The spectral changes in EMG during a second bout eccentric contraction could be due to adaptation in muscle fibres themselves: a simulation study.

The mechanism of marked reduction in damage symptoms after repeated bout of similar eccentric contractions is still unknown. The neuronal adaptation leading to reduction of muscle fibre propagation velocity (MFPV) due to increased activation of slow-twitch motor units (MUs), decrease in activation of fast-twitch MUs, and/or increase in MU synchronization was suggested as a cause for lower EMG frequency characteristics. However, the repeated bout effect could occur also after electrically stimulated exercise. Prolonged elevation of cytoplasmic Ca(2+) due to the increased membrane permeability after eccentric contractions was reported. Elevated Ca(2+) induced peripheral changes that included alteration of intracellular action potential and MFPV reduction. We simulated and compared changes in EMG frequency characteristics related to effects of central nervous system (CNS) or to peripheral changes. The simulations were performed for different electrode arrangements and positions. The results showed that the peripheral effects could be similar or even stronger than the effects related to CNS. We hypothesised that the repeated bout effect was a consequence of the adaptation in muscle fibres necessary for avoiding Ca(2+)-induced protein and lipid degradation due to Ca(2+) overload resulting from the increased membrane permeability after eccentric contraction. The possibilities for noninvasive testing of this hypothesis were discussed.

Fatigue analysis of interference EMG signals obtained from biceps brachii during isometric voluntary contraction at various force levels.

The aim of the present study was to test the applicability of indices of muscle fatigue to interference EMG signals detected at various distances from the end-plate region during isometric voluntary contractions at different force levels. Bar electrode with 12 leading off surfaces and 5mm inter-pole distance was used to detect EMG from human m. biceps brachii. The sensitivity of the new spectral indices to detect muscle fatigue was higher than that of mean or median frequencies. Considerable variations in the characteristic frequencies and values of spectral indices that could reflect recruitment and/or rotation of MUs were found under submaximal efforts. The increase of the indices was considered as a sign of peripheral muscle fatigue while their decreasing could be a sign of de-recruitment of fatigued or/and recruitment of new MUs reflecting central fatigue. The sensitivity of the indices to fatigue depended on the electrode arrangement and its longitudinal position in respect of the end-plate region and ends of the muscle fibres. It was larger for the electrodes placed in the middle of the semi-fibre. To overcome the problem with inappropriate position of the electrode, one could use an electrode whose longitudinal dimension would cover the entire semi-length of the analyzed fibres.

Simulation analysis of interference EMG during fatiguing voluntary contractions. Part II--changes in amplitude and spectral characteristics.

Capabilities of amplitude and spectral methods for information extraction from interference EMG signals were assessed through simulation and preliminary experiment. Muscle was composed of 4 types of motor units (MUs). Different hypotheses on changes in firing frequency of individual MUs, intracellular action potential (IAP) and muscle fibre propagation velocity (MFPV) during fatigue were analyzed. It was found that changes in amplitude characteristics of interference signals (root mean square, RMS, or integrated rectified value, IEMG) detected by intramuscular and surface electrodes differed. RMS and IEMG of surface detected interference signals could increase even under MU firing rate reduction and without MU synchronisation. IAP profile lengthening can affect amplitude characteristics more significantly than MU firing frequency. Thus, an increase of interference EMG amplitude is unreliable to reflect changes in the neural drive. The ratio between EMG amplitude and contraction response can hardly characterise the so-called 'neuromuscular efficiency'. The recently proposed spectral fatigue indices can be used for quantification of interference EMG signals. The indices are practically insensitive to MU firing frequency. IAP profile lengthening and decrease in MFPV enhanced the index value, while recruitment of fast fatigable MUs reduced it. Sensitivity of the indices was higher than that of indices traditionally used.

Simulation analysis of interference EMG during fatiguing voluntary contractions. Part I: What do the intramuscular spike amplitude-frequency histograms reflect?

Decline in amplitude of EMG signals and in the rate of counts of intramuscularly recorded spikes during fatigue is often attributed to a progressive reduction of the neural drive only. As a rule, alterations in intracellular action potential (IAP) are not taken into account. To test correctness of the hypothesis, the effect of various discharge frequency patterns as well as changes in IAP shape and muscle fibre propagation velocity (MFPV) on the spike amplitude-frequency histogram of intramuscular interference EMG signals were simulated and analyzed. It was assumed that muscle was composed of four types of motor units (MUs): slow-twitch fatigue resistant, fast-twitch fatigue resistant, fast intermediate, and fast fatigable. MFPV and IAP duration at initial stage before fatigue as well as their changes differed for individual MU types. Fatigability of individual MU types in normal conditions as well as in the case of ischaemic or low oxygen conditions due to restricted blood flow was also taken into account. It was found that spike amplitude-frequency histogram is poorly sensitive to MU firing frequency, while it is highly sensitive to IAP profile lengthening. It is concluded that spike amplitude-frequency analysis can hardly provide a correct measure of MU rate-coding pattern during fatigue.

