Experimental Simulation of Cat Electromyogram: Evidence for Algebraic Summation of Motor-Unit Action-Potential Trains

Scott J. Day1,2 and Manuel Hulliger1

 1Department of Clinical Neurosciences, Faculty of Medicine, University of Calgary, Calgary, Alberta T2N 4N1, Canada; and  2Center for Musculoskeletal Research, National Institute for Working Life, S907 13 Umeå, Sweden


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Day, Scott J. and Manuel Hulliger. Experimental Simulation of Cat Electromyogram: Evidence for Algebraic Summation of Motor-Unit Action-Potential Trains. J. Neurophysiol. 86: 2144-2158, 2001. Prompted by the observation that the slope of the relationship between average rectified electromyography (EMG) and the ensemble activation rate of a pool of motor units progressively decreased (showing a downward nonlinearity), an experimental study was carried out to test the widely held notion that the EMG is the simple algebraic sum of motor-unit action-potential trains. The experiments were performed on the cat soleus muscle under isometric conditions, using electrical stimulation of alpha -motor axons isolated in ventral root filaments. The EMG signals were simulated experimentally under conditions where the activation of nearly the entire pool of motor units or of subsets of motor units was completely controlled by the experimenter. Sets of individual motor units or of small groups of motor units were stimulated independently, using stimulation profiles that were strictly repeatable between trials. This permitted a rigorous quantitative comparison of EMGs that were recorded during combined activation of multiple motor filaments with EMGs that were synthesized from the algebraic summation of motor unit action potential trains generated by individual nerve filaments. These were recorded separately by individually stimulating the same filaments with the same activation profiles that were employed during combined stimulation. During combined activation of up to 10 motor filaments, experimentally recorded and computationally synthesized EMGs were virtually identical. This indicates that EMG signals indeed are the outcome of the simple algebraic summation of motor-unit action-potential trains generated by concurrently active motor units. For both recorded and synthesized EMGs, it was confirmed that EMG magnitude increased nonlinearly with the ensemble activation rate of a pool of motor units. The nonlinearity was largely abolished when EMG magnitude was estimated as the sum of rectified, instead of raw, motor-unit action-potential trains. This suggests that the downward nonlinearity in the EMG-ensemble activation rate relation is due to signal cancellation arising from the perfectly linear summation of positive and negative components of action-potential waveforms. The findings provide a much needed post hoc validation of the concept of EMG generation by strict algebraic summation of motor unit action potentials that is generally relied on in theoretical modeling studies of EMG and in EMG decomposition algorithms.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The electromyogram (EMG) is a complex signal that is thought to result from the summation of trains of action potentials generated by active motor units (MUs) in the vicinity of the recording electrode. It is generally assumed that summation is linear, but this has never been directly demonstrated. The issue is relevant because linear (or algebraic) summation of motor-unit action-potential trains (MUAPs) underlies a number of widely used signal processing techniques, for instance when extracting single MUAPs from whole-muscle EMG using spike- or stimulus-triggered averaging (Cheney and Fetz 1985; Fetz and Cheney 1980; Fortier 1994; Milner-Brown et al. 1973b), when decomposing multi-unit EMG into constituent MUAP trains using template matching techniques (Guiheneuc et al. 1983, 1989; LeFever and De Luca 1982; Mambrito and De Luca 1984; McGill et al. 1985; ), or when analyzing signal properties in computer simulations or mathematical models of EMG (Day et al. 1996; Fuglevand et al. 1993; Libkind 1968, 1969; Milner-Brown and Stein 1975; Person and Libkind 1970; Yao et al. 2000).

In a previous study, we recorded the EMG evoked by electrical stimulation of MUs in ventral root filaments. The relationship between the ensemble activity in motor axons (simulated peripheral motor drive) and the magnitude of EMG could be analyzed because the firing rates of all MUs were known. EMG magnitude (e.g., average rectified EMG, AEMG) increased nonlinearly with ensemble activation rate (EAR), with the slope of the relationship progressively decreasing with EAR (Hulliger et al. 2001). This nonlinearity could be due to at least two separate mechanisms: first, it might be a manifestation of signal cancellation arising from increased probability of MUAP overlap as the ensemble activation rate increased; second, it might arise from a progressive decrease in muscle electrical impedance because the proportion of muscle fibers undergoing temporary reduction of membrane impedance during action-potential transients would increase as the activation of the pool of MUs increased. The second possibility is addressed in more detail in a separate paper where it is shown that alterations in membrane impedance apparently do not influence MUAP train summation. In contrast, considering the numbers and mean discharge rates of MUs active during a voluntary contraction and the average duration of MUAPs (5-10 ms), the incidence of overlaps of MUAPs was bound to increase significantly, even in the absence of synchronization.

Is the extent of signal cancellation sufficient to account exclusively for the nonlinearity of the AEMG-EAR relation and, as a corollary, does this occur as a result of strict algebraic summation of MUAP trains. To address these questions, an experimental simulation technique was used that permitted the controlled and parallel activation of single MUs and groups of MUs (multi-motor units, MMUs) in independent stimulation channels. The pulse trains of individual stimulation profiles were stored digitally and could be reproduced repeatedly and identically. Thus the contribution of individual MUs to EMG signals that were recorded during the concurrent activation of several MUs could be assessed independently when they were activated individually. Therefore a strict quantitative comparison between two types of MMU EMG signals could be made: one that was generated and recorded during combined activation of a number of MUs and one that was synthesized by algebraic summation of the MUAP trains evoked when each of the MUs was activated separately.

The results clearly demonstrate that the electromyographic interference signal is indeed the result of strict algebraic summation of individual MUAP trains and that the nonlinear relationship between EMG magnitude and EAR of the MU pool is almost exclusively due to signal cancellation.

A preliminary account of selected aspects of this study has been published previously (Hulliger et al. 1995).


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Animals and preparation

An acute soleus nerve-muscle preparation, as fully described elsewhere (Hulliger et al. 2001), was used in 14 cats deeply anesthetized with pentobarbitone (initial dose: 40 mg/kg). The hind limb was completely denervated except for the soleus muscle. The distal 2 cm of the soleus nerve was dissected and carefully freed from connective tissue to permit sensitive neurogram recording for MU identification. The muscle was exposed by removing both heads of the gastrocnemius and freeing it from the plantaris muscle. The fine fascia surrounding the soleus muscle was resected to fully expose the posterior surface of the muscle belly and its tendon. The calcaneus was cut distal to the tendon insertion and used to anchor the tendon to the force transducer of an electromagnetic stretching device. After dissection, the hip, knee, and ankle were rigidly fixed to a stereotactic frame using steel pins.

Following lumbo-sacral laminectomy the ventral roots (L5-S3) were exposed and cut. The roots containing motor axons to the soleus muscle (typically L7, S1) were divided into smaller filaments, with the goal of isolating either small groups of MUs (MMU) or single MUs. Particular care was taken to establish the single-unit nature of putative single MU filaments. A filament was accepted as containing a functionally single motor axon only if four independent criteria of singleness were satisfied: at threshold of activation by electrical stimulation at 30/s all-or none force steps, all-or-none surface EMG potentials, all-or-none intramuscular EMG potentials, and all-or-none neurogram potentials (recorded from the distal muscle nerve) had to be observed. MMU filaments were divided and/or recombined until 10 filaments were prepared; this generated between 6 and 15% of whole muscle force (as observed on tetanic muscle nerve stimulation). For different 10 filament sets, there was some variation in the largest/smallest filament ratio (between 1.5 and 2.5).

Up to 10 filaments of the same type (either all MMU or all single MU) were selected for experimental trials, rank-ordered inversely according to size (tetanic force) and mounted on separate stimulating electrodes. The electrodes were organized on one of two multi-channel arrays (see Hulliger et al. 2001). For all trials, the muscle was moderately stretched and kept at a fixed length, corresponding to an in-vivo ankle joint angle of 90°. Between trials the muscle was allowed to shorten by 5 mm to minimize interference with circulation.

