The simple frequency response of human stretch reflexes in which either short- or long-latency components predominate

The spinal cord facilitates cerebellar upper limb motor learning and control; inputs from neuromusculoskeletal simulation

Complex interactions between brain regions and the spinal cord (SC) govern body motion, which is ultimately driven by muscle activation. Motor planning or learning are mainly conducted at higher brain regions, whilst the SC acts as a brain-muscle gateway and as a motor control centre providing fast reflexes and muscle activity regulation. Thus, higher brain areas need to cope with the SC as an inherent and evolutionary older part of the body dynamics. Here, we address the question of how SC dynamics affects motor learning within the cerebellum; in particular, does the SC facilitate cerebellar motor learning or constitute a biological constraint? We provide an exploratory framework by integrating biologically plausible cerebellar and SC computational models in a musculoskeletal upper limb control loop. The cerebellar model, equipped with the main form of cerebellar plasticity, provides motor adaptation; whilst the SC model implements stretch reflex and reciprocal inhibition between antagonist muscles. The resulting spino-cerebellar model is tested performing a set of upper limb motor tasks, including external perturbation studies. A cerebellar model, lacking the implemented SC model and directly controlling the simulated muscles, was also tested in the same. The performances of the spino-cerebellar and cerebellar models were then compared, thus allowing directly addressing the SC influence on cerebellar motor adaptation and learning, and on handling external motor perturbations. Performance was assessed in both joint and muscle space, and compared with kinematic and EMG recordings from healthy participants. The differences in cerebellar synaptic adaptation between both models were also studied. We conclude that the SC facilitates cerebellar motor learning; when the SC circuits are in the loop, faster convergence in motor learning is achieved with simpler cerebellar synaptic weight distributions. The SC is also found to improve robustness against external perturbations, by better reproducing and modulating muscle cocontraction patterns.

Functional force stimulation alters motor neuron discharge patterns

Introduction

Beneficial effects have been observed for mechanical vibration stimulation (MVS), which are mainly attributed to tonic vibration reflex (TVR). TVR is reported to elicit synchronized motor unit activation during locally applied vibration. Similar effects are also observed in a novel vibration system referred to as functional force stimulation (FFS). However, the manifestation of TVR in FFS is doubted due to the use of global electromyography (EMG) features in previous analysis. Our study aims to investigate the effects of FFS on motor unit discharge patterns of the human biceps brachii by analyzing the motor unit spike trains decoded from the high-density surface EMG.

Methods

Eighteen healthy subjects volunteered in FFS training with different amplitudes and frequencies. One hundred and twenty-eight channel surface EMG was recorded from the biceps brachii and then decoded after motion-artifact removal. The discharge timings were extracted and the coherence between different motor unit spike trains was calculated to quantify synchronized activation.

Results and discussion

Significant synchronization within the vibration cycle and/or its integer multiples is observed for all FFS trials, which increases with increased FFS amplitude. Our results reveal the basic physiological mechanism involved in FFS, providing a theoretical foundation for analyzing and introducing FFS into clinical rehabilitation programs.

Frequency characteristics of human muscle and cortical responses evoked by noisy Achilles tendon vibration

