Motor unit firing rate during static contraction indicated by the surface EMG power spectrum

Complexity Analysis of Surface Electromyography for Assessing the Myoelectric Manifestation of Muscle Fatigue: A Review

The surface electromyography (sEMG) records the electrical activity of muscle fibers during contraction: one of its uses is to assess changes taking place within muscles in the course of a fatiguing contraction to provide insights into our understanding of muscle fatigue in training protocols and rehabilitation medicine. Until recently, these myoelectric manifestations of muscle fatigue (MMF) have been assessed essentially by linear sEMG analyses. However, sEMG shows a complex behavior, due to many concurrent factors. Therefore, in the last years, complexity-based methods have been tentatively applied to the sEMG signal to better individuate the MMF onset during sustained contractions. In this review, after describing concisely the traditional linear methods employed to assess MMF we present the complexity methods used for sEMG analysis based on an extensive literature search. We show that some of these indices, like those derived from recurrence plots, from entropy or fractal analysis, can detect MMF efficiently. However, we also show that more work remains to be done to compare the complexity indices in terms of reliability and sensibility; to optimize the choice of embedding dimension, time delay and threshold distance in reconstructing the phase space; and to elucidate the relationship between complexity estimators and the physiologic phenomena underlying the onset of MMF in exercising muscles.

Single channel surface electromyogram deconvolution to explore motor unit discharges

Interference surface electromyogram (EMG) reflects many bioelectric properties of active motor units (MU), which are however difficult to estimate due to the asynchronous summation of their discharges. This paper introduces a deconvolution technique to estimate the cumulative firings of MUs. Tests in simulations show that the power spectral density of the estimated MU firings has a low-frequency peak corresponding to the mean firing rate of MUs in the detection volume of the recording system, weighted by the amplitudes of MU action potentials. The peak increases in amplitude and its centroid shifts to a higher frequency when MU synchronization is simulated (mainly due to the shift of discharges of large MUs). The peak is found even at high force levels, when such a contribution does not emerge from the EMG. This result is also confirmed in preliminary applications to experimental data. Moreover, the simulated cumulative firings of MUs are estimated with a correlation above 90% (considering frequency contributions up to 150 Hz), for all force levels. The method requires a single EMG channel, thus being feasible even in applied studies using simple recording systems. It may open many potential applications, e.g., in the study of the modulation of MU firing rate induced by either fatigue or pathology and in coherency analysis. Graphical Abstract Examples of application of the deconvolution (Deconv) algorithm and comparison with the cumulative firings and the cumulated weighted firings (CWF, i.e., each firing pattern is weighted by the root mean squared amplitude of the corresponding MU action potential). Portions of data are shown on the left, the power spectral densities (PSD) on the right (Welch method applied to 3 s of data, sub-epochs of 0.5 s, mean value removed from each of them, 50% of overlap). A) Simulated signal (50% of maximal voluntary contraction, MVC) with random MU firings. B) Simulated signal (50% MVC) with a level of synchronization equal to 10%. C) Experimental data from vastus medialis at 40% MVC (data decomposed by the algorithm of Holobar and Zazula, IEEE Trans. Sig. Proc. 2007; PSD of the cumulated firings almost identical to that of CWF, as few MUs were identified).

Monitoring voluntary blink magnitude through a wearable eye-tracking system: A preliminary study

This study proposes a novel approach to measure the contractile force of eye blink that is generally obtained from the orbicularis oculi activity through Ocular ElectroMyo-Graphy (O-EMG). Here, O-EMG is compared with the eye information acquired through a wearable head-mounted eye-tracking system in order to investigate the possibility of using the eye-tracking in place of the O-EMG. Eight subjects were simultaneously monitored through an O-EMG and the eye-tracker while they were performing a structured protocol implying a variation in the blink contractile strength. Results showed that eye-tracking features were able to statistically discriminate three kinds of contractile forces similarly to EMG features. The consequent correlation analysis revealed that all the EMG-related features were significantly correlated with the eye-tracking ones with a p-value <;10^-6. Moreover, considering the extracted eye-tracking features, i.e. Integrated Gaze Path (IGP) and Eye-closed Duration (ECD), IGP reported a higher Spearman's correlation values with eye-blink reflex magnitude (EBM) than ECD. These encouraging results suggest that the ocular information extracted from the eye-tracking could be profitably used in non-invasive ecological environments where wearability and comfortability play a crucial role in detecting spontaneous response.

