Biomedical Engineering Reference
In-Depth Information
Chapter 6
A Unified Bayesian Framework
for MEG/EEG Source Imaging
6.1 Introduction
Magnetoencephalography (MEG) and related electroencephalography (EEG) use
an array of sensors to take electromagnetic field (or voltage) measurements from
on or near the scalp surface with excellent temporal resolution. In both MEG and
EEG, the observed field can in many cases be explained by synchronous, compact
current sources located within the brain. Although useful for research and clinical
purposes, accurately determining the spatial distribution of these unknown sources
is a challenging inverse problem. The relevant estimation problem can be posed
as follows: The measured electromagnetic signal is
y
d
t
, where
d
y
equals
the number of sensors and
d
t
is the number of time points at which measurements
are made. Each unknown source
s
r
d
y
×
∈ R
d
t
is a
d
c
-dimensional neural current
dipole, at
d
t
timepoints, projecting from the
r
th (discretized) voxel or candidate
location distributed throughout the brain. These candidate locations can be obtained
by segmenting a structural MR scan of a human subject and tessellating the brain
volume with a set of vertices,
y
and each
s
r
are related by the likelihood model
d
c
×
∈ R
d
s
y
=
L
r
s
r
+
ʵ
,
(6.1)
r
=
1
d
y
×
d
c
is the
so-called lead-field matrix for the
r
th voxel. The
k
th column of
L
r
represents the
signal vector that would be observed at the scalp given a unit current source/dipole
at the
r
th vertex with a orientation in the
k
th direction. It is common to assume
d
c
=
where
d
s
is the number of voxels under consideration and
L
r
∈ R
3 (for EEG), which
allows flexible source orientations to be estimated in 2D or 3D space. Multiple
methods based on the physical properties of the brain and Maxwell's equations are
available for the computation of each
L
i
, as described in Appendix A. Finally,
2 (for MEG with a single spherical shell model) or
d
c
=
ʵ
is a noise-plus-interference term where we assume, for simplicity, that the columns
