Computer simulation study of the shape of motor unit action potential

Motor unit action potentials (MUAPs) of brachial biceps were simulated. A simulated MUAP was obtained as a sum of single fibre action potentials (SFAPs) from all the muscle fibres of a motor unit (MU). The influence of the following factors on MUAP shape for different kinds of recording electrode was studied: fibre density, neuromuscular jitter, temporal dispersion and electrode displacements. The simulation confirms that typical MUAPs recorded with needle electrodes from muscles of low fibre density such as brachial biceps are usually triphasic. Increased fibre density produces MUAPs of more complex shape and higher amplitude. Normal neuromuscular jitter is responsible for the variability of shape of subsequent potentials from the same MU as well as for electromyographic shimmer. Pathologic (increased) jitter makes the shapes of subsequent potentials unrecognizable. The influence of temporal dispersion is interconnected with other factors but rather of minor importance. The simulation shows how big changes in MUAP shape can be expected due to electrode displacements during single experiment or during estimation of MU territory.     

Detection of motor unit action potentials with surface electrodes: influence of electrode size and spacing

A model of the motor unit action potential was developed to investigate the amplitude and frequency spectrum contributions of motor units, located at various depths within muscle, to the surface detected electromyographic (EMG) signal. A dipole representation of the transmembrane current in a three-dimensional muscle volume was used to estimate detected individual muscle fiber action potentials. The effects of anisotropic muscle conductance, innervation zone location, propagation velocity, fiber length, electrode area, and electrode configuration were included in the fiber action potential model. A motor unit action potential was assumed to be the sum of the individual muscle fiber action potentials. A computational procedure, based on the notion of isopotential layers, was developed which substantially reduced the calculation time required to estimate motor unit action potentials. The simulations indicated that: 1) only those motor units with muscle fibers located within 10–12 mm of the electrodes would contribute significant signal energy to the surface EMG, 2) variation in surface area of electrodes has little effect on the detection depth of motor unit action potentials, 3) increased interelectrode spacing moderately increases detection depth, and 4) the frequency content of action potentials decreases steeply with increased electrode-motor unit territory distance.     

End plate spikes in the human electromyogram. Revision of the fusimotor theory.

'End plate spike' (EPS) is a spontaneous action potential of a normal striated muscle. EPSs are found in local 'active spots' of the muscle. The prevailing hypothesis about the origin of EPSs states that when a needle electrode affects a motor nerve branch near the neuromuscular junction at the end plate zone, an increased leakage of acetylcholine to the synaptic cleft ensues. This elicits postsynaptic action potentials of the muscle fibre which can be recorded as EPSs with the same needle electrode. Thus EPSs are thought to be caused by needle injury or irritation of the motor axon. We suggest that EPSs are action potentials of intrafusal muscle fibres and that 'active spots' are in fact muscle spindles. Waveform analysis reveals three types of EPSs: small EPSs, not propagated outside the active spot either: i) with negative onset; or ii) with short positive initial deflection; and iii) large EPSs resembling propagated motor unit potentials (MUPs) but with a typical EPS firing pattern, distinctly different from that of the MUPs. Study of EPS activation in different manoeuvres associates small EPSs with intrafusal gamma motor units and large MUP-like EPSs with beta motor units.     

Spatial analysis of motor unit potentials of the rat medial gastrocnemius

The spatial analysis of the potentials of single motor units of the rat medial gastrocnemius muscle evoked by stimulation of the fibres of split ventral roots was carried out with a bipolar electrode moving in the direction perpendicular to the longitudinal axis of the muscle fibres. During this movement of the electrode a variability was observed in the time of the biphasic potential from its maximum to minimum, and in the peak-to-peak amplitude of these potentials. The potentials recorded outside the territory of the motor unit had a lower amplitude in relation to the potentials from the territory of the unit. This made localization of the motor unit on the cross-section of the muscle possible. Differences in the duration of the potential from maximal to minimal amplitude (maximum-minimum amplitude time--M-MAT) of each investigated motor unit from successive recording sites reflected the number of fibres contributing to the action potential and the distance of the recording surface of the electrode from the zone of the motor end-plates of this motor unit. The greatest diameter of the territory of the observed motor units reached 2.5 mm.     

