Tremor-related motor unit firing in Parkinson's disease: implications for tremor genesis.

Muscle tremors reflect rhythmical motor unit (MU) activities. Therefore, the MU firing patterns and synchrony determine the properties of the parkinsonian force tremor (FT) and the neurogenic components of associated limb tremors. They may also be indicative of the neural mechanisms of tremor genesis which to date remain uncertain. We examined these MU behaviours during isometric contractions of a finger muscle in 19 parkinsonian subjects. Our results reveal that the parkinsonian FT is abnormally large. Like the physiological FT, it is accompanied by in-phase rhythms in all MU activities. However, there exist two important differences. Firstly, the synchrony during the parkinsonian FT is stronger than the normal one and therefore contributes to the FT enhancement. Secondly, the synchronous MU components partly represent rhythmical sequences of spike doublets and triplets whose incidences directly reflect the differences of the MU firing rates to the FT frequency. According to our analyses, the latter frequency coincides with the MU recruitment rate. Consequently, the numerous medium- and small-sized active MUs contribute rhythmical twitch doublets and triplets, i.e. large force pulses, to the parkinsonian FT. The impact of this effect on the FT amplitude is found to predominate over the impact of the augmented synchrony. Importantly, apart from the rule governing the occurrence of doublets/triplets, the mean interspike intervals within such spike events are fairly fixed around 50 ms. Such regularities in MU activities may reflect properties of the neural input underlying the FT, and thus represent a basis for more focused studies of the generator(s) of parkinsonian tremors.

Analysis of synchrony (correlations) in neural populations by means of unit-to-aggregate coherence computations.

This paper presents a general outline of the mathematical basis of an approach for analysis of population synchrony by means of coherence computations, a demonstration of the use of this approach, and a discussion of the potential utility and limitations of the approach. The coherence function for the pair single-unit activity and population-aggregate activity is studied in the light of theoretical considerations on the superposition of partially correlated unitary activities. The theoretical analysis, as well as computer simulations, indicate that when a subset of units in a population are correlated around some frequency, the unit-to-aggregate coherence function for members of this subset shows, in a wide range of conditions, a clear peak around that frequency (and possibly harmonic peaks), being very low at other frequencies where there is no synchrony. Specifically, the value of the peak coherence at the frequency of synchrony reflects the strength of the unitary correlations and their extent within the population, the numerical size of the population, and the degree of phase concentration for the units of the correlated subset. This value remains substantial, or at least significant, for wide ranges of values of these parameters. In contrast, the unit-to-aggregate coherence function for the remaining uncorrelated units has very low values at all frequencies, and tends to zero in the case of a large population. On the basis of these properties, an approach is presented for analysis of synchrony (correlations) in a neural population, which is simple and efficient, particularly when the population is large in numerical size. This approach utilizes unit-to-aggregate coherence computations for a sample of recorded unitary activities as a means for detecting population synchrony and estimating the extent of synchrony. In addition, this analysis can provide useful information on other characteristics of synchrony, such as the strengths of the unitary correlations. The use of the approach is demonstrated with an example from a study of fast rhythms in inspiratory activities, and other applications are also briefly described. The main advantage of unit-to-aggregate coherence analysis is that by using readily recorded activities, it efficiently identifies correlated units in a population and provides information on characteristics of synchrony, at every frequency within the range of interest.

Frequency response of spinal Renshaw cells activated by stochastic motor axon stimulation.

In anaesthetized or decerebrate cats, motor axons in lumbosacral ventral roots or hindlimb muscle nerves were stimulated with random trains of brief electrical pulses, and Renshaw cell spike sequences were recorded. Spectral analysis was used to determine the range of linear operation of Renshaw cells, via coherence computations, and to calculate their frequency-dependent gains and phases. The analysis showed that the dynamic behaviour of Renshaw cells was different for different strengths of their synaptic input from motor axons and for different mean stimulus rates. In general, the changes in dynamics associated with variation of these two input parameters followed a common trend. This can be related to the average response of Renshaw cells per stimulus, as assessed by peri-stimulus time histograms. For axons having a strong excitatory effect on a Renshaw cell (as judged from the size of early peri-stimulus time histogram peaks), and for low mean stimulus rates (10-23 pulses per second), the linear range of signal transmission (assessed by coherence computation) was usually very broad (from zero sometimes up to over 100 Hz, but mostly up to 50-100 Hz). Following an initial elevation in the range 2-15 Hz, the gain showed first a rapid decrease with frequency, down to a value which at 30-50 Hz could be a tenth of the gain at lower frequencies (2-15 Hz); it then continued to decline slowly. Otherwise the linear range was narrower and/or the coherence was generally lower; the gain was lower and showed little decline with frequency. The phase curves of Renshaw cells generally showed a low-frequency phase lead (up to roughly 10 Hz) and an increasing phase lag thereabove that was generated in part by the conduction delay. The results show that Renshaw cells can follow, particularly sensitively, inputs in a frequency range encompassing the steady firing rates of many alpha-motoneurons. This range of high gain also covers that of a component of physiological tremor (ca. 6-12 Hz), a basic mechanism of which is probably related to unfused contractions of newly recruited motor units firing in this range. It can therefore be expected that recurrent inhibition via Renshaw cells is especially powerful in this physiologically important range of alpha-motoneuron firing.

