Influence of inhomogeneities in muscle tissue on single-fibre action potentials: a model study.

The influence of changes in electrical conductivity, due to the muscle boundary, layers and compartments of intramuscular connective tissue and blood vessels, on computed single-muscle fibre action potentials (SFAPs) in rat hindleg muscle is calculated. The position of the active fibre is varied throughout the muscle. For fibres close to the muscle boundary, peak-to-peak voltages of SFAPs increase by up to a factor of 3 compared with the unbounded situation. For inner fibres, the presence of nearby connective tissue compartments causes an increase of up to 40%. A blood vessel in the neighbourhood of the active fibre leads to a decrease of at most 20%, for recording sites between the active fibre and the blood vessel. For recording sites beyond the blood vessel, peak-to-peak voltages increase by up to 20%.

Conduction velocity distributions compared to fiber size distributions in normal human sural nerve.

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 normal sural nerve biopsies. Coefficients of variation (CoVs) revealed the statistical relationship between morphological data (diameter histograms) 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 inherent 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 modeling increases the reliability of the estimation of the number of active fibers as compared to direct CAP amplitude interpretation.

Single fibre action potentials in skeletal muscle related to recording distances.

Single muscle fibre action potentials (SFAPs) are considered to be functions of a bioelectrical source and electrical conductivity parameters of the medium. In most model studies SFAPs are computed as a convolution of the bioelectrical source with a transfer function. Calculated peak-to-peak amplitudes of SFAPs decrease with increasing recording distances. In this paper an experimental validation of model results is presented. Experiments were carried out on the m. extensor digitorum longus (EDL) of the rat. Using a method including fluorescent labelling of the active fibre, the distance between the active fibre and the recording electrode was derived. With another method, the decline of the peak-to-peak amplitude of SFAPs detected along a multi-electrode was obtained. With both experimental methods, in general peak-to-peak amplitudes of SFAPs decreased with increasing recording distances, as was found in model results with present volume conduction theory. However, this behaviour was not found in all experiments. The rate of decline of the peak-to-peak amplitudes with recording distance was always less than in models.

A statistical approach to fiber diameter distribution in human sural nerve.

Fifty-one normal sural nerve biopsies were obtained from 800 diagnostic biopsies. The external diameter distribution of myelinated fibers was described using the sum of two beta probability density functions, describing the thin as well as the thick fiber group. A cross-sectional study using these distribution functions showed increasing values of the peak of the larger fiber group, the diameter of the thickest fibers, and the separation between the smaller and the larger groups until the beginning of adult life. The transition from a uni- into a bimodal histogram occurred gradually between 7 and 13 months. Total transverse fascicular area increased with age, whereas fiber density decreased significantly with age. The number of fibers remained stable over age. The relative proportion of the numbers of fibers in both groups described by one of the beta distributions remained constant over age. This occurred despite a marked decrease in the number of small fibers with a diameter less than, e.g., 6.5 microns. The results indicated an outgrowth of especially the larger myelinated fibers with age. This process continues with decreasing intensity into adult life.

The bioelectrical source in computing single muscle fiber action potentials.

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.

Muscle conduction velocity and morphology after prolonged hypoxemia and diabetes in rats.

One of the electrophysiological abnormalities in the experimental rat model of chronic hypoxia (10% O2) and in the experimental rat model of diabetes is an increase in jitter in the stimulated single fibre EMG, which is thought to result from a primary disorder of the axon with its terminal branches. But muscle fibre alterations that influence the propagation of muscle action potentials can also increase jitter. The contribution of possible changes in muscle conduction velocity and muscle morphology to jitter were investigated in the present study. Muscle conduction velocities were determined and compared with the morphological properties of muscle fibers in muscles of control, chronic hypoxic and terminal-stage diabetic rats. The mean muscle conduction velocities were in the same range in the three groups. The muscle fibre type composition and the mean muscle fibre diameters were about the same in the hypoxic and the control rats, whereas the muscles of the diabetic rats showed a higher percentage of intermediate type muscle fibres, which is suggestive of muscle degeneration, and a smaller mean muscle fibre diameter in comparison with muscles of the hypoxic and the control rats. It is concluded that the similarities between the electrophysiological properties of the muscles despite differences in their morphology, indicate that there is primary axonal degeneration in diabetic hypoxic rats.

Potential distribution and single-fibre action potentials in a radially bounded muscle model.

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.

Epidural spinal cord stimulation: calculation of field potentials with special reference to dorsal column nerve fibers.

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 modeling study of nerve fascicle stimulation.

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.