The use of frequency domain techniques in the study of signal transmission in skeletal muscle

Characteristics of Rest and Postural Tremors in Parkinson's Disease: An Analysis of Motor Unit Firing Synchrony and Patterns

The neural mechanisms responsible for resting and postural tremor in Parkinson’s disease (PD) have been the object of considerable study, much of it focusing on supraspinal sites. Here, we adopted an alternative approach that emphasizes motor unit (MU) firing synchrony and patterns of discharge. To explore if these could account for known features of PD tremor, we recorded the instantaneous acceleration of the upper limb of 23 PD patients at rest or while they tried to hold a stable posture together with surface EMG and single MU discharges of upper limb muscles. Spectral, coherence and cross-correlation analyses of the recorded signals demonstrated alternating epoch-I and epoch-II intervals in PD patients both at rest and while they held a stable posture. Epoch-II intervals are characterized by the presence of 4–8 Hz overt tremor, enhanced MU synchrony and spike-doublets or triplets bearing a one-to-one relation to each tremor cycle. Epoch-I resembled physiological tremor in that it was characterized by 6–10 Hz non-overt tremor, lower MU synchrony and rhythmical MU firing at the intrinsic rate of the unit. The frequency of overt and non-overt tremor remained the same whether the patient was at rest or held a stable posture and the same was true of the remaining characteristics of epoch-I and epoch-II. The mean interval between spikes of a doublet/triplet varied between 30 and 50 ms and, for any given patient, remained roughly constant throughout measurements. This is the first time that enhanced MU synchrony and spike doublets/triplets characterized by relatively stable interspike intervals, are shown to accompany the overt tremor of PD patients. To account for our findings we propose that a two-state oscillatory spinal stretch reflex loop generates overt parkinsonian tremor in response to intermittent, descending, relatively high frequency oscillatory signals.

Neuromuscular mechanisms and neural strategies in the control of time-varying muscle contractions

The organization of the neural input to motoneurons that underlies time-varying muscle force is assumed to depend on muscle transfer characteristics and neural strategies or control modes utilizing sensory signals. We jointly addressed these interlinked, but previously studied individually and partially, issues for sinusoidal (range 0.5–5.0 Hz) force-tracking contractions of a human finger muscle. Using spectral and correlation analyses of target signal, force signal, and motor unit (MU) discharges, we studied 1) patterns of such discharges, allowing inferences on the motoneuronal input; 2) transformation of MU population activity (EMG) into quasi-sinusoidal force; and 3) relation of force oscillation to target, carrying information on the input's organization. A broad view of force control mechanisms and strategies emerged. Specifically, synchronized MU and EMG modulations, reflecting a frequency-modulated motoneuronal input, accompanied the force variations. Gain and delay drops between EMG modulation and force oscillation, critical for the appropriate organization of this input, occurred with increasing target frequency. According to our analyses, gain compensation was achieved primarily through rhythmical activation/deactivation of higher-threshold MUs and secondarily through the adaptation of the input's strength expected during tracking tasks. However, the input's timing was not adapted to delay behaviors and seemed to depend on the control modes employed. Thus, for low-frequency targets, the force oscillation was highly coherent with, but led, a target, this timing error being compatible with predictive feedforward control partly based on the target's derivatives. In contrast, the force oscillation was weakly coherent, but in phase, with high-frequency targets, suggesting control mainly based on a target's rhythm.

