The effect of electrical stimulation with several electrode combinations on nerve fibers with different orientations in the spinal cord was investigated by computing the steady-state field potentials and activating functions. At first an infinite homogeneous model was used while secondly the spinal cord and its surrounding tissues were modeled as an inhomogeneous anisotropic volume conductor. The effect of mediodorsal epidural stimulation was calculated. It was concluded that with cathodal stimulation, mediodorsally in the epidural space, longitudinal fibers are depolarized, but dorsoventral ones are hyperpolarized. With anodal stimulation the opposite will occur. It was found that parameters substantially affecting the potential distribution in the dorsal columns are the conductivity of the white matter and the width and the conductivity of the csf layer.
A nerve stimulation model has been developed, incorporating realistic cross-sectional nerve geometries and conductivities. The potential field in the volume conductor was calculated numerically using the variational method. Nerve fiber excitation was described by the model of McNeal. Cross-sectional geometries of small monofascicular rat common peroneal nerve and multifascicular human deep peroneal nerve were taken as sample geometries. Selective stimulation of a fascicle was theoretically analyzed for several electrode positions: outside the nerve, in the connective tissue of the nerve, and inside a fascicle. The model results predict that the use of intraneural or even intrafascicular electrodes is necessary for selective stimulation of fascicles not lying at the surface of the nerve. Model predictions corresponded with experimental results of Veltink et al. on intrafascicular and extraneural stimulation of rat common peroneal nerve and to results of McNeal and Bowman on muscle selective stimulation in multifascicular dog sciatic nerve using an extraneural multielectrode configuration.
Generally, single muscle fiber action potentials (SFAPs) are modeled as a convolution of the bioelectrical source (being the transmembrane current) with a weighting or transfer function, representing the electrical volume conduction. In practice, the intracellular action potential (IAP) rather than the transmembrane current is often used as the source, because the IAP is relatively easy to obtain under experimental conditions. Using a core conductor assumption, the transmembrane current equals the second derivative of the IAP. In previous articles, discrepancies were found between experimental and simulated SFAPs. Adaptations in the volume conductor slightly altered the simulation results. Another origin of discrepancy might be an erroneous description of the source. Therefore, in the present article, different sources were studied. First, an analytical description of the IAP was used. Furthermore, an experimental IAP, a special experimental SFAP, and a measured transmembrane current scaled to our experimental situation were applied. The results for the experimental IAP were comparable to those with the analytical IAP. The best agreement between experimental and simulated data was found for a measured transmembrane current as source, but differences are still apparent.
In modelling the electrical behaviour of muscle tissue, we used to employ a frequency-dependent volume conductor network model, which was infinitely extended in all directions. Equations in this model could be solved using a finite-difference approach. The most important restriction of this model was the fact that no boundary effects could be incorporated. Analytical models of muscle tissue normally do not have this disadvantage, but in those models the microscopic structure of muscle tissue cannot be taken into account. In the paper, we present a combined numerical/analytical approach, which enables the study of potential distributions and SFAPs in simulated microscopic muscle tissue in which the influence of the muscle boundary has been considered. We considered muscle models with radii of 1.5 mm and 10 mm. Both models were compared with an unbounded network model. In the model with a radius of 1.5 mm we varied the position of the active fibre relative to the muscle surface. It appeared that in most cases the presence of a boundary had a considerable effect on the potential distribution. An increase in the peak-to-peak value of the SFAP amplitude up to 300 per cent was noticed when the active fibre was positioned 500 microns beneath the muscle surface in a model with a radius of 1.5 mm.
Compound action potentials (CAPs) were recorded from the sural nerve of healthy volunteers. A mathematical technique (inverse modeling) was used to compute conduction velocity (CV) histograms from the data. Results were compared to the morphology of age-matched nor mal sural nerve biopsies. Coefficients of variation (CoVs) revealed the statistical relationship between morphological data (diameter histo grams) and electrophysiological data (CV histograms and conventional CAP parameters). No differences were found for the thick fiber group when comparing the CoVs of the diameter histogram parameters with the corresponding CV histogram parameters. Apparently, the same in herent biological interindividual variability is encountered. The CoVs of the CVs of the CAP'S main phases are in good agreement with the CoVs of the estimated mean velocity of the thick fiber group. Inverse model ing increases the reliability of the estimation of the number of active fibers as compared to direct CAP amplitude interpretation.
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