An EMG study of functional cortico-motoneuronal connections in humans.

We set out to decompose the EMG signal into its constituent motor unit action potential components to track motor unit firing rates with a high degree of accuracy and extract their average firing rate. We were able to show that this average firing rate tracks the subject's force trajectory from beginning to end. We propose that this average firing rate is a volitional control signal pointing to the existence of a 'volitional unit'. This volitional unit has to do with the projection of a group of functionally related cortico-motoneurons on a group of spinal motoneurons in the motoneuronal pool of a muscle. Our study of motor unit firing patterns during their steady state showed that spinal motoneurons respond to a descending central input in a Gaussian manner. We have further shown that the central drive itself, as represented by the average firing rate of the active motor units, also displays a Gaussian firing behavior. We have also described the existence of a 'translation factor', highly correlated to the motor unit size, which is unique to each spinal motoneuron and determines the motoneuronal response, and its resulting firing rate, to the descending inputs. As for force generation, we have shown that expressing the twitch force of a motor unit in a dynamic fashion using the 'electrotwitch' concept of firing rate x macro area, approximates motor unit force output better and accounts for firing rate related force changes more effectively than force estimates based on the mechanical twitch.     

Periodontal mechanoreceptor input reduces synchronous discharge of voluntarily activated masseter motor units in man

The control exerted by inputs from periodontal mechanoreceptors (PMRs) on the tonic activity of 35 pairs of single motor units in the left masseter muscle was investigated with and without the presence of continuous pressure on the upper left central incisor tooth. Crosscorrelograms were computed to assess the temporal coupling between the discharges of the motor unit pairs. In the absence of continuous pressure, central peaks in the cross-correlograms revealed the presence of significant synchronous discharge in 16 out of the 35 pairs tested. In contrast, during PMR stimulation only nine pairs were found to discharge with a significant amount of synchronization. It is concluded that short-term synchronization due to common, partially common and synchronized inputs shared by the motoneurons was reduced whenever extraneous periodontal inputs were superimposed on the voluntary command. This indicates that the interneurons which mediate the periodontal inputs arising from one single tooth are not distributed widely throughout the masseter motoneuron pool. In contrast, it appears that periodontal inputs are liable to reduce the efficiency of common inputs distributed to the masseter motoneurons during voluntary contraction ("desynchronization").     

Periodontal mechanoreceptor input reduces synchronous discharge of voluntarily activated masseter motor units in man

The control exerted by inputs from periodontal mechanoreceptors (PMRs) on the tonic activity of 35 pairs of single motor units in the left masseter muscle was investigated with and without the presence of continuous pressure on the upper left central incisor tooth. Cross-correlograms were computed to assess the temporal coupling between the discharges of the motor unit pairs. In the absence of continuous pressure, central peaks in the cross-correlograms revealed the presence of significant synchronous discharge in 16 out of the 35 pairs tested. In contrast, during PMR stimulation only nine pairs were found to discharge with a significant amount of synchronization. It is concluded that short-term synchronization due to common, partially common and synchronized inputs shared by the motoneurons was reduced whenever extraneous periodontal inputs were superimposed on the voluntary command. This indicates that the interneurons which mediate the periodontal inputs arising from one single tooth are not distributed widely throughout the masseter motoneuron pool. In contrast, it appears that periodontal inputs are liable to reduce the efficiency of common inputs distributed to the masseter motoneurons during voluntary contraction ("desynchronization").     