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.

Spindle gain increase during muscle unit fatigue.

In anaesthetized cats, medial gastrocnemius motor units (MUs) were stimulated with random sequences (mean rates between 6 and 12 pps) of electrical pulses delivered to their axons in small ventral root filaments. Muscle tension was recorded under isometric conditions, and spike trains of muscle spindle afferents were recorded from small dorsal root filaments during prolonged MU activation. Time-domain (PSTH) and frequency-domain (gain) computations were performed to study the effects of fatiguing muscle unit contractions on the signal transmission from skeletomotor efferents to spindle afferents. In the course of muscle unit fatigue, during which the gain of the force-producing sub-system decreased, the gain of the sub-system transforming force to afferent discharge increased so that the overall gain between skeletomotor efferents and spindle afferents remained relatively high. This could be a mechanism that preserves a high quality of afferent information on MU contractions.

Fast rhythms in the discharges of medullary inspiratory neurons.

The discharges of 44 medullary inspiratory (I) neurons in decerebrate paralyzed cats were studied using interval and spectral analysis. Most neurons had a rhythm in their discharge. In 31 the rhythm was at the frequency of, and coherent to, the high-frequency oscillations (HFOs) of I nerves, and in 7 the rhythm was in the range of medium-frequency oscillations (MFOs), with no coherence to nerve MFOs. Thus, correlated HFOs are characteristic of the I system at all levels, whereas MFOs are uncommon in medullary neurons and seem to be unrelated to general mechanisms.

Intracellular potentials and discharge patterns of expiratory neurons in the caudal ventral respiratory group: influence of phasic pulmonary afferent input.

In decerebrate paralyzed cats, the membrane potential (MP) patterns of 12 augmenting expiratory (E) neurons in the caudal ventral respiratory group, and phrenic and recurrent laryngeal activities, were compared for inspiratory (I) phases with and without lung inflation. No-inflation produced, in the MPs of E neurons, larger hyperpolarization during I and during early E (associated with increased early-E laryngeal activity), suggesting an increase of inhibitory inputs from I neurons and early-E neurons, respectively.

Changes in frequency content of inspiratory neuron and nerve activities in the course of inspiration.

In decerebrate paralyzed cats, the spectra and coherences of inspiratory (I) nerve activities and of medullary I neuron discharges were compared between different stages of I. The correlated high-frequency oscillations (HFOs) in the activities had common time courses of frequency and strength, which were influenced by lung afferent input; whereas the time courses for the uncorrelated medium-frequency oscillations (MFOs) depended on individual activity patterns. These results indicate that HFOs are characteristic of the common I pattern generator, whereas MFOs are specific to individual activities.

High-frequency and medium-frequency components of different inspiratory nerve discharges and their modification by various inputs.

In decerebrate paralyzed cats, spectral analysis was performed on simultaneous recordings of efferent inspiratory nerves (phrenic, recurrent laryngeal, hypoglossal). Spectral peaks were present both in the high-frequency (HFO) range (50-100 Hz) and the medium-frequency (MFO) range (20-50 Hz). Different activities were coherent only in the HFO range, indicating that the HFOs arise in a common inspiratory pattern generator that drives the different motoneuron populations, whereas the MFOs are specific to different systems.

Amplitude reduction of motor unit twitches during repetitive activation is accompanied by relative increase of hyperpolarizing membrane potential trajectories in homonymous alpha-motoneurons.

In anaesthetized cats, medial gastrocnemius motor units (MUs) were electrically stimulated via their ventral-root axons with independent random patterns. Isometric muscle tension and homonymous alpha-motoneuron (MN) membrane-potential fluctuations in response to these stimuli were recorded simultaneously, usually for periods of about 2 min. The tension and membrane potential were averaged with respect to a stimulus train over two disjoint time intervals, one stretching 20-40 s at record beginning, and the other a similar duration at the end of recording. Whereas average MU twitch amplitudes usually decreased between these periods, average membrane potential trajectories did not do so, such that, when normalized to the change in twitch amplitude, the membrane potential trajectories usually increased in size. This suggests that the decline in the mechanical effect of MU activation was accompanied by an increase in the gain of the afferent pathway to homonymous MNs, which was confirmed by gain computations in the frequency domain. This compensation could be a mechanism to maintain the high quality of information about MU contractions transmitted to MNs in the course of MU fatigue.

Coherent modulations of human motor unit discharges during quasi-sinusoidal isometric muscle contractions.

Spectral analysis of single-unit discharges, multi-unit EMG and muscle force during voluntary quasi-sinusoidal isometric contractions of two hand muscles revealed corresponding modulations of the firing rates of motor units at the frequency of the force oscillation. These rate modulations were correlated; and they showed a phase advance over the force oscillation, which is consistent with a cause-effect relationship between changes in firing rate and variations in force. These effects, observed over wide ranges of modulation amplitudes and frequencies, confirm the role of rate coding in the generation of time-varying muscle contractions; and they support the idea that during voluntary contraction of a given muscle, the motoneuron pool is subject to a common drive.