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.

Estimation of the muscle fibre semi-length under varying joint positions on the basis of non-invasively extracted motor unit action potentials.

Changes in muscle fibre length and surface electrode position with respect to the muscle fibres affect the amplitude and frequency characteristics of surface electromyography (SEMG) in different ways. Knowledge of changes in muscle fibre length would help towards a better interpretation of the signals. The possibility of estimating the length through SEMG during voluntary contractions was checked in this study. The fibres' semi-length was estimated from the product of the conduction velocity and conduction time during which the wave of excitation propagated from the end-plate region to the ends of the fibres. Short (10 s), moderate (30% of maximum voluntary contraction) isometric contractions were performed by 10 subjects at different elbow joint angles (80-140 degrees in steps of 20 degrees ). Monopolar signals were detected non-invasively, using a two-dimensional electrode array. High spatial resolution EMG and a decomposition technique were utilised to extract single motor unit activities for triggered averaging and to estimate conduction velocity. A significant increase with joint angle was found in conduction time and estimated fibre semi-length. Changes in conduction velocity with joint angle were found to be not significant. The methodology described allows the relative changes in fibres' semi-length to be estimated from SEMG data.

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.

Intracellular action potential generation and extinction strongly affect the sensitivity of M-wave characteristic frequencies to changes in the peripheral parameters with muscle fatigue.

Changes in muscle fibre propagation velocity (MFPV) and shape of intracellular action potentials (IAPs) accompany peripheral muscle fatigue. We have shown through mathematical simulations that the effects of IAP generation and extinction reduced the sensitivity of the mean (fmean) and median (fmed) frequency of M-wave power spectra to individual changes in MFPV. Due to the differences in weighting of the spectral components used for calculation of the characteristic frequencies, the highest spectral components of the M-wave affected the fmean more than the fmed. These components are related to the M-wave leading edge that reflects the IAP depolarization phase. They reduced the sensitivity of the spectral moment of order 1 to individual changes in MFPV and increased its sensitivity to IAP changes. Since the changes of the IAP depolarization phase during the final stages of peripheral muscle fatigue affected the fmean more, the range of the relative reductions of the fmean and fmed were approximately the same under combined changes in IAP and MFPV. The sensitivities of M-wave characteristic frequencies depended also on the electrode arrangement and position as well as on the length of active muscle fibres.

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.

Simulation analysis of the ability to estimate motor unit propagation velocity non-invasively by different two-channel methods and types of multi-electrodes.

Ability to estimate motor unit propagation velocity correctly using different two-channel methods for delay estimation and different non-invasive spatial filters was analysed by simulation. It was established that longitudinal double difference electrodes could be not a better choice than simple bipolar parallel electrodes. Spatial filtration with a new multi-electrode (performing difference between signals detected by two transversal double difference electrodes positioned along the muscle fibres) promises to give the best estimate. Delay estimation between reference points is more preferable than that based on the cross-correlation technique, which is considerably sensitive to the fundamental properties of the muscle fibre extracellular fields. Preliminary averaging and approximation of the appropriate parts of the signals around chosen reference points could reduce the larger noise sensitivity and the effects of local tissue inhomogeneities as well as eliminate the sampling problem. A correct estimate of the propagation velocity could be impossible, even in the case of not very deep motor units (15 or 10 mm, depending on the spatial filter used) with relatively long (about 120 mm) muscle fibres. In the case of fibres with asymmetrical location of the end-plates in respect to the fibre ends, the propagation velocity estimates could be additionally biased above the longer semilength of the motor unit fibres.

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.

Amplitude-related characteristics of motor unit and M-wave potentials during fatigue. A simulation study using literature data on intracellular potential changes found in vitro.

To realize possible reasons for changes in EMG amplitude characteristics with fatigue, we analyzed motor unit potentials (MUPs) and M-waves under simultaneous variations of the intracellular action potential (IAP) amplitude, duration, and shape as well as of the muscle fiber propagation velocity and desynchronization in activation of individual muscle fibers. Analysis was performed through computer simulation of MUPs and M-waves detected at different distances from active fibers in infinite anisotropic volume conductor. Changes in the IAP spike and negative after-potential were taken from in vitro experiments reported in the literature. It was shown that the amplitudes of MUP and M-wave detected simultaneously at different distances could decrease close to the active fibers, be almost unchanged at middle distances, and increase far from the fibers even under IAP amplitude decreasing. This reflected the distance-dependent effects of changes in the IAP profile along the fiber. Electrode position affected sensitivity of MUP and M-wave durations to changes in the IAP duration and propagation velocity. Thus, the signal area and RMS depended on electrode position and could change with fatigue in a way different from that of signal amplitude. The results can help to avoid misleading interpretation of EMG changes.

