5 EEG Source Imaging and Multimodal Neuroimaging
91
and J is the source term obtained from the right hand side integration of (5.18). This
system of equations can then be solved using a number of iterative linear methods.
A comprehensive review of these methods is given in [38].
5.1.5 A Note on Tissue Conductivity Values
The conductivity values for the different tissues in the brain contribute significantly
to the accuracy of the forward model. The conductivity for the cerebro-spinal fluid
(CSF) is widely accepted to be 1.79 S/m [8]. The conductivity values for the brain
and scalp compartment were also reported to be 0.33 S/m with good agreement
in the field [33, 36, 45], while the soft tissue to skull conductivity ratio remains a
subject of debate, leading to a multitude of studies conducted to arrive at a more
accurate number. For instance, the brain-to-skull ratio was originally suggested to
be 80 by multiple research groups using different analysis techniques [16, 31, 72].
More recently, however, the ratio was estimated to be 15 based on in vitro and in vivo
experiments performed by Oostendorp et al. [62]. In 2004, Guttierrez et al. reported
the soft tissue to skull conductivity of 26 using EEG scalp measurement and a 4sphere head model [36], while Lai et al. suggested using spherical head model a
ratio of 25 from the in vivo cortical imaging of 5 epilepsy patients in 2005 [45].
Subsequently, using a realistic geometry inhomogeneous head model, Zhang et al.
estimated a brain-to-skull conductivity ratio of 18.7 through in vivo experiments of
intracranial electrical stimulation in two epilepsy patients [83, 84].
5.2 From the Scalp to the Brain—The Inverse Problem
Now that we have defined the relationship between dipoles and the potentials they
generate on the scalp layer, we can attempt to invert this relationship to determine
which parts of the brain are active from their associated scalp potentials. This process
is referred to as EEG source localization. EEG source localization begins at the
forward problem (see 5.15):
V G J + n
and formulates the inverse problem as:
ˆ
J M V
(5.20)
where V ∈ R
N ×T is the measurement matrix of N electrodes and T time samples, G ∈
R
N ×P is the gain or the lead-field matrix, J ∈ R
P×T depicts the dipole magnitude
of P dipoles over T time samples, M ∈ R
P×N is the inverse operator, and ˆ
J is
91
and J is the source term obtained from the right hand side integration of (5.18). This
system of equations can then be solved using a number of iterative linear methods.
A comprehensive review of these methods is given in [38].
5.1.5 A Note on Tissue Conductivity Values
The conductivity values for the different tissues in the brain contribute significantly
to the accuracy of the forward model. The conductivity for the cerebro-spinal fluid
(CSF) is widely accepted to be 1.79 S/m [8]. The conductivity values for the brain
and scalp compartment were also reported to be 0.33 S/m with good agreement
in the field [33, 36, 45], while the soft tissue to skull conductivity ratio remains a
subject of debate, leading to a multitude of studies conducted to arrive at a more
accurate number. For instance, the brain-to-skull ratio was originally suggested to
be 80 by multiple research groups using different analysis techniques [16, 31, 72].
More recently, however, the ratio was estimated to be 15 based on in vitro and in vivo
experiments performed by Oostendorp et al. [62]. In 2004, Guttierrez et al. reported
the soft tissue to skull conductivity of 26 using EEG scalp measurement and a 4sphere head model [36], while Lai et al. suggested using spherical head model a
ratio of 25 from the in vivo cortical imaging of 5 epilepsy patients in 2005 [45].
Subsequently, using a realistic geometry inhomogeneous head model, Zhang et al.
estimated a brain-to-skull conductivity ratio of 18.7 through in vivo experiments of
intracranial electrical stimulation in two epilepsy patients [83, 84].
5.2 From the Scalp to the Brain—The Inverse Problem
Now that we have defined the relationship between dipoles and the potentials they
generate on the scalp layer, we can attempt to invert this relationship to determine
which parts of the brain are active from their associated scalp potentials. This process
is referred to as EEG source localization. EEG source localization begins at the
forward problem (see 5.15):
V G J + n
and formulates the inverse problem as:
ˆ
J M V
(5.20)
where V ∈ R
N ×T is the measurement matrix of N electrodes and T time samples, G ∈
R
N ×P is the gain or the lead-field matrix, J ∈ R
P×T depicts the dipole magnitude
of P dipoles over T time samples, M ∈ R
P×N is the inverse operator, and ˆ
J is