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.

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.

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.

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.

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.

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.

Effect of recording electrode position along a muscle fibre on surface potential power spectrum.

Extracellular action potentials produced by a muscle fibre of finite length were calculated for recordings at the skin surface. The sensitivity of power spectra to variations in propagation velocity (ν) and intracellular action potential (IAP) duration (T(in)) was studied theoretically. The magnitude and distribution of the spectral power of muscle fibre potentials depend on the electrode longitudinal position. The relative shifts of the spectra in dB induced by variation in ν or T(in) hardly depend on the longitudinal position of the electrode. A variation in ν affects only the power spectrum positive slope and the initial part of the high-frequency roll-off and a variation in T(in) affects only the remaining part of the high-frequency roll-off. The total spectral amplitude is practically non-sensitive to variations in the wavelength, b = ν.T(in). The total power is sensitive to variations in ν, T(in) as well as in b, and its relative changes depend on the electrode longitudinal position. The whole power spectrum is shifted along the frequency axis and mode (F(max)), median (F(med)) and mean (F(mean)) frequencies have practically equal percentage changes only when ν and T(in) vary jointly in such a way that the product ν.T(in) keeps unchanged.

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.

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.

Use of surface potential spectral characteristics for solving the inverse problem in electroneurography.

The changes in the power spectra of single-fibre extracellular action potentials (SFEAPs) generated in an infinite anisotropic frequency-dependent volume conductor, which occurred as a result of alterations in the propagation velocity v and duration T(in) of the intracellular action potential (IAP) were analytically determined. Effects of the temporal and spatial dispersions of almost synchronously activated fibres on the power spectrum of compound extracellular potentials (CEPs) were analysed for different shapes and sizes of the activated fibres' territory. It was found that, as a result of desynchronisation in the fibres' activation, dips existed in the CEP power spectra and that the frequencies of the dips depended on the degree of desynchronisation but did not depend on the velocity. It was shown that the hypothetical power spectrum of compound IAP was sensitive to the variations in the desynchronisation in the fibres' activation and in the risetime and duration of IAP even at a great fibre electrode distance typical for surface recordings.

Radial changes of extracellular potential amplitude and integral characteristics and the inverse problem in electroneurography.

The possibility of solving the inverse problem in electroneurography, i.e. of estimating the main parameters specifying the activated fibre's functional state, using the amplitude and integral characteristics of the surface potentials generated by infinite homogeneous fibres, has been analysed. An analytical expression has been found for the amplitude of the negative phase Anph of the single fibre extracellular action potential (SFEAP) as a function of the wavelength b, the fibre-electrode distance y and a scale factor Ao proportional to the intracellular action potential amplitude Vm, to the square of the fibre radius a and to the ratio of the axoplasm conductivity sigma a and volume conductor conductivity sigma e. For a large fibre-electrode distance, typical of surface recordings, an analytical expression of the integral of the negative phase Inph of the SFEAP as a function of Ao, b, y and the propagation velocity v was also found. Simple methods are proposed for estimating v, the location of the electrical centre of the activated fibres' territory and the product of the number of activated fibres N, duration T(in) of the intracellular action potential and of the factor Ao. The estimation errors due to the temporal and spatial dispersion of the activated fibres were analysed as a function of the fibre-electrode distance and the territory shape.

Power spectra of extracellular potentials generated by an infinite, homogeneous excitable fibre.

The power spectra of the extracellular potentials (EPs) generated under activation of an infinite, homogeneous excitable fibre immersed into an infinite, resistive, isotropic and homogeneous volume conductor are theoretically analysed. The changes in the power spectrum related to the changes in the propagation velocity v, amplitudes Vm and duration Tin of the intracellular action potential (IAP) are analytically determined. It is found that in the ultra-low-frequency region the EP spectral power follows the course of alteration in the square of the modified Bessel function of the second kind and order zero multiplied by the fourth power of the frequency, and the Tin can be assessed by the deviation of the EP power spectrum from this function. It is shown why the sensitivity of the spectral characteristics depends substantially on the radial distance yo from the activated fibre to the point of observation; why the total spectral amplitude depends directly on the IAP wavelength but the total spectral power depends on the IAP wavelength as well as on its duration and propagation velocity; and why the EPs are not proportional to the IAP second spatial derivative even in close proximity to the fibre.

Power spectra of single infinite fibre extracellular potentials recorded by a bipolar electrode.

The power spectra of bipolarly recorded extracellular action potentials (EAPs) generated by an infinite, homogeneous, excitable fibre in an infinite, resistive, isotropic and homogeneous volume conductor were theoretically analysed. The changes in the power spectrum of EAP, which occurred as a result of alterations in the propagation velocity v and duration Tin of the intracellular action potential IAP, were analytically determined for bipolar parallel and radial electrodes with a small interpole distance. It was found that the sensitivity of the spectral characteristics to alterations in v, Tin and/or the IAP asymmetry substantially depends on the fibre-electrode distance; information on the IAP fast changes, that seems to be lost in unipolar recording as a result of the filtering effect of the fibre-electrode distance, can be restored. The orientation of the recording electrode need not be taken into account when a qualitative analysis is carried out, but when a quantitative analysis has to be performed, then the electrode orientation has a significant influence. A method is suggested for determination of the fibres' orientation by means of the spectrum of EAPs recorded bipolarly. The selectivity of the bipolar electrodes is analysed.

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.

Fundamentals of power spectra of extracellular potentials produced by a skeletal muscle fibre of finite length. Part II: Effect of parameters altering with functional state.

The reasons for dependence of the power spectra of extracellular potentials (EPs) produced by a skeletal muscle fibre of finite length, on parameters altering with functional state was analysed. The sensitivity of the EP power spectra to alterations in the parameters depends on the distance of the observation point from the fibre. At large distances the sensitivity can change with longitudinal position as well. The differences in the sensitivity are due to the changes in the inter-relations between the power spectra of the input signal (the first temporal derivative of the intracellular action potential) and of the impulse response (IR) of the fibre of finite length as a linear system of EP generation. It was shown that not only the parameters affecting the IR (propagation velocity of the waves of depolarisation), but also the parameters determining the input signal (intracellular action potential duration and after-potential) can affect the characteristic frequencies of the EP power spectra.

Fundamentals of power spectra of extracellular potentials produced by a skeletal muscle fibre of finite length. Part I: Effect of fibre anatomy.

To provide a thorough understanding of the changes in the power spectrum of electromyographic (EMG) signals, the formation of the power spectrum (PS) of extracellular potentials (EPs) produced by a skeletal muscle fibre of finite length was analysed. It was shown that, as in the case of an infinite fibre, the PS could be represented as the product of power spectra of the input signal (the first temporal derivative of the intracellular action potential, IAP) and of the impulse response (IR) of the fibre of finite length as a system of EP generation. The interrelations between the two multipliers determine the sensitivity of the EP power spectrum to alterations in parameters. The anatomical parameters of the fibre (length, depth, position of the end-plate in respect of the fibre ends) affect the EP power spectrum through IR power spectrum. Variations of the EP characteristic frequencies along the fibre length as well as oscillations in the PS are intrinsic properties of the fibre of finite length.