W. Wallinga

Modelling action potentials and membrane currents of mammalian skeletal muscle fibres in coherence with potassium concentration changes in the T-tubular system

Abstract During prolonged activity the action potentials of skeletal muscle fibres change their shape. A model study was made as to whether potassium accumulation and removal in the tubular space is important with respect to those variations. Classical Hodgkin-Huxley type sodium and (potassium) delayed rectifier currents were used to determine the sarcolemmal and tubular action potentials. The resting membrane potential was described with a chloride conductance, a potassium conductance (inward rather than outward rectifier) and a sodium conductance (minor influence) in both sarcolemmal and tubular membranes. The two potassium conductances, the Na-K pump and the potassium diffusion between tubular compartments and to the external medium contributed to the settlement of the potassium concentration in the tubular space. This space was divided into 20 coupled concentric compartments. In the longitudinal direction the fibre was a cable series of 56 short segments. All the results are concerned with one of the middle segments. During action potentials, potassium accumulates in the tubular space by outward current through both the delayed and inward rectifier potassium conductances. In between the action potentials the potassium concentration decreases in all compartments owing to potassium removal processes. In the outer tubular compartment the diffusion-driven potassium export to the bathing solution is the main process. In the inner tubular compartment, potassium removal is mainly effected by re-uptake into the sarcoplasm by means of the inward rectifier and the Na-K pump. This inward transport of potassium strongly reduces the positive shift of the tubular resting membrane potential and the consequent decrease of the action potential amplitude caused by inactivation of the sodium channels. Therefore, both potassium removal processes maintain excitability of the tubular membrane in the centre of the fibre, promote excitation-contraction coupling and contribute to the prevention of fatigue.

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.

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 10mm. Both models were compared with an unbounded network model. In the model with a radius of 1·5mm 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 μm beneath the muscle surface in a model with a radius of 1·5mm.

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.

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%.

In vivo magnetomyograms of skeletal muscle

Magnetomyography (MMG) is a new noninvasive technique inspired by the magnetoneurographic method of J.P. Wikswo (IEEE Trans. Biomed. Eng., Vol.BME-30, p.215-21, 1983). MMG is used to detect action currents in a muscle, which is immersed in a highly conducting fluid. The detection coil is of a toroidal shape, with the muscle passing through the center of the coil. For a long muscle which fits tightly in the toroid, it is to be expected that magnetic fields correspond almost completely to the intracellular longitudinal (axial) currents in active muscle fibers. An experimental setup with specific coils for rat and mouse skeletal muscles was developed. It is sensitive enough to detect currents from single motor units. The technique can be used to record stimulated twitch activity in live muscle as a function of force level, coil position along the muscle, temperature, etc. By simulating the response with a finite-element forward model, it is possible to calculate action currents under various experimental conditions.<<ETX>>

Modeling removal of accumulated potassium from T-tubules by inward rectifier potassium channels

The membrane models of Cannon et al. (1993) and Alberink et al. (1995) for mammalian skeletal muscle fibers are based upon Hodgkin-Huxley descriptions of sodium, potassium delayed rectifier and leak conductances and the capacitive current taking into account fast inactivation of sodium channels. Now inward rectifier and chloride ion currents, sodium-potassium pump and slow inactivation of sodium channels have been inserted. The behavior of the model with respect to resting membrane potential and action potential firing does not differ remarkably from Alberink et al. The model has been used to study the removal of potassium from the T-tubular space. The inward rectifier current significantly contributes to the restoration of the normal potassium concentration after prolonged action potential firing. This may be an important mechanism to avoid muscle fatigue.

Changes in time and frequency related aspects of motor unit action potentials during fatigue

During fatigue the shape of motor unit action potentials (MUAPs) change. Characteristics of the MUAPs described before concern several time related aspects. No attention has been given to the frequency spectrum changes of MUAPS. The median frequency of MUAPS has now been determined for motor units in the extensor digitorum longus muscle of the rat. Some examples of the changes are shown during a fatiguing stimulation pattern (250 s of 40 Hz stimulation during one third of each second). In general the median frequency tends to change more quickly than the time characteristics of the MUAPs. The results do not allow to draw yet conclusions about the time and frequency characteristics during fatigue for mechanically identified types of motor units.

Source characteristics from inverse modeling of EMG signals

If one tries to solve the inverse problem in single fiber electromyography (SFEMG), the question is which signal to consider as the proper source signal. Often the intracellular action potential (IAP) is taken as such. Measuring shape parameters and distances of Single Fiber Action Potentials and active fibers in muscle and comparing them with muscle structure model predictions reveals that it is transmembrane current which is the true source of the SFEMG.

The effect of fiber-electrode distance on single fiber action potentials

The distance between active fibers and measuring electrodes as occuring during single fiber electromyomyography was assessed. SFAP amplitudes were calculated with a volume conduction model of skeletal muscle. Calculated SFAPs had smaller peak to peak voltages than the measured ones, the latter showed large spread. There is thus a discordance between experiment and theory in single fiber electromyography.