Biomedical Engineering Reference
In-Depth Information
is known as the forward problem. The estimation of generator
strength, location and timecourse from the EEG and MEG signal
and the knowledge of electrical properties of their biological envi-
ronment and the configuration of the measuring devices is known
as the inverse problem. The laws of electromagnetism define what
can be asked of the data and how the forward and inverse prob-
lems should be tackled, in particular what a priori assumptions can
be made about the generators. The forward and inverse problem
will be considered, describing in each case the theoretical frame-
work established by the laws of electromagnetism and its implica-
tions for useful MEG (and sometimes EEG) applications
3.1. The Forward
Problem
It is useful to separate the full current density into two terms. In
general, we are interested in the first term known as impressed
currents because they describe the active currents generated
by energy-demanding neuronal activity. The remaining currents
make up the second term; they describe the passive currents
that flow as a result of the impressed currents in the biological
medium. Impressed currents of an individual neuron cannot be
directly detected by either MEG or EEG because they are too
weak. Even under the most favorable conditions, a detectable sig-
nal can only be generated by the collective activity of at least many
hundreds of neurons spread over 1 mm
2
or larger cortical patches.
At this spatial scale, the appropriate terms that best separate the
full current density into active and passive elements are referred to
as primary current density and volume or return currents respec-
tively. The primary current density depends on both intracellu-
lar currents and the local extracellular currents. The intracellular
currents are closely related to the local impressed currents. Since
these ionic flows are along axons and dendrites, the net contribu-
tion from a single neuron is a sum of vectors each pointing along
the long axis of the corresponding active dendrite or axon. The
overall primary current density generated by intracellular currents
is the vector sum of contributions from active neurons, which
is therefore strongly dependent on the overall arrangement of
neurons. The flow of extracellular currents along the local con-
ductivity gradients is determined mainly by cell membranes. For
each focal neuronal activity, the local arrangement of cells deter-
mines the combined effect of both intracellular and extracellu-
lar currents and therefore shapes the resulting primary current
density. The source space is a convenient label for the region of
space where the primary current density can be non-zero, and
it includes the entire brain. Primary currents can be thought of
as the generators of the volume or return currents, i.e., the large-
scale passive electrical current flowing in the “volume conductor”,
in the brain at large and bounded by the highly resistive skull.
These large-scale passive electrical currents do not contribute to
the magnetic field, except where they “twist” at boundaries with