Some properties of motor unit action potential trains recorded during constant force isometric contractions in man

A specially designed needle electrode was used to record motor unit action potentials for the complete time duration of constant force isometric contractions varying in discrete steps from minimum to maximum force levels. A total of 70 motor unit action potential trains were recorded and analyzed.Several properties of the motor unit action potentials were observed. The inter-pulse intervals between adjacent motor unit action potentials of a particular motor unit action potential train were measured and subsequently analyzed as a real continuous random variable. The distribution of the values of the inter-pulse intervals was described by the Weibull probability distribution function with time and force dependent parameters. Furthermore the Survivor function and the Hazard function of the Weibull probability distribution function described certain characteristics of the motor unit firing intervals. Most important of all, it became possible to derive an equation that would generate a real continuous random variable whose properties would be identical to those of the inter-pulse intervals.     

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.     

Neuromuscular adjustments that constrain submaximal EMG amplitude at task failure of sustained isometric contractions

The amplitude of the surface EMG does not reach the level achieved during a maximal voluntary contraction force at the end of a sustained, submaximal contraction, despite near-maximal levels of voluntary effort. The depression of EMG amplitude may be explained by several neural and muscular adjustments during fatiguing contractions, including decreased net neural drive to the muscle, changes in the shape of the motor unit action potentials, and EMG amplitude cancellation. The changes in these parameters for the entire motor unit pool, however, cannot be measured experimentally. The present study used a computational model to simulate the adjustments during sustained isometric contractions and thereby determine the relative importance of these factors in explaining the submaximal levels of EMG amplitude at task failure. The simulation results indicated that the amount of amplitude cancellation in the simulated EMG (～ 40%) exhibited a negligible change during the fatiguing contractions. Instead, the main determinant of the submaximal EMG amplitude at task failure was a decrease in muscle activation (number of muscle fiber action potentials), due to a reduction in the net synaptic input to motor neurons, with a lesser contribution from changes in the shape of the motor unit action potentials. Despite the association between the submaximal EMG amplitude and reduced muscle activation, the deficit in EMG amplitude at task failure was not consistently associated with the decrease in neural drive (number of motor unit action potentials) to the muscle. This indicates that the EMG amplitude cannot be used as an index of neural drive.     

Comparative analysis of motor unit action potentials of the medial gastrocnemius muscle in cats and rats

Properties of motor unit action potentials (MUAPs) were compared for medial gastrocnemius (MG) motor units (MUs) in cats and rats. The experiments on functionally isolated MUs were performed under general anaesthesia, under comparable conditions (surgery, stimulating protocol and recording methods) for both species investigated. The proportions of motor units and contractile properties of the sample used in the study were consistent with previous studies performed on the MG muscle in both animal species, so comparisons of action potentials of individual types of MUs were acknowledged as fully reliable. The most prominent differences concerning MUAPs were observed in total duration and peak-to-peak times which for all MU types were about twice longer in cat MUs, in comparison to the rat MUs. The considerable disproportions were observed between the MUAP amplitudes of FF (fast fatigable), FR (fast resistant to fatigue) and S (slow) MUs in each species (the highest amplitudes were measured for FF and the lowest for S MUs), but there were no significant differences between cat and rat when respective types of MUs were compared. The shapes of MUAPs were commonly characterized by biphasic waveforms composed of two or three turns in all types of units, and no interspecies differences were revealed. Several factors influencing MUAP parameters were discussed indicating most of all importance of variable length of cat and rat muscle fibres and ambiguous influence of motor unit size, thickness of muscle fibres and their density around the recording electrode in the MG muscle of both species.     

Spectral and time domain characteristics of single muscle fibre action potentials during continuous activity extracted from model considerations

A model of the muscle fibre extracellular action potentials (ECAPs) calculation using experimentally recorded intracellular action potentials (ICAPs) has been applied to investigate the effect of repetitive stimulation on the electrical activity of isolated frog muscle fibres. The ECAPs were calculated both at small (0.01 mm) and at large (5 mm) radial distances to the fibre axis, and their relationship with the original ICAP parameters has been inferred. Fourier transformation of the calculated ECAPs in order to obtain the spectral characteristics and to trace out their behaviour during continuous fibre activity was performed. Stimulation frequency dependence on the ECAP time characteristics and on the shift of the maximum spectral density towards low frequencies at small and large radial distance were observed. The spectral density peak frequency is propagation velocity (PV)-dependent. The advantage of the presented method over the available experimental extracellular recording techniques from isolated muscle fibers is the possibility to show the effect of continuous muscle fibre activity on the parameters of the ECAPs and their spectral characteristics at large radial distance, which is not experimentally accessible. Our results are in agreement with those experimentally obtained. The results from the model prove the role of changes in PV of excitation along the muscle fibres (representing the last link in the complex organized motor system) in the development of fatigue. Received: 24 July 1997 / Accepted in revised form: 2 July 1998     