The aim of the study was the quantitative comparison of EMGs that were generated by combined stimulation of several motor filaments with EMGs that were synthesized from individual filament contributions. Therefore it was crucial that filament properties remained stable. Stability was monitored at regular intervals (typically 30 min) by measuring the tetanic forces elicited by stimulation of each filament at 30/s. Stability of sets of filaments was assessed at similar intervals by measuring tetanic forces during combined activation, using a standard multi-channel stimulation protocol. The absence of cross talk between neighboring filaments was verified in tests with staggered activation of each filament of a set at 30/s, the criterion being a staircase force profile, in which the number of steps equaled the number of stimulated filaments. Forces were measured with customized force transducers with a resolution of 5 mN (see Hulliger et al. 2001). If force estimates differed by more than 5% from the initial measurements, filaments or sets of filaments were discarded. Moreover, stability was reassessed off-line, mainly by quantitative analysis of EMG signals during repeated single- and multi-filament stimulation trials (see RESULTS).

Stimulation

Up to 10 ventral root filaments were stimulated independently, individually, or in combination, using 10 separate voltage-controlled isolated stimulators. These were operated by software-generated transistor-transistor logic (TTL) pulse trains, representing filament-specific activation profiles (see following text). The number of filaments stimulated in a given trial was determined by the experimental design and ranged between 1 and 10. In trials where several filaments were stimulated together, the smallest filament (MMU or MU) was recruited first and the largest filament last, broadly imitating orderly recruitment according to size (Henneman and Mendell 1981; Henneman et al. 1965).

Multi-channel activation encompassed stationary and transient stimulation designs. Both were used for the MMU studies, while single MU studies were restricted to transient activation designs. The stationary design featured, in successive brief trials, the stimulation of increasing numbers (up to 10) of MMU filaments at increasing mean rates. For each trial, individual filaments were activated at a fixed mean stimulation rate (see Fig. 1, A1 and B1, and Experimental protocols). Stimulation commenced 1-2 s before 2 s of data recording (see following text). In the transient activation design, the number of filaments activated increased within each trial over an 8-s period (recruitment; see Fig. 1A2), with or without an additional progressive increase in the rate of stimulation (rate modulation; see Fig. 1B2). Therefore to vary the amount of isometric force over the entire range that could be generated by a given set of filaments, only a single trial was required for the transient activation design. In contrast, in the stationary design multiple 2-s trials were necessary to study a range of activation levels.



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Fig. 1. Schematic illustration of the stimulation protocols. Top: stimulation rates and patterns used for stationary activation tests; middle and bottom: stimulation patterns of 2 separate protocols used for transient activation tests. A1: schematic illustration of mean stimulation rates used in 27 consecutive measurements using concurrent stimulation of multi-motor unit (MMU) filaments (see METHODS) (see also Hulliger et al. 2001); the thick vertical lines (a-e) identify the tests, for which both combined multi-channel and up to 10 single channel stimulation trials were carried out. B1: individual stimulation profiles of the 10 channels of test c (in A1) illustrating the inter-stimulus interval (ISI) variability of individual pulse trains (see also text and Fig. 4). Middle: background components of individual transient stimulation profiles; bottom: instantaneous rate displays of individual stimulation profiles, with pseudo-random Gaussian noise added to the background components of middle (see text). A, 2 and 3: imitation of a pure recruitment strategy, featuring staggered activation of filaments at a relatively high rate (28/s) but without subsequent increase of activation rate; the 4 profiles were used for activation of MMU filaments. B, 2 and 3: imitation of a combined recruitment and rate modulation strategy, featuring staggered activation of MUs at a low rate (7/s) combined with a subsequent systematic increase in activation rate. The 10-channel pattern of B3 was used for activation of single motor units (MUs; see Fig. 8). A reduced version (channels 1, 4, 7, and 10) was used for trials with activation of MMU filaments (see Fig. 6).

Unique sets of single-channel stimulation profiles and multi-channel stimulation patterns were used to ensure the independent and asynchronous activation of individual filaments (both MMU and single MU). All profiles were digitally generated, stored, and reproduced to guarantee the precise replication of all stimulus patterns in repeated trials, both within and between experiments.

Each profile was characterized by a background component, which represented the mean rate of stimulation (window averaged) and, in most cases, by an added component of Gaussian noise (coefficient of variation, CV, 12.5%), which varied the timing of successive stimulus events (see Fig. 1, A3 and B3). For the stationary patterns, the mean stimulation rate was kept constant. For the transient activation patterns, the background profiles were either rectangles (for a protocol imitating pure recruitment; see Fig. 1A2) or ramps of various slopes (for a protocol imitating a combination of recruitment and rate modulation; see Fig. 1B2). The addition of Gaussian noise altered the duration of inter-stimulus intervals (ISI) up to a maximum of around 40% (compared with the intervals of the background profiles). ISI variability of this size is consistent with inter-impulse interval variability observed in MU firing patterns during voluntary contractions (CV, 12.5% or larger) (Dorfman et al. 1988, 1989; Person and Kudina 1972). More recent data suggest that the ISI variability averages around 20% (Erim et al. 1999; Laidlaw et al. 2000); nevertheless, the variability chosen is within the physiological range for humans. Customized software, implemented in Unix, was used to generate suitable stimulation profiles as lists of inter-stimulus intervals, which were stored as binary files (for details, see Hulliger et al. 2001).

Using either an 8-channel hybrid signal generator (Frei et al. 1981; Hulliger et al. 1987) or a 16-channel VME processor, the inter-stimulus interval files were converted (in real time) into standard TTL pulse trains. Up to 10 of these pulse trains were generated in parallel, each being used to trigger its assigned stimulation unit. In either case, pulse trains could be generated repetitively or in single sweep mode. Signal generator memories stored impulse patterns with a resolution of 4,096 bins per sweep. For pulse trains lasting 2 s, temporal resolution was therefore limited to 0.488 ms. This was adequate for the generation of short stimulation profiles (as used in the stationary design, see the preceding text), but it ruled out the use of this technology for the generation of longer lasting stimulation profiles (13 s) as required for the transient stimulation protocol. To achieve this, we used a 16-channel digital I/O board operated by a fast VME microprocessor. This permitted, in strict real-time operation, the simultaneous generation of 10 independent stimulation profiles with a resolution of 0.1 ms. In both cases, digital clock pulses were used to read successive values of the pulse train signals from digital memories. To minimize the jitter in stimulus-related averaging and summation procedures (see Analysis), the readout clock pulses operating on VME files were synchronized with the master clock of the data acquisition computer (see following text), which controlled A/D sampling of EMG and force signals. Thus the occurrence of each stimulus pulse was synchronized with an A/D clock pulse. However, in the initial experiments (4/12), where stimulus pulse trains were read from the signal generator memories, this technology was not available. This limited the resolution of the signal averaging and summation methods that were used for the recordings dealing with waveform interaction and stationary activation of multiple filaments (see RESULTS).

The hybrid signal generator was limited to eight independent channels. To activate 10 separate filaments, the outputs (pulse trains) of two signal generator channels were time delayed (by 5 and 10 ms), and each was used to activate a second filament (see Fig. 1B1: stimulation channels 1-4). As a result, for two pairs, the two constituent filaments were activated with a single stimulation profile, but in an asynchronous manner (see also Hulliger et al. 2001).

Recording

EMG signals were always recorded in two parallel channels using bipolar surface and intramuscular wire electrodes. The surface electrode was a customized patch electrode with two wires (Cooner, 0.012-mm diameter, Teflon coated, stainless steel) that formed loops of 10-mm circumference. The wires were anchored in a thin sheet of silastic (10 × 10 mm), with 2-mm segments of the wires of each loop bared. The inter-electrode distance (between the bared wire segments) was 4 mm. The patch was carefully stitched to the epimysium of the exposed muscle. In addition, the electrode was always mounted in the same topographic location (proximal, midline), at about 30% along the proximo-distal axis of the soleus muscle. The intramuscular electrode consisted of a pair of wires (as for the patch electrode; Teflon insulated, with 1-mm bared tips). They were inserted approximately 3-5 mm apart, also in a midline position, at about 50% along the proximo-distal axis. Care was taken to ensure that the electrodes were mounted at a safe distance from the nerve entry zone (for soleus typically at 10-15% along the axis).

