Biomedical Engineering Reference
In-Depth Information
sharp changes in conductivity, especially the skull. In the special
case that only concentric spherical boundaries of changes in con-
ductivity are present, the magnetic field generated outside a con-
ductor is given by an analytical expression
(17)
.Furthermore,the
laws of electromagnetism and spherical symmetry define explic-
itly which generators can produce an external magnetic field and
which are magnetically silent, i.e. they do not produce an exter-
nal magnetic field no matter how strong they are. Specifically,
radial components of the current density are magnetically silent
sources. The magnetic field generated by tangential components
of the current density can be written analytically in a form that
depends on the center of the conducting sphere(s) and it does
not depend on either the conductivities of the different com-
partments or the radii of the concentric shell(s), as long as the
magnetic field is computed outside the conductor (last spheri-
cal shell). Finally, for a spherical conductor, the radial magnetic
field, i.e. the component of the magnetic field (outside the head)
pointing away from the center of the conducting sphere depends
only on the primary currents. The magnetic field for realistic head
shapes can be computed accurately and fast using a set of overlap-
ping spheres appropriately chosen for each sensor
(18)
. The skull
is smooth and nearly spherical; so, the convenient and relatively
simple spherical model can provide an excellent estimate for the
second term, except around openings like the eye sockets or parts
of the skull that deviate substantially from the spherical model.
The EEG forward problem poses real difficulties in practice.
The accurate computation of EEG signal is more demanding
because it depends strongly on details of the conductivity profile.
The differences in the forward problem for MEG and EEG sig-
nals have two main consequences. First, the relationship between
neuronal activity is easier to model for MEG. On the one hand,
the skull is transparent to magnetic fields and highly resistive to
electrical currents (that must cross it to produce the scalp EEG)
and, on the other, the effect of the conducting medium can be
approximated by simple models for accurate computations of the
magnetic field but have to be described in detail for the com-
putation of the surface potential. Second, the EEG is influenced
strongly by both radial and tangential electric currents while MEG
is only sensitive to tangential ones.
The laws of electromagnetism endow both EEG and MEG
signals with a direct relationship with the neuronal sources.
Specifically, the electric and magnetic fields propagate from the
(neuronal source) generator site with the speed of light. Since
the sensors are just some centimeters away, for all practical pur-
poses, the effect is immediate: a change in the source electrical
activity in the brain produces an immediate change in the MEG
and EEG signal. This is in sharp contrast with other neuroimaging
methods like positron emission tomography (PET) and functional