Noisy stimuli, along with linear systems analysis, have proven to be effective for mapping functional neural connections. We explored the use of noisy (10-115 Hz) Achilles tendon vibration to examine somatosensory reflexes in the triceps surae muscles in standing healthy young adults (n = 8). We also examined the association between noisy vibration and electrical activity recorded over the sensorimotor cortex using electroencephalography. We applied 2 min of vibration and recorded ongoing muscle activity of the soleus and gastrocnemii using surface electromyography (EMG). Vibration amplitude was varied to characterize reflex scaling and to examine how different stimulus levels affected postural sway. Muscle activity from the soleus and gastrocnemii was significantly correlated with the tendon vibration across a broad frequency range (~10-80 Hz), with a peak located at ~40 Hz. Vibration-EMG coherence positively scaled with stimulus amplitude in all three muscles, with soleus displaying the strongest coupling and steepest scaling. EMG responses lagged the vibration by ~38 ms, a delay that paralleled observed response latencies to tendon taps. Vibration-evoked cortical oscillations were observed at frequencies ~40-70 Hz (peak ~54 Hz) in most subjects, a finding in line with previous reports of sensory-evoked γ-band oscillations. Further examination of the method revealed 1) accurate reflex estimates could be obtained with <60 s of low-level (root mean square = 10 m/s²) vibration; 2) responses did not habituate over 2 min of exposure; and importantly, 3) noisy vibration had a minimal influence on standing balance. Our findings suggest noisy tendon vibration is an effective novel approach to characterize somatosensory reflexes during standing.NEW & NOTEWORTHY We applied noisy (10-115 Hz) vibration to the Achilles tendon to examine the frequency characteristics of lower limb somatosensory reflexes during standing. Ongoing muscle activity was coherent with the noisy vibration (peak coherence ~40 Hz), and coherence positively scaled with increases in stimulus amplitude. Our findings suggest that noisy tendon vibration, along with linear systems analysis, is an effective novel approach to study somatosensory reflex actions in active muscles.

Frequency response of vestibular reflexes in neck, back, and lower limb muscles

Vestibular pathways form short-latency disynaptic connections with neck motoneurons, whereas they form longer-latency disynaptic and polysynaptic connections with lower limb motoneurons. We quantified frequency responses of vestibular reflexes in neck, back, and lower limb muscles to explain between-muscle differences. Two hypotheses were evaluated: 1) that muscle-specific motor-unit properties influence the bandwidth of vestibular reflexes; and 2) that frequency responses of vestibular reflexes differ between neck, back, and lower limb muscles because of neural filtering. Subjects were exposed to electrical vestibular stimuli over bandwidths of 0–25 and 0–75 Hz while recording activity in sternocleidomastoid, splenius capitis, erector spinae, soleus, and medial gastrocnemius muscles. Coherence between stimulus and muscle activity revealed markedly larger vestibular reflex bandwidths in neck muscles (0–70 Hz) than back (0–15 Hz) or lower limb muscles (0–20 Hz). In addition, vestibular reflexes in back and lower limb muscles undergo low-pass filtering compared with neck-muscle responses, which span a broader dynamic range. These results suggest that the wider bandwidth of head-neck biomechanics requires a vestibular influence on neck-muscle activation across a larger dynamic range than lower limb muscles. A computational model of vestibular afferents and a motoneuron pool indicates that motor-unit properties are not primary contributors to the bandwidth filtering of vestibular reflexes in different muscles. Instead, our experimental findings suggest that pathway-dependent neural filtering, not captured in our model, contributes to these muscle-specific responses. Furthermore, gain-phase discontinuities in the neck-muscle vestibular reflexes provide evidence of destructive interaction between different reflex components, likely via indirect vestibular-motor pathways.

Computation and study of the low-frequency oscillation of surface electromyogram recorded in biceps during isometric upper limb contraction

This study has experimentally studied the low frequency oscillation in surface electromyogram (sEMG) during isometric muscle contraction for Biceps brachii muscle. The time constant corresponding to this low frequency oscillation was computed for sEMG. Experiments were repeated for 25 subjects, and for isometric muscle contraction, ranging between 25% and 100 % maximum voluntary contraction (MVC), while the subjects were given real-time visual feedback of the force of contraction, recorded at 1000 samples/ second. The time constant (Tc) corresponding to the variability of sEMG was computed using the Hilbert transform and envelope detection. The results show that the time constant, Tc of sEMG recorded from the biceps during isometric contraction was the same for all the subjects, and for different levels of force of muscle contraction, and was 78 ms (± 1.1). This suggests that the low frequency oscillation of sEMG of the biceps brachii muscles is a fundamental property of that muscle, and corresponds to a fundamental phenomenon, which has never been observed earlier. By comparison from delays reported in literature, this delay is similar to M2 stretch reflex latency, and may be attributed to the neural pathway delay.