High-impedance (1 GOmega ) differential preamplifiers (gain 10) located close to the muscle were used as buffer amplifiers and to remove DC and low-frequency drift components (1st-order high-pass filter at 0.1 Hz). Main amplifiers provided band-pass filtering of the EMG signals, using first order RC (high-pass, 3 Hz) and second-order Bessel (low-pass, 1 kHz) filters. At the beginning of each experiment, their gains were optimized (typically around 100) to permit distortion-free digitization of the largest signals that were expected and then kept fixed for the remainder of the experiment.

EMG signals were digitized at 2 kHz using a laboratory computer (LSI 11/73) with a customized multi-channel amplifier and A/D board. The magnitudes of the EMG signals spanned a wide range, as they encompassed signals elicited by multi- and single-channel activation of ventral root filaments. Especially for single filament activation, signal size strongly depended on the location of the active muscle fibers relative to the recording electrode. Therefore prior to A/D conversion the signals were subjected to a final stage of gain optimization (using the digitally controlled amplifiers of the A/D board) to maximize, for each individual trial, the resolution of the digital recordings. The gain settings were recorded digitally, along with EMG and force data, so that the global recording gain of the cascade of amplifiers could be calculated off-line. The 12-bit A/D converter provided 4,096 point resolution. Digitization encompassed both surface and intramuscular EMG signals for the stationary designs but was restricted to the surface EMG signal for the transient designs. All data were transferred to Sun workstations for off-line analysis.

Experimental protocols

Four separate experimental protocols were used to assess how contributions from individual MUs interact to produce the composite EMG signal recorded during activation of multiple MUs. All four protocols specifically addressed the question whether action-potential trains of individual or small groups of MUs interacted on the basis of linear summation. To this end a quantitative comparison was carried out between recorded MMU EMGs, which were obtained during combined activation of several independently controlled ventral root filaments, and synthesized MMU EMGs, which were obtained by algebraic summation of the AP trains recorded separately during isolated stimulation of each individual filament using the same stimulation profile.

INTERACTION OF TWO WAVEFORMS. It was known from pilot studies (Hulliger et al. 2001), and amply confirmed in the present study, that the magnitude of the EMG signal (measured as AEMG) did not increase linearly with the level of activation of the entire pool of MUs. The latter was quantified as an EAR, defined as the sum of individual stimulation rates across all filaments of a multi-channel stimulation trial. Instead AEMG showed pronounced saturation with increasing EAR (see, for instance, Figs. 5, 7, and 10). As outlined in the INTRODUCTION, this could be due to signal cancellation, nonlinear summation of single-channel potentials, or a combination of the two. To assess the magnitude of cancellation effects in the simplest case of waveform interaction and to address the question whether cancellation resulted from linear summation alone, a simple test based on systematic variation of the degree of overlap between two separate waveforms was designed. To this end, two separate filaments were stimulated at a constant rate of 20/s (CV 0%). The stimuli of one pulse train were systematically time-shifted in relation to those of the other (reference) pulse train and were advanced or delayed by a fixed interval (0, 1, 2, 3, 4, 6, 8, 12, or 20 ms).

STATIONARY ACTIVATION OF MULTIPLE FILAMENTS. Stationary multi-filament activation entailed 59 brief activation episodes (3-4 s, see preceding text). The degree of MU pool activation varied widely (EAR: 3-452/s; cf. Fig. 1A1). To monitor filament stability and to collect data to evaluate the extent of linearity of summation of single filament EMG contributions, on five occasions, the trials with combined stimulation (of 4, 7, or 10 filaments) were supplemented by a set of trials with separate stimulation of each individual filament (vertical bars in Fig. 1A: corresponding EAR values: 16, 55, 112, 252, and 393/s). This was followed by a repetition of the combined stimulation trial. These recordings were then used in off-line comparisons of recorded and synthesized multi-channel EMG signals.

Confirmation of a linear summation of APs under steady-state conditions would not necessarily imply that the same held true during transient activation. It was often observed, especially at the onset of activation at low rates (both for single MUs and especially MMU filaments), that the gradual build-up of force (over 100-200 ms) was accompanied by an initial transient in the AP shape with a similar time course (see DISCUSSION). Two experimental protocols were therefore used to further investigate the issue of linearity of summation of EMG contributions under conditions of transient activation, one dealing with relatively large MMU contributions, the other with smaller single MU contributions.

LINEARITY OF SUMMATION: TRANSIENT ACTIVATION OF MMU FILAMENTS. Transient activation trials were based on single episodes of stimulation (lasting 12 s) in which four MMU filaments of intermediate size (tetanic force, around 2 N) were recruited successively. The activation patterns imitated either pure recruitment at a relatively high rate (28/s) without additional rate modulation (Fig. 1A, 2 and 3) or a combination of recruitment (at much lower initial rate, 7/s) and subsequent rate modulation (Fig. 1B, 2 and 3; see also Fig. 6A). The protocol encompassed six single trials: combined multi-channel stimulation trials at the beginning and end and four single-channel activation trials, one for each of the four MMU filaments.

LINEARITY OF SUMMATION: TRANSIENT ACTIVATION OF SINGLE MU FILAMENTS. As in the case of MMU filaments, trials with transient activation of single MU filaments were based on a single 12-s episode of stimulation. However, only a single, combined recruitment and rate modulation strategy was investigated (Fig. 1B, 2 and 3; cf. Fig. 8A), 10 (instead of only 4) independently controlled filaments were stimulated, and each filament contained only one soleus alpha -motor axon. The protocol encompassed 12 trials: combined multi-channel stimulation trials at the beginning and at the end, and 10 single-channel activation trials in between, one for each of the 10 single MU filaments.

Analysis

Data analysis of digitized EMG signals was performed with custom and commercial software (ACE Graphics, P. J. Turner, Beaverton, OR) for display and statistical analysis. Full-wave rectification was performed by a simple software routine. No additional digital filtering was used.

Theoretical predictions of EMG signals (i.e., synthesized EMG) from experimentally recorded MUAP trains were based on algebraic summation of digitized records collected during stimulation of single motor filaments. AEMG was computed from segments of rectified EMG. The time windows used were either 2 s for stationary or 120 ms for transient EMG records (see also RESULTS).

For combined activation of multiple filaments, the recorded and computationally synthesized EMG signals were compared with a linear regression analysis. This was based on large numbers (up to 24,000) of pairs of corresponding data points (see Fig. 9A1). For the statistical analysis of differences (between recorded and synthesized EMG signals) in the AEMG-EAR relations, curvilinear regression analysis was used (e.g., Snedecor and Cochran 1967). No attempt was made to describe data sets from different experimental protocols with a single describing function. Instead for each set of data from a given stimulation protocol, a few alternatives were explored to find the best-fitting describing function. In practice, it turned out that both power functions and quadratic functions (polynomials) adequately served the purpose for the statistical analysis. Standard computational algorithms were then used for the implementation of the analysis and computation of confidence limits (Snedecor and Cochran 1967).


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Whether global EMG resulted from simple algebraic summation of unitary APs was investigated in acute experiments on 14 cats. Four separate protocols were studied. The main methodological feature was the use of strictly controlled electrical stimulation of motor filaments containing single or small sets of MUs and of digitally generated stimulation profiles that were identical between trials. This permitted rigorous quantitative comparison of two forms of MMU EMG signals, one that was recorded during combined activation of multiple motor filaments and one that was synthesized during off-line analysis as the algebraic sum of the EMG signals generated by each filament individually. The latter were recorded experimentally in a series of separate measurements using stimulation profiles, which, for each filament, were identical with those used during combined activation. Although both surface and intramuscular EMGs were recorded, the data presented are restricted to the surface EMG signal because exploratory analysis did not reveal any fundamental differences between the surface and intramuscular data.