Modulation and transmission of peripheral inputs in monkey cuneate and external cuneate nuclei

Somatosensory signals undergo substantial modulation in the dorsal column nuclei. We examined transmission of signals from forelimb afferents in primate cuneate and external cuneate nuclei. In anesthetized macaque monkeys, the median, ulnar, deep radial, and superficial radial nerves were electrically stimulated at 1.5-2× motor threshold with independent Poisson trains whereas extracellular recordings were made from 317 cells. Responses to peripheral stimulation included instances of both brief facilitation and long lasting suppression. A high proportion of cells (87%) responded to stimulation of two or more peripheral nerves, suggesting a large amount of convergence. Facilitated cells showed coherence with the peripheral stimulation across a broad frequency range; coherence was especially high in cells that responded with a burst of action potentials. Cells that responded with suppression also showed significant coherence, but this fell rapidly for frequencies above 25 Hz. Similar results were seen in both the main and external cuneate. When stimulation of one nerve was conditioned by a preceding nerve stimulus, the response to the second stimulus was attenuated for around 40 ms. This occurred independently of whether the first stimulus produced an initial facilitation or suppression or whether the same or a different nerve served as a conditioning stimulus. Mechanical stimulation of a receptive field suppressed responses to a second identical mechanical stimulus over a similar timescale. We conclude that the primate cuneate nucleus is capable of transmitting temporal information about stimuli with high fidelity; stimuli interact both temporally and spatially to modulate the onward transmission of information.

Assessment of across-muscle coherence using multi-unit vs. single-unit recordings

Coherence between electromyographic (EMG) signals has been used to identify correlated neural inputs to motor units (MUs) innervating different muscles. Simulations using a motor-unit model (Fuglevand et al. 1992) were performed to determine the ability of coherence between two multi-unit EMGs (mEMG) to detect correlated MU activity and the range of correlation strengths in which mEMG coherence can be usefully employed. Coherence between motor-unit and mEMG activities in two muscles was determined as we varied the strength of a 30-Hz periodic common input, the number of correlated MU pairs and variability of MU discharge relative to the common input. Pooled and mEMG coherence amplitudes positively and negatively accelerated, respectively, toward the strongest and most widespread correlating inputs. Furthermore, the relation between pooled and mEMG coherence was also nonlinear and was essentially the same whether correlation strength varied by changing common input strength or its distribution. However, the most important finding is that while the mEMG coherence saturates at the strongest common input strengths, this occurs at common input strengths greater than found in most physiological studies. Thus, we conclude that mEMG coherence would be a useful measure in many experimental conditions and our simulation results suggest further guidelines for using and interpreting coherence between mEMG signals.

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.

Coherent Motor Unit Rhythms in the 6–10 Hz Range During Time-Varying Voluntary Muscle Contractions: Neural Mechanism and Relation to Rhythmical Motor Control

In quasi-sinusoidal (0.5–3.0 Hz) voluntary muscle contractions, we studied the 6- to 10-Hz motor unit (MU) firing synchrony and muscle force oscillation with emphasis on their neural substrate and relation to rhythmical motor control. Our analyses were performed on data from 121 contractions of a finger muscle in 24 human subjects. They demonstrate that coherent 6- to 10-Hz components of MU discharges coexist with carrier components and coherent modulation components underlying the voluntary force variations. The 6- to 10-Hz synchrony has the frequency of the tremor synchrony in steady contractions and is also widespread and in-phase. Its strength ranges from very small to very large (MU/MU coherence >0.50) among contractions; moreover, it is not related to the contraction parameters, in accord with the notion of a distinct 6- to 10-Hz synaptic input to the MUs. Unlike the coherent MU modulations and the voluntary force variations, the in-phase 6- to 10-Hz MU components are suppressed or even eliminated during ischemia, while the respective force component is drastically reduced. These findings agree with the widely assumed supraspinal origin of the MU modulations, but they also strongly suggest a key role for muscle spindle feedback in the generation of the 6- to 10-Hz synaptic input. They therefore provide important information for the study of generators of the 6- to 10-Hz rhythm which subserves the postulated rhythmical control and is manifested as force and movement components. Moreover, they argue for a participation of oscillating spinal stretch reflex loops in the rhythm generation, possibly in interaction with supraspinal oscillators.