Extracellular potentials of single active muscle fibres: Effects of finite fibre length

The extracellular action potentials (ECAPs) of single active muscle fibres immersed an isotropic volume conductor were investigated. The origination of excitation in the motor end-plate and its reaching the fibre end were taken into consideration. It was explained why at short radial distances the ECAPs over the fibre at points close to the end were similar in shape to the first time derivative and at points close to the motor end-plate-to the first time derivative of the intracellular action potential (ICAP) taken with minus sign. The fibre end changed the ECAP which would be recorded if the fibre was infinite and this change called pure termination potential (PTP) was a biphase positive-negative potential, proportional to the first time derivative of the ICAP at points close to the membrane and over the very end. With increasing the radial and axial distances PTP decreases in amplitude. Taking into account the PTP, the genesis of the terminal positive phase of the ECAPs (Gydikov and Kosarov 1972a, b) can be explained. The onset of the fibre or the motor end-plate also changed the potential which would be recorded if the fibre was infinite. This change was given the term of pure onset potential (POP)-a biphase negative-positive potential, proportional to the first time derivative of the ICAP taken with minus sign at a point close to the membrane and over the motor end-plate. With increasing the radial and the axial distance POP decreased in amplitude.Close to the membrane PTP and POP were commensurable with the potential of an infinite fibre only at points close to the ends or to the motor end-plate. At long radial distances they were commensurable with the potential of an infinite fibre for all axial distances.     

The size index as a motor unit identifier in electromyography examined by numerical calculation.

A computer simulation was performed to investigate the size index as a motor unit identifier in electromyography. The size index calculated from the amplitude and area of the simulated motor unit action potential (MUP) was plotted against the distance between the needle electrode and current source to show how the index changes as a function of the distance. The index of the MUP also was plotted against the number of muscle fibers belonging to a single motor unit, the size of the motor unit territory, and the diameter of the muscle fibers in order to establish the major determinants of the index. The index was relatively constant for the distance less than 2 mm between the needle electrode and closest edge of the current source. It changed logarithmically with the number of muscle fibers and with the diameter of the fibers.     

Estimation of monopolar signals from sphincter muscles and removal of common mode interference

The detection of surface electromyogram (EMG) by multi-electrode systems is applied in many research studies. The signal is usually recorded by means of spatial filters (linear combination of the potential under at least two electrodes) with vanishing sum of weights. Nevertheless, more information could be extracted from monopolar signals measured with respect to a reference electrode away from the muscle. Under certain conditions, surface EMG signal along a curve parallel to the fibre path has zero mean (property approximately satisfied when EMG is sampled by an array of electrodes that covers the entire support of the signal in space). This property allows estimating monopolar from single differential (SD) signals by pseudoinversion of the matrix relating monopolar to SD signals. The method applies to EMG signals from the external anal sphincter muscle, recorded using a specific cylindrical probe with an array of electrodes located along the circular path of the fibres. The performance of the algorithm for the estimation of monopolar from SD signals is tested on simulated signals. The estimation error of monopolar signals decreases by increasing the number of channels. Using at least 12 electrodes, the estimation error is negligible. The method applies to single fibre action potentials, single motor unit action potentials, and interference signals.The same method can also be applied to reduce common mode interference from SD signals from muscles with rectilinear fibres. In this case, the last SD channel defined as the difference between the potentials of the last and the first electrodes must be recorded, so that the sum of all the SD signals vanishes. The SD signals estimated from the double differential signals by pseudoinvertion are free of common mode.     

Branched EMG electrodes for stable and selective recording of single motor unit potentials in humans.

Branched surface EMG electrodes are bipolar electrodes with the hot signal pole referenced to two or more short-circuited leading-off surfaces. This technique provides stable recording of single motor unit potentials during real movements, up to maximal muscle contractions. The selective characteristic of branched electrodes is based on the same principles as the double differential detection system and spatial filtering technique proposed later. Equi-weight calculations to assess the selectivity of different electrode types and their position are used. The main advantage of branched electrodes, especially high stability, is achieved by the wire electrode version. The design, manufacture, implementation, and application of wire electrodes are discussed in detail. During recording of motor unit potentials, electrodes are positioned subcutaneously over the muscle fascia. This positioning maximizes electrode stability. Appropriate orientation of the electrode relative to the muscle architecture ensures adequate selectivity for single motor unit recordings. Branched electrodes require ordinary EMG equipment (two or even one amplifier).     