Waveform interaction

The complexity of the EMG signal arises in part from interference or signal cancellation due to the temporal overlap of APs with opposite polarity. The goal was to assess the magnitude of this effect and to determine whether the global EMG could be accounted for by simple linear summation.

Waveform interaction was studied in tests where two MMU filaments were stimulated at constant rate (20/s), with one stimulus pulse train systematically time-shifted relative to the other (see METHODS). For each of five pairs of filaments studied in two experiments, recordings were made for 17 different time shifts. Figure 2 illustrates five selected time shifts of stimulus pulses (top), the APs elicited by separate stimulation of two MMU filaments (middle), and the potentials elicited by combined stimulation (bottom). Both waveforms consisted of four distinguishable phases with the first phase positive. Qualitatively, their interaction (bottom) was therefore predictable from the time shifts (middle): summation prevailed when dominant waveform components were in phase (in this example at 0-ms shift), cancellation and waveform distortion prevailed at a critical time shift (2 ms), and a mixed effect was seen at a slightly larger shift (-3 ms). For time shifts larger than the duration of the MMUAPs (about 10 ms), the two waveform's contributions during combined stimulation appeared to be the same as during single filament stimulation.



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Fig. 2. Controlled waveform interaction to evaluate the effect of action potential overlap and signal cancellation. Top: illustration of selected examples of stimulus timing; 2 MMU filaments were activated at the same constant rate (20/s), while time shifts between the 2 were systematically varied between -20 and 20 ms (see METHODS). Examples were selected to illustrate interactions between AP segments with the same or opposite phase polarities (see also text). Middle: MMU action potentials (MMUAPs) evoked by separate stimulation of 2 ventral root filaments. Bottom: waveform interaction on combined activation of the 2 filaments. See also text.

A quantitative measure of the effects of overlap on signal magnitude was obtained by computing, for each time shift, an AEMG value for the entire 2-s data segment. The results for the filament pair of Fig. 2, bottom, are plotted in Fig. 3A1 as normalized values of AEMG. Normalization was relative to the AEMG value at maximum shift (20 ms), for which the two MMUAPs did not overlap. It can be seen that waveform overlap caused signal reduction but never signal enhancement. Signal reduction was modest (maximally 25%), and its dependence on time shift was complex. The generality of these observations is illustrated in Fig. 3B1 in the graph of average AEMG during combined stimulation of all five pairs. Averaging of AEMG profiles across pairs was only meaningful because, in spite of the complex features of individual interaction patterns, all individual pairs had an AEMG maximum (minimum reduction) at 0-ms time shift and local minima for immediately adjacent values of shift (1-2 ms).



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Fig. 3. Signal cancellation due to AP overlap and interaction. Averaged rectified electromyogram (AEMG) calculated over 2-s segments of recorded and synthesized EMG generated by activation of 2 MMU filaments. A: data from the pair of Fig. 2. B: data from all 5 pairs of filaments, for which waveform interaction tests were performed, averaged after separate calculation of AEMG values for each pair and each time shift value. Top: AEMG values as a function of the time shift between stimulus pulse trains (see Fig. 2) during combined electrical stimulation of the 2 filaments. Bottom: AEMG values of EMG traces that were synthesized from the records obtained during separate stimulation of each filament (see Fig. 2, middle). Thick lines, synthesized data; thin lines, data recorded during combined activation (added for comparison; same traces as in top).

Whether this signal reduction was attributable to signal cancellation due to the linear summation of constituent MMUAPs was evaluated by comparing the magnitude of experimentally recorded EMG with that of analytically synthesized EMG. To this end, the MMUAP trains recorded during separate single filament stimulation were added algebraically and then analyzed identically. In Fig. 3, bottom, no systematic differences were found between the recorded (thin lines, same as in Fig. 3, top) and the synthetic (thick lines) AEMG. Thus signal reduction due to AP overlap was accounted for by linear cancellation. The small differences between the two sets of lines can be attributed to sampling inaccuracy. As indicated in METHODS, at the time of these initial experiments, stimulus pulses could not be synchronized with the A/D clock pulses. For a sampling rate of 2 kHz and individual MMUAP phases as short as 2-3 ms, this led to appreciable jitter of sampled waveforms. This was evident in stimulus triggered superpositions of successive MUAPs (not illustrated) and evidently limited the accuracy of the waveform synthesis of Fig. 3, bottom.

Stationary activation of multiple filaments

Given the evidence that pairs of APs summed linearly, we asked whether linear interaction was also present during combined activation of larger numbers of filaments and over a wider range of stimulation rates. Recordings during stationary activation were made in three experiments. In each case, between 4 and 10 MMU filaments were activated under steady-state conditions in five separate tests, each encompassing initial and final trials with combined activation of multiple filaments and trials with selective activation of individual filaments (see METHODS, Experimental protocols, and Fig. 1A1, vertical lines identifying tests a-e). Figure 4 shows an example of the EMG signals recorded in a test at EAR 252/s (Fig. 4A; see also Fig. 1A1, test c, and Fig. 1B1). The 10 MMUAP trains elicited by activation of each filament are illustrated in Fig. 4C. The multi-channel EMG elicited by concurrent activation of all 10 filaments (using the same stimulation profiles as in C) is shown in Fig. 4B. In Fig. 4D, a similar multi-channel EMG signal is illustrated, but in this case, the signal was synthesized off-line by algebraic summation of the 10 MMUAP trains shown in Fig. 4C. Qualitatively the recorded and synthesized multi-channel EMGs were very similar, although comparison of individual spike sequences on an expanded time scale (not shown, but cf. Fig. 8) revealed some minor discrepancies, which again were attributable to jitter, arising from limited A/D sampling resolution. Clearly this observation had to be corroborated by quantitative analysis.



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Fig. 4. Comparison of recorded and synthesized EMG during stationary activation of 10 MMU filaments. A: stimulation protocol, featuring separate and combined activation of 10 filaments at intermediate rates, ranging from 17/s to 31/s (cf. also C, and Fig. 1A, test d). B: surface EMG recorded during combined electrical stimulation. C: MMUAP trains evoked by separate stimulation of each filament. D: EMG synthesized off-line by algebraic summation of the individual MUAP trains shown in C. Note, in C, the absence of a clear correlation between MMUAP amplitude and filament size (tetanic force), as the filaments were ordered according to their size (channel 1, smallest; channel 10, largest). See also text.

Notably, although the filaments of Fig. 4 were rank ordered by size (tetanic force; filament 1 smallest, filament 10 largest; see METHODS), it is evident that there was no close relationship between MMU tetanic force and AP magnitude (e.g., filaments 1 and 2 had larger MMUAPs than filaments 3, 4, and 7). Tetanic forces of the filaments of Fig. 4C ranged from 1.28 to 3.04 N. Qualitatively similar observations were made in all three experiments. This observation has recently been corroborated in recordings from 250 single MUs from cat soleus where regression analysis revealed that there was no correlation at all between MUAP size (measured as the AP area) and tetanic force (A. F. Ware, M. Hulliger, and S. J. Day, unpublished data).

The ability of the synthesized EMG signal to reproduce the original recording, obtained during combined stimulation of multiple filaments was evaluated by linear regression analysis of the clusters of corresponding data points (synthesized vs. recorded; cf. Fig. 9A1, and see also Analysis). The analysis was carried out separately for each test condition defined by its EAR value. The correlation coefficients for comparisons of initial and final recordings during combined stimulation (averaged across experiments) were 0.934, 0.965, 0.954, 0.971, and 0.971 for EAR values of 16, 55, 112, 252, and 392/s, respectively. For the same EAR values, comparisons of combined and synthesized records revealed average correlation coefficients of 0.954, 0.911, 0.912, 0.906, and 0.910. Averaged across EAR values, the coefficients for comparisons between combined records and combined and synthesized records were 0.959 and 0.919.

