Biological Effects - RF/Microwave Interaction with Biological Tissues - page 107

extracellular potential is negligible, so that the transmembrane potential
equals the intracellular potential.
These linear models assume an infinitely long fiber, that is, a fiber whose
length is large relative to the distance to the electrode. In a number of usual
applications, this condition does not apply and it is necessary to consider the
termination conditions of fibers in the field of a focal electrode. An analytical
model of a fiber terminal in the field of a monopolar, time-varying, spherical
or point source has been presented, and the effects of the termination imped-
ance of an axon on the membrane polarization induced by extracellular stimuli
have been shown [68]. The significance of any termination current is deter-
mined by the ratio of the termination impedance to the axon's input imped-
ance. If the ratio is large, the fiber is effectively “sealed” and the termination
current is insignificant. If it is small, the fiber is “unsealed” and the membrane
potential at the terminal is zero. If the ratio is of the order of 1, there is sig-
nificant termination current and the fiber is in an intermediate state between
sealed and unsealed. For a myelinated fiber terminating with nodal membrane,
this latter situation appears to apply. An important feature of end-structure
stimulation is its time constant.
Analyses of magnetic stimulation of finite-length neuronal structures have
been performed using computer simulations [69]. Models of finite neuronal
structures in the presence of extrinsically applied electric fields indicate that
excitation can be characterized by two driving functions: one due to field gra-
dients and the other to fields at the boundaries. It was found that boundary
field-driving functions play an important role in governing excitation charac-
teristics during magnetic stimulation. Simulations have indicated that axons
whose length is short compared to the spatial extent of the induced field are
easier to excite than longer axons of the same diameter and also that inde-
pendent cellular dendritic processes are probably not excited during magnetic
stimulation. Analysis of the temporal distribution of induced fields indicated
that the temporal shape of the stimulus waveform modulates excitation
thresholds and propagation of action potentials. Those results are based on
simulations only and need to be confirmed by experimental results.
As mentioned in Section 2.1.2, there are excellent discussions of various
models, including Hodgkin-Huxley, Frankenhaeuser-Huxley, Chiu-
Ritchie-Rogert-Staff-Stagg, and Schwarz-Eikhof [7]. Large differences in
model behavior are obvious for strong signals. The results also depend on fiber
parameters, influence of myelin, irregularities, branching, electrode geometry,
and so on.
A number of questions remain unanswered. There is a lack of quantitative
results illustrating the significant differences, if any, between CW, pulsed, and
ELF-modulated waves. Systematic experiments are necessary to illustrate pos-
sible significant differences at different frequencies. Little information is avail-
able about the quantitative effects of millimeter waves either on the nervous
system or on its constituents, although there might be fundamental differences
between microwave and millimeter-wave excitation. The wavelength of these