Preliminary investigation of energy comparation between gyroscope, electromyography and VO2 wearable sensors

Building on previous experiments in the domain of energy expenditure estimation using wearable sensors, the measurements of energy ratios of a runner on a treadmill were analyzed to observe any commonalities between an inertia measurement unit and an electromyograph sensor. The subjects were equipped with a VO2 gas measurement device, an Inertial Measurement Unit (IMU) measuring gyroscopic activity and an electromyography (EMG) sensor network whilst running at 5 different speeds on a calibrated treadmill. The observed results established a co-linear relationship with the gyroscope based measurements, EMG based measurements with the VO2 measurements.

Increases of quadriceps inter-muscular cross-correlation and coherence during exhausting stepping exercise

The aim of this study was to examine the change of the intermuscular cross-correlation and coherence of the rectus femoris (RF), vastus medialis (VM) and vastus lateralis (VL) during exhausting stepping exercise. Eleven healthy adults repeated the stepping exercise up to their individual endurance limits (RPE score reached 20), and the cross-correlation and coherence were assessed by surface electromyography (EMG) recordings. The coefficient and time lag of cross-correlation and the coherence areas in the alpha (8–12 Hz), beta (15–30 Hz), gamma (30–60 Hz) and high-gamma (60–150 Hz) bands among the three muscle pairs (RF-VM, RF-VL and VM-VL) were calculated. As muscle fatigue, RF-VM and VM-VL showed increases of coefficients and the shortening of time lags. RF-VM and RF-VL showed increases of beta-band coherence in the ascent and descent phases, respectively. The increased intermuscular cross-correlation and beta-band coherence may be a compensatory strategy for maintaining the coordination of knee synergistic muscles during fatigue due to the fatigue-related disturbance of the corticospinal transmission. Therefore, the intermuscular cross-correlation and beta-band coherence may be a potential index for assessing muscle fatigue and monitoring the central control of motor function during dynamic fatiguing exercise.

Multi-scale surface electromyography modeling to identify changes in neuromuscular activation with myofascial pain

To solve the limitations in using the conventional parametric measures to define myofascial pain, a 3-D multi-scale wavelet energy variation graph is proposed as a way to inspect the pattern of surface electromyography (SEMG) variation between the dominant and nondominant sides at different frequency scales during a muscle contraction cycle and the associated changes with the upper-back myofascial pain. The model was developed based on the property of the wavelet energy of the SEMG signal revealing the degree of correspondence between the shape of the motor unit action potential and the wavelet waveform at a certain scale in terms of the frequency band. The characteristic pattern of the graph for each group (30 normal and 26 patient subjects) was first derived and revealed the dominant-hand effect and the changes with myofascial pain. Through comparison of individual graphs across subjects, we found that the graph pattern reveals a sensitivity of 53.85% at a specificity of 83.33% in the identification of myofascial pain. The changes in these patterns provide insight into the transformation between different fiber recruitment, which cannot be explored using conventional SEMG features. Therefore, this multi-scale analysis model could provide a reliable SEMG features to identify myofascial pain.

Spectral properties of electromyographic and mechanomyographic signals during isometric ramp and step contractions in biceps brachii

The purposes of this study were: (1) to apply wavelet and principal component analysis to quantify the spectral properties of the surface EMG and MMG signals from biceps brachii during isometric ramp and step muscle contractions when the motor units are recruited in an orderly manner, and (2) to compare the recruitment patterns of motor unit during isometric ramp and step muscle contractions. Twenty healthy participants (age = 34 ± 10.7 years) performed step and ramped isometric contractions. Surface EMG and MMG were recorded from biceps brachii. The EMGs and MMGs were decomposed into their intensities in time-frequency space using a wavelet technique. The EMG and MMG spectra were then compared using principal component analysis (PCA) and ANCOVA. Wavelet combined PCA offers a quantitative measure of the contribution of high and low frequency content within the EMG and MMG. The ANCOVA indicated that there was no significant difference in EMG total intensity, EMG(MPF), first and second principal component loading scores (PCI and PCII) between ramp and step contractions, whereas the MMG(MPF) and MMG PCI loading scores were significantly higher during ramp contractions than during step contractions. These findings suggested that EMG and MMG may offer complimentary information regarding the interactions between motor unit recruitment and firing rate that control muscle force production. In addition, our results support the hypothesis that different motor unit recruitment strategy was used by the muscle when contracting under different conditions.