The similarity of the recorded and synthesized EMGs does not indicate to what extent the data were attenuated by signal cancellation. This was assessed by comparing the magnitude of the multi-channel signal with the sum of magnitudes of the constituent single-channel signals (cf. Fortier 1994). Signal magnitude was estimated as the AEMG calculated over finite time windows (2 s for the data of Fig. 4). Figure 5A shows pooled data from all three experiments. Mean AEMG is plotted for EMGs obtained using combined stimulation (thick line, bottom trace), summation of MMUAP trains followed by rectification (synthesized EMG, thin broken line) and summation of rectified individual MMUAP trains (top trace). Both recorded and synthesized multi-channel EMG increase monotonically with EAR but show a distinct downward nonlinearity (i.e., a gain compression where gain = EMG/EAR). The sum of constituent magnitudes was consistently larger than the magnitude of the two multi-channel signals. As highlighted by the shaded area, this difference increased with EAR, indicating that signal loss increases with increasing levels of activation of a pool of MUs. The size of the signal loss was appreciable, reaching 50% for the highest EARs studied. Given that the EMG is the result of algebraic summation of MUAP trains, this signal loss can only be attributed to MUAP phase cancellation (see DISCUSSION).



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Fig. 5. Quantitative analysis of the magnitude of recorded and synthesized EMG for stationary activation of 10 MMU filaments. A: dependence of AEMG on ensemble activation rate; thick line (C), recorded during combined stimulation; thick broken line (Sigma ), synthesized from individual MMUAP trains (recorded separately); thin line, sum of rectified MUAP trains. Shaded area, the amount of signal loss attributable to signal cancellation. For each trace, AEMG was normalized to the maximum recorded level during combined stimulation. Note the residual nonlinearity in the sum of rectified MUAP trains (see DISCUSSION). B: power function regression analysis of pooled AEMG values. Filled squares, recorded EMG; open triangles, synthesized EMG; measurements at (from 3 different 10-channel sets) each of 5 EAR values. Power functions were fitted separately to the pooled data sets (recorded, synthesized). Note the close agreement of the fitted functions: thick line, recorded EMG; broken line, synthesized EMG; thin solid lines, 80% confidence limits calculated from population regression coefficients and variance (see text and METHODS).

Figure 5 also illustrates that, for stationary activation of MMU filaments, the magnitudes of the recorded and synthesized EMG were indistinguishable (cf. thick with broken lines in A). The largest difference in magnitude between the two traces was 3% (mean values in A). However, this difference was not statistically significant (Fig. 5B). For each condition (recorded vs. synthesized), all individual AEMG measurements were pooled and summarized by a general describing function of the relation between AEMG and EAR. A simple power function relationship appeared to be most suitable to describe both data sets with a limited number of parameters. Best-fitting power functions, calculated by regression analysis, are shown in Fig. 5B as thick (recorded) and broken (synthesized) lines. The fitted functions describing recorded and synthesized EMG are indistinguishable. Confidence limits were then calculated from the estimates of standard deviation of the regression parameters and are illustrated by the thin lines in B. Eighty percent rather than 95% limits are shown because, owing to very large variability of AEMG estimates between experiments, standard deviations of parameters and size of confidence limits were large. Nevertheless regardless of the limited resolution of this analysis, the main observation was that differences between the fitted describing functions of recorded and synthesized EMG magnitude were extremely small and not significant, statistically.

Nonstationary activation

At the onset of an episode of stimulation, MUAP waveforms often revealed small transients in shape, offset, or magnitude, which appeared to run parallel to the gradual build-up of force. This phenomenon was clearly recognizable during activation of single filaments (see Fig. 6C) and occasionally visible at the onset of multi-channel stimulation, when the different MUAPs were sufficiently distinct and the level of ensemble activation was sufficiently low. The apparent similarity of the time course of force (not shown) and MUAP transients suggests they may be caused by mechanical changes in the muscle during the development of isometric force (see DISCUSSION).



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Fig. 6. Comparison of recorded and synthesized EMG during transient activation of MMU filaments. A: stimulation profiles of the protocol imitating recruitment of rate modulation of 4 activation channels. B: EMG recorded during combined stimulation of 4 MMU filaments. C: MMUAP trains recorded during separate stimulation of each of the 4 filaments, using the same stimulation profiles (shown in A) as used during combined stimulation (B). D: synthesized EMG obtained by algebraic summation of the 4 MMUAP trains (C).

Transient activation of MMU filaments

Figure 6 illustrates the experimental design and the main qualitative observation of the stimulation protocol based on transient activation of four MMU filaments (see METHODS). These filaments were prepared so as to contain on average about 10 MUs as judged from the tetanic forces at 30/s, which ranged between 2 and 2.5 N. The individual stimulation profiles (Fig. 6A) were ramp-shaped transients with added Gaussian noise (see METHODS and Fig. 1B, 2 and 3). Trials with separate stimulation of the individual filaments (C) were flanked by trials with concurrent activation of all four filaments (B). The EMG recorded during combined activation (B) was compared with the signal that was synthesized off-line (D) by algebraic summation of the MMUAP trains recorded during separate activation of each individual filament (C). A qualitative comparison of the synthesized (D) with the recorded (B) EMG reveals a remarkable degree of similarity, including minute detail of prominent segments of recording. The similarity is more readily apparent on an expanded time scale (not shown, but cf. Fig. 8C). Similar observations were made in 12 tests from six experiments. These tests included the stimulation protocol of Fig. 6 (imitating recruitment of filaments at low rate, combined with rate modulation) and the related protocol of Fig. 1 (A, 2 and 3), imitating recruitment alone.

The extent to which the temporal structure of the recorded EMG was reproduced by the synthesized EMG was again assessed by linear regression analysis of pairs of corresponding data points (not illustrated, but cf. Fig. 9A). This was done separately for the measurements of each experiment and for the two stimulation protocols. The average regression coefficients for comparisons of initial and final EMGs during combined stimulation were 0.991 and 0.993 for the pure recruitment and the recruitment and rate modulation protocol. In contrast, for comparisons of combined and synthesized records, average values of 0.967 and 0.963 were obtained for the two respective stimulation protocols. Generally, the values were very high, indicating that the relationship between synthesized and recorded EMG signals was linear. The resolution of this analysis is characterized by comparing the initial and final recordings of EMG obtained during combined activation (using the same 4 filaments and stimulation patterns): the correlation coefficients were more than 0.99. Moreover, the correlation between synthesized and recorded signals was nearly as strong, with mean correlation coefficients more than 0.96. This indicates that the two signals are either essentially identical or linearly scaled versions of each other. Analysis of the slopes of the regression lines revealed a marginal, but consistent, deviation from unity: for both stimulation protocols mean slopes were 1.05, with the recorded signal being smaller than the synthesized signal. At face value this indicates a 5% deviation of the recorded from the linearly synthesized EMG. However, deviations from unitary slope can also arise from factors other than linear attenuation (see DISCUSSION). In fact, the analysis of signal magnitude did not support the notion that simple linear attenuation was solely responsible for this effect (see Fig. 7).



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Fig. 7. Quantitative analysis of the magnitude of recorded and synthesized EMG for transient activation of 4 MMU filaments, using the combined recruitment and rate modulation protocol. A: dependence of AEMG on ensemble activation rate; thick line (C), recorded during combined stimulation; thick broken line (Sigma ), synthesized from individual MMUAP trains (recorded separately); thin solid line, sum of rectified MMUAP trains. Shaded area, the amount of signal loss attributable to signal cancellation. For each trace, AEMG was normalized to the maximum recorded level during combined stimulation. B: power function regression analysis of pooled AEMG values. Power functions were fitted separately to the pooled data sets (recorded, synthesized). Note the close agreement of the fitted functions: thick line, recorded EMG; broken line, synthesized EMG; thin solid lines, 95% confidence limits calculated from population regression coefficients and variance (see text). The underlying stimulation patterns and examples of EMG signals are shown in Fig. 6.

Figure 7 summarizes the results of the EMG magnitude analysis for the data that were collected during concurrent MMU filament stimulation or synthesized from control measurements with single-filament activation. The data shown are those obtained with the activation scheme imitating combined recruitment and rate modulation, which featured transient activation patterns (Fig. 6). The same analysis was carried out for the parallel observations on the imitation of pure recruitment. The results were similar to those shown in Fig. 7 and are therefore not illustrated.