On theory of motor synergies

Recently Latash, Scholz, and Schöner (2007) proposed a new view of motor synergies which stresses the idea that the nervous system does not seek a unique solution to eliminate redundant degrees of freedom but rather uses redundant sets of elemental variables that each correct for errors in the other to achieve a performance goal. This is an attractive concept because the resulting flexibility in the synergy also provides for performance stability. But although Latash et al. construe this concept as the consequence of a "neural organization" they do not say what that may be, nor how it comes about. Adaptive model theory (AMT) is a computational theory developed in our laboratory to account for observed sensory-motor behavior. It gives a detailed account, in terms of biologically feasible neural adaptive filters, of the formation of motor synergies and control of synergistic movements. This account is amplified here to show specifically how the processes within the AMT computational framework lead directly to the flexibility/stability ratios of Latash et al. (2007). Accordingly, we show that quantitative analyses of experimental data, based on the uncontrolled manifold method, do not and indeed cannot refute the possibility that the nervous system tries to find a unique (optimal) solution to eliminate redundant degrees of freedom. We show that the desirable interplay between flexibility and stability demonstrated by uncontrolled manifold analysis can be equally well achieved by a system that forms and deploys optimized motor synergies, as in AMT.

Stretch reflexes and joint dynamics in rheumatoid arthritis

In clinically diagnosed rheumatoid arthritis (RA), studies were conducted to investigate the reflex and passive tissue contribution to measured increases in joint stiffness in the resting upper limb and during constant contractions of an attached muscle. The tonic stretch reflex was induced by a servo-controlled sinusoidal stretch perturbation of the metacarpophalangeal joint of RA patients, and age- and sex-matched controls. The resulting reflexes and mechanical changes in the RA affected joint were explored. Surface electromyographic (EMG) measurements were obtained from first dorsal interosseus muscle. Reflex gain (EMG/joint angle amplitude ratio), phase difference (reflex delay after stretch), coherence square (proportion of EMG variance accounted for by joint angle changes), joint mechanical gain (torque-joint angle amplitude ratio) and mechanical phase difference (torque response delay after stretch) were determined. RA patients showed decreased reflex gain that was partly due to coexistent severe muscle weakness, as determined from maximum voluntary contraction and grip pressure estimates. The decreased reflex gain was most evident at high stretch frequency suggesting a disproportionate loss of the large diameter afferent response and also increased reflex delay in the patients. These changes ensemble suggest significant loss of neural drive to the motor unit population. Patients also showed increased joint stiffness (measured as torque gain) in the contracting muscle, but there was no evidence of reflex activity or increased stiffness at rest. This suggests that the increased joint stiffness in RA was due to changes in the mechanical properties of the active muscle-joint system rather than changes in reflex properties.