Simulation system of spinal cord motor nuclei and associated nerves and muscles,in a Web-based architecture

A Web-based simulation system of the spinal cord circuitry responsible for muscle control is described. The simulator employs two-compartment motoneuron models for S, FR and FF types, with synaptic inputs acting through conductance variations. Four motoneuron pools with their associated interneurons are represented in the simulator, with the possibility of inclusion of more than 2,000 neurons and 2,000,000 synapses. Each motoneuron action potential is followed, after a conduction delay, by a motor unit potential and a motor unit twitch. The sums of all motor unit potentials and twitches result in the electromyogram (EMG), and the muscle force, respectively. Inputs to the motoneuron pool come from populations of interneurons (Ia reciprocal inhibitory interneurons, Ib interneurons, and Renshaw cells) and from stochastic point processes associated with descending tracts. To simulate human electrophysiological experiments, the simulator incorporates external nerve stimulation with orthodromic and antidromic propagation. This provides the mechanisms for reflex generation and activation of spinal neuronal circuits that modulate the activity of another motoneuron pool (e.g., by reciprocal inhibition). The generation of the H-reflex by the Ia-motoneuron pool system and its modulation by spinal cord interneurons is included in the simulation system. Studies with the simulator may include the statistics of individual motoneuron or interneuron spike trains or the collective effect of a motor nucleus on the dynamics of muscle force control. Properties associated with motor-unit recruitment, motor-unit synchronization, recurrent inhibition and reciprocal inhibition may be investigated.     

Influence of motoneuron firing synchronization on SEMG characteristics in dependence of electrode position.

The frequency content of the surface electromyography (SEMG) signal, expressed as median frequency (MF), is often assumed to reflect the decline of muscle fiber conduction velocity in fatigue. MF also decreases when motor unit firings synchronize, and we hypothesized that this effect can explain the electrode-dependent pattern in our previous recordings from the trapezius muscle. An existing motoneuron (MN) model describes the afterhyperpolarization following a spike as an exponential function on which membrane noise is superimposed. Splitting the noise into a common and an individual component extended the model to a MN pool with a tunable level of firing synchrony. An analytical volume conduction model was used to generate motor unit action potentials to simulate SEMG. A realistic level of synchrony decreased the MF of the simulated bipolar SEMG by approximately 30% midway between endplate position and tendon but not above the endplate. This is in accordance with experimental data from the biceps brachii muscle. It was concluded that the pattern of decrease of MF during sustained contractions indeed reflects MN synchronization.     

Enhanced motor unit rate coding with improvements in a force-matching task

These data describe improved modulation of discharge rates (rate coding) of first dorsal interosseous motor units throughout the acquisition of a complex force-matching skill involving isometric index finger abduction. In each of 15 consecutive trials, subjects attempted to match their force to a trajectory consisting of the sum of two sine waves (0.15 and 0.5 Hz) and random oscillations (overall mean force level ˜20% MVC). Reductions in root-mean-square (RMS) error of each subject’s force relative to the trajectory indicated substantial improvements in force-matching ability (F=33.8, p<0.001). With the acquisition of this new skill, there was increased amplitude modulation of muscular force near both dominant frequencies of the force-matching trajectory (F=10.6, p=0.008). The standard deviation and coefficient of variation of motor unit inter-spike intervals both decreased with improved performance indicating a general reduction in the amplitude of firing rate modulations (SD: F=18.69, p=0.001; CV: F=43.6, p<0.001). After skill acquisition, there was decreased firing rate modulation outside of the two dominant frequencies and increased amplitude of firing rate modulation at the higher of the two dominant frequencies (0.5 Hz, F=8.23, p=0.015). These findings indicate that improved precision of rate coding was a contributor to the acquisition of the new force-matching task. That the change in rate coding was frequency dependent suggests that factors other than frequency coding may contribute to the improved force matching at 0.15 Hz.     

Efficient “Communication through Coherence” Requires Oscillations Structured to Minimize Interference between Signals

