Anatomical constraints applied to MEG beamformers

1
Anatomical constraints applied to MEG
beamformers A. Hillebrand and G. R. Barnes The
Wellcome Trust Laboratory for MEG studies,
Neurosciences Research Institute, Aston
University, Birmingham B4 7ET, U.K.
hillebra_at_aston.ac.uk
Introduction Synthetic Aperture Magnetometry
(SAM1) is a beamformer approach2 for the
localisation of neuronal activity from EEG/MEG
data1,3. SAM estimates the orientation of each
source in a pre-defined sourcespace by a
non-linear search for the optimum orientation.
However, MEG is most sensitive to cortical
sources4 and most detectable sources are oriented
perpendicular to the surface5. The reconstructed
neuronal activity can therefore reasonably be
constrained to the cortical surface, orientated
perpendicular to it. This work compares the
performance of a constrained and unconstrained
beamformer with respect to the localisation
accuracy of the source reconstructions and the
spatial resolution.

• Methods
• An unconstrained beamformer (SAM) and a
  constrained beamformer (with the sources
  orientated perpendicular to the cortical surface)
  were both applied to simulated datasets (N50).
  Two performance measures were obtained from the
  images of reconstructed source activity
  (Statistical Parametric Maps or SPMs)
• Spread of the peak in the SPM, based on the
  resel estimate6.
• Localisation error ( Euclidean distance between
  the location of the peak in the SPM and the
  target location).
• The performance of the beamformers was examined
  in the following situations
• Using accurate anatomical constraints.
• Adding perturbations to the surface normals
  (representing local segmentation errors when the
  cortical surface is extracted from the MRI).
• Perturbing the surface location and sphere
  origin (representing MRI/MEG co-registration
  errors).

Figure 1 Reconstructed source activity for one
of the representative target sources with
different source strengths, using SAM (a, b, c)
and the constrained beamformer (d, e, f). The
SPMs are displayed on an inflated cortical patch
formed around the target source (white circle).
The spatial resolution increases and the
localisation error decreases with increasing
source strength. Moreover, the anatomical
constraints force the lead fields of neighbouring
elements to be more dissimilar, resulting in a
reduced correlation between the beamformer
weights and therefore an improved spatial
resolution for the constrained beamformer6.
Figure 3 SAM output versus the orientation of a
target source, using two different source
strengths. The beamformer output reduces rapidly
for the stronger target source when its estimated
orientation deviates from the optimum
orientation. Consequently, this beamformer has a
higher selectivity than the beamformer for the
weaker source, but would also be more sensitive
to erroneous orientation constraints.
Figure 2 Influence of inaccurate orientation
constraints (?10?, 20?, and 30? respectively)
(a, b) and location errors (shift2, 4 and 8mm
respectively) (c, d) on the performance of SAM
and the constrained beamformer. The advantage in
spatial resolution (a, c) of the constrained
beamformer reduces when inaccurate constraints
are used with medium SNR data and disappears for
large SNR data. Additionally, SAM and the
constrained beamformer obtain very similar
localisation errors for data with low SNR (b, d).
For large SNR, SAM obtains an average
localisation error of zero, whereas the
inaccurately constrained beamformer fails to
obtain accurate localisation (b, d). This is
caused by a difference between the actual and
modelled lead fields due to the inaccurate
constraints (see also figure 3). These
differences cause the beamformer to attenuate the
signal from the target source2, resulting in
noisy source images and large localisation
errors. Also note that a shift in the location
constraints increases the localisation errors,
being of almost equal magnitude for the
constrained beamformer and SAM for corresponding
shifts (d). Furthermore, the minimum localisation
error that is obtainable is approximately as
large as the shift in the location constraints
(d).
Conclusions The spatial resolution of the
beamformer improves, typically by a factor of 4,
by applying anatomical constraints, and the
localisation accuracy improves marginally.
However, this advantage disappears when errors
are introduced in the orientation and location
constraints, and, moreover, the localisation
accuracy of the inaccurately constrained
beamformer becomes worse than for SAM.
Consequently, the MEG/MRI co-registration and
local segmentation errors should be smaller than
2mm and 10? respectively for the constrained
beamformer to improve on the performance of SAM.
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638-650. 2 van Veen BD, van Drongelen W,
Yuchtman M and Suzuki A (1997) IEEE T. Biomed.
Eng. 44(9) 867-880. 5 Okada Y (1982) In
Biomagnetism An Interdiciplinary Approach.
Pergamon Press, New York. 399-408. 3 Singh KD,
Barnes GR, Hillebrand A, Forde EME and Williams
AL (2002) NeuroImage 16 103-114. 6 Barnes
GR and Hillebrand A (2003) Human Brain Mapping.
18(1) 1-12.