As before, EMG magnitude was estimated as the AEMG. However, averaging was restricted to shorter time windows (120 ms) than for the stationary data (2 s), producing 100 segments from the 12-s recordings. Window duration was adjusted qualitatively to provide a magnitude estimate that captured the dynamic features of the EMG while limiting the variability of estimates between successive windows. For each segment, the EAR was calculated as the simple probability density of stimulus pulse occurrence across all channels (see Experimental protocol). For the analysis of the general trends (Fig. 7A), the AEMG estimates were averaged for each window across experiments.

The main finding was that, as in the case of stationary activation of MMU filaments (Fig. 5), the estimates of EMG magnitude (AEMG) were practically identical for the experimentally recorded and the computationally synthesized signals. This is illustrated in Fig. 7A by the almost completely overlapping graphs of recorded (bottom trace, thick line) and synthesized (broken line) AEMG plotted against EAR. The synthesized EMG tended to be marginally larger, but the mean difference over the entire range of EAR of the transient activation protocol was less than 2%. Further, there was a weak tendency of these---very small---differences to be more pronounced at EARs less than 70/s, i.e., in the region where filaments were being recruited. Likewise, in spite of the low values of EAR (only 4, compared with the 10 independent activation channels of Fig. 5), the relation between AEMG and EAR revealed a similar downward nonlinearity. Comparison with the average magnitude of the summed rectified constituent EMGs (top trace) again indicates that the downward nonlinearity was largely attributable to signal cancellation. However, at the highest activation rates the signal loss due to cancellation was smaller than for the 10-channel data of Fig. 5A. This difference was mainly related to the smaller range of EAR values of Fig. 7A and much less pronounced for comparable EARs (cf. Figs. 7A with 5A at 120/s). Finally, the same power function regression analysis was carried out separately for the two data sets (recorded and synthesized) after pooling observations across experiments. The two data sets were best fitted by practically identical power functions (Fig. 7B, thick and interrupted lines). The differences between the best fitting describing functions were minute and the relationships could not be distinguished statistically.

Transient activation of single-MU filaments

Figures 8-10 illustrate the results obtained with multi-channel transient activation of single MUs. Apart from the range of forces investigated, the main difference of design was the use of 10 (compared with 4) independent transient stimulation profiles (see Figs. 1B3 and 8A). Observations from eight preparations on 10 separate sets of 10 single MUs are summarized in Figs. 9 and 10.



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Fig. 8. Comparison of the surface EMG produced by combined stimulation and algebraic summation of single MUs. Top: the 10 single MU, transient recruitment and rate modulation protocol. Middle: qualitative assessment (single experiment) of the EMG superimposed from the combined stimulation and algebraic summation conditions for an entire data sweep. Bottom: 2 selected segments of the superimposed traces with increased temporal resolution (thick black line, combined stimulation; white thin line, algebraic summation). These segments are highlighted in the middle row (width exaggerated for clarity). Note the qualitative similarity even of individual peaks and troughs of the combined-activation and synthesized signals. See also text.



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Fig. 9. Linear regression analysis to compare recorded with synthesized EMG signals during combined activation of 10 single MUs. A: scatter plots of pairs of corresponding data points (recorded, synthesized) sampled at the same point in time. Dashed line in A1, reference with unitary slope. B: fitted linear regression lines. Top: data of the example illustrated in Fig. 8. Bottom: data from all 10 10-channel sets superimposed. Since EMGs were sampled and synthesized at a resolution of 2,000/s, superposition of 10 12-s episodes would have yielded 240,000 data points in A2; therefore only each third data point was plotted in A. Note the remarkable degree of correlation and the extremely small number of outlier points in A2. In line with this, the fitted regression lines (10) in B2 cannot all be recognized individually.



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Fig. 10. Quantitative analysis of the magnitude of recorded and synthesized EMG for transient activation of 10 single MU filaments. Activation pattern imitating recruitment and rate modulation (see Fig. 8A). A: dependence of averaged rectified EMG (AEMG) on ensemble activation rate; thick line (C), recorded during combined stimulation; thick broken line (Sigma ), synthesized from individual MMUAP trains (recorded separately); thin solid line, sum of rectified MUAP trains. Shaded area, the amount of signal loss attributable to signal cancellation. For each trace, AEMG was normalized to the maximum recorded level during combined stimulation. B: quadratic regression analysis of pooled AEMG values. Data from 10 different sets of single MUs. Quadratic functions were fitted separately to the pooled data sets (recorded, synthesized). Note the close agreement of the fitted functions: thick line, recorded EMG; broken line, synthesized EMG; thin solid lines, 95% confidence limits calculated from population regression coefficients and variance (see text and METHODS).

Figure 8 gives a qualitative illustration of the high degree of similarity between experimentally recorded and computationally synthesized EMG signals during independent activation of 10 single MUs. The superimposed (recorded and synthesized) EMG transients were consistently indistinguishable qualitatively as illustrated in Fig. 8B. Even on expanded time scale, consistent differences could not be recognized (Fig. 8C). Linear regression analysis of data sets consisting of pairs of corresponding samples (synthesized vs. recorded) was again performed separately for all 10 sets. An example of a cluster of such data points, which represents a complete 12-s episode of activation, is shown in Fig. 9A1 for data from a single 10-MU set. The very high degree of correlation is evident, and it is obvious from the graphic display that the slope of the underlying relationship would be very close to 1.0, as indeed was observed from the slope of the linear regression (Fig. 9B1, calculated slope 0.979). In Fig. 9A2, data from all 10 sets are superimposed to emphasize the very high consistency of the observations of Figs. 8 and 9A1. Figure 9A2 shows 80,000 data points (one-third of those sampled and used for regression analysis). Against this background the number of outlier points (about 10) is very small.

Results of the linear regression analysis are shown in Fig. 9. The mean coefficient of correlation from the 10 sets of data were very high (0.984), less than 1% below the figure of 0.991 for the control measurements comparing data from initial and final trials with combined stimulation (see METHODS). The linear regression lines that were calculated from data clusters of the type illustrated in Fig. 9A1 are illustrated in Fig. 9B2 as superimposed line segments, each drawn over the range of the original data points. At most, four individual regression lines can be distinguished, again strongly emphasizing that the slopes of the fitted regression lines were all close to 1.0: individual values of slope ranged from 0.99 to 1.03, with a mean of 1.01. The observation of unitary linear regression slopes combined with very high regression coefficients strongly suggests that for practical purposes the synthesized and recorded EMG signals during activation of up to 10 single MUs were identical. This was further borne out by the analysis of EMG magnitude.

Figure 10 summarizes the results of EMG magnitude analysis, comparing recorded with synthesized EMGs obtained by activation of 10 single MUs. The data are presented in the same general format as in Figs. 5 and 7, using the same window-averaging technique as in Fig. 7 (see preceding text). In contrast to the MMU data of Fig. 7, it emerged that the single MU data were most effectively summarized by quadratic (instead of power function) expressions (see METHODS). Regardless of the particular describing function, the main observations were that means of EMG magnitude of recorded and synthesized signals were identical, and that signal loss (attributable to MUAP waveform cancellation) was appreciable, even for a small number of MUs activated at low rates: in Fig. 10A the graphs of AEMG versus EAR were identical in minute detail (broken line, synthesized EMG; thick solid line, recorded EMG, largely obscured due to superposition). The absence of qualitative differences between combined and synthetic records was confirmed statistically. These graphs also reveal a similar degree of downward nonlinearity as shown in Fig. 5 for data based on MMU filament activation. This was in contrast to the linear increase of the summed constituent AEMG estimate, indicating that (for the single MU data) the nonlinearity was nearly exclusively attributable to signal loss arising from waveform cancellation. Its size is highlighted by the shaded area, whose width increases with EAR.