The tonic stretch reflex and spastic hypertonia after spinal cord injury

The operational definition of spasticity is focused on increased resistance of joints to passive rotation and the possible origin of this increased resistance in the induced tonic stretch reflex (TSR). This term is applied in the context of both cerebral and spinal injury, implying that a similar reflex mechanism underlies the two disorders. From recent studies it is clear that increased passive joint resistance in resting limbs following stroke is highly correlated with the induced TSR, but this evidence is lacking in spinal injury. The contribution of the TSR to hypertonia in spinal cord injury (SCI) is unclear and it is possible that hypertonia has a different origin in SCI. The contribution of resting and activated TSR activity to joint stiffness was compared in SCI and normal subjects. The magnitude of the TSR in ankle dorsiflexors (DF) and plantarflexors (PF) and mechanical ankle resistive torque were measured at rest and over a range of contraction levels in normal subjects. Similar measures were made in 13 subjects with SCI to the limits of their range of voluntary contraction. Normals and SCI received a pseudo-sinusoidal stretch perturbation of maximum amplitude +/- 20 degrees and frequency band 0.1-3.5 Hz that was comparable to that used in manual clinical testing of muscle tone. Elastic resistance and resonant frequency of the ankle joint, after normalization for limb volume, were significantly lower in complete and incomplete SCI than normal subjects. No reflex response related to stretch velocity was observed. Resting DF and PF TSR gain, when averaged over the tested band of frequencies, were significantly lower in complete SCI than in resting normal subjects (<0.5 microV/deg). Linear regression analysis found no significant relationship between TSR gain and resting joint stiffness in SCI. Mean TSR gain of DFs and PFs at rest was not correlated with the subject variables: age, time since SCI, level of injury, Frankel score, number of spasms per day, Ashworth score or anti-spastic medication. DF and PF reflex gain were linearly related to voluntary contraction level and regression analysis produced similar slopes in incomplete SCI and normal subjects. Hence TSR loop gain was not significantly increased in SCI at any equivalent contraction level. Extrapolation of the regression lines to zero contraction level predicted that reflex threshold was not reduced in SCI. Low frequency passive stretches did not induce significant TSR activity in the resting limbs of any member of this SCI group. The TSR thus did not contribute to their clinical hypertonia. Other reflex mechanisms must contribute to hypertonia as assessed clinically. This result contrasts with our similar study of cerebral spasticity after stroke, where a comparable low frequency stretch perturbation produced clear evidence of increased TSR gain that was correlated with the hypertonia at rest. We conclude that a low frequency stretch perturbation clearly distinguished between spasticity after stroke and SCI. Spasticity in the two conditions is not equivalent and care should be taken in generalizing results between them.

Entrainment to extinction of physiological tremor by spindle afferent input

In this study the systematic modulation of wrist flexor muscle activity by imposed joint movement was examined. Ten subjects maintained a constant contraction level (25% of the maximum; trial duration: 20 s) in flexor carpi radialis while their wrists were perturbed with 50 different quasi-sinusoidal signals (frequency range: 0.5-9.5 Hz; amplitude: 0.3-4.2 degrees ). The frequency spectra of wrist position and the rectified and filtered electromyogram (EMG) were determined. The muscle activity was only weakly entrained to imposed movements of small amplitude and low frequency, as shown by a small peak in the EMG spectrum at the frequency of movement, while the most prominent peak in the spectrum was between 9 and 15 Hz, corresponding to the frequency range of physiological tremor. The entrainment of muscle activity increased markedly as the amplitude and frequency of the imposed movement increased, to the point of saturation of modulation and harmonic peaks in the spectrum. In parallel with this increase in entrainment, the 9-15 Hz tremor peak was progressively extinguished. The results are consistent with a coupled oscillator model in which the central oscillatory source(s) of tremor became fully entrained to the imposed movement at the highest amplitudes and frequencies. Such coupling depends on communication between the external forcing oscillator and the central oscillator(s), the I (a) afferent signal from the imposed movement being the most likely candidate to provide the entraining signal for the central oscillator(s).

Variation of magnitude and timing of wrist flexor stretch reflex across the full range of voluntary activation