The ‘communication through coherence’ (CTC) hypothesis proposes that selective communication among neural networks is achieved by coherence between firing rate oscillation in a sending region and gain modulation in a receiving region. Although this hypothesis has stimulated extensive work, it remains unclear whether the mechanism can in principle allow reliable and selective information transfer. Here we use a simple mathematical model to investigate how accurately coherent gain modulation can filter a population-coded target signal from task-irrelevant distracting inputs. We show that selective communication can indeed be achieved, although the structure of oscillatory activity in the target and distracting networks must satisfy certain previously unrecognized constraints. Firstly, the target input must be differentiated from distractors by the amplitude, phase or frequency of its oscillatory modulation. When distracting inputs oscillate incoherently in the same frequency band as the target, communication accuracy is severely degraded because of varying overlap between the firing rate oscillations of distracting inputs and the gain modulation in the receiving region. Secondly, the oscillatory modulation of the target input must be strong in order to achieve a high signal-to-noise ratio relative to stochastic spiking of individual neurons. Thus, whilst providing a quantitative demonstration of the power of coherent oscillatory gain modulation to flexibly control information flow, our results identify constraints imposed by the need to avoid interference between signals, and reveal a likely organizing principle for the structure of neural oscillations in the brain.     

Synaptic integration in motoneurons with hyper-excitable dendrites

Motoneurons have extensive dendritic trees that receive the numerous inputs required to produce movement. These dendrites are highly active, containing voltage-sensitive channels that generate persistent inward currents (PICs) that can enhance synaptic input 5-fold or more. However, this enhancement is proportional to the level of activity of monoaminergic inputs from the brainstem that release serotonin and noradrenalin. The higher this activity, the larger the dendritic PIC and the higher the firing rate evoked by a given amount of excitatory synaptic input. This brainstem control of motoneuron input-output gain translates directly into control of system gain of a motor pool and its muscle. Because large dendritic PICs are probably necessary for motoneurons to have sufficient gain to generate large forces, it is possible that descending monoaminergic inputs scale in proportion to voluntary force. Inhibition from sensory inputs has a strong suppressive effect on dendritic PICs: the stronger the inhibition, the smaller the PIC. Thus, local inhibitory inputs within the cord may oppose the descending monoaminergic control of PICs. Most motor behaviors evoke a mixture of excitation and inhibition (e.g., the reciprocal inhibition between antagonists). Therefore, normal joint movements may involve constant adjustment of PIC amplitude.     

A Canonical Circuit for Generating Phase-Amplitude Coupling

‘Phase amplitude coupling’ (PAC) in oscillatory neural activity describes a phenomenon whereby the amplitude of higher frequency activity is modulated by the phase of lower frequency activity. Such coupled oscillatory activity – also referred to as ‘cross-frequency coupling’ or ‘nested rhythms’ – has been shown to occur in a number of brain regions and at behaviorally relevant time points during cognitive tasks; this suggests functional relevance, but the circuit mechanisms of PAC generation remain unclear. In this paper we present a model of a canonical circuit for generating PAC activity, showing how interconnected excitatory and inhibitory neural populations can be periodically shifted in to and out of oscillatory firing patterns by afferent drive, hence generating higher frequency oscillations phase-locked to a lower frequency, oscillating input signal. Since many brain regions contain mutually connected excitatory-inhibitory populations receiving oscillatory input, the simplicity of the mechanism generating PAC in such networks may explain the ubiquity of PAC across diverse neural systems and behaviors. Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. Consequently, this model can inform attempts to associate distinct types of PAC with different network topologies and physiologies in real data.     

Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

The synchronized firings of active motor units (MUs) increase the oscillations of muscle force, observed as physiological tremor. This study aimed to investigate the effects of synchronizing the firings within three types of MUs (slow—S, fast resistant to fatigue–FR, and fast fatigable–FF) on the muscle force production using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including 8 S, 23 FR, and 26 FF) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.     

Modulation of motor unit firing rates during a complex sinusoidal force task in young and older adults.