Area-to-amplitude ratio of the terminal phase of the belly-tendon detected motor unit potentials could be used to recognize reinnervated motor units.

Besides the increased number of fibres, the reinnervated motor units (MUs) are characterised by an increased scattering the end-plates, greater desynchronization in the fibres' activation, greater dispersion in the diameters of the MU fibres and thus in propagation velocities along them. As a result, desynchronization in the moments, at which the excitation waves reach the fibres' ends, increases in reinnervated MUs. The possibility to recognize reinnervated MUs in short (hand) muscles on the basis of changes in duration of the terminal (second) phase of the belly-tendon detected motor unit potentials (MUPs) was examined by numerical experiments. A convolution model that took into account the finite fibre length, was used to calculate MUPs for distances typical of surface detection. It was shown that the ratio between the area of the terminal phase and its amplitude, as a measure of duration of the terminal phase, was sensitive to desynchronisation of the waves of excitation. The ratio was independent of the distance from the MU axis and of the volume conductor properties. Basing on the results obtained, we can conclude that the ratio reflects main functional compensations in reinnervated MUs and could be used for discrimination between reinnervated and normal MUs.

Neither high-pass filtering nor mathematical differentiation of the EMG signals can considerably reduce cross-talk.

Using mathematical simulation of motor unit potentials (MUPs), detected by a point and rectangular plate electrode, we have shown that the muscle tissue does not act like a low-pass frequency filter on MUPs. Depending on the electrode type and its longitudinal position, the relative weight of the terminal phases (reflecting the excitation extinction) in MUPs and thus of high frequencies in the MUP power spectrum, increase with the MU depth. Therefore, high-pass filtering or differentiating signals detected neither monopolarly nor bipolarly could eliminate the cross-talk produced by high frequency components of MUPs from deep MUs. Such methods could be effective against the main components but not against the MUP leading edge and terminal phases. To reduce the cross-talk, position of the detecting electrodes should correspond to anatomy of muscles producing the cross-talk. Monopolar electrode should be located above the ends of the muscles. Cross-talk of the muscles located beyond the muscle of interest could be higher than that produced above the end-plate of deep muscles. On the contrary, under detection by a longitudinal bipolar electrode, the cross-talk is much smaller above the end-plate region or beyond deep muscles. The cross-talk is the greatest above the ends of the deep muscles.

Surface detected potentials of normal and reinnervated motor units: a simulation study for muscles consisted of short fibres.

We aimed to check whether the characteristics used up to now in macro EMG to distinguish between normal and reinnervated motor unit potentials (MUPs), were suitable for surface detected MUPs. MUPs produced by normal and reinnervated MUs were simulated with a fast and precise convolution model. An increased number of fibres in the MU territory enhanced the amplitude, area and RMS of the MUP proportionally irrespective of the MU-electrode distance. An increased scatter of the end-plates and greater desynchronization in the fibres' activation decreased the MUP amplitude and affected the temporal characteristics of the MUP (duration of the negative phase and its area to amplitude ratio). The effects were more pronounced at shorter distances. At larger distances, the effect of the MU-electrode distance on temporal and amplitude characteristics of MUPs was much stronger than that of the parameters changed with reinnervation. We conclude that reinnervated MUs consisting of short fibres can not be distinguished from the normal ones by means of characteristics of MUP used in macro EMG. To discriminate reinnervated MUs non-invasively, the MUP amplitude should be normalized in respect of the MU-electrode distance or other MUP characteristics (independent of MU-electrode distance and sensitive to reinnervation) should be used.

The presence of unknown layer of skin and fat is an obstacle to a correct estimation of the motor unit size from surface detected potentials.

To overcome problems with a strong distance-dependence of the motor unit potentials (MUPs), different methods to estimate the MU location and size have been proposed. Distance-independence of the exponent of the power function, that describes the MUP distance decline, and homogeneity of the volume conductor, are assumed in all methods. Some of them consider the exponent value as unique, irrespective of persons, muscles and their functional state. One method estimates the current exponent value. We evaluate this method by computer simulation of MUPs in infinite and semi-infinite volume conductor. Our results show that although the first assumption is not fulfilled, it does not affect considerably the estimate of the MU location and size obtained for infinite or semi-infinite homogeneous volume conductor. The errors of the MU location can be insignificant even in inhomogeneous volume conductor with a layer of lower conductivity (skin and fat) between the muscle tissue and electrode. The accurate location of the MU electrical axis is, however, not a sufficient condition for a correct MU size estimation that depends considerably on actual parameters of the layer. Thus, the surface EMG could hardly be considered as non-invasive alternative to macro EMG for detection of the enlarged MUs.