Periodontal-Masseteric Reflexes Decrease with Tooth Pre-load

The responses of incisal periodontal mechanoreceptors to increasing mechanical stimulation are known to follow a hyperbolic-saturating course. The implications of these properties for the reflexive control of bite-force have not been examined directly. In line with the abovementioned receptor characteristics, we hypothesized that the periodontal-masseteric reflex will reduce as a function of increasing incisal pre-load. In 10 participants, a central incisor was repeatedly tapped (0.4 N). We measured the modulation by pre-load (0.2–2.0 N) of the reflex frequency-response at and between 3 and 20 Hz. The entrainment of the reflex increased with frequency up to 20 Hz and diminished with increasing pre-load. Importantly, the hyperbolic relationship shown here between the periodontal-masseteric reflex and tooth pre-load agreed with the load/response relationships predicted by single-receptor and tooth movement studies. This study demonstrated that periodontal mechano-receptors are able to contribute to the ongoing control of only small bite-forces.

Mandibular physiological tremor is reduced by increasing-force ramp contractions and periodontal anaesthesia

We have previously shown that the application of anaesthesia to periodontal mechanoreceptors (PMRs) dramatically reduces the 6-12 Hz physiological tremor (PT) in the human mandible during constant isometric contractions where visual feedback is provided. This current study shows that during a ramp contraction where force is slowly increased, the amplitude of mandibular PT is almost five times smaller on average than when the same force ramp is performed in reverse, i.e. force is slowly decreased. This smaller tremor is associated with a higher mean firing rate of motor units (MUs) as measured by the sub-30 Hz peak in the multi-unit power spectrum. The decrease in the amplitude of PT following PMR anaesthetisation is associated in some instances with a similar increase in the overall firing rate; however this change does not match the diminution of tremor. The authors postulate that the decrease in mandibular PT during increasing force ramps may be due to a change in the mean firing rate of the MUs. The change in tremor seen during PMR anaesthetisation may in part be due to a similar mechanism; however other factors must also contribute to this.

Application of spectral entropy to EEG and facial EMG frequency bands for the assessment of level of sedation in ICU

The applicability and performance of spectral entropy as a measure of the depth of sedation was studied by comparison to the Richmond sedation and agitation scale (RASS). A biopotential signal was measured from the forehead of eight ICU patients. From this biopotential four different frequency bands were defined using trend fitting to the low and high frequency limits of the pooled power spectra, two frequency bands representing EEG and the other two representing fEMG. The spectral entropy from the EEG bands correlated very well with the sedation levels of RASS. From levels 0 to -5 the decrease was almost linear (r=0.51 and r=0.53). A similar comparison for the spectral entropy of the fEMG bands did not produce any clear correlation (r=0.07 for both fEMG bands), however there was still some clear interaction at some levels. It seems that the RASS is dependent upon both EEG and fEMG effects. That is; RASS is related to both cortical and sub-cortical components of sedation.

Surface EMG models: properties and applications

After a general introduction on the kind of models and the use of models in the natural sciences, the main body of this paper reviews potential properties of structure based surface EMG (sEMG) models. The specific peculiarities of the categories (i) source description, (ii) motor unit structure, (iii) volume conduction, (iv) recording configurations and (v) recruitment and firing behaviour are discussed. For a specific goal, not all aspects conceivable have to be part of a model description. Therefore, finally an attempt is made to integrate the 'question level' and the 'model property level' in a matrix providing direction to the development and application of sEMG models with different characteristics and varying complexity. From this overview it appears that the least complex are models describing how the morphological muscle features are reflected in multi-channel EMG measurements. The most challenging questions in terms of model complexity are related to supporting the diagnosis of neuromuscular disorders.

Dysgraphia in children: lasting psychomotor deficiency or transient developmental delay?

A longitudinal design was applied to differentiate between normal variations of psychomotor development and lasting handwriting deficiency (dysgraphia). Sixteen primary school children were tested with writing tasks that were recorded on a computer-monitored'XY tablet. These tasks represented different modules of the handwriting model of Van Galen (1991). Dependent variables were spatial errors, movement time, movement dysfluencies, trajectory length, stroke curvature, and the degree of neuromotor noise in the movement velocity profiles. The latter variable was measured by means of Power Spectral Density Analysis of the movement velocity signal, which revealed that movements of poor writers were substantially more noisy than those of proficient writers, with a noise peak in the region of neuromotor tremor. At the same time, the poor writers were less accurate. It was concluded that control of spatial accuracy rather than allograph retrieval or size control is the discriminating feature in dysgraphic children. Moreover, poor writers do not catch up with their peers within the 1 year time span tested.

