Biological Effects - RF/Microwave Interaction with Biological Tissues - page 106

tivity of the CSF layer. The CSF has a major influence on the potential distri-
bution on the spinal cord. Although limited to the analysis of electrode con-
figurations and the design of alternative electrodes for spinal cord DC
stimulation, these results are important in that they give an insight on the field
potential distribution in the dorsal column.
Interest in neural excitation by EM induction has grown in recent years.
Magnetic stimulation of the CNS is a painless alternative to electrical stimu-
lation and is finding increasing use. The spatial distribution of the currents
induced by the stimulating coil has been calculated from a computer model
[65]. Two configurations of a plane circular coil are considered: parallel to the
tissue surface and perpendicular to the surface. The surface is assumed planar
and infinite in extent. The tissue is modeled as a uniform, isotropic volume
conductor. A quasi-static approximation is made in calculating the electric
field. The current density is mapped as a function of position, including depth.
In both configurations, it is always parallel to the surface and maximum at
the surface. There is no perpendicular (vertical) current. The stimulation of a
nerve fiber requires that the component of the surrounding electric field, and
hence bulk current flow, is parallel to the fiber and should exceed a particular
threshold value. These results suggest that nerve fibers running parallel to the
skin surface are more likely to be stimulated than those running obliquely and
that it is extremely difficult to stimulate nerve fibers running perpendicularly.
On the other hand, it was found that, for a given coil, the current density
at a particular point in the tissue is only dependent on its distance from the
coil. This current density is independent of the distances of the point and of
the coil from the tissue surface. In this analysis, the magnetic field produced
by the induced current in the tissue has been ignored because it is much
smaller than that produced by the primary current in the coil. The frequency
components of the coil current waveform are at about 10 kHz. At this fre-
quency, the skin depth is approximately 10 m, that is, much larger than the
object.
A model of magnetic stimulation of an unmyelinated nerve fiber that pre-
dicts where and when excitation occurs has been proposed [66]. It consists of
a one-dimensional cable equation that is forced by a term analogous to the
activating function for electrical stimulation with extracellular electrodes.
While neural stimulation is caused by a three-dimensional electric field distri-
bution, a one-dimensional cable model generally describes the response. These
one- and three-dimensional representations have been reconciled, and an acti-
vating function for magnetic stimulation was derived which was consistent
with both [67]. From a three-dimensional volume conductor model of mag-
netic stimulation, the induced electric field and its resultant transmembrane
potential distribution along an axon were derived analytically. This model
validated several simplified assumptions on which the one-dimensional model
was based: (1) The electric field within the axon is axial, (2) the field in the
membrane is radial, (3) the electric field in the membrane due to induction is
negligible compared to the electric field due to charge separation, and (4) the