Independent vasomotor control of rat tail and proximal hairy skin

Quantitative differences are known to exist between the vasomotor control of hairy and hairless skin, but it is unknown whether they are regulated by common central mechanisms. We made simultaneous recordings from sympathetic cutaneous vasoconstrictor (CVC-type) fibres supplying back skin (hairy) and tail (hairless) in urethane-anaesthetized, artificially ventilated rats. The animal's trunk was shaved and encased in a water-perfused jacket. Both tail and back skin CVC-type fibres were activated by cooling the trunk skin, and independently by the resultant fall in core (rectal) temperature, but their thresholds for activation differed (skin temperatures 38.8 +/- 0.4 degrees C versus 36.8 +/- 0.4 degrees C, core temperatures 38.1 +/- 0.2 degrees C versus 36.8 +/- 0.2 degrees C, respectively; P < 0.01). Back skin CVC-type fibres were more responsive to skin than to core cooling, while the reverse applied to tail fibres. Back skin CVC-type fibres were less responsive than tail fibres to prostaglandin E2 (PGE2) microinjected into the preoptic area. Spectral analysis showed no significant coherence between tail and back skin CVC-type fibre activities during cooling. After preoptic PGE2 injection, a coherent peak at 1 Hz appeared in some animals; this disappeared after partialization with respect to ventilatory pressure, indicating that it was attributable to common ventilatory modulation. Neuronal inhibition in the rostral medullary raphé by microinjected muscimol (2 mM, 60-120 nl) suppressed both tail and back skin CVC-type fibre activities, and prevented their responses to subsequent skin cooling. These results indicate that thermoregulatory responses of hairless and hairy skin vessels are controlled by independent neural pathways, although both depend on synaptic relays in the medullary raphé.

Comparison between two rat sympathetic pathways activated in cold defense

In cold defense and fever, activity increases in sympathetic nerves supplying both tail vessels and interscapular brown adipose tissue (iBAT). These mediate cutaneous vasoconstrictor and thermogenic responses, respectively, and both depend upon neurons in the rostral medullary raphé. To examine the commonality of brain circuits driving these two outflows, sympathetic nerve activity (SNA) was recorded simultaneously from sympathetic fibers in the ventral tail artery (tail SNA) and the nerve to iBAT (iBAT SNA) in urethane-anesthetized rats. From a warm baseline, cold-defense responses were evoked by intermittently circulating cold water through a water jacket around the animal's shaved trunk. Repeated episodes of trunk skin cooling decreased core (rectal) temperature. The threshold skin temperature to activate iBAT SNA was 37.3 +/- 0.5 degrees C (n = 7), significantly lower than that to activate tail SNA (40.1 +/- 0.4 degrees C; P < 0.01, n = 7). A fall in core temperature always strongly activated tail SNA (threshold 38.3 +/- 0.2 degrees C, n = 7), but its effect on iBAT SNA was absent (2 of 7 rats) or weak (threshold 36.9 +/- 0.1 degrees C, n = 5). The relative sensitivity to core vs. skin cooling (K-ratio) was significantly greater for tail SNA than for iBAT SNA. Spectral analysis of paired recordings showed significant coherence between tail SNA and iBAT SNA only at 1.0 +/- 0.1 Hz. The coherence was due entirely to the modulation of both signals by the ventilatory cycle because it disappeared when the coherence spectrum was partialized with respect to airway pressure. These findings indicate that independent central pathways drive cutaneous vasoconstrictor and thermogenic sympathetic pathways during cold defense.

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.

Population and unit synchrony of fast rhythms in expiratory recurrent laryngeal discharges

In a decerebrate, vagotomized, gallamine-paralyzed cat that had a prominent bilaterally coherent fast rhythm (50 Hz) in expiratory (E) recurrent laryngeal (RL) nerve discharges, recordings were taken of the firing of nine RL E fibers. This rhythm (called E high-frequency oscillation or EHFO) was seen as a sharp peak in all unit autospectra, all unit-nerve coherence spectra (value range 0.39-0. 91), and all unit-unit coherence spectra (value range 0.27-0.85). In addition, 8/9 units had a sharp autospectral peak in a lower frequency range (19-35 Hz) called E medium-frequency oscillation (EMFO), but there was no coherence at this frequency between signal pairs (unit-unit, unit-nerve, nerve-nerve). The MFOs are specific for each unit and are considered to arise from asynchronous inputs and membrane properties. The HFOs are considered to arise from widespread network interactions that produce a common (correlated) rhythm in virtually all neurons of the RL E network. These phenomena suggest the use of the RL E network as a model system for analyzing rhythmic neural interactions.