In summary, the observations from single MU experimental simulations of graded MU pool activation strongly suggest that the EMG interference signal is the result of nearly perfect algebraic summation of constituent MUAP trains and that signal loss due to waveform overlap and cancellation introduces a significant downward nonlinearity that is manifest already at low firing rates and recruitment levels.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

It is widely assumed that the global EMG is the outcome of a process of simple linear summation of multiple AP trains that are generated by concurrently active MUs. However, this concept has never been tested experimentally in a systematic manner. The main reason is that suitable experimental techniques have only recently become available (see following text).

As MUs are recruited and possibly increase their firing rate during progressive muscle activation, increasing numbers of MUAPs contribute to the global EMG signal at any one time. One might predict that EMG magnitude should increase approximately linearly with EAR. However, the matter is complicated by increasing MUAP overlap and signal cancellation, which would reduce EMG, and by the possibility that the late recruited larger MUs might contribute larger MUAPs, which would augment EMG. The latter is controversial (see RESULTS), the former had not previously been measured, and the extent of any cancellation between the two was difficult to assess. Yet in an experimental simulation of EMG, where EAR was explicitly controlled, it was recently shown that EMG magnitude increased at a progressively slower rate with EAR, revealing a downward nonlinearity (Hulliger et al. 2001) (see also Figs. 5, 7, and 10).

This observation of a nonlinear increase in EMG with EAR motivated the present study. While it was clear that this could arise in principle from signal cancellation on the basis of perfectly linear summation of MUAPs, the possibility of additional mechanisms of genuinely nonlinear signal interaction could not be ruled out a priori nor could the relative contributions of these various sources of nonlinearity be estimated reliably.

Experimental design

The new methodological feature of the present study was the quantitative comparison of EMGs recorded during combined activation of multiple motor filaments with EMGs that were synthesized by the algebraic summation of MUAP trains generated individually by the same filaments. Ideally such comparisons would be carried out in experiments where each MU of a given pool could be stimulated independently during combined activation in tests encompassing both stationary and nonstationary segments of activation. However, limitations of present experimental methodology rule out such an undertaking. In the present study, the assessment of the issue of linearity of unitary contributions to the EMG was therefore carried out in four separate experimental protocols, which together covered important conditions of MU pool activation: first, under conditions of stationary as opposed to nonstationary or transient activation; second, during activation of sets of single MUs (encompassing only a fraction of the pool, and generating relatively small MUAPs) as opposed to activation of sets of MU groups (encompassing most of the pool, and generating larger MMUAPs).

EMG as the algebraic sum of MUAPs

It is important to distinguish between linear summation and algebraic summation. The latter is a special case of the former. The simple concept that was used in the design and analysis of the experiments is represented formally by
<IT>C</IT><SUB>1,10</SUB>(<IT>t</IT>) = <IT>kS</IT><SUB>1,10</SUB>[muap<SUB>i</SUB>(<IT>t</IT>)] (1)
where C(t) is the experimentally recorded EMG signal obtained during combined activation, S[muapi(t)] is the algebraic sum of the individual single- or MMUAP trains, recorded separately, and k is a constant scale factor (k =1 for algebraic summation but not necessarily for linear summation).

The presence of linearity of summation of MUAP contributions was assessed by determining the goodness of fit of the recorded data, C(t), by the synthesized data, S[muapi(t)], using linear regression and correlation analysis. The question whether, in addition to being linear, the summation was also algebraic, was assessed by examining the value of the scale factor k. For algebraic summation, it would have to be close to 1.0. It bears emphasis that the only deviation of the interaction function from a process of strict algebraic summation that could still yield consistently high linear correlations is that of a globally scaled algebraic sum. The scale factor k in Eq. 1 would then have a value different from 1.0. Alternatively, consider the case of some hypothetical process of unevenly weighted summation of contributions; the recorded EMG, C(t), would be the sum of weighted (ki) constituent MUAP trains, S[kimuapi(t)]. Thus the EMG would still be the result of linear summation of MUAPs, but a strong correlation and linear relation between the individually weighted sum and the scaled sum of Eq. 1 could not generally be expected.

The results of the present study demonstrate that under isometric conditions and for the cat soleus muscle, the temporal profile of a complex EMG signal appears to be the outcome of nearly perfectly linear, in fact algebraic, summation of the contributing MUAP trains. This was generally true for all four experimental protocols that were examined: during stationary activation of pairs of MMU filaments and for sets of up to 10 MMU filaments, which encompassed between 80 and 100% of the entire pool of MUs, and during transient activation of up to 10 individual filaments, both for relatively large MMUAPs, as elicited by activation of MMU filaments and for smaller MUAPs as elicited by activation of single MUs. However, rather minor deviations from a process of strict algebraic summation were noted in some circumstances (see following text).

These results have important implications. They provide an essential post hoc validation of the notion that the electromyogram is the product of algebraic summation of MUAP trains. This assumption has been was widely relied on in the design of EMG decomposition algorithms, in theoretical modeling studies of EMG, and when extracting MUAP waveforms from global EMG using spike triggered averaging (see INTRODUCTION).

Limitations of the experimental method

The main shortcoming of the experimental simulation method is that only a limited number of MUs can be activated independently. To imitate higher levels of muscle activation and the associated larger myoelectric signals, filaments containing several motor axons to the muscle had to be stimulated. The main artifact introduced by electrical stimulation of MMU filaments is the complete synchronization among the subsets of MUs activated in each filament (referred to below as "group synchronization"). Clearly, this is not physiological, as all the evidence from MU recordings during voluntary activation indicates that pools of MUs normally are largely desynchronized (e.g., De Luca et al. 1993; Milner-Brown et al. 1973).

Recent evidence from a computer simulation study (Yao et al. 2000) indicates that a progressive increase in the level of synchronization between MU's results in a proportional increase in the magnitude of the EMG signal. The authors attribute the increase in EMG magnitude to a progressive decrease in the amount of signal cancellation with MU synchronization. One of the main differences between this and the current study is that the entire pool of MUAPs had homogenous AP phase properties (i.e., same sequence in the polarity of AP phases), so synchronization resulted in primarily additive effects between AP signals rather than the more reductive (cancellation) or mixed effects expected with synchronized overlaps between APs with heterogenous waveform properties. In separate study in the cat soleus using surface electrode recordings as in the present study (Ware et al., unpublished data), it was observed that the AP phase properties of a pool of 250 recorded MUs was highly heterogenous, varying in both the number and sequence of distinguishable AP phases. The observations of Yao et al. (2000) suggest that the group synchronization decreased the level of signal cancellation in the present study.

To what extent then did group synchronization affect the signal loss due to cancellation and hence the extent of the downward nonlinearity seen in the AEMG-EAR relationship? This was evaluated for data from both MMU (Fig. 5) and single MU (Fig. 10) activation. For comparable values of EAR (300/s), signal cancellation was larger for MMU simulations (50% in Fig. 5 vs. 30% in Fig. 10). However, with combined MMU filament stimulation some 120-150 MUs were activated. Preliminary computer simulations using experimentally recorded MUAP waveforms have shown that for a pool of this size cancellation loss can be as high as 80% of the total signal of constituent MUAPs (Day et al. 1996). Thus cancellation loss during combined activation of MMU filaments was comparatively small (50%). This suggests that group synchronization was associated with appreciable cancellation loss. This may be attributed to the heterogeneity and nonuniform polarity profiles of MUAP waveforms, but at present it cannot be assessed whether the data from cat soleus are at variance with the theoretical study of Yao et al. (2000). For cat soleus, the effects of synchronization on signal cancellation remain to be examined more directly in computer simulations of MU synchronization.

However, for the issue of linearity of summation, signal loss due to group synchronization is not a major concern. The same group synchronization of the MU pool was present when MMU filaments were activated alone and in combination. Thus in principle the comparison of recorded with synthesized multi-filament EMGs still is methodologically valid. But could the minor deviations from linearity seen with combined activation of MMU filaments be attributed to less obvious consequences of group synchronization? Synchronization could have direct electrical and more indirect mechanical effects on AP interaction. These two are now considered separately.

