Model of the slow components of skeletal muscle potentials

Estimate of M-wave changes in human biceps brachii during continuous stimulation

The purpose of the present study was to validate the capability of new fatigue indexes (in the time and frequency domain) applied to experimental recordings and thus, to test some assumptions made in previous simulations. The indexes were applied to M-waves detected non-invasively from human m.biceps brachii during repetitive slightly above threshold stimulations. It was found that distance between the motor point and middle of the end-plate region could be relatively large. Under identical conditions (signals detected by monopolar electrodes and high-pass filtered at 1 Hz), the relative changes of the indexes obtained in electrophysiological experiments and simulations were similar. Changes of the intracellular action potential profile during fatigue used in the simulations were consequently supposed to be close to the actual ones for the muscle analyzed. When the high-pass cut-off frequency was higher than 1 Hz, the sensitivity of the index in the time domain was higher, while that in the frequency domain was lower. If the normalizing spectral moment was of higher order, the sensitivity of the spectral index could be even 150-times greater than that of the fatigue indexes traditionally used. Thus, the spectral index promises high capability to assess fatigue during functional electrical stimulation.

Simulation analysis of the performance of a novel high sensitive spectral index for quantifying M-wave changes during fatigue

A high sensitive fatigue index is desired to improve stimulation strategy and to prevent muscle damage in functional electrical simulations. The great number of indexes used shows that there is no index that satisfies all investigators. A way to develop a high sensitive index for quantifying M-wave changes during fatigue and to estimate its performance was analyzed. The changes in M-wave and its frequency distribution due to variations of intracellular action potential (IAP) and muscle fibre propagation velocity (MFPV) with fatigue were simulated. It was found that the ratio between the spectral moments of order -1 and 2 was considerably more sensitive to peripheral muscle fatigue than the mean (the ratio between the spectral moments of order 1 and 0) and median frequency traditionally used. The sensitivity of the new index depended on the electrode arrangement and position in respect to the active fibres. The belly-tendon detection promised the highest index sensitivity. The length of the active fibres also affected the index sensitivity. The shorter the fibres the lower was the index sensitivity. The sensitivity of the new index could be relatively high even in the case of traditionally used high-pass cut-off frequencies that could distort the M-wave shape.

The cross-correlation and phase-difference methods are not equivalent under noninvasive estimation of the motor unit propagation velocity

Noninvasive estimation of motor unit propagation velocity (MUPV) was reduced to that of the time delay between signals detected by two surface EMG electrodes placed along the muscle fibres. When the cross-correlation function between the signals was used, the problem with temporal resolution arose. Estimation of the time delay in the frequency domain was proposed to overcome this problem. To check whether the cross-correlation and phase-difference methods give the same estimates, the results obtained by both methods were compared through simulation. A different sensitivity of the two methods to the effects of the excitation origin and extinction was found. Besides, the quality of the estimate depended on the electrode arrangement. The longitudinal double difference electrodes were preferable with the phase-difference method, while the MUPV estimates obtained by the cross-correlation technique were more correct when the longitudinal single difference or bipolar transversal double difference electrodes were used. In addition, the estimates obtained by the phase-difference method were more sensitive to the longitudinal scattering of motor end-plates and ends of the fibres, to the fibre lengths and to the negative after-potential magnitude. Such sensitivity could make MUPV estimates incorrect even under a relatively small distance between the motor unit axis and electrode.

Interpretation of EMG changes with fatigue: facts, pitfalls, and fallacies

Failure to maintain the required or expected force, defined as muscle fatigue, is accompanied by changes in muscle electrical activity. Although studied for a long time, reasons for EMG changes in time and frequency domain have not been clear until now. Many authors considered that theory predicted linear relation between the characteristic frequencies and muscle fibre propagation velocity (MFPV), irrespective of the fact that spectral characteristics can drop even without any changes in MFPV, or in proportion exceeding the MFPV changes. The amplitude changes seem to be more complicated and contradictory since data on increased, almost unchanged, and decreased amplitude characteristics of the EMG, M-wave or motor unit potential (MUP) during fatigue can be found in literature. Moreover, simultaneous decrease and increase in amplitude of MUP and M-wave, detected with indwelling and surface electrodes, were referred to as paradoxical. In spite of this, EMG amplitude characteristics are predominantly used when causes for fatigue are analysed. We aimed to demonstrate theoretical grounds for pitfalls and fallacies in analysis of experimental results if changes in intracellular action potential (IAP), i.e. in peripheral factors of muscle fatigue, were not taken into consideration. We based on convolution model of potentials produced by a motor unit and detected by a point or rectangular plate electrode in a homogeneous anisotropic infinite volume conductor. Presentation of MUP in the convolution form gave us a chance to consider power spectrum (PS) of MUP as a product of two terms. The first one, PS of the input signal, represented PS of the first temporal derivative of intracellular action potential (IAP). The second term, PS of the impulse response, took into account MFPV, differences in instants of activation of each fibre, MU anatomy, and MU position in the volume conductor in respect to the detecting electrode. PS presentation through product means that not only changes in MFPV could be responsible for PS shift as is usually assumed. Changes in IAP duration and IAP after-potential magnitude, affecting the first term of the product, influence the product and thus MUP PS. Moreover, the interrelations between the two spectra and thus sensitivity of spectrum to different parameters change with MU-electrode distance because the second term depends on it. Thus, we have demonstrated that theory does not predict a linear relation between the characteristic frequencies (maximum, mean and median) and MFPV. IAP duration and after-potential magnitude are among parameters affecting MUP or M-wave PS and thus, EMG PS detected by monopolar and bipolar electrodes. Usage of single fibre action potential models instead of MUP ones can result in false dependencies of frequency characteristics. The MUP amplitude characteristics are determined not only by amplitude of IAP, but also by the length of the IAP profile and source-electrode distance. Due to the IAP profile lengthening and an increase in the negative after-potential, surface detected EMG amplitude characteristics can increase even when IAP amplitude decreases considerably during fatigue. Increase in surface detected MUP or M-wave amplitude should not be attributed to a weaker attenuation of the low-frequency components with distance. Simultaneous decrease and increase in amplitude of MUP and M-wave detected with indwelling and surface electrodes are regular, not paradoxical. Corner frequency of the high pass filter should be 0.5 or 1 Hz when muscle fatigue is analyzed. The area of MUP or M-wave normalized in respect of the amplitude of the terminal phase (that is produced during extinction of the depolarized zones at the ends of the fibres) could be useful as a fatigue index. Analysing literature data on IAP changes due to Ca(2+) increasing, we hypothesised that the ability of muscle fibres to uptake Ca(2+) back into the sarcoplasmic reticulum could be the limiting site for fatigue. If this hypothesis is valid, IAP changes are not a cause of fatigue; they are due to it.