Synchronized fast rhythms in inspiratory and expiratory nerve discharges during fictive vocalization

In precollicular decerebrate and paralyzed cats, respiratory nerve activities were recorded during fictive vocalization (FV), which consisted of a distinctive pattern of 1) decreased inspiratory (I) and expiratory (E) phase durations, 2) marked increase of phrenic activity and moderate changes of recurrent laryngeal (RL) and superior laryngeal (SL) I activities, and 3) massive recruitment of laryngeal and abdominal (ABD; lumbar) E activities. FV was produced by electrical stimulation (100 Hz) in the midbrain periaqueductal gray (PAG) or its putative descending pathways in the ventrolateral pons (VLP). Spectral and correlation analyses revealed three types of effect on fast rhythms during FV. 1) I activities: the coherent high-frequency oscillations in I (I-HFO, 60-90 Hz) present in phrenic and RL discharges during the control state did not change qualitatively, but there was an increase of power and a moderate increase (4-10 Hz) of frequency. Sometimes a distinct relatively weak stimulus-locked rhythm appeared. 2) RL and SL activities during E: in recruited discharges, a prominent intrinsic rhythm (coherent E-HFOs at 50-70 Hz) appeared; sometimes a distinct relatively strong stimulus-locked rhythm appeared. 3) ABD activities during E: this recruited activity had no intrinsic rhythm but had an evoked oscillation locked to the stimulus frequency. Thus FV is characterized by 1) appearance of prominent coherent intrinsic rhythms in RL and SL E discharges, which presumably arise as a result of excitation and increased interactions in laryngeal networks; 2) modification of intrinsic rhythmic interactions in inspiratory networks; and 3) evoked rhythms in augmenting-E neuron networks without occurrence of intrinsic rhythms.

Altered frequency characteristic of central vasomotor control in SHR

Previous work from our laboratory has demonstrated that the very low-frequency (VLF: 0-0.25 Hz) and low-frequency (LF: 0.25-0.8 Hz) power of arterial pressure variability (APV) are related to vasomotor reactivity in response to control signals from the rostral ventrolateral medulla (RVLM) via the sympathetic system in the rat. The present study evaluated the differences in the dynamic property of central vasomotor control between spontaneously hypertensive rats (SHR) and normotensive Wistar-Kyoto rats (WKY). Experiments were carried out in 10- to 12-wk-old rats that were anesthetized with continuous infusion of pentobarbital sodium, paralyzed with pancuronium, and maintained on mechanical ventilation. We found that SHR exhibited significantly higher arterial pressure (AP), heart rate (HR), and VLF, LF, and high-frequency (0.8-2.4 Hz) power of APV than WKY under resting state. Broad-band electrical stimulation of the RVLM elicited parallel APV in the VLF and LF ranges in both rat strains. The evoked APV and transfer magnitude of the APV to stimulus spike rate variability (RVLM-AP magnitude) were significantly higher in SHR, especially in the LF range. The response frequency of central vasomotor control, represented by the high-cut frequency of RVLM-AP magnitude, was also extended in SHR. The disparity in RVLM-AP transfer magnitude between SHR and WKY became virtually absent after combined alpha- and beta-adrenoceptor blockade by phentolamine and propranolol. These results suggest that the dynamic control of RVLM on AP reactivity is enhanced in SHR, in which the adrenergic system may play a major role.

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.

