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This paper presents a method for co-evolving neuro-inspired developmental programs for playing checkers. Each player's program is represented by seven chromosomes encoding digital circuits, using a form of genetic programming, called Cartesian Genetic Programming (CGP). The neural network that occurs by running the genetic programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to situations encountered on the checkers board. The results show that, after a number of generations, by playing each other the agents play much better than those from earlier generations. Such learning abilities are encoded at a geneticlevel rather than at the phenotype level of neural connections.

There is now a great interest in exploiting the capabilities of hardware devices; especially the reconfigurable properties of FPGA to implement and study the dynamics of neural networks, specifically a biological inspired neural network. FPGA has a much greater appeal than other modes of implementation because an FPGA implementation offers the flexibility of simple software (re-)configuration in comparison to other digital ASICs. In this paper a hippocampus-inspired spiking neural network is implemented on an FPGA, in order to take advantage of these two characteristics as well as to achieve autonomy for a neuro-controller device.

A developmental model of neural network is presented and evaluated in the game of Checkers. The network is developed using cartesian genetic programs (CGP) as genotypes. Two agents are provided with this network and allowed to co-evolve untill they start playing better. The network that occurs by running theses genetic programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to situations encountered on the checkers board. The method has no board evaluation function, no explicit learning rules and no human expertise at playing checkers is used. The results show that, after a number of generations, by playing each other the agents begin to play much better and can easily beat agents that occur in earlier generations. Such learning abilities are encoded at a genetic level rather than at the phenotype level of neural connections.

Changes in coherence and cumulant calculated between electroencephalograph (EEG) recorded from the scalp over primary motor cortex and rectified surface electromyograph (EMG) recorded from the contralateral wrist extensor muscles have been studied during development in humans (48 subjects, age 0-59 years). Using the techniques of EEG-EMG coherence and cumulant analysis and pooled coherence and cumulant analysis we demonstrate that between childhood, adolescence and adulthood there are increases in the prevalence and magnitude of coherence at frequencies between 15 and 35 Hz with corresponding development of a tri-phasic feature in the EEG-EMG cumulant. The results show for the first time that changes in the cortical approximately 20 Hz oscillatory drive to human motoneurone pools take place during motor development.

A novel method of optimal spectral tracking is presented which permits the characterisation of trial-varying parameters. Many experimental studies suffer from the limitations of available analysis methodologies, which often impose a condition of stationarity. This severely limits our ability to track slow varying or dynamic responses with any statistical certainty. Presented is a complete framework for the non-stationary analysis of trial-varying data. Theory is introduced and developed in the characterisation of speed dependent neural modulation of the locomotor drive to tibialis anterior (TA) during healthy treadmill locomotion. The approach adopts adaptive filter theory while retaining a spectral focus, thus remaining compatible with much of the current literature. Spectral tracking procedures are evaluated using both surrogate and neurophysiological time-series. Confidence intervals are derived in both empiric and numerical form. Analysis of the pre-synaptic drive to TA under the modulation of treadmill belt speed follows, with results demonstrating clear speed dependent influences on the spectral content of TA, suggesting dynamic neural modulation of the locomotor drive. Findings include speed-modulated components at 7-12 Hz (early swing) and 15-20 Hz (pre-stance). Speed invariant components were identified at 8-15 and 15-20 Hz during early and late swing, in agreement with previous studies. Modification to the method permits a sub-optimal alternative, encouraging the exploration of short epoched data.

The hippocampus region may help in the design of a neuro-controller used for path navigation of a robot. The spatial representation of the hippocampus can help provide a spatial mapping of the environment. The representation used is the place cell/place field representation. Place cell represents a population of neurons and place fields provide the spatial mapping of the environment. A place cell fires if the agent is believed to be in the environment for which its respective place field is representing. The hippocampus-inspired neural network model is not only spatially motivated but is also directionally driven. This model will be fully implemented onto an FPGA device to provide autonomy.

This study uses models of pyramidal neurons in the hippocampus to design a hardware spiking neural network neuro-controller model for the purpose of navigation. The neural network model consists of individual neurons modeled using the two-dimensional bio-inspired Izhikevich algorithm. The network is connected according to the connectivity within the hippocampus region, as this region is one of the regions in the brain that is responsible for path navigation. The information processed by the model helps provide navigation and creates memories. The neural network model is intended to be implemented onto a field programmable gate array (FPGA) device. This eliminates the need of an operating system to run the network, thus achieving autonomy.