This paper reports an investigation of the magnitude and timing of the stretch reflex over the full range of activation of flexor carpi radialis. While it is well established that the magnitude of the reflex increases with the level of muscle activation, there have been few studies of reflex magnitude above 50% of maximum voluntary contraction (MVC) and virtually no study of the timing of the response in relation to activation level. Continuous small amplitude (approximately 2 degrees) perturbations were applied to the wrist of 12 normal subjects while they maintained contraction levels between 2.5-95% MVC, monitored via surface electromyography (EMG). Both narrow band (4-5 Hz) and broad band (0-10 Hz) stretch perturbations were employed. The gain (EMG output/stretch input) and phase advance of the reflex varied with the level of muscle activation in a similar manner for both types of stretch, but there were significant differences in the patterns of change due to stretch bandwidth. Consistent with previous studies, the group average reflex gain initially increased with muscle activation level and then saturated. Inspection of individual data, however, revealed that the gain reached a peak at about 60% MVC and then decreased at higher contraction levels, the pattern across the full range of activation being well described by quadratic functions (mean r2=0.82). This quadratic pattern has not been reported previously for the neural reflex response in any muscle but is consistent with the pattern that has been reliably observed in studies of the mechanical reflex response in lower limb muscles. In contrast to the pattern for reflex gain, the phase advance of the reflex (at a stretch frequency of 4.5 Hz) decreased linearly from approximately 130 degrees at the lowest contraction levels to approximately 50 degrees as maximum voluntary contraction was reached (mean r2=0.69). This decrease corresponds to a delay of 49 ms introduced centrally in reflex pathways. All subjects showed clearly defined quadratic functions relating reflex gain and linear functions relating reflex phase to activation level, but there were considerable individual differences in the slopes of these functions which point to systematic differences in synaptic behaviour of the motoneuron pool. Thus, there was wide inter-subject variation in both the contraction level at which the reflex gain reached a peak (31-69% MVC) and the highest target contraction level that could be sustained during reflex measurement (47-95% MVC). A high correlation between these variables (r2=0.78) suggests a linear relation between afferent support of contraction and muscle fatigability. The decline in reflex gain at high levels of muscle activation signals a failure of muscle afferent input and subjects in whom the gain reached a peak and declined early were unable to sustain higher target contraction levels. The results of the study show that both the timing and magnitude of the stretch reflex vary markedly over the full range of voluntary muscle activation. The pattern of variation may account for why the stretch reflex contributes most effectively to muscle mechanics over the lower half of the range of activation, while progressive reductions in both gain and phase advance at higher levels render the reflex mechanically less effective and make tremor more likely.

Blink reflexes and the silent period in tetanus

Abnormalities of the silent period (SP) and blink reflexes occur in diseases that interfere with inhibitory pathways, such as tetanus and stiff-person syndrome (SPS). The SP is abnormal in tetanus but not in SPS. Studies of the blink reflex in tetanus are limited. In this report, a patient with generalized tetanus is described. The masseteric-and mixed-nerve SP was absent or truncated. In contrast to SPS, blink reflex studies revealed no bilateral R1 component, and a discrete R3 was only present ipsilateral to right supraorbital stimulation. This reflects the distinct inhibitory pathways underlying these disorders.

The period of latency before a muscle receptor generates an action potential as a response to a muscle stretch

Six primary (Ia) and seven secondary (II) muscle spindle afferents and eight Golgi tendon organ afferents (Ib) from the tibial anterior muscle of the cat, recorded at the dorsal roots, were subjected to a sinusoidal stretch of the host muscle, the frequency of which increased linearly from 2 to 80 Hz over four different lengths of time. Both the amplitude of the sinusoidal stretch and the prestretch of the muscle were varied. The phase of the action potentials was determined. The phase of the action potential, driven 1:1, increased linearly with frequency. From the gradient of the phase of this action potential the muscle-muscle receptor latency was determined, i.e., the period of latency between the stretch of the muscle and the occurrence of the action potential at the muscle nerve where it enters the muscle. The muscle-muscle receptor latency had values lying between 3 and 8 ms: it was dependent on the experimental parameters and became shorter as the conduction velocity of the afferent fiber increased. In three experiments the muscle latency was determined, i.e., the period of latency before the stretch was transferred from the tendon of the muscle to the proximal third of the muscle belly. The muscle was stretched sinusoidally under the same varying parameters as given above. The length changes occurring in the proximal third of the muscle were measured with a piezo element. The muscle latency was determined from the slope of the phase of the zero points of the sinusoidal piezo length changes; the phase increases linearly with frequency. The muscle latency had values lying between 6 and 15 ms: it was dependent on the experimental parameters. The muscle spindle latency, i.e., the period of latency between the stretch of the polar parts of the intrafusal muscle fibers and the recording of the action potentials from the spindle nerve near the spindle capsule, was determined from 5 Ia fibers and 1 II fiber of isolated muscle spindles. The isolated muscle spindle was stretched under the same varying parameters as given above. The muscle spindle latency was determined from the slope of the phase of the phase-locked action potential. The muscle spindle latency as measured by our method proved to be 0 ms. The latencies of the three elements and their dependence on the experimental parameters are discussed in the light of the transfer properties of the muscle and the muscle receptors.