A model of the muscle action potential for describing the leading edge, terminal wave, and slow afterwave

The leading edge, terminal wave, and slow afterwave of the motor-unit action potential (MUAP) are produced by changes in the strength of electrical sources in the muscle fibers rather than by movement of sources. The latencies and shapes of these features are, therefore, determined primarily by the motor-unit (MU) architecture and the intracellular action potential (IAP), rather than by the volume-conduction characteristics of the limb. We present a simple model to explain these relationships. The MUAP is modeled as the convolution of a source function related to the IAP and a weighting function related to the MU architecture. The IAP waveform is modeled as the sum of a spike and a slow repolarization phase. The MU architecture is modeled by assuming that the individual fibers lie along a single equivalent axis but that their action potentials have dispersed initiation and termination times. The model is illustrated by simulating experimentally recorded MUAPs and compound muscle action potentials.

A model of the muscle-fiber intracellular action potential waveform, including the slow repolarization phase

Recent studies have shown that the slow repolarization phase or "negative afterpotential" of the intracellular muscle-fiber action potential (IAP) plays an important role in determining the shape of the extracellularly recorded motor-unit action potential (MUAP). This paper presents a model of the IAP waveform as the sum of a spike and an afterpotential, both represented by simple analytical expressions. The model parameters that specify the sizes of the spike and afterpotential are shown to be proportional to the quadrupole and dipole moments of the transmembrane current distribution associated with the spike of the wave of excitation. The model provides a computationally efficient method for simulating the MUAP, and it can be reliably inverted to estimate the model parameters from empirical IAP and MUAP waveforms.

The physiological origin of the slow afterwave in muscle action potentials

OBJECTIVE

Both intramuscularly-recorded motor unit action potentials (MUAPs) and surface recorded MUAPs and compound muscle action potentials (CMAPs) have slow afterwaves which can contribute as much as half their measured duration. This study tested the hypothesis that the slow afterwave has its physiological origin in the negative afterpotential of the muscle fiber intracellular action potential (IAP).

METHODS

We investigated the slow afterwave in MUAPs and CMAPs from brachial biceps, tibialis anterior, first dorsal interosseous, thenar and hypothenar muscles in 15 normal subjects, and using computer simulations.

RESULTS

The slow afterwaves did not match the time constant of the amplifier's high-pass filter, and so were not filtering artifacts. They lasted long after propagation had terminated at the muscle/tendon junction, and so were not due to the temporal or spatial dispersion of propagating single-fiber potentials. Their amplitude and polarity varied with the recording site as predicted by computer simulations that modeled the IAP as having a negative afterpotential. They also changed with double-pulse stimulation and decreasing temperature in ways consistent with the results of intracellular studies of the IAP negative afterpotential.

CONCLUSIONS

The presented results support our hypothesis that the slow afterwave is a manifestation of the IAP negative afterpotential.

Anatomical and electrophysiological determinants of the human thenar compound muscle action potential

Clinical interpretation of the compound muscle action potential (CMAP) requires a precise understanding of its underlying mechanisms. We recorded normal thenar CMAP5 and motor unit action potentials using different electrode configurations and different thumb positions. Computer simulations show that the CMAP has four parts: rising edge, negative phase, positive phase, and tail which correspond to four distinct stages of electrical activity in the muscle: initiation at the end-plate, propagation, termination at the muscle/tendon junctions, and slow repolarization. The shapes of volume-conducted signals recorded beyond the muscle are also explained by these four stages. Changes in CMAP shape associated with thumb abduction are due to changes in termination times resulting from changes in muscle-fiber lengths. These findings demonstrate that the negative and positive phases of the CMAP are due to different mechanisms, and that anatomical factors, particularly muscle-fiber lengths, play an important role in determining CMAP shape.