A model is presented for the calculation of single myelinated fiber action potentials in an unbounded homogeneous medium and in nerve cuff electrodes. The model consists of a fiber model, used to calculate the action currents at the nodes of Ranvier, and a cylindrically symmetrical volume conductor model in which the fiber's nodes are represented as point current sources. The extracellular action potentials were shown to remain unchanged if the fiber diameter and the volume conductor geometry are scaled by the same factor (principle of corresponding states), both in an unbounded homogeneous medium and in an inhomogeneous volume conductor. The influence of several cuff electrode parameters, among others, cuff length and cuff diameter, were studied, and the results were compared, where possible, with theoretical and experimental results as reported in the literature.
SummaryThe perception threshold for epidural spinal cord stimulation in chronic pain management was analyzed on 3923 testing data obtained from 136 implanted patients. The initial areas of paresthesiae due to stimulation were recorded and reported as the stimulation map according to the location of electrodes. Measurement of dorsal thickness of the cerebrospinal fluid (CSF) layer was obtained from 26 subjects using magnetic resonance imaging (MRI). The results indicate that the perception threshold is a function of the spinal level of the implanted electrodes, of the mediolateral position in the spinal canal and the contact separation of electrode. Differences in perception threshold at various vertebral levels are mainly due to varying depths of the dorsal CSF layer. The medially placed electrodes caudal to the mid-cervical levels have a higher perception threshold than more laterally placed ones. The electrodes at high and mid-cervical levels, however, have a smaller perception threshold if placed medially. The information obtained from this investigation has important implications for the design of a new-generation stimulation system and clinical application to maximize the longevity of the power source.
Effects of both anatomic and electrode geometry on the recruitment of rostrocaudal fibers in the spinal cord were investigated by computer simulation of epidural spinal cord stimulation. A three-dimensional model was used, representing the geometry and electrical conductivity of the spinal cord and surrounding tissues, in combination with a model representing the electrical properties of a myelinated nerve fiber. Recruitment contours in the dorsal columns were calculated at various spinal geometries as a function of electrode position, combination and area. Cathodal position appeared to be most significant. Recruitment areas resulting from different contact combinations of a mediodorsal array were almost identical. It was shown that peception threshold largely depends on both dorsal cerebrospinal fluid width and fiber size. The usual bipolar contact separation appeared to approximate the theoretically optimal value, resulting in maximum fiber recruitment at minimum stimulus.
Mathematical models of myelinated nerve fibres are highly stylized abstractions of real nerve fibres. For example, nerve fibres are usually assumed to be perfectly straight. Such idealizations can cause discrepancies between theoretical predictions and experimental results. One well-known discrepancy is that the currently used models predict (contradictory to experimental findings) that an activation of nerve fibres is not possible with a pure transverse electric field. This situation occurs when a magnetic coil is placed symmetrically above a straight nerve fibre for magnetic nerve stimulation, or when an anode and a cathode are placed equidistantly on a line perpendicular to the fibre in the case of electrical stimulation. It is shown that this discrepancy does not occur if the physiological undulation of peripheral nerve fibres is included in the models. Even for small undulation amplitudes (e.g. 0.02 mm), it is possible to activate the fibre in these positions. For physiological undulations, as found in the literature, and favourable (off-centre) positions, the typical reduction of the thresholds is in a range between one and five, compared with perfectly straight fibres.
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