The 'M2' electromyographic response to random perturbations of arm movements is missing in long-trained monkeys.

Adult monkeys who have been under training over a long period of time show a loss of the M2 component in their biceps electromyographic response to brief, random perturbations of an alternating arm movement, the M1 component being apparently enhanced. These changes of the stretch-induced responses indicate a long-term plasticity of the sensorimotor system of monkeys. This result also provides hints for the origin and possible functional significance of the short- and long-latency components of the electromyographic response in subjects with less experience.

A linear stochastic model of the single motor unit.

The production of force and of the electrical signal by an active motor unit is theoretically described. Neural spikes are modelled using the Dirac delta function. Mechanisms for the generation of random impulse trains and the properties of the corresponding stochastic processes are discussed; the "renewal" model is proposed as the most appropriate. The possibility of using a linear model for the systems that produce force and electrical signal in the unit is examined. It is concluded that the linear assumption is justifiable during steady, constant-strength contractions of muscle. This linear stochastic model of the motor unit is used in two subsequent papers to study the muscle force and the electromyogram.

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.

Note on the estimation of the correlation function of neural spike trains.

The use of time-bins in the estimation of the correlation function of neural spike trains has a filtering effect on the estimate and results in distortion and aliasing. Prior low-pass filtering of the spike trains, on the other hand, and computation of the correlation function of the emerging waveforms in the standard way result in an estimate that is also a filtered version of the original function but distortion- and alias -free. In addition, the correlation function so computed can be normalized. An analogous definition of the correlation coefficient for the first technique enables the comparison of these various correlation estimates and clarifies their properties.

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.

The mathematical basis of population rhythms in nervous and neuromuscular systems.

The mechanism underlying rhythmical aggregate activity of a population of neural or neuromuscular elements is examined in this report. By making use of the spectral properties of stochastic processes (Papoulis, 1965), it is shown that such population rhythms are the inevitable effect of the rhythmical activities of the individual elements, irrespective of the phase relations of the latter. This result applies to both "discrete" signals, such as spike trains, and "continuous" ones, such as membrane potential fluctuations. It has implications regarding the generation of common physiological rhythms and the preservation of rhythms when converging activity of one of the above two types is transformed into activity of the other type.

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.

Occurrence of widespread motor-unit firing correlations in muscle contractions: their role in the generation of tremor and time-varying voluntary force.

The firing behavior of motor units (MUs) of the first dorsal interrosseus muscle of the hand was examined during both constant-force and varying-force (sinusoidal or broadband random variations) isometric contractions in healthy adults. The emphasis was on the analysis of MU synchrony with an efficient and sensitive method. In static contractions, widespread and strong MU firing correlations, with the MUs in phase, were present at the frequency of muscle tremor, when the tremor was regular (narrowband) and large. MU correlations could also exist in contractions where the tremor of a subject was irregular (broadband) overall, but they were generally weak. These correlations were at the frequency of the subject's regular tremor, and the corresponding distinct tremor component was sometimes discernible within the broad tremor-band. In contrast, the MUs did not show any such correlations in the case of purely irregular and small tremor. On the basis of these observations, it is concluded that the rhythms in the force contributions of the last- recruited, large MUs, which fire near their threshold rate, compose the broadband frequency content of physiological muscle tremor in every contraction. Within this band, there is an additional distinct tremor component when MU correlations are present. For widespread and strong MU correlations, this component dominates and constitutes the observed regular tremor. In dynamic contractions, the firing of all MUs was modulated in the frequency band of both the sinusoidal and the complex variations of the force. The MU modulations showed a time-lead over the force variations and were strongly correlated both to these variations and among themselves. Thus widespread and strong correlations of MU firing modulations seem to provide a mechanism for generation of time-varying voluntary force, under general dynamic conditions. Finally, when regular tremor was present in dynamic contractions, widespread and fairly strong MU correlations also existed at the tremor frequency. It is concluded that at least two mechanisms can cause widespread MU synchrony, and they can act in parallel. They involve two types of correlated inputs to the alpha-motoneurons (presumably from the muscle spindles and the cortex), whose effects combine at the level of the membrane potential of the cells.

Force predictions relating to tremor and other consequences of a 'distributed' model of skeletal muscle.

In this brief report, a 'distributed' computer model of skeletal muscle is described, and its predictions regarding muscle force and EMG are presented. The force and myo-electric signals are produced as the sum of the contributions of independently activated motor units possessing a distribution of properties. The results of the simulation as well as theoretical study show that: (a) asynchronous activity of motor units can be responsible for the fairly regular oscillations observed in muscle tremor; (b) the use, in the case of muscle, of the limit theorem for the superposition of independent point processes leads to erroneous conclusions with respect to the frequency characteristics of the muscle force waveform, and possibly, with regard to those of the EMG.