The brain has long been seen as a powerful analogy from which novel computational techniques could be devised. However, most artificial neural network approaches have ignored the genetic basis of neural functions. In this paper we describe a radically different approach. We have devised a compartmental model of a neuron as a collection of seven chromosomes encoding distinct computational functions representing aspects of real neurons. This model allows neurons, dendrites, and axon branches to grow, die and change while solving a computational problem. This also causes the synaptic morphology to change and affect the information processing. Since the appropriate computational equivalent functions of neural computation are unknown, we have used a form of genetic programming known as Cartesian Genetic Programming (CGP) to obtain these functions. We have evaluated the learning potential of this system in the context of solving a well known agent based learning scenario, known as wumpus world and obtained promising results.

A coevolutionary competitive learning environment for two antagonistic agents is presented. The agents are controlled by a new kind of computational network based on a compartmentalised model of neurons. We have taken the view that the genetic basis of neurons is an important [27] and neglected aspect of previous approaches. Accordingly, we have defined a collection of chromosomes representing various aspects of the neuron: soma, dendrites and axon branches, and synaptic connections. Chromosomes are represented and evolved using a form of genetic programming known as Cartesian Genetic Programming. The network formed by running the chromosomal programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to environmental interactions. The idea of this paper is to demonstrate the importance of the genetic transfer of learned experience and life time learning. The learning is a consequence of the complex dynamics produced as a result of interaction (coevolution) between two intelligent agents. Our results show that both agents exhibit interesting learning capabilities.

This work presents a model of minimal time-continuous target-cell specific use-dependent short-term synaptic plasticity (STP) observed in the pyramidal cells that can account for both short-term depression and facilitation. In general it provides a concise and portable description that is useful for predicting synaptic responses to more complex patterns of simulation, for studies relating to circuit dynamics and for equating dynamic properties across different synaptic pathways between or within preparations. This model allows computation of postsynaptic responses by either facilitation or depression in the synapse thus exhibiting characteristics of dynamic synapses as that found during short-term synaptic plasticity, for any arbitrary pre-synaptic spike train in the presence of realistic background synaptic noise. Thus it allows us to see specific effect of the spike train on a neuronal lattice both small-scale and large-scale, so as to reveal the short-term plastic behavior in neurons.

In adults, motoneurone pools of synergistic muscles that act around a common joint share a common presynaptic drive. Common drive can be revealed by both time domain and frequency domain analysis of EMG signals. Analysis in the frequency domain reveals significant coherence in the range 1-45 Hz, with maximal coherence in low (1-12 Hz) and high (16-32 Hz) ranges. The high-frequency range depends on cortical drive to motoneurones and is coherent with cortical oscillations at approximately 20 Hz frequencies. It is of interest to know whether oscillatory drive to human motoneurone pools changes with development. In the present study we examined age-related changes in coherence between rectified surface EMG signals recorded from the short and long thumb abductor muscles during steady isometric contraction obtained while subjects abducted the thumb against a manipulandum. We analysed EMG data from 36 subjects aged between 4 and 14 years, and 11 adult subjects aged between 22 and 59 years. Using the techniques of pooled coherence analysis and the chi(2) difference of coherence test we demonstrate that between the ages of 7 and 9 years, and 12 and 14 years, there are marked increases in the prevalence and magnitude of coherence at frequencies between 11 and 45 Hz. The data from subjects aged 12-14 years were similar to those obtained from adult controls. The most significant differences between younger children and the older age groups were detected at frequencies close to 20 Hz. We believe that these are the first reported results demonstrating significant late maturational changes in the approximately 20 Hz common oscillatory drive to human motoneurone pools.

A comparison of previously defined spike train synchronization indices is undertaken within a stochastic point process framework. The second-order cumulant density (covariance density) is shown to be common to all the indices. Simulation studies were used to investigate the sampling variability of a single index based on the second-order cumulant. The simulations used a paired motoneurone model and a paired regular spiking cortical neurone model. The sampling variability of spike trains generated under identical conditions from the paired motoneurone model varied from 50% to 160% of the estimated value. On theoretical grounds, and on the basis of simulated data a rate dependence is present in all synchronization indices. The application of coherence and pooled coherence estimates to the issue of synchronization indices is considered. This alternative frequency domain approach allows an arbitrary number of spike train pairs to be evaluated for statistically significant differences, and combined into a single population measure. The pooled coherence framework allows pooled time domain measures to be derived, application of this to the simulated data is illustrated. Data from the cortical neurone model is generated over a wide range of firing rates (1-250 spikes/s). The pooled coherence framework correctly characterizes the sampling variability as not significant over this wide operating range. The broader applicability of this approach to multielectrode array data is briefly discussed.