Functional characterization of caudal hypoglossal neurons by spectral patterns of neuronal discharges in the rat

This study evaluated the spectral characteristics of neuronal discharges in the caudal hypoglossal nucleus and their physiological relevance in adult, male Sprague Dawley rats which were anaesthetized and maintained with pentobarbital sodium. Based on auto-spectral analysis of extracellular single-neuron activity, three spectral patterns were identified in the spontaneous discharges of hypoglossal neurons. Neurons that exhibited a rhythmic pattern manifested a concentrated peak in the auto-spectrogram that corresponded to the mean discharge rate. A majority of hypoglossal neurons displayed the modulated pattern, which was manifested either as scattered power densities (wide-band modulated pattern) or with a peak frequency component that was different from the mean discharge rate (narrow-band modulated pattern). Neurons that exhibited a mixed pattern displayed both rhythmic and modulated spectral patterns. Cross-spectral analysis further revealed that respiratory modulation constituted a major physiological influence on caudal hypoglossal neurons. The respiratory modulated pattern, however, could be converted to a mixed pattern in the presence of a central dipsogen, angiotensin III. The results suggest that the spectral patterns of neuronal discharges in caudal hypoglossal neurons represent manifestations of multiple physiological information, including that regarding respiration and dipsogenesis, which is encoded in these neurons. It was also shown that this information may only be revealed by auto-spectral and cross-spectral analysis of neuronal discharge signals.

Medial septal unit firing characteristics following injections of 8-OH-DPAT into the median raphe nucleus

Extracellular single-unit recording techniques were used to examine the firing characteristics of neurons in the medial septum/diagnol band of Broca complex (MS/DB) following injections of the 5-HT1A agonist, 8-OH-DPAT, into the median raphe nucleus (MRN) of urethane-anesthetized rats. It had previously been shown that MRN injections of 8-OH-DPAT produce hippocampal theta rhythm. Injections of 8-OH-DPAT into the MRN produced a change in firing characteristics of MS/DB neurons from an irregular discharge to a pattern of rhythmical bursting in synchrony with hippocampal theta rhythm. Cross-correlational and coherence analyses demonstrated that the rhythmical firing pattern of MS/DB neurons strongly correlated with rhythmical fluctuations in the hippocampal EEG during periods of hippocampal theta produced by 8-OH-DPAT injections, but not during baseline conditions (i.e. hippocampal desynchronization). The results suggest that MRN control of the hippocampal EEG is modulated by the MS/DB. Serotonergic projections from the MRN to the MS/DB may normally act to inhibit the rhythmical bursting of MS/DB neurons, thereby producing hippocampal desynchronization. Suppression of MRN 5-HT neurons by MRN injections of 8-OH-DPAT would disinhibit MS/DB neurons, allowing them to burst rhythmically and thereby produce hippocampal theta rhythm.

Identification and characterization of rhythmic nociceptive and non-nociceptive spinal dorsal horn neurons in the rat

The properties of rhythmic low-threshold and multireceptive spinal dorsal horn neurons were determined. Multiple neuron recordings were made via a single electrode in the lumbar spinal cord of pentobarbital-anesthetized or decerebrate, unanesthetized, spinalized rats. The background activity of a total of 223 neurons was analysed: 21.0% of 176 fully characterized neurons were low threshold, 73.3% multireceptive and 5.7% nociceptive-specific neurons. Twenty of 100 neurons tested were driven by antidromic stimulation at the upper cervical cord. To identify and evaluate rhythmic harmonic oscillations in the discharges of spinal dorsal horn neurons during background activity and steady-state noxious heat-evoked responses, interspike interval, autocorrelation and autospectral analysis were performed. The background activity of 99 of the 223 neurons (44.4%) of our sample was rhythmic. The distribution of the fundamental spectral frequencies has a bimodal shape, the first band between 0.5 and 2 Hz and the second between 6 and 13 Hz. Low-threshold and multireceptive neurons had a similar incidence of rhythmicity (54.1 and 43.4%, respectively). Only one of 20 neurons with long ascending projections presented rhythmic background activity. Activation of heat-sensitive nociceptors within the cutaneous receptive fields of the neurons had a strong anti-rhythmic effect in nine of 15 (60%) neurons. No change was observed in the pattern of autospectra of non-rhythmic neurons or low-threshold neurons during noxious stimulation. Twenty-four of 37 (66.6%) rhythmic neurons retained their rhythmic background discharges during reversible cold-block spinalization at the upper thoracic cord. The incidence of neurons with burst-like discharges was highest among multireceptive neurons (98/129, 75.9%) and non-rhythmic neurons (89/124, 71.8%). Thus, rhythmicity exists in sensory neurons of the spinal dorsal horn probably generated within its local neuronal network and partially modulated by supraspinal descending systems. Rhythmicity is depressed by activity in primary afferent nociceptors. The role of rhythmicity for information transfer and neuronal plasticity is discussed.