This study compared motor unit rate coding and muscular force control in the first dorsal interosseous muscle of older (n = 11, mean 72.3 yr) and young (n = 12, mean 18.7 yr) adults. Rate coding during a sinusoidal isometric force-matching task was evaluated using spectral analysis of the time-varying changes in firing rate. The task required force modulations to match a trajectory comprising the sum of 0.15- and 0.45-Hz sine waves. Based on the amplitude of spectral peaks at 0.15 and 0.45 Hz, the amplitude of force modulation was similar in young and older adults at both frequencies (F = 1.9, P = 0.17). Force modulation gain (FMG) was computed as the ratio of the amplitude of force modulation to the amplitude of firing rate modulation. To account for rate coding differences related to the properties of the motoneuron, recruitment threshold force was used as a covariate in age-group comparisons. At both task frequencies, firing rate was modulated with less amplitude (F = 0 14, P < 0.001) and FMG was greater (F = 0 27, P < 0.001) in the older adults. In its transformation of neural input to mechanical output, muscle is known to act as a low-pass filter. Compared with modulation at 0.15 Hz, less change in force per change in firing rate at 0.45 Hz (lower FMG; F = 0 67, P < 0.001), independent of age group, is consistent with this filtering effect. Our conclusion is that there is a reduced amplitude of firing rate modulation in older adults.     

Mono-synaptic reflex responses of individual motoneurons

Individual motoneuron responses to a variety of afferent inputs have been examined. At a given input some motoneurons respond to every trial, some to no trial, and some respond to a certain percentage of trials that is characteristic for the motoneuron at that input. The performance of a motoneuron is expressed by means of a firing index that relates the number of responses to the number of trials. In a representative assemblage of individual motoneurons some 20 to 30 per cent display intermediate firing indices. This number, comprising an "intermediate zone" remains fairly constant at different levels of input although the individuals within it may be entirely different at two different levels of input. Frequency distribution of individuals with respect to firing indices is U-shaped. Intermediacy of firing indices depends upon temporal fluctuation of excitability which, in the first approximation, is normal. The individual motoneurons are approximately equally frequently distributed with respect to transmitter potentiality of their monosynaptic reflex afferent connections. The distribution of motoneurons with respect to transmitter potentiality of their monosynaptic reflex connections is considered representative of a natural pool in that the sum of their individual post-tetanic response behaviors accurately reproduces the course of post-tetanic potentiation in a natural pool.     

Simulations of the alpha motoneuron pool electromyogram reflex at different preactivation levels in man

The alpha motoneuron pool and the surface electromyogram (EMG) of the human soleus muscle are modelled, respectively, by an alpha motoneuron pool model generating the firing patterns in the motor units of e muscle and by a muscle model using these discharge patterns to simulate the surface EMG. In the alpha motoneuron pool model, we use a population of motoneurons in which cellular properties like cell size and membrane conductance are distributed according to experimentally observed data. By calculating the contribution from each motor unit, the muscle model predicts the EMG. Wave forms of the motor unit action potentials in the surface EMG are obtained from experimental data. Using the model, we are able to give a quantitative prediction of the motoneuron pool activity and the reflex EMG output at different preactivation levels. The simulated data are consistent with experimentally obtained results in healthy humans. During static isometric muscle preactivations, the simulations show that the reflex strength is highly dependent on the intrinsic threshold properties of the alpha motoneuron pool. Received: 27 April 1993/Accepted in revised form: 8 September 1993     

Factors affecting phase synchronization in integrate-and-fire oscillators

Step changes in input current are known to induce partial phase synchrony in ensembles of leaky integrate-and-fire neurons operating in the oscillatory or “regular firing” regime. An analysis of this phenomenon in the absence of noise is presented based on the probability flux within an ensemble of generalized integrate-and-fire neurons. It is shown that the induction of phase synchrony by a step input can be determined by calculating the ratio of the voltage densities obtained from fully desynchronized ensembles firing at the pre and post-step firing rates. In the limit of low noise and in the absence of phase synchrony, the probability density as a function of voltage is inversely proportional to the time derivative along the voltage trajectory. It follows that the magnitude of phase synchronization depends on the degree to which a change in input leads to a uniform multiplication of the voltage derivative over the range from reset to spike threshold. This analysis is used to investigate several factors affecting phase synchronization including high firing rates, inputs modeled as conductances rather than currents, peri-threshold sodium currents, and spike-triggered potassium currents. Finally, we show that without noise, the equilibrium ensemble density is proportional to the phase response curve commonly used to analyze oscillatory systems. Action Editor: John Rinzel     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Synchronous cortical oscillatory activity during motor action