Various time-frequency methods have been used to study time-varying properties of non-stationary neurophysiological signals. In the present study, a time-frequency coherence estimate using continuous wavelet transform (CWT) together with its confidence intervals are proposed to evaluate the correlation between two non-stationary processes. The approach is based on averaging over repeat trials. A systematic comparison between approaches using CWT and short-time Fourier transform (STFT) is carried out. Simulated data are generated to test the performance of these methods when estimating time-frequency based coherence. In contrast to some recent studies, we find that CWT based coherence estimates do not supersede STFT based estimates. We suggest that a combination of STFT and CWT would be most suitable for analysing non-stationary neural data. Tests are presented to investigate the time and frequency discrimination capabilities of the two approaches. The methods are applied to two experimental data sets: electroencephalogram (EEG) and surface electromyogram (EMG) during wrist movements in a healthy subject, and local field potential (LFP) and surface EMG recordings during resting tremor in a Parkinsonian patient. Supporting software is available at and .

It is possible to obtain information about the synaptic drive to motoneurons during walking by analyzing motor-unit coupling in the time and frequency domains. The purpose of the present study was to compare motor-unit coupling during walking in healthy subjects and patients with incomplete spinal cord lesion to obtain evidence of differences in the motoneuronal drive that result from the lesion. Such information is of importance for development of new strategies for gait restoration. Twenty patients with incomplete spinal cord lesion (SCL) participated in the study. Control experiments were performed in 11 healthy subjects. In all healthy subjects, short-term synchronization was evident in the discharge of tibialis anterior (TA) motor units during the swing phase of treadmill walking. This was identified from the presence of a narrow central peak in cumulant densities constructed from paired EMG recordings and from the presence of significant coherence between these signals in the 10- to 20-Hz band. Such indicators of short-term synchrony were either absent or very small in the patient group. The relationship between the amount of short-term synchrony and the magnitude of the 10- to 20-Hz coherence in the patients is discussed in relation to gait ability. It is suggested that supraspinal drive to the spinal cord is responsible for short-term synchrony and coherence in the 10- to 20-Hz frequency band during walking in healthy subjects. Absence or reduction of these features may serve as physiological markers of impaired supraspinal control of gait in SCL patients. Such markers could have diagnostic and prognostic value in relation to the recovery of locomotion in patients with central motor lesions.

This simulation study examines the possibility that dendritic sub units can be defined according to temporal aspects in the timing of populations of synaptic inputs. A two cell model with passive dendritic trees is used, which is subject to both common and independent synaptic inputs, the presence of common synaptic input results in a tendency for correlated firing in the two cell model. The strength of this correlation is used to measure the efficacy of the common synaptic inputs in modulating the output discharge of each neurone. Our results suggest that a small fraction of the total synaptic input can effectively modulate the timing of output spikes, this phenomenon is not dependent on the physical location of the inputs on the dendritic tree. This phenomenon depends on the presence of temporal correlation between the pre-synaptic spike trains that provide the common input. We propose to refer to these as temporal sub units.

High frequency oscillations (> 80–90 Hz) occur in neocortex and hippocampus in vivo where they are associated with specific behavioural states and more classical EEG frequency bands. In the hippocampus in vitro these oscillations can occur in the absence of pyramidal neuronal somatodendritic compartments and are temporally correlated with on-going, persistent gamma frequency oscillations. Their occurrence in the hippocampus is dependent on gap-junctional communication and it has been suggested that these high frequency oscillations originate as collective behaviour in populations of electrically coupled principal cell axonal compartments. Here we demonstrate that the superficial layers of medial entorhinal cortex can also generate high frequency oscillations associated with gamma rhythms. During persistent gamma frequency oscillations high frequency oscillations occur with a high bispectral coherence with the field gamma activity. Bursts of high frequency oscillations are temporally correlated with both the onset of compound excitatory postsynaptic potentials in fast-spiking interneurones and spikelet potentials in both pyramidal and stellate principal neurones. Both the gamma frequency and high frequency oscillations were attenuated by the gap junction blocker carbenoxolone. These data suggest that high frequency oscillations may represent the substrate for phasic drive to interneurones during persistent gamma oscillations in the medial entorhinal cortex.