Spatio-temporal representation of multichannel EMG firing patterns and its clinical applications

Analyzing motor unit (MU) activity is essential for studying the neurological dysfunction of upper motor neuron disorders (UMND). This study employs multichannel surface electromyographic (EMG) signals, as recorded from the upper arm during elbow flexion and extension, to analyze the temporal changes and spatial distribution of the dominant firing rate. To estimate the dominant firing rate, the autoregressive (AR) spectrum analysis method is utilized to detect the peaks and poles of the AR model, of the surface EMG spectrum below 40 Hz. The temporal changes in firing rates are also observed by using the spectrogram representation of low-frequency EMG spectra. The EMG spectrogram facilitates examination of the time-varying characteristics of firing rates and recruitment of MUs from surface EMG signal. The low-frequency spectra of multichannel EMG are then represented in a polar form to visualize the spatial distribution of firing patterns across muscles. Via spatio-temporal representation techniques, this study provides a viable approach of observing both the spatial and temporal patterns of MU activities in normal subjects and patients with UMND, including cerebrovascular disease and Parkinson's disease.

AR modeling of myoelectric interference signals during a ramp contraction

We investigated the time-varying behaviour of the autoregressive (AR) parameters in a myoelectric (ME) signal detected during a linear force increasing contraction. The AR parameters of interest were the reflection coefficients, the AR model spectrum, and the prediction errors. We used well-conditioned ME signals for which the complete time record of the motor units firings was available. In addition, the influence of the recruitment of a new motor unit, the conduction velocity of action potentials, and additive broad-band noise were investigated using simulated ME signals. The simulated ME signals were constructed from a selected group of the available motor unit action potential trains. The results revealed that, as the contraction progressed, the AR parameters displayed a time-varying behavior which coincided with the recruitment of newly recruited motor units whose spectrum of the waveform differed from that of the rest of the ME signal. This property of the AR parameters was obscured by the presence of broad-band noise and low-amplitude motor unit action potentials, both of which are more pronounced during low-level force contractions.

Rate modulation of jaw-elevator motor units as revealed from the low-frequency power spectrum of the surface electromyogram in myogenous CMD patients

The firing pattern of the motor units (MUs) in jaw-elevator muscles was studied within a wide range of isometric contraction levels by means of changes in the frequency and broadness of the primary peak in the low-frequency (5-40 Hz) power spectral density function of the surface EMG. EMG was recorded from both masseter and anterior temporal muscles in 11 myogenous CMD patients as well as in 11 gender- and age-matched controls who clenched in intercuspal occlusion under the control of visual feedback at various levels (0.5-67% MVC for the various muscles studied). The EMG was digitized for 12 periods of 1.6 s per condition; the power spectrum was averaged and smoothed for the various clenching levels. Linear regression analysis showed that the positive slope in the peak frequency (PF)/% MVC relationship, a measure of rate modulation of the MUs, did not differ significantly between patients and controls. At a low clenching level, PF was smaller (p < 0.01) for the anterior temporal muscles of the patients, suggesting lower firing rates for a wide range of clenching levels of the patients because of a similar rate modulation for patients and controls. Furthermore, the variance in the slope values was larger (p < 0.05) for the masseteric muscles of the patients, which may be explained by more heterogeneity of the masseteric rate modulation in the patient group. The broadness of the primary peak was smallest at a low clenching level (p < 0.001) for the anterior temporal muscles of the patients, suggesting a more uniform firing rate or more synchronization between MUs.

Single motor unit myoelectric signal analysis with nonstationary data

The information content of the myoelectric signal (MES) is commonly revealed by statistical measures in the time or frequency domain. Empirical analyses of the MES from a single motor unit have generally assumed that features are invariant with time. Theoretical and experimental work has been done to demonstrate how nonstationary behavior in the discharge statistics of a motor neuron may affect estimates of features extracted from the motor unit's contribution to the MES. Specifically, it has been shown that nonstationary behavior can markedly influence estimates of features describing motor neuron firing behavior and consequently, the low-frequency portion of the MES power spectral density. These results may help to explain the discrepancies in the literature which report empirical models of motor neuron firing statistics.