Effect of parameters altering with muscle fibre functional state on power spectra of spatially filtered extracellular potentials.

We aimed to analyse the effect of parameters altered with muscle fibre functional state on power spectra (PS) and spectral characteristics of the signals detected from skeletal muscle fibres of finite length by bipolar or one-dimensional multi-electrodes oriented in parallel to the muscle fibres. The PS were calculated as the product of the power spectrum of the input signal (the first temporal derivative of the intracellular action potential (IAP)) and spatially filtered impulse response. A multi-electrode with an even number of poles, located above the end-plate or fibre end, reduces the effect of alterations in the propagation velocity and increases that of the IAP duration and after-potentials. Detection of the signals far from the end-plate and fibre ends reduces the effect of the IAP spike duration and increases that of the propagation velocity. Increasing the number of poles reduces the effect of after-potentials. A proper multi-electrode arrangement and position could help to separate and assess the relative alteration of individual parameters.

Calculation of spatially filtered signals produced by a motor unit comprising muscle fibres with non-uniform propagation.

Simulation of actual muscle potentials is necessary to understand processes that underlie changes in electromyographic signals. The work reported aims to analyse existing methods and suggest new ways of calculating precisely the signals (MUS) detected by a multielectrode from motor units (MUs) consisting of homogeneous or inhomogeneous (functionally and geometrically) fibres. Simulation (based on cable equations) of intracellular action potential (IAP) in a muscle fibre with a moderate geometrical inhomogeneity demonstrates that considerable changes in propagation velocity (more than 3.5 times) are accompanied by insignificant changes in the IAP amplitude (< 5%) and IAP shape in the temporal domain. MUS can therefore be considered as the output signal of a timeshift-invariant system whose input signal is the first temporal derivative of the IAP. As a result, calculation of MUS is reduced to a single convolution in the case of muscle composed of both homogeneous and inhomogeneous fibres. The suggested approach is valid for simulation of recordings obtained with points or rectangular plates leading off surfaces from muscles consisting of fibres that are parallel or inclined to the skin surface. The MUS terminal phases are prolonged because of fibre inhomogeneities. The presence of geometrical inhomogeneities results in additional positive-negative phases in MUS.

Calculation of extracellular potentials produced by an inclined muscle fibre at a rectangular plate electrode.

Generally the anatomy of muscles is rather complex, and the fibres have various inclination angles within the muscles. We suggest a fast and reliable way to calculate extracellular potentials produced at a point or rectangular plate electrode by a muscle fibre of finite length with an arbitrary inclination. A muscle fibre was considered to be a linear timeshift-invariant system of potential generation. Then, similar to the fibre without inclination, the extracellular potential produced by an inclined fibre was represented as the output signal of the system; it was calculated as the convolution of the input signal and impulse response. Irrespective of the inclination, the input signal of the system was the first temporal derivative of the intracellular action potential. The impulse response of the system differed for the fibres with inclination. This required a new method of analytical integration over the rectangular electrode area. The approach provides a chance to simulate and analyze motor unit potentials or F-, H- or M-responses produced by muscles of complicated anatomy (circum-pennate or complex pennate type) at electrodes of actual size and location in normals and patients with neuro-muscular disorders.

Effect of electrode dimensions on motor unit potentials.

Different effects of longitudinal and transversal electrode dimensions on nerve or muscle single fibre action potentials detected monopolarly, were reported in the literature. The results were contradictory. We studied motor unit potentials (MUPs) detected at a large distance (typical of surface recording) on the basis of a mathematical model without source simplification. The MUPs were calculated as a single convolution of the first temporal derivative of a realistic intracellular action potential and MU impulse response. The spatial averaging of the MUPs by rectangular plate electrodes was performed through analytical integration of the MU impulse response over the electrode area. The effects of longitudinal dimension of the electrode were stronger than those of a transversal one. The effects were distance dependent. The longitudinal dimension of the electrode influenced the main phases (that reflected the excitation origin and propagation) more than the terminal phases (that reflected the excitation extinction at the muscle fibers' ends). This was due to differences in the character of the potential fields (quadrupole or dipole) during generation of individual MUP phases. It was shown that the relative weight of the individual MUP phases could be stressed or suppressed by a proper choice of electrode dimensions, position and orientation.