Oscillations of the motor cortex interact with similar activity of the spinal motoneuron pool in the 15-30 Hertz frequency range. Recent observations have demonstrated how this interaction affects the firing of single corticospinal neurons. The interaction, reflected as corticomuscular coherence, occurs for both distal and proximal muscles and it constitutes one connection in a larger web of oscillatory interactions, including several other motor areas in the cortex, thalamus, and cerebellum. New results cast light on the possible functional significance of this interaction. The rhythmic interaction may reveal interesting information in several motor disorders, including essential tremor, Parkinson's disease, myoclonus epilepsy, and mirror movements.     

The muscle sound properties of different muscle fiber types during voluntary and electrically induced contractions.

Soundmyogram (SMG) and electromyogram signals were recorded simultaneously from the relatively fast medial gastrocnemius (MG) and slow soleus (SOL) during voluntary and electrically induced contractions. Using a spike-triggered averaging technique, the averaged elementary sound and corresponding MU spikes were also obtained from about 35 different MUs identified. The rms-SMG of MG increased as a function of force (P < 0.01). On the contrary, these values for SOL increased up to 60% MVC (P < 0.01), but decreased at 80% MVC. The relationship between the peak to peak amplitude of SMG and MU spike indicated significant positive correlations (r = 0.631 to approximately 0.657, P < 0.01). During electrical stimulation at 5 Hz, the SMG power spectral peak frequency (PF) was matched with stimulation frequency in both muscles. At higher stimulation frequencies, e.g., > 15 Hz, only in the MG was SMG-PF synchronized with stimulation frequency; the slow SOL did not show such synchronization. Our data suggest that the SMG frequency components might reflect active motor unit firing rates, and that the SMG amplitude depends upon mechanical properties of contraction, muscle fiber composition, and firing rate during voluntary and electrically induced contractions.     

Relationship between the discharge rate of a firing motoneuron and the effectiveness of excitatory la afferent volleys in man

The H-reflex was evoked after producing regular unit firing in the flexor carpi ulnaris set up by moderate voluntary isometric muscular contraction. The firing index was used to quantify the effectiveness of the monosynaptic afferent signal traveling to the firing motoneuron. An analysis was made of the 3.3–16.0 spikes/sec firing range characteristic of naturally occurring muscular contraction. Effectiveness of afferent signals for motor units in the "fast" muscles under study were found to depend on motoneuronal background firing rate; the former declined as the latter rose, as previously discovered during research into "slow" soleus muscle units [2]. Afferent signals were most effective for motoneurons belonging to the "fast" muscles over the entire range of firing rates. It was found from analyzing afferent signal efficacy in relation to its point of occurrence within the interspike interval that variations in motoneuronal excitability within this interval are the reason for this relationship.Institute for Research into Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 19, No. 5, pp. 595–600, September–October, 1987.     

Membrane Resonance and Stochastic Resonance Modulate Firing Patterns of Thalamocortical Neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.     

Analysis of the effects of firing rate and synchronization on spike-triggered averaging of multidirectional motor unit torque

Spike-triggered averaging (STA) of muscle force transients has often been used to estimate motor unit contractile properties, using the discharge of a motor unit within the muscle as the triggering events. For motor units that exert torque about multiple degrees-of-freedom, STA has also been used to estimate motor unit pulling direction. It is well known that motor unit firing rate and weak synchronization of motor unit discharges with other motor units in the muscle can distort STA estimates of contractile properties, but the distortion of STA estimates of motor unit pulling direction has not been thoroughly evaluated. Here, we derive exact equations that predict that STA decouples firing rate and synchronization distortion when used to estimate motor unit pulling direction. We derive a framework for analyzing synchronization, consider whether the distortion due to synchronization can be removed from STA estimates of pulling direction, and show that there are distributions of motor unit pulling directions for which STA is insensitive to synchronization. We conclude that STA may give insight into how motoneuronal synchronization is organized with respect to motor unit pulling direction. Action Editor: David Terman