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.     

Influence of timing variability between motor unit potentials on M-wave characteristics

The transient enlargement of the compound muscle action potential (M wave) after a conditioning contraction is referred to as potentiation. It has been recently shown that the potentiation of the first and second phases of a monopolar M wave differed drastically; namely, the first phase remained largely unchanged, whereas the second phase underwent a marked enlargement and shortening. This dissimilar potentiation of the first and second phases has been suggested to be attributed to a transient increase in conduction velocity after the contraction. Here, we present a series of simulations to test if changes in the timing variability between motor unit potentials (MUPs) can be responsible for the unequal potentiation (and shortening) of the first and the second M-wave phases. We found that an increase in the mean motor unit conduction velocity resulted in a marked enlargement and narrowing of both the first and second M-wave phases. The enlargement of the first phase caused by a global increase in motor unit conduction velocities was apparent even for the electrode located over the innervation zone and became more pronounced with increasing distance to the innervation zone, whereas the potentiation of the second phase was largely independent of electrode position. Our simulations indicate that it is unlikely that an increase in motor unit conduction velocities (accompanied or not by changes in their distribution) could account for the experimental observation that only the second phase of a monopolar M wave, but not the first, is enlarged after a brief contraction. However, the combination of an increase in the motor unit conduction velocities and a spreading of the motor unit activation times could potentially explain the asymmetric potentiation of the M-wave phases.     

Influence of amplitude cancellation on the simulated surface electromyogram.

The purpose of the study was to quantify the influence of selected motor unit properties and patterns of activity on amplitude cancellation in the simulated surface electromyogram (EMG). The study involved computer simulations of a motor unit population with physiologically defined recruitment and rate coding characteristics that activated muscle fibers whose potentials were recorded on the skin over the muscle. Amplitude cancellation was quantified as the percent difference in signal amplitude when motor unit potentials were summed before and after rectification. The simulations involved varying the level of activation for the motor unit population, the recording configuration, the upper limit of motor unit recruitment, peak discharge rates, the amount of motor unit synchronization, muscle fiber length, the thickness of the subcutaneous tissue, and the motor unit properties that change with advancing age. The results confirmed a previous experimental report (Day SJ and Hulliger M, J Neurophysiol 86: 2144-2158, 2001) that amplitude cancellation in the surface EMG can reach 62% at maximal activation. A decrease in the range of amplitudes of the motor unit potentials, as can occur during fatiguing contractions, increased amplitude cancellation up to approximately 85%. Differences in the amount of amplitude cancellation were observed across all simulated conditions, and resulted in substantial changes in the absolute magnitude of the EMG signal. The most profound factors influencing amplitude cancellation were the number of active motor units and the duration of the action potentials. The effects of amplitude cancellation were minimal (<5%) when the EMG amplitude was normalized to maximal values, with the exception of variations in peak discharge rate and recruitment range, which resulted in differences up to 17% in the normalized EMG signal across conditions. These results indicate the amount of amplitude cancellation that can occur in various experimental conditions and its influence on absolute and relative measures of EMG amplitude.     

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.     

Separation of propagating and non propagating components in surface EMG

Surface electromyogram (EMG) detected by electrode arrays along the muscle fibre direction can be approximated by the sum of propagating and non propagating components. A technique to separate propagating and non propagating components in surface EMG signals is developed. The first step is an adaptive filter, which allows obtaining an estimation of the delay between signals detected at different channels and a first estimate of propagating and non propagating components; the second step is used to optimise the estimation of the two components. The method is applicable to signals with one propagating and one non propagating component. It was optimised on simulated signals, and then applied to single motor unit action potentials (MUAP) and to electrically elicited EMG (M-waves).

The new method was first tested on phenomenological signals constituted by the sum of a propagating and a non propagating signal and then applied to simulated and experimental EMG signals. Simulated signals were generated by a cylindrical, layered volume conductor model. Experimental signals were monopolar surface EMG signals collected from the abductor pollicis brevis muscle and M-waves recorded during transcutaneous electrical stimulation of the biceps muscle. The technique may find different applications: in single motor unit (MU) studies (a) for decreasing the variability and bias of CV estimates due to the presence of the non propagating components, (b) for estimating automatically the length of the muscle fibres from only three detected channels and (c) for removal of the stimulation artifact M-waves.