Investigation on parametric analysis of dynamic EMG signals by a muscle-structured simulation model

In the analysis of electromyographic (EMG) signals during dynamic movement, we have proposed an estimation algorithm for the time-varying parameters of an autoregressive model. The parameters correspond to less biased time-varying reflection coefficients. We determined the less biased estimation using a locally quasi-stationary model and named these parameters "k parameters." We estimated k parameters up to the fifth order for the surface EMG signals of a masseter muscle during rapid open-close movement of the lower jaw, a ballistic contraction, and fatigue. According to the results, the time courses of the k parameters displayed remarkable properties. In order to study the behavior of k parameters physiologically, we produced a muscle-structured simulation model based on anatomical and physiological data. The simulation results suggested that the behavior of the third parameter is related to the number of active motor units (MU's) at the shallow layer of a muscle. The detailed recruitment mechanism in terms of the MU's types has not yet been solved. Although further study is required, the parametric analysis using k parameters offers a new perspective for evaluation of muscle dynamics during several movements.

Frequency analysis of electromyographically measured covert speech behavior

Eleven subjects were asked to silently read slides of the letters "P" and "T," and to view meaningless control slides similarly as they were presented visually. One-eighth-second electromyographic excerpts were sampled from the baseline and response periods. The data were then transformed into the frequency domain for inferential analyses. The mean power spectral frequencies for the response period were significantly lower than those for the base-line in the overall analysis. There were, however, no significant changes from baseline as a function of kind of stimulus (T, P, or Control) or muscle activated (lips or tongue). It was concluded that there was a generalized responding, not unique to the processing of the specific stimuli studied. Frequency analysis of EMG measures of covert behavior holds some promise of yielding unique information not available through traditional analysis procedures, but more sensitive methods than those used here would be required to demonstrate this.

Quantitative surface electromyography in anesthesia and critical care

The frontalis muscle spontaneous (SEMG) and electrically evoked (EEMG) electromyograms were recorded in 4 different clinical settings. Using a standardized isoflurane-based anesthetic protocol. Study 1 examined the SEMG response to both surgical and acoustic stimuli. The acoustic SEMG response was also examined in comatose head-injured patients. Study 2 used the EEMG to compare the extent of vecuronium-induced neuromuscular blockade on the frontalis and hypothenar muscles in both anesthetized and comatose patients. In Study 3 head-injured comatose patients were used to investigate the relationship between SEMG changes and transient elevations in intracranial pressure (ICP). The effect of opiate analgesics on the pain-activated SEMG in conscious post-operative patients was investigated in Study 4. These studies illustrate the following phenomena. First, in conscious, unparalyzed or lightly anesthetized patients, painful (stressful) stimuli are associated with increases in SEMG amplitude. Thus, the SEMG may indicate periods of inadequate analgesia, not only post-operatively (Study 4) but also intra-operatively (Study 1), since we found the frontalis to be relatively insensitive to a non-depolarizing neuromuscular blocker (Study 2). However, the interpretation of intra-operative SEMG changes may be confounded by opiates (Study 4) and perhaps other agents capable of influencing the frontalis through either non-nociceptive central or peripheral mechanisms. Second, the opiate analgesics consistently decreased SEMG amplitude in non-tolerant conscious patients (Study 4. Although this opiate-induced decrease is not necessarily indicative of opiate analgesia, it may provide an objective, quantifiable measure of a central opiate effect. The SEMG is particularly well-suited to determine the precise timecourse of this effect. Third, in deeply anesthetized or comatose patients, unresponsive to either surgical or electrical stimulation. SEMG amplitude may increase in response to elevated ICP or certain sounds (Study 3). The stress (pain) and auditory-evoked SEMGs may thus provide measures of brainstem function that are independent of the level of consciousness.