The current peaks underlying APs must have been larger with synchronized activation than they would have been without. By the same token, the associated muscle fiber electrical impedance minima would have been lower. If AP-related impedance minima were capable of causing nonlinear MUAP summation, the group synchronization during MMU filament stimulation should have unmasked and exaggerated any nonlinearity of this type. The only very minor deviations from algebraic summation with combined activation of MMU filaments indicates that effects due to impedance reduction by group synchronization were very small.

Group synchronization of MU subsets also has mechanical consequences, especially at low activation rates, when force ripple is bound to be more pronounced than with asynchronous activation. It was repeatedly observed that the onset of activation of MUs was associated with transients in amplitude, shape, or offset of MUAPs. These appeared to have the same time course as the gradual build-up of force. This raises the possibility of a mechanical origin of the transients in MUAP shape. These could plausibly be attributed to alterations in the spatial relationship between MUAP current source and the recording electrode, so that current dipoles would be seen by the recording electrode under a different angle. Such configuration changes would indeed be expected from the large changes in fiber pennation angle that have been reported in contracting, compared with resting muscle (Hoffer et al. 1989). MUAP waveform transients due to fiber re-orientation might be most pronounced during activation of MUs in an otherwise passive muscle, and they might be smaller in predominantly active muscle because fiber orientation changes in a majority of contracting MUs are bound to be imposed mechanically on a minority of noncontracting MUs. Thus for mechanical reasons, the MUAPs contributed by a given MU to the EMG would be different at low compared with high levels of background activation. In the extreme, this could invalidate the comparison of recorded with synthesized multi-filament EMGs.

The question here is whether group synchronization could exaggerate the mechanical impact of different levels of background contraction on MUAP properties. At present, there is no simple answer nor is the issue easily resolved experimentally. However, even if group-synchronized activation exaggerated any distortion of MUAP waveforms by background activation, in the present study, its effects must have been very small because deviations from linearity were small.

Limitations of the generality of findings

The linearity of summation of MUAPs was close to perfect when small numbers of single MUs were activated. The extent to which this finding can be extrapolated to larger numbers of single MUs cannot be assessed with certainty. However, it seems unlikely that massive nonlinearities would be encountered if significantly larger numbers of MUs could be controlled independently and activated in combination. The concurrent activation of four MMU filaments, each of which contained on average about 10 MUs, revealed a marginal deviation from linear summation of constituent MMUAPs that on average was no worse than 5%. Since the cat soleus muscle on average contains about 150 MUs (Boyd and Davey 1968; Burke et al. 1977), a deviation of around 20% might be expected for near maximum activation of a muscle, assuming---for simplicity---that the deviation was proportional to active muscle force. However, in an independent assessment based on stimulus-triggered averaging and extraction of MMUAPs against a background of increasing whole muscle activation, the deviations from linearity of summation were smaller than 5% even at maximum muscle activation (S. J. Day, M. Hulliger, P. Sjölander, and K. A. Scheepstra, unpublished results).

Alternatively, the level of background activation of the muscle might impact the contribution of single MUAPs to the global EMG signal on the basis of mechanical interactions leading to muscle fiber realignment (see preceding text). For single MUs, the deviations from algebraic summation were negligible. This suggests that this realignment mechanism was either not very powerful or cancelled by some other process. The latter seems more likely because the MUAP waveform transients (see preceding text) clearly were present when single MUs were activated individually. How could they fail to cause deviations from linearity? The transients did not reveal any uniform pattern nor would they be expected to because different MUs occupy different territories and have different topographic relations to the site of the recording electrode. Conceivably to some extent, waxing and waning transients cancelled each other, thus reducing the size of the overall effect. Whichever applies, the main point is that MUAP interaction was strictly algebraic. For MMU filaments, the minor deviations from algebraic summation can readily be attributed to fiber realignment effects and perhaps less effective mutual cancellation among multiple filaments. Although this is speculative, the difference (between MMU and single MU filaments) in the importance of these putative mechanical coupling effects could easily be due to the presence of some critical intermediate range of background force, where realignment effects are most pronounced.

The present findings are limited to isometric conditions and a uniformly slow muscle (soleus) in the cat. To what extent the conclusion of an essentially linear process of MUAP interaction can be extrapolated to other muscles and, in particular, dynamic conditions must remain speculative. As for nonisometric conditions, suffice it to emphasize that prediction of EMG from single MUAP waveforms is bound to be complicated by dynamic muscle activation. Alterations of fiber orientation and the current source-electrode relationship under dynamic conditions are likely to have a significant impact on the shape and magnitude of MUAPs.

As for muscles other than soleus, the simplest solution might be to repeat the experiments in a mixed muscle, also under isometric conditions. However, this could be more challenging than might be apparent because it would be appreciably more difficult to elicit reproducible MUAP waveforms in consecutive stimulation trials: both potentiation and fatigue are more pronounced in type FF than type S MUs, and the effects of these phenomena on MUAP shapes are more difficult to standardize experimentally (M. Djupsjöbacka and M. Hulliger, unpublished observations). Yet the present analysis rests on the very feature of repeatability because otherwise any comparison of recorded with synthesized EMG signals during combined activation of multiple MUs would be invalid.

Linear summation versus downwardly nonlinear EMG

The present findings confirm the observation from other EMG simulation experiments (Day et al. 1996; Hulliger et al. 2001) that the slope of the relationship between EMG magnitude (AEMG) and ensemble activation rate of a pool of MUs decreases progressively (i.e., downward nonlinearity; see also INTRODUCTION). This was true both for experimentally recorded and computationally synthesized EMG. In addition, it was shown that this downward nonlinearity can largely if not exclusively be attributed to signal loss owing to MUAP phase cancellation because the nonlinearity was almost completely abolished on summation of rectified, instead of raw, MUAP trains (Day et al. 1996; see also Fortier 1994).

The linearity of the relationship between the summed rectified MUAP signal and EAR (Fig. 10A) may be a specific and somewhat accidental feature of the uniformly slow cat soleus muscle. In soleus, there is no correlation between MU size (tetanic force) and MUAP size (Ware et al., unpublished observations), so that statistically the contribution to the EMG signal of large and late recruited MUs is the same as that of the smaller MUs, which easily accounts for the preceding linear relationship. However, this does not necessarily hold true for other muscles or for MMUAP filaments in soleus. The latter probably contributes to the residual nonlinearity in the summed rectified EMG-EAR relation of Figs. 5 and 7. This issue was not further pursued experimentally, given the limitations of MMU filament stimulation (see preceding text).

The downward nonlinearity is a specific property (if not artifact) of the particular measures of EMG magnitude that are widely used (AEMG; REMG: r.m.s. magnitude of EMG). Indeed it was shown long ago that the variance of an EMG interference signal, if it is based on-linear summation of APs, increases linearly with ensemble activation rate (Milner-Brown and Stein 1975). However, for the commonly used measures of AEMG and REMG, the downward nonlinearity can be very significant, increasing progressively with the number of MUs that are recorded from a given electrode site: in computer simulations, it was shown that for a pool of 150 MUs up to 80% of the constituent signal can be lost, based on signal cancellation alone (Day et al. 1996; unpublished observations). Thus simple measures of EMG magnitude are poor indicators of peripheral motor drive.


    ACKNOWLEDGMENTS

We are most grateful to W. M. Morrow and B. Kacmar for valuable technical assistance with software and electronic hardware, and we thank Drs. R. Hawkes, A. Prochazka, and U. Windhorst for valuable comments on the manuscript.

This study was supported by the Alberta Heritage Foundation for Medical Research (AHFMR) and Medical Research Council Canada. S. J. Day was a recipient of an AHFMR studentship.


    FOOTNOTES

Address for reprint requests: M. Hulliger, Dept. of Clinical Neurosciences, Faculty of Medicine, University of Calgary, Health Sciences Centre, 3330 Hospital Dr. N.W., Calgary, Alberta T2N 4N1, Canada (E-mail: mhullige{at}ucalgary.ca).

Received 22 March 2000; accepted in final form 6 June 2001.


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ABSTRACT
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0022-3077/01 $5.00 Copyright © 2001 The American Physiological Society