Vertebrate and most invertebrate organisms interact with their environment through processes of adaptation and learning. Such processes are generally controlled by complex networks of nerve cells, or neurons, and their interactions. Neurons are characterized by all-or-none discharges - the spikes - and the time series corresponding to the sequences of the discharges - the spike trains - carry most of the information used for intercellular communication. This paper describes biologically inspired spiking neural network models suitable for digital hardware implementation. We consider bio-realism, hardware friendliness, and performance as factors which influence the ability of these models to integrate into a flexible computational substrate inspired by evolutionary, developmental and learning aspects of living organisms. Both software and hardware simulations have been used to assess and compare the different models to determine the most suitable spiking neural network model.

We have studied human stereopsis by analysing magnetoencephalographic signals during the presentation of stereograms using frequency analysis. The study of synchronised firing of cortical neurones is a new way of understanding information processing in the brain and it is hypothesised that frequencies greater than 35 Hz are used for higher-order processing. We report the response of cortical neurones involved in stereopsis recorded from over the occipital and parietal cortices using a single channel axial superconducting quantum interference device neuromagnetometer. Our main result was increased cortical activity in the gamma-band at frequencies apparently related to stereopsis and the perception of depth. Our results are consistent with reports in the literature that suggest that frequencies above 40 Hz are involved in attention, pattern recognition and higher order visual activity.

Summary Background In healthy people, rhythmic activation of the motor cortex in the 15–30 Hz frequency range accompanies and contributes to voluntarily-generated postural contractions of contralateral muscle. In patients with Parkinson's disease, an abnormal low-frequency activation of the motor areas of the cortex occurs and has been directly linked to the characteristic 3–6 Hz rest tremor of this disease. We therefore investigated whether the motor cortex is involved in the transmission of the rhythmic motor drive responsible for generating essential tremor. Methods Non-invasive recordings of activity from the hand area of the motor cortex were made from six patients with essential tremor by magnetoencephalography. The recordings were made simultaneously with the electromyogram recorded from contralateral finger muscles during periods of postural tremor. A statistical spectral analysis was done to determine at which frequencies the two signals were correlated. Findings Spectral analysis of the electromyogram signals showed a significant low-frequency component at the frequency of the tremor bursts. However, there was no coherence between magnetoencephalogram and electromyogram recordings at the tremor frequency, indicating that no correlation existed between the tremor signal and low-frequency activity recorded from the primary motor cortex in individuals with essential tremor. Coherence at frequencies higher than the tremor frequency was similar to that in healthy individuals performing voluntary postural contractions. Interpretation The absence of significant coherence between the magnetoencephalogram and electromyogram at tremor frequencies suggests that in essential tremor the tremor is imposed on the active muscle through descending pathways other than those originating in the primary motor cortex. These findings challenge the model widely used to explain the efficacy of neurosurgical treatment of essential tremor, are in contrast to those of previous studies of parkinsonian rest tremor, and highlight an important difference in the pathophysiology of essential and parkinsonian tremor.

Stereopsis implies the perception of solid form and is generally used to denote the perception of solid objects by the human visual system. Although monocular cues are important for depth perception at a distance, for objects less than a 100 feet away, this process is also mediated by stereoscopic vision. Fixation at a point with both eyes renders the image of that point falling on the centre of the retina in each eye. However, because the two eyes are about six centimetres apart, three-dimensional objects produce slightly different images on different parts of the 2 retinae. The degree of this binocular disparity depends on the distance of the object from the plane of fixation of the 2 eyes. Thus, points on a three-dimensional object just outside the fixation plane stimulate different points on each eye and multiple disparities provide cues for stereopsis — which results in the perception of depth. The hypothesis that binocular disparity is the effective stimulus for depth perception is attributed to Kepler, the astronomer but the demonstration of that disparity alone can produce depth sensation was first provided by Wheatstone in 1838 with his invention of the stereoscope [1]. Bela Julesz[2] discovered that apparent three-dimensionality’ of objects can be perceived by the human visual system in random-dot stereograms which contain hidden images. This fact suggests that the main clue required for the perception of stereopsis is retinal disparity which excites the “cyclopean” group of neurones in the brain. These neurones force fusion of the discrete retinal images to give the perception of apparent third dimension in an essentially two-dimensional image.

