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In-Depth Information
8.4.4 Forward Modeling
In order to obtain an estimate of the primary current density, one needs to model
the EM signals produced by both the primary (i.e., impressed) and the secondary
(i.e., volume, return) current density throughout the head volume conductor, which
in reality has an inhomogenous and anisotropic conductivity profile. Analytic MEG
forward solutions can be computed if the volume conductor is approximated by an
isotropic sphere or a set of overlapping spheres [78, 36]. The same is true for EEG
but using concentric spherical shells with different isotropic conductivities. Most
MEG and EEG studies assume a spherically symmetric volume conduction model.
Solutions and software exist to improve the level of realism of the forward volume
conduction head model, as the measured signals - especially with EEG - may have
significant contributions from volume currents.
Much progress has been made toward realistic EM forward modeling using nu-
merical techniques such as the boundary element method (BEM) and the finite el-
ement method (FEM) [32, 3, 102]. The BEM assumes a homogenous and isotropic
conductivity profile through the volume of each tissue shell (e.g., brain, CSF, skull,
skin), but with a conductivity inhomogeneity across the boundaries of the shells.
The FEM usually also assumes homogeneity and isotropy within each tissue type,
but in contrast to BEM, can also be used to model the conductivity anisotropy of
white matter and that of the skull's spongiform and compact layers. Although real-
istic modeling exploits any available subject-specific information from MRI (e.g.,
T1, T2, PD, DTI) or CT, standardized BEM or FEM head models can be used as a
first approximation for subjects without an MR scan [19, 16]. We should note, how-
ever, that realistic modeling is ultimately limited by the uncertainty in parameters
such as the in vivo individual distribution of electrical conductivity throughout head
tissues, which is yet to be accessible reliably to MRI techniques [90] and electrical
impedance tomography [24].
8.4.5 Inverse Modeling
The goal of inverse modeling is to estimate the location and strengths of the sources
that generated the measured EM data. As in many other problems in physics, this is
a so-called
ill-posed
inverse problem, which essentially means there are an infinite
number of solutions that explain the measured data equally well. The main reason is
that some source configurations produce no EM signals at the sensors. This means
that these silent source configurations can always be added to an existing solution
without affecting the fit to the data [33]. This nonuniqueness forces us to make
a priori assumptions, additional to the experimental data, to further constrain the
number of feasible source patterns to one unique solution [78, 31].
These additional constraints are usually handled within the general framework of
regularization, which is also common to most medical imaging applications where
reconstruction of source signals of measured data is required. In NSI, these con-