Properties of human motoneurones and their synaptic noise deduced from motor unit recordings with the aid of computer modelling

This paper reviews two new facets of the behaviour of human motoneurones; these were demonstrated by modelling combined with analysis of long periods of low-frequency tonic motor unit firing (sub-primary range). 1) A novel transformation of the interval histogram has shown that the effective part of the membrane's post-spike voltage trajectory is a segment of an exponential (rather than linear), with most spikes being triggered by synaptic noise before the mean potential reaches threshold. The curvature of the motoneurone's trajectory affects virtually all measures of its behaviour and response to stimulation. The 'trajectory' is measured from threshold, and so includes any changes in threshold during the interspike interval. 2) A novel rhythmic stimulus (amplitude-modulated pulsed vibration) has been used to show that the motoneurone produces appreciable phase-advance during sinusoidal excitation. At low frequencies, the advance increases with rising stimulus frequency but then, slightly below the motoneurones mean firing rate, it suddenly becomes smaller. The gain has a maximum for stimuli at the mean firing rate (the 'carrier'). Such behaviour is functionally important since it affects the motoneurone's response to any rhythmic input, whether generated peripherally by the receptors (as in tremor) or by the CNS (as with cortical oscillations). Low mean firing rates favour tremor, since the high gain and reduced phase advance at the 'carrier' reduce the stability of the stretch reflex.

Spindle and motoneuronal contributions to the phase advance of the human stretch reflex and the reduction of tremor

1. The human stretch reflex is known to produce a phase advance in the EMG reflexly evoked by sinusoidal stretching, after allowing for the phase lag introduced by simple conduction. Such phase advance counteracts the tendency to tremor introduced by the combined effect of the conduction delay and the slowness of muscle contraction. The present experiments confirm that the EMG advance cannot be attributed solely to the phase advance introduced by the muscle spindles, and show that a major additional contribution is provided by the dynamic properties of individual motoneurones. 2. The surface EMG was recorded from biceps brachii when two different types of sinusoidally varying mechanical stimuli were applied to its tendon at 2-40 Hz. The first was conventional sinusoidal displacement ('stretch'); the spindle discharge would then have been phase advanced. The second was a series of weak taps at 103 Hz, with their amplitude modulated sinusoidally ('modulated vibration'). The overall spindle discharge should then have been in phase with the modulating signal, since the probability of any individual 1 a fibre responding to a tap would increase with its amplitude. The findings with this new stimulus apply to motoneurone excitation by any rhythmic input, whether generated centrally or peripherally. 3. The sinusoidal variation of the EMG elicited by the modulated vibration still showed a delay-adjusted phase advance, but the value was less than that for simple stretching. At 10 Hz the difference was 70-80 deg. This was taken to be the phase advance introduced by the spindles, very slightly underestimated because of the lags produced by tendon compliance in transmitting sinusoidal stretch to the muscle proper. The adjusted phase advance with modulated vibration was taken to represent that introduced by the reflex centres, undistorted by tendon compliance. At 10 Hz the reflex centres produced about the same amount of phase advance as the muscle spindles. 4. At modulation frequencies above 10 Hz the adjusted central phase advance remained approximately constant. However, when the frequency was reduced to below 6 Hz the central phase advance decreased. The depth of EMG modulation (reflex gain) also fell rapidly, starting from a slightly higher frequency. Thus the central phase advance mechanisms behave like a high-pass filter. 5. A simple model of the motoneurone, incorporating synaptic noise and an after-hyperpolarization, was tested with sinusoidal inputs and gave a phase advance over a wide range of frequencies. The effect was tightly linked to two particular facets of the motor discharge; these were the ratio between the stimulus frequency and the mean firing rate (the 'carrier frequency' of the unit), and the coefficient of variation of the interspike interval distribution. The gain rose to a maximum at the carrier frequency, while the phase advance showed a maximum at 0.8 of the carrier. The more regular the discharge, the greater were these effects. The phase advance might increase to above 90 deg, showing that the motoneurone potentially provides a major contribution to the phase advance of the stretch reflex. Related effects have already been observed in other neuronal models and for the discharge of the muscle spindle, without their significance for the motoneurone being appreciated. In essence, a rhythmically firing neurone is particularly affected by a rhythmic stimulus when the two frequencies approximately coincide. 6. Recording from single human motor units confirmed the role of the 'carrier frequency' in determining the phase advance with sinusoidal inputs. In particular, for both stretching and modulated vibration, the phase advance of the response elicited by a fixed sinusoidal stimulus changed appropriately when the firing rate of the unit varied 'spontaneously' over a long recording period. 7. Thus a combination of modelling and experiment has shown that the motoneurones themselves produce a significant phase advance.

