as constraints for a beamformer in
order to estimate local activations inside the
brain during a certain task on a time scale of
milliseconds.
The gray-white matter boundary defines the
locations and directions of the primary currents
in the cortex and can be used as an anatomical
constraint for various kinds of beamforming
algorithms 4. Here we show results using an
extension of the algorithm known as SAM
(synthetic aperture magnetometry) 5 which can
be applied to averaged data. A beamforming filter
HT is calculated by minimizing the power from all
locations and directions while keeping the signal
constant from a location and direction of
interest T T(x,y,z,?,f). In general the
beamformer and the power at T are given by
where C represents the covariance matrix of
the data and GT is the forward solution from T.
For averaged data C cannot be inverted and the
procedure has to be restricted to the signal
subspace by expanding GT and HT into the
eigenvectors ?(k) of C. The expansion
coefficients hk for the beamformer and the source
power can then be expressed in terms of gl and
the eigenvalues ?l of C.
An MRI scan is transformed into a coordinate
system defined by the nasion, and the left and
right preauricular points on the subjects head.
Freesurfer 1,2 is used to extract the surface
which defines the gray-white matter boundary and
to inflate it into a sphere.
That way, we have a quasi-continuous
representation of the brain surface and can
sample and tessellate it at any desired accuracy.
The vectors perpendicular to this surface are of
particular interest because due to the columnar
organization of the cortex, the primary currents
are oriented in these directions.
References 1 Dale A.M., Fischl B.,Sereno M.I.,
Neuroimage 9 179-194 (1999) 2 Fischl B.,
Sereno M.I., Dale A.M,, Neuroimage 9 195-207
(1999) 3 Fischl B., Sereno M.I., Tootell
R.B.M., Human Brain Mapping 8 272-285 (1999) 4
Dale A.M., Sereno M.I., Journal of Cognitive
Neuroscience 5/2 162-176 (1993) 5 Robinson
S.E., Vrba J., in Recent Advances in
Biomagnetism, Tohoku University Press, Sendai
(1999)
The transformation into a sphere is unique and
invertible, i.e. every point on the gray-white
matter boundary corresponds to a single point on
the sphere and vice versa because both surfaces
are singly connected and therefore topologically
equivalent 3. The spherical coordinate system
of latitude ? and longitude f can now be mapped
onto the brain surface.
Comparison of fMRI and MEG activity recorded
during an experiment where subjects were asked to
synchronize with an external metronome. Left
Signal intensity masked with a correlation
threshold of 0.5. MiddleSignal intensity at
locations along the gray-white matter boundary.
Right Global power calculated from the
beamformer using MEG data recorded from the same
subject performing the same task.
Acknowledgement Work supported by NINDS (grant
NS39845), NIMH (grant MH42900) and the Human
Frontier Science Program.