Biomedical Engineering Reference
In-Depth Information
special geometries of the volume conductor, such as the sphere or an ellipsoid. A
concise review on the spherical homogeneous conductor model is found in Appen-
dixA. For realistic volume conductors, various numerical techniques such as finite-
element and boundary-element methods may be employed, although these methods
are generally time-consuming.
Measurement models refer to the specific measurement systems used in EEG and
MEG including the position of the sensors relative to the head. For instance, dif-
ferent MEG systems measure axial versus planar gradients of the magnetic fields
with respect to different locations of sensors. The measurement model incorporates
such information about the type of measurement and the geometry of the sensors.
Measurement of the position of the head relative to the sensor array is accomplished
by attaching head-localization coils to fiducial landmarks on the scalp. ModernMEG
systems are sometimes equipped with continuous head-localization procedures that
enable constant updating of sensor locations relative to the head to compensate for
subjects head movements. The source, volume conductor, and measurement models
are typically combined into a concept called the lead field that describes a linear rela-
tionship between sources and the measurements. When discussing inverse methods,
we assume that the lead field matrix is known.
1.3.2 Inverse Algorithms
Inverse algorithms are used for solving the bioelectromagnetic inverse problem,
i.e., for estimating the parameters of neural sources from MEG and EEG sensor
data. When implementing electromagnetic brain imaging, this estimation of spatial
locations and timing of brain sources is a challenging problem because it involves
solving for unknown brain activity across thousands of voxels from the recordings
of just a few hundred sensors. In general, there are no unique solutions to the inverse
problem because there are many source configurations that could produce sensor
data equal to the sensor observations, even in the absence of noise and (if given)
infinite spatial or temporal sampling. This nonuniqueness is referred to as the ill-
posed nature of the inverse problem. Nevertheless, to get around this nonuniqueness,
various estimation procedures incorporate prior knowledge and constraints about
source characteristics.
Inverse algorithms can be classified into two categories: model-based dipole fit-
ting and (non-model-based) imaging methods. Dipole fitting methods assume that
a small set of current dipoles can adequately represent an unknown source distri-
bution. In this case, the dipole locations and its moments form a set of unknown
parameters, which are typically estimated using the least-squares fit. The dipole fit-
ting method—particularly the single-dipole fitting method—has clinically been used
for localization of early sensory responses in somatosensory and auditory cortices.
However, two major problems exist in a dipole fitting procedure. First, the
nonlinear optimization causes a problem of local minima when more than two dipole
parameters are estimated. A second, more difficult problem is that the dipole fitting
methods require a priori knowledge of the number of dipoles. Often, such information