A novel technique for the study of human eye movements was used to investigate the frequency components of ocular drift and microtremor in both eyes simultaneously. The tangential components of horizontal eye accelerations were recorded in seven healthy subjects using light-weight accelerometers mounted on scleral contact lenses during smooth pursuit movements, vestibulo-ocular reflexes and eccentric gaze with and without fixation. Spectral peaks were observed at low (up to 25 Hz) and high (60-90 Hz) frequencies. A multivariate analysis based on partial coherence analysis was used to correct for head movement. After correction, the signals were found to be coherent between the eyes over both low- and high-frequency ranges, irrespective of task, convergence or fixation. It is concluded that the frequency content of ocular drift and microtremor reflects the patterning of low-level drives to the extra-ocular muscle motor units.

Neuronal modelling is the process by which a biological neuron is represented by a mathematical structure that incorporates its biophysical and geometrical characteristics. This structure is referred to as the mathematical model or the model of the neuron. The behavior of this representation may serve a number of purposes: for example, it may be used as the basis for estimating the biophysical parameters of real neurons or it may be used to define the computational and information processing properties of a neuron. Neuronal modelling requires not only an understanding of mathematical and computational techniques, but also an understanding of the what the process of modelling entails. A general treatment of models, however, would necessarily lead to the examination of a number of philosophical questions. Here we simply discuss some aspects of modelling that in our experience have proved to be useful in the construction and application of models. These topics are not usually considered in the neurophysiological modelling literature, but an understanding of the basic assumptions of modelling, and the presumed relation between model and reality is essential for constructive work in computational neuroscience.

Publisher Summary The work of Stiles and Randall and that of Elble and Randall established that the spectrum of a tremor signal consists of two components: an inertial load dependent component and a neurogenic component. The former is a property of the structure exhibiting the tremor and shifts toward lower frequencies with increased inertial loading. The neurogenic component is load independent and was first attributed to central descending processes in the frequency range 8–12 Hz. During a maintained postural task, an additional 15–30-Hz neurogenic component of tremor was identified and associated with motor unit synchronization. Farmer et al . inferred, on the basis of indirect evidence, that the common drive to the synchronized motor units was of descending origin. Conway et al. , using magnetoencephalographic (MEG) techniques, and Halliday et al ., with conventional electroencephalographic (EEG) techniques, demonstrated a correlation between localized cortical activity in the 15–30-Hz frequency band and the neurogenic component of tremor associated with motor unit synchronization. These results imply that the localized rhythmic cortical activity in the 15–30-Hz frequency band that occurs during maintained postural tasks accounts for the 15–30-Hz component of neurogenic tremor, which in turn is a consequence of motor unit synchronization. The analysis of the correlation between the 15–30-Hz rhythmic cortical oscillations and the neurogenic component of tremor is equivalent to an investigation of the descending drive that synchronizes motor units during maintained postural tasks. The application of spectral and coherence analyses therefore provides a powerful procedure for characterizing the central drive associated with rhythmic cortical activity and motor unit synchrony in normal and pathological tremors. The application of these analytical methods reveals significant differences in the correlation between cortical drive and tremor in normal subjects with that observed in the cases of essential tremor and Parkinsonian tremor.

The cross-correlation histogram has provided the primary tool for inferring the structure of common inputs to pairs of neurones. While this technique has produced useful results it not clear how it may be extended to complex networks. In this report we introduce a linear model for point process systems. The finite Fourier transform of this model leads to a regression type analysis of the relations between spike trains. An advantage of this approach is that the full range of techniques for multivariate regression analyses becomes available for spike train analysis. The two main parameters used for the identification of neural networks are the coherence and partial coherences. The coherence defines a bounded measure of association between two spike trains and plays the role of a squared correlation coefficient defined at each frequency lambda. The partial coherences, analogous to the partial correlations of multiple regression analysis, allow an assessment of how any number of putative input processes may influence the relation between any two output processes. In many cases analytic solutions may be found for coherences and partial coherences for simple neural networks, and in combination with simulations may be used to test hypotheses concerning proposed networks inferred from spike train analyses.

