A linear stochastic model of the single motor unit

Parallel neuronal mechanisms underlying physiological force tremor in steady muscle contractions of humans

We present results from a study of the 6-to 12-Hz force tremor in relation to motor unit (MU) firing synchrony. Our experimental observations from 32 subjects, 321 contractions, and 427 recorded MUs reveal that tremor is accompanied by corresponding, in-phase MU rhythms that are additional to the ones at the MU intrinsic firing rates. This rhythmical synchrony is widespread and has a uniform strength that ranges from near zero to very large (MU/MU coherence > 0.50) in different contractions. Both the synchrony and the tremor are suppressed during ischemia, and this strongly suggests an involvement of spindle feedback in their generation. Furthermore, in the presence of substantial synchrony, the tremor enhancement, relative to the minimal tremor of ischemia, reflects the strength of the synchrony. Theoretical considerations based on these observations indicate that the muscle force signal is expected to show 1) frequency components in the band of the firing rates of the last-recruited, large MUs, and 2) because of the synchronized MU rhythms, an additional, distinct component with a size reflecting the strength of synchrony. Furthermore, synchronized MU rhythms, with frequencies in the 6- to 12-Hz range, are expected to arise from self-oscillations in the monosynaptic stretch reflex loop, due primarily to the associated muscle delay (several tens of milliseconds). Our results therefore reveal the parallel action of two tremor mechanisms, one of which involves MU synchrony probably caused by loop action. Clearly, the results on the synchrony and its impact also apply to other possible generators of tremor synchrony, including supraspinal ones.

Nonuniform activation of the agonist muscle does not covary with index finger acceleration in old adults

This study examined the patterns of activation in the superficial and deep parts of the first dorsal interosseus muscle and in the antagonist muscle, second palmar interosseus, during postural tasks (position holding) and slow movements (position tracking) of the index finger performed by young and old adults. The position-tracking task involved the index finger lifting light loads (2.5, 10, and 35% of maximum) with shortening and lengthening contractions as steadily as possible. Steadiness was quantified in both tasks as the standard deviation of index finger acceleration. The fluctuations in acceleration during the two tasks were greater for the old subjects (62-72 yr) compared with young subjects (19-27 yr), especially with the lightest loads. The two groups of subjects activated the superficial and deep parts of first dorsal interosseus at similar intensities during the position-holding task, whereas the deep part was more active during the shortening and lengthening contractions of the position-tracking task. The nonuniform activation of first dorsal interosseus, therefore, was not associated with the difference in the standard deviation of acceleration between the young and old subjects. Furthermore, there was no association between the average level of coactivation by the antagonist muscle and the standard deviation of acceleration for either group of subjects across these tasks. Thus the greater variability in motor output exhibited by the older adults could not be explained by either the nonuniform activation of the agonist muscle or the average level of coactivation by the antagonist muscle.

On the detection and measurement of synchrony in neural populations by coherence analysis

This study considers the possibility of using coherence analysis for detection and measurement of synchrony (correlations) in large neural populations, applied to activities that are relatively easy to record in parallel. Mathematical analysis and computer simulations are used to examine the behavior of the coherence function between both unitary and population-aggregate activity (UTA coherence) and the aggregate activities of two populations (ATA coherence). The results indicate that for a large population showing partial correlations, the UTA coherence function is almost zero at all frequencies for the uncorrelated units. However, unless the synchrony is very restricted, its value is nonzero (i.e., statistically significant by common criteria) at each frequency of synchrony for the units that show correlations to other units. Moreover, this value is indicative of the strength of synchrony for any given unit. These properties enable the identification of the correlated units in a sample of unit/population activities simultaneously recorded in a series of experiments, and hence the detection of synchrony. The extent of synchrony can then be estimated as the fraction of such units in the sample, whereas the values of the UTA coherences in the sample can be used to estimate the strength and its distribution within the population. Similarly, the ATA coherence function is generally nonzero (significant) at the frequencies where there are correlations between members of two large populations. This enables the easy detection of such correlations from simultaneously recorded population activities. However, this function is a very sensitive index of synchrony and even shows saturation effects. It may therefore be used as a general measure of synchrony only under restricted conditions.

Surface EMG recordings during maximum static shoulder forward flexion in different positions

This study investigated how position in the range of motion influences the power spectral density function during static shoulder forward flexion. 23 healthy females (20-30 years) volunteered as subjects. They performed maximum static shoulder forward flexions in three positions: 45, 65 and 90 degrees of shoulder flexion. An isokinetic dynamometer was used and the subjects were seated in a specially constructed chair to enable adequate fixation. The elbow was extended and the hand pronated. Electromyographic (EMG) signals (using surface electrodes) were obtained from the descending part of the right trapezius, the anterior portion of the right deltoid, the right infraspinatus and the common belly of the right biceps brachii. The four EMG-signals and the torque and shoulder angle were analyzed by computer. For each 256 ms, mean power frequency, root mean square value and mean torque were calculated. At each of the three positions four 256 ms periods were analyzed and the data are presented as their means. In the trapezius and the biceps brachii the mean power frequency did not change between the three positions. Deltoid and infraspinatus had significantly higher mean power frequencies at 90 degrees than at 45 degrees of flexion. Different factors behind the change in mean power frequency are discussed. The need to standardize the range of motion when studying dynamic fatiguing contractions is emphasised.

The information carried by spindle afferents on motor unit activity as revealed by spectral analysis

Spectral analysis was used to study the effects of motor unit activity on the discharge patterns of muscle spindle endings. Spindle afferents of hind-limb muscles of the cat were recorded during electrical stimulation of one or more motor units, and, for comparison, while the receptors discharged in the absence of induced extrafusal activity ('background discharge'). The stimulus sequences used were random, but had characteristic frequency components representing an underlying rhythm, similar to those of trains in real alpha-motoneuron output. The computed afferent spectra and coherences between stimulus and afferent trains indicate that the discharge patterns of muscle spindles carry information on the activity of particular subsets of motor units. The spectra also demonstrate a complex interaction of internal spindle (pacemaker) mechanisms and external (modulating) processes which determine the discharge patterns of primary and secondary endings. In addition, they reveal interesting differences between primaries and secondaries, possibly indicative of a particular role for each type of ending in motor control.

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.

A study of the electromyogram using a population stochastic model of skeletal muscle

The features of the electromyogram (EMG) are studied using a population model of skeletal muscle based on the differing properties and the independent activation of motor units (MUs). It is shown, both analytically and by computer simulation, that: (a) The power spectrum of the EMG is determined by the distribution of filtering and firing properties of the active MUs. (b) A tendency towards a rhythmical grouping of action potentials is to be expected from a set of asynchronous MUs firing semiregularly at similar rates; the grouped electrical activity has a phase-lead over the force output of the set of about 180 degrees. A unified explanation of the properties of the muscle force waveform and the electromyogram, in terms of asynchronous activity of MUs, is proposed. The explanation covers the relationship and the differences between the two signals.

A study of the muscle force waveform using a population stochastic model of skeletal muscle

A population stochastic model based on the differing properties and the independent activation of motor units is used to describe the production of force in the contracting skeletal muscle. Detailed force predictions of the model concerning a hand muscle are obtained by computer simulation. General features of the force signal are established analytically on the basis of the general properties of the neuromuscular system which the population model takes into account. The results show that the asynchronous activity of motor units and the distribution of their filtering and firing properties at various levels of muscle contraction are responsible, at least partially, for the main features of the muscle force waveform, including tremor.