Relationship of firing intervals of human motor units to the trajectory of post-spike after-hyperpolarization and synaptic noise

1. Interspike interval distributions from human motor units of a variety of muscles were analysed to assess the role of synaptic noise in excitation. The time course of the underlying post-spike after-hyperpolarization (AHP) was deduced by applying a specially developed transform to the interval data. Different firing rates were studied both by varying the firing voluntarily, and by selecting subpopulations of spikes for a given firing rate from long recordings with slight variations in frequency. 2. At low firing rates the interval histograms had an exponential tail. Thus at long intervals, the motoneurone was randomly excited by noise and its post-spike AHP was complete. This contrasts with the firing produced by intracellular current injection in the cat, when the membrane potential increases linearly until threshold is reached. The interval histogram was therefore analysed with the aid of a model of synaptic excitation to deduce the mean 'trajectory' of membrane voltage in the last part of the interspike interval. 3. The computer model, described in the Appendix, was used to determine the effect of the mean level of membrane potential on the probability of a spike being excited, per unit time, during an on-going interspike interval. All variables were treated as voltages, with synaptic noise simulated by time-smoothed Gaussian noise. This enabled an interval distribution to be transformed into a segment of the underlying trajectory of the membrane potential; the potential was expressed in terms of the noise amplitude and the spike threshold. 4. At low firing rates, the equilibrium value of the membrane voltage trajectory lay well below threshold; the deviation typically corresponded to the standard deviation of the noise or more. The noise standard deviation was estimated to be about 2 mV. 5. With increasing mean firing rate, the near-threshold portion of the trajectory obtainable from the histogram occurred earlier, was steeper and rose to a higher level. Trajectories for different firing rates fell on the same curve after shifting them vertically by varying amounts. The curve was taken to represent the AHP of the motoneurone and was closely exponential. The shift of the trajectory gave its mean synaptic drive. The duration of the AHP varied between units and was longer than average for units from soleus muscle. 6. Further modelling showed that summation of noise with the AHP can explain the well-known changes in discharge variability that occur as firing rate increases. 7. It is concluded that synaptic noise plays a major role in the excitation of tonically firing human motoneurones and that the noiseless motoneurone with a linear trajectory provides an inadequate model for the conscious human. This is of interest in relation to various standard measures of human motor unit activity such as short-term synchronization.