Signal transmission from motor axons to group Ia muscle spindle afferents: frequency responses and second-order non-linearities

Spinal recurrent inhibition via Renshaw cells and proprioceptive feedback via skeletal muscle and muscle spindle afferents have been hypothesized to constitute a compound feedback system [Windhorst (1989) Afferent Control of Posture and Locomotion; Windhorst (1993) Robots and Biological Systems--Towards a New Bionics]. To assess their detailed functions, it is necessary to know their dynamic characteristics. Previously we have extensively described the properties of signal transmission from motor axons to Renshaw cells using random motor axon stimulation and data analysis methods based thereupon. Using the same methods, we here compare these properties, in the cat, with those between motor axons and group Ia muscle spindle afferents in terms of frequency responses and nonlinear features. The frequency responses depend on the mean rate (carrier rate) of activation of motor axons and on the strength of coupling between motor units and spindles. In general, they are those of a second-order low-pass system with a cut-off at fairly low frequencies. This contrasts with the dynamics of motor axon-Renshaw cell couplings which are those of a much broader band-pass with its peak in the range of c. 2-15 Hz [Christakos (1987) Neuroscience 23, 613-623]. The second-order non-linearities in motor unit-muscle spindle signal lines are much more diverse than those in motor axon-Renshaw cell couplings. Although the average strength of response declines with mean stimulus rate in both subsystems, there is no systematic relationship between the amount of non-linearity and the average response in the former, whilst there is in the latter. The qualitative appearance of motor unit-muscle spindle non-linearities was complicated as was the average response to motor unit twitches. Thus, whilst Renshaw cells appear to dynamically reflect motor output rather faithfully, muscle spindles seem to signal local muscle fibre length changes and their dynamics. This would be consistent with the hypothesis that the two feedback pathways monitor different state variables determining the production of muscle force: neural input and length and its changes. Specifically, the dynamic properties of both subsystems may combine favourably to decrease the risk of instability (tremor) in the motoneuron-muscle spindle loop.

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.

Dynamic behaviour of alpha-motoneurons subjected to recurrent inhibition and reflex feedback via muscle spindles

The dynamic transfer characteristics of mammalian spinal skeleto-motoneurons are determined by intrinsic properties and various sorts of feedback. Here, recurrent inhibition via Renshaw cells and reflex feedback via muscle units and muscle spindle (in particular Ia) afferents, in the cat, are considered. The dynamic properties of the motor axon-Renshaw cell and the motor unit-spindle afferent subsystems were experimentally determined by stimulating motor axons with pseudo-random patterns of electrical pulses at two mean rates (low: 9.5-13 pulses/s; high: 20-23 pulses/s) and recording discharges of the two output elements. Spectral analysis yielded frequency responses to which transfer functions were fitted. These transfer functions in conjunction with those previously derived for alpha-motoneurons were used to study the stability and input-output characteristics of motoneurons with regard to two issues: stability and input-output relations of the combined (recurrent plus reflex) system as compared with each subsystem alone, with (i) each feedback path consisting of a single loop at some moderate level of force production, and (ii) each pathway consisting of two loops related to two motoneuron subpopulations active at a higher level of recruitment. It is shown that Renshaw cells have frequency characteristics well suited to contribute to the stabilization of the reflex loop. They can do so at low gains of recurrent inhibition.

