IGCAR : Annual Report - Indira Gandhi Centre for Atomic Research

IGC
Annual Report 2007
VI.13. Identification and Localization of Dipoles
for Magnetoencephalography
Magnetoencephalography
(MEG) is a technique for noninvasive
functional imaging
of the brain using
Superconducting Quantum
Interference Devices (SQUIDs).
In MEG, the neural current
sources have to be determined
based on the magnetic field
distribution measured outside
the brain. To obtain an
approximate solution to this
inverse problem, the brain is
typically modeled as a set of
concentric spheres and the
neural currents that cause the
magnetic field are represented
as current dipoles which are
either rotating or stationary.
The identification of the
locations of dipoles and their
temporal characteristics
(rotating and non-rotating) in
the presence of noise has been
done using the MUltiple Signal
Classification (MUSIC)
approach. With the
development of SQUID sensors
at IGCAR and setting up of
MEG facility, these results will
be of practical importance for
the analysis of MEG signals.
The radial component of the
magnetic field b r produced
outside the skull at (xn',yn',zn')
by a set of equivalent current
dipoles of strength qi's situated
inside the cortex at (xi,yi,zi)
can be written as a product of
a gain matrix M and the
column vector Q representing
their strength (Fig.1).
For four dipoles, 118
measurement locations and
100 time slices, b r is a
118x100 matrix, M is a
118x12 matrix and Q is a
12x100 matrix. To simulate a
realistic measurement, we add
to b r a Gaussian noise term
with mean zero and variance
10% of the maximum magnetic
field due to the source to
obtain the noisy data matrix b rn .
An approximate solution to
the problem of deducing the
locations and the strengths of
the equivalent current dipoles
can be obtained by minimizing
the residual error between the
simulated magnetic field b rn
and the calculated field. If brn
is decomposed into [UΣV T ] by
singular value decomposition
(SVD) and is seen to have a
rank r, then the
noise subspace can
be approximated by
U m-r U T m-r (U m-r is the matrix
containing of m-r columns at
the extreme right of the
decomposed matrix U). To find
the dipole locations by MUSIC
approach,Gi, the single dipole
Table 1 : Results of inversion calculation for four dipoles with 10% noise.
168 BASIC RESEARCH