The muscle activity spectrum: spectral analysis of muscle force as an estimator of overall motor unit activity

Starting from the observation that the part above 6 Hz of the power spectrum of force tremor during isometric contractions can be related to the unfused twitches of motor units firing asynchronously, an attempt was made to study the usefulness of force tremor spectral analysis as a global descriptor of motoneurone pool activity. To compensate for the mechanical low-pass filter characteristic of skeletal muscle which leads to increased damping of mechanical ripples at higher frequencies, a numerical compensation rule was derived from data obtained by electrical microstimulation of small ensembles of motor units (MUs). Hidden line plots of consecutive partially overlapping spectra allowed visualization of changes in spectral composition during ongoing muscle activity. The resulting muscle activity spectra (MAS) showed broad peaks according to the range of onset firing rates in normal subjects. These tended to shift to higher frequencies with increasing force. Under conditions with increased synchronization of the MUs these broad peaks were replaced by sharp peaks corresponding to the burst repetition rate. Patients with different motor dysfunctions were selected to illustrate how alterations of MU activity are reflected in the MAS. Decreased or increased firing rates were observed as well as abnormal states of synchronization. It is concluded that the MAS provides useful information about some aspects of the discharge characteristics of ensembles of MUs and therefore represents a method to monitor some qualitative 'image' of the MU activities within a muscle.

A surface electrode array for detecting action potential trains of single motor units

Action potentials of single motor units were detected by a linear surface electrode array placed perpendicular to the longitudinal axis of the biceps brachii. Twelve myoelectric signals were derived simultaneously from a voluntarily contracting muscle. Using a visual feedback control, 3 subjects produced spike trains of single motor unit action potentials (MUAPs) at a weak contraction. When the myoelectric signals showed an interference pattern at a moderate contraction, several MUAPs were isolated by a visual analysis. MUAPs occurring at about fixed intervals with constant amplitudes and with identical wave forms were presumed to be the action potential trains of single motor units. Reliable estimates of single MUAP wave forms were obtained by averaging and superimposing the detected signals at a timing of characteristic potential peaks. Then not only the firing rate of the spikes but also the territory and the wave form of single MUAPs were investigated. Most MUAPs had a sharp and symmetrical distribution of potentials on a skin surface along the muscle circumference, while some MUAPs showed complex wave forms with some separate potential peaks. The possible arrangement of muscle fibers belonging to the motor units was estimated from the MUAP wave forms.

Influence of motor unit firing statistics on the median frequency of the EMG power spectrum

Changes in the EMG power spectrum during static fatiguing contractions are often attributed to changes in muscle fibre action potential conduction velocity. Mathematical models of the EMG power spectrum, which have been empirically confirmed, predict that under certain conditions a distinct maximum occurs in the low-frequency part of the spectrum, indicating the dominant firing rate of the motor units. The present study investigated the influence of this firing rate peak on the spectral changes during a static fatiguing contraction at 50% of maximum EMG amplitude in the frontalis and corrugator supercilii muscles. An exponential decrease of the median frequency (MF) of the EMG power spectrum was observed when the firing rate peak was absent. When the firing rate peak was present, an exaggerated decrease of MF in the beginning of the contraction was found, which was associated with an increase in firing rate peak magnitude. In later stages of the contraction, a partial recovery of MF occurred, concomitant with a decrease in firing rate peak magnitude. The influence of the firing rate peak on MF was also investigated during nonfatiguing contractions of the frontalis muscle at 20, 40, 60, and 80% of maximum EMG amplitude. A curvilinear relationship between MF and contraction strength was found, whether firing rate peaks were present or absent. The presence of firing rate peaks, however, was associated with a decrease in MF which was inversely related to contraction strength, due to the inverse relationship between firing rate peak magnitude and contraction strength.

The effects of motor unit synchronization on the power spectrum of the electromyogram

A realistic model for two synchronized motor unit action potential trains (MUAPT) is presented in which the variability of the time difference between corresponding action potentials (hereafter denoted by delay) is taken into account. Specifically, this delay is modeled as a continuous random variable that may assume both positive and negative values. Expressions are derived for the auto- and cross-power spectra of two such trains using their relations with the auto- and cross-correlation functions, respectively, with which they form Fourier transform pairs. The results show that the auto- and the cross-power spectra of two such synchronized MUAPTs differ from the auto- and the cross-spectra of two independent MUAPTs. The contribution of the statistics of the interpulse intervals to one of the auto-power spectra is smaller and the cross-power spectra no longer reduce to a Dirac sigma-function at the origin but are now determined by the other auto-power spectrum and by the Fourier transform of the density function associated with the time difference between corresponding action potentials. As a consequence of this change in the cross-power spectra synchronization leads to an absolute increase of power at low frequencies and to a relative decrease of power at high frequencies. The results are then generalized to electromyograms (EMG) composed of more than just two MUAPTs and illustrated with simulated power spectra with which the theory shows excellent agreement.