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.

The relationship between coherence and nonlinear characteristics in Renshaw cell responses to random motor axon stimulation

Cat spinal Renshaw cells were activated by stimulating muscle nerves or ventral roots with random (pseudo-Poisson) patterns of brief electrical stimuli. This input pattern is optimal for a comparative study in both the frequency- and time-domain. The frequency-dependent variable of particular interest in this study was the coherence as a measure of the degree to which signal transmission is linear and noise-free; it was estimated via spectral analysis. Time-domain analysis consisted of calculating peri-stimulus time histograms in order to estimate the amount of nonlinearity in the cell responses to pairs of stimuli. The main result was that the amount of nonlinearity measured in this way did not profoundly depress the coherence. Two types of peri-stimulus time histogram were calculated: the "conventional" peri-stimulus time histogram (as a reference) computed with respect to all the stimuli in a train, and the "conditional" peri-stimulus time histogram computed with respect to the second in pairs of stimuli which were separated from each other by varied intervals delta. The latter type of peri-stimulus time histogram showed that Renshaw cell responses to stimuli were conditioned by preceding stimuli, which could facilitate (at small delta s) and/or more often depress (up to several hundreds of milliseconds) the subsequent responses in a nonlinear manner. The objective of this study was to test the hypothesis that nonlinear characteristics contribute significantly to depress the coherence from its optimal value (1).(ABSTRACT TRUNCATED AT 250 WORDS)

A framework for the analysis of neuronal networks

The object of this work is to consider the application of some methods of spike train analysis that are not widely known, and are concerned with the description of the interaction between spike trains and the determination of causal connections between them. The notation and terminology follow conventions established in the statistical literature. The examples given are based on in-continuity recordings of the spontaneous activity of single Ia afferents from the soleus muscle and single motor units from the same muscle. Cumulant densities are shown to be simple extensions of the traditional cross-correlation methods, and are useful in characterizing the pattern of activity in one spike train that influences that in another, and to reveal interactions between spike trains that would not be apparent from the correlation histogram alone. Parameters based on the Fourier transforms of the spike trains are shown to be useful in determining timing relations between them, and in inferring patterns of connectivity not possible by correlation methods alone.

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.

Relations between time-and frequency-domain measures of signal transmission from cutaneous afferents to dorsal horn neurons

In pentobarbitone-anesthetized cats, the spike sequences of dorsal horn neurons were recorded in response to random stimulation of branches of the suralis nerve. Combined frequency- and time-domain analysis was performed on the stimulus and spike trains. Coherence function estimates computed by spectral analysis were compared with peristimulus time histograms (PSTHs). The cell responses were divided into 4 main types: PSTHs with a single high and narrow peak were associated with broad-range high coherence; PSTHs with two (or sometimes 3) distinct peaks concurred with a coherence which was high a low frequencies, low at intermediate ones and higher again at high frequencies; broad unstructured PSTH peaks of varying height concurred with coherence declining from high values at low frequencies to lower values at higher ones; and small and broad PSTH peaks were associated with generally low coherence. Thus, the variation of coherence with frequency depends on the precise pattern of cell discharge.

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.

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.

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.

Neural activity states in different forms of physiological tremor. Facts and hypotheses

This paper attempts to combine (and thereby briefly review) various sets of physiological data in order to outline a qualitative model of the different states of stochastic neural activity underlying different forms of physiological tremor. Particular emphasis in put on spatial distributions of the properties of neural elements and their interconnexions , and on discharge characteristics of motor units and muscle spindle afferents including so-called "early discharges" and nonlinearities. It is argued that the wide variety of internal anatomical and functional structures of skeletal muscles and of their reflex organization must be considered when dealing with stability problems. Computer simulations of stochastic population models of the involved neuromuscular elements are advocated as means to investigate the relative importance of the many factors possibly contributing to stabilizing or de-stabilizing neuromuscular systems.