Biological Effects - RF/Microwave Interaction with Biological Tissues - page 105

simulation of neural reactions to electrical stimuli in 1976. He used a popular
spatial model consisting in a network of lumped circuit models [60]. An excel-
lent discussion of various models is found in [61].
The propagation of neural activity in an axon is a consequence of the elec-
trical properties of the axonal cell membrane. An electric circuit consisting of
a capacitance, a voltage source, and nonlinear resistances, which represent the
gating of the ionic channels, can model a small segment of the membrane.
Potentials within and on the surface of a finite cylindrical volume conductor
due to a single-fiber along its center have been calculated by solving Laplace's
equation using a relaxation model [62]. The results have led to the estimation
of the variation of the single-fiber surface potential (SFSP) that would be
recorded from a surface electrode for differing nerve depths and conduction
velocities. A conduction velocity of 60 m s -1 was chosen, which results in an
instantaneous active length of 30 mm on the fiber. A length of 150 mm was
chosen for the model to reduce end effects. The model radius was taken as
10 mm, which corresponds to the approximate depth of the ulnar nerve at
superficial sites such as the elbow and axilla. Results are that the SFSP is more
elongated than the transmembrane current waveform and the relative ampli-
tude of its first positive phase is considerably decreased. The SFSP wave shape
is independent of fiber velocity and its amplitude is proportional to the veloc-
ity squared.
The computation of the steady-state field potentials and activating functions
led to the evaluation of the effect of electrical stimulation with several elec-
trode combinations on nerve fibers and different orientations in the spinal
cord [63]. The model comprises gray matter, white matter, CSF, epidural fat,
and a low-conductivity layer around the epidural space. This layer represents
the peripheral parts, like the vertebral bone, muscle, fat, and skin. Dura mater,
pia mater, and arachnoid were not incorporated in the model, estimating that
these membranes have only negligible influence on the field potential distri-
bution in the spinal cord [64].
First, an infinite homogeneous model was used, solving Laplace's equation.
Second, the spinal cord and its surrounding tissues were modeled as an
inhomogeneous anisotropic volume conductor using a variational principle by
which a functional representing the power dissipation of the potential fields
must be minimized to obtain the solution. Applying this method, inhomo-
geneities, anisotropy, and various boundary conditions can easily be incorpo-
rated and only first-order derivatives are used, while in direct discretization
methods of Laplace's equation second-order derivatives appear. The effect on
spinal nerve fibers was approximated using the activating function that, for
myelinated fibers, is the second-order difference of the extracellular potentials
along the fiber. The effect of mediodorsal epidural stimulation was calculated.
It was concluded that with cathodal simulation, mediodorsally in the epidural
space, longitudinal fibers are depolarized while dorsoventral ones are hyper-
polarized. The opposite occurs with anodal stimulation. It was found that
parameters substantially affecting the potential distribution in the dorsal
column are the conductivity of the white matter and the width and conduc-