The aim of this study was to examine the pathophysiological mechanisms underlying co-contraction in patients with dystonia (n = 6) and writer's cramp (n = 5). Multi-unit needle and surface EMGs were recorded from extensor carpi radialis (ECR) and flexor carpi radialis (FCR) muscles during motor tasks that elicited dystonia or writer's cramp. The EMGs from ECR and FCR were recorded simultaneously and analysed using cross-correlation analysis. Similar recordings were obtained from healthy age- and sex-matched control subjects (n = 8). Despite co-contraction of the muscles, cross-correlograms from the healthy subjects did not reveal evidence of motor unit synchronization. Cross-correlograms from the dystonic subjects revealed a central peak with a median duration of 37 ms, indicating broad-peak motor unit synchronization. Cross-correlograms from patients with writer's cramp were either flat or modulated by a 11-12-Hz tremor. Frequency-domain analysis of ECR and FCR EMGs demonstrated significant coherence in the patients with dystonia and writer's cramp. These results indicate that co-contraction in dystonia is neurophysiologically distinct from voluntary co-contraction and is produced by abnormal synchronization of presynaptic inputs to antagonist motor neuron pools. ECR and FCR co-contraction in writer's cramp may be a compensatory process under voluntary control.

This article reviews some recent applications of time and frequency domain cross-correlation techniques to human motor unit recording. These techniques may be used to examine the pre-synaptic mechanisms involved in control of motoneuron activity during on-going motor tasks in man without the need for imposed and artificial perturbations of the system. In this review we examine, through several examples, areas in which insights have been gained into the basic neurophysiological processes that bring about motoneuron firing in man and illustrate how these processes are affected by central nervous system pathology. We will demonstrate that synchronization and coherence may be revealed between human motor unit discharges and give examples that support the hypothesis that these phenomena are generated by activity in a focused common corticospinal input to spinal motoneurons. Disruption of central motor pathways due to diseases of the nervous system leads to pathophysiological alterations in the activity of these pre-synaptic motoneuron inputs that can be revealed by cross-correlation analysis of motor unit discharges. The significance of these studies and outstanding questions in this field are discussed

Muscle spindle discharge in the cat is sensitive to the mechanical activity of anatomically close motor units (e.g. Binder & Stuart, 1980; Conway, Halliday & Rosenberg, 1993). In man similar have been demonstrated by electrical stimulation of skeletomotor axons (McKeon & Burke, 1983). However, studies of voluntary contractions in man have failed to reveal effects of this nature when single afferent firing was correlated with gross surface EMG in leg muscles (Gandevia, Burke & McKeon, 1986). Here we examine this problem in the case of finger extensor muscles during low force voluntary isometric contractions.

Physiological tremor has two main spectral components. One is a consequence of mechanical resonance and its frequency changes with inertial loading (Stiles & Randall, 1967). The other is load independent (referred to as neurogenic) and contributes to two distinct frequency bands of the spectrum (Amjad, Conway, Farmer, O’Leary, Halliday & Rosenberg, 1994). Here we describe the relation between the neurogenic components of tremor and the discharges of single motor-units. While Elble & Randall (1976) studied extensor digitorum communis with a single load of between 200 – 250g or an equivalent voluntarily generated force, we have been concerned with loads not exceeding 25g, which is less than a 10% maximum voluntary contraction.

Distal synaptic inputs to motoneurones produce Post Synaptic Potentials (PSP) at the soma with longer rise times and half widths than proximal inputs. This is due to electrotonic spread of the PSP. Previous studies have concentrated on the time course of a single compound EPSP at the soma for a variety of pre-synaptic input configurations (e.g. Segev, Fleshman & Burke, 1990). The EPSP represents only an intermediate variable in determining the output discharge of a cell. Simulation studies with compartmental models of motoneurones were used to investigate the functional consequences of synaptic location on synaptic transmission during repetitive firing.

1. Spike trains from identified single Ia afferents from soleus and lateral gastrocnemius muscles were recorded (while 'in continuity' with the spinal cord) simultaneously with single-motor-unit EMG spike trains from the same muscles in decerebrate cats. 2. A total of 143 Ia afferent-motor-unit pairs were examined for the presence of correlated activity between the Ia afferent and motor-unit and between the motor-unit and Ia afferent. Four types of correlation were identified on the basis of the cross-intensity function estimated for individual Ia afferent-motor-unit pairs. These correlations were attributed to the absence or presence of a central Ia afferent-motoneurone interaction or a peripheral motor-unit-muscle spindle interaction. 3. In addition to the cross-correlation-based second-order cross-intensity function, third-order cumulants were defined and used further to investigate Ia afferent-motor-unit interactions. A third-order cumulant density-based approach to signal processing offers improved signal-to-noise ratios, compared with the traditional product density approach, for parameters characterizing certain kinds of linear processes as well as a description of non-linear interactions. Two classes of third-order relations were described. One class was associated with a strong central connection and the other with a weak central connection. 4. Third-order cumulants estimated for Ia afferent-motor-unit pairs with significant second-order central correlations were able to detect a period of decreased motoneuronal excitability. In addition, temporal summation prior to spike initiation could be identified in cases where the afferent discharge was suitably high. 5. Third-order cumulants estimated for Ia afferent-motor-unit pairs in which no significant second-order central correlation existed identified the presence of weak synaptic interactions. It is argued that these interactions result from the summation from the recorded Ia afferent discharge and other spontaneous synaptic inputs to the motoneurone. 6. The results of the second-order cross-intensity analysis of Ia afferent-motor-unit interactions, combined with those from the third-order cumulant density analysis, showed that 77% of the recorded afferents had a detectable influence on motor-unit behaviour. 7. The results of this study suggest that the third-order cumulant, based on the analysis of spike trains, will provide a useful tool for detecting synaptic interactions not found by the use of the second-order cross-correlation histogram alone, and may also be used to estimate the time course of post-spike depression in motoneurones, as well as other non-linear regions of motoneurone membrane trajectory.

1. The discharges of pairs of individual motor units were recorded from intrinsic hand muscles in man. Single motor unit recordings were obtained either when both members of the motor unit pair were within first dorsal interosseous muscle (1DI:1DI recordings) or where one motor unit was within 1DI and the other in second dorsal interosseous muscle (1DI:2DI recordings). The pairs of motor unit spike trains were cross-correlated in the time domain and the results compared to those of coherence analysis performed on the same spike train data. Central peaks were present in the cross-intensity functions, indicating the presence of common synaptic input to the motoneurone pair. Coherence analysis of these data indicated significant association between motor unit firing in the frequency ranges 1-12 and 16-32 Hz. 2. Analysis of sequential non-overlapping segments of data recorded from individual motor unit pairs, demonstrated that both the central cross-intensity peak and coherence in the frequency bands 1-12 and 16-32 Hz were consistent features throughout a long recording. In these sequential recordings, the size of the central cross-intensity peak and the maximal value of coherence in the frequency band 16-32 Hz covaried from segment to segment. Analysis of the entire population of motor unit pairs confirmed a positive relationship between the magnitude of peak coherence and the size of the central cross-intensity peak. 3. Voluntary sinusoidal co-modulation of the firing rates of pairs of individual motor units recorded from within 1DI was found to produce significant values of coherence corresponding to the frequency of the common modulation. However, firing rate co-modulation was not found to affect either the size of the central cross-intensity peak or the maximum value of coherence in the frequency band 16-32 Hz. 4. Pairs of single motor units were recorded from within 1DI and biceps brachii muscles of healthy subjects. The number and size of the central cross-intensity peaks and coherence peaks detected were compared for the two muscles. The incidence and size of central cross-intensity peaks and the incidence and magnitude of 16-32 Hz coherence peaks were both found to be greater for 1DI recordings when compared to biceps brachii recordings. 5. Single motor unit recordings were made from the intrinsic hand muscles of a patient with severe peripheral deafferentation. Time- and frequency-domain analysis of these recordings revealed cross-intensity peaks and frequency bands of coherence similar to those seen in healthy subjects.(ABSTRACT TRUNCATED AT 400 WORDS)

to the editor: The electromyogram (EMG) as an indirect measure of motor unit activity has proved invaluable in motor control studies. Increasingly, the application of frequency domain techniques to EMG signals has provided important insight into the structure and function of the human motor system.

Coherence and related functions are powerful tools in the study of neurophysiological data. Amjad et al. (1997) introduced two measures which allow an arbitrary number of independent coherence functions to be evaluated for statistically significant differences and combined into a single population measure. This latter measure they termed ‘pooled coherence’. Baker (2000) presents an example of the application of pooled coherence to a population of simulated data which does not describe accurately the correlation structure within the data. The estimation of pooled coherence, as defined by Eq. (2.11) in Amjad et al. (1997) and Eq. (1) in Baker (2000), is equivalent to joining the separate records into a single long record and estimating the coherence for this single pooled record using a periodogram approach (e.g. Halliday et al., 1995). Thus, once the context of an analysis has been determined, the terms coherence and pooled coherence are interchangeable. Asymptotic confidence limits allow coherence estimates to be assessed for the presence of significant correlation at each Fourier frequency. In the case of periodogram estimates formed from disjoint sections this confidence limit can be estimated from a simple expression which depends on the number of sections averaged (Amjad et al., 1997). This approach is based on the extensively developed theory for the properties of Fourier transforms of stationary stochastic data (e.g. Brillinger, 1981). Why should a coherence estimate and confidence limit which are appropriate for single records fail to describe the correlation structure in a single record formed from 100 separate sections (Baker 2000)? Consider a plot of the two simulated signals constructed in Baker (2000), each consisting of 100 sections, with the amplitude of each section scaled by a normally distributed factor of 1098 (mean92 SD). The fine detail will be lost, but the two traces will exhibit step changes in their envelope at transition points between sections. In statistical terms the data exhibits a nonstationarity, in fact nonstationarity is built into the construction of such data. Second order stationarity (invariance of second order moments) is one of the assumptions underlying the application of coherence analysis (e.g. Brillinger, 1981). As described below, it is the violation of the assumption of stationarity which underlies the result reported in Baker (2000). The analogy between spectrum analysis and analysis of variance has long been recognized (e.g. Tukey, 1961). The spectrum of a signal can be interpreted as providing a measure of the fraction of the total variance (power) at a Fourier frequency. Scaling the amplitude of different sections of data by a constant is equivalent to scaling the variance of each signal resulting in an increase or decrease in the relative power at each frequency. Following this line of reasoning we can see that a pooled coherence estimate (calculated from pooled cross and auto spectra) will be dominated by the sections with the largest variance, and the sampling fluctuations will be determined mostly by the subset of sections with the largest variance. A confidence limit * Corresponding author. Present address: Department of Electronics, University of York, Heslington, York YO10 5DD, UK. Tel.: +44-1904-432345; fax: +44-1904-432335. E-mail address: dh20@ohm.york.ac.uk (D.M. Halliday).

It has been widely assumed that joint receptors contribute to the reflex regulation of movement and posture, although there have been few clear demonstrations of joint-mediated reflex actions on alpha-motoneurones other than those attributable to flexor reflex afferents. The present study extends our recent work on joint-mediated reflexes by using Fourier analysis of spike train interactions to demonstrate that restricted mechanical activation of a small number (one to five) of knee joint receptors by localized indentation of the joint capsule can modify the firing pattern of quadriceps motoneurones in decerebrated cats. The modulation of this discharge pattern can be reversibly abolished by application of droplets of lignocaine directly to the joint nerve and consequently can be attributed unambiguously to articular afferents. Activation of single joint afferents could on occasion produce changes in motor unit firing patterns, but usually activation of two or more was required before secure effects were observed. Increasing the intensity of indentation (resulting in activation of greater numbers of joint receptors) increases the strength of coupling between joint afferent input and motor unit responses, although the relationship is not linear. The relation between the discharge patterns of pairs of motor units was also examined, and it was found that significant coupling occurred at the stimulus frequency, superimposed on a 'background' coupling from unidentified sources. The phase relationship between pairs of motor units was not affected by the periodic stimulus. However, it was observed that if two motor units were firing independently of one another in the absence of capsule probing, maintained capsular indentation produced a striking synchronization between the discharges of the two motor units. These experiments show strong joint-mediated reflex effects on motor unit firing indicating that joint receptors may have an important role to play in motor control.

Muscle spindles are complex biological receptors involved in the maintenance of posture. Such receptors have several inputs, some of which are point process like (neural signals), whereas others are continuous (e.g. muscle length). These inputs combine to produce a neural output which is also a point-process. Frequency domain analysis of the point-process signals has revealed features not apparent by other methods of investigation. Processes occurring within the muscle spindle which may not be directly accessible experimentally have been studied successfully using a combination of simulation and identification techniques.

There is both direct and indirect evidence that stretch activation occurs in the dynamic bag1 fibres of the mammalian muscle spindle and that it is responsible for maintaining the high sensitivity of primary sensory endings in stretches great enough to break the resting actomyosin bonds responsible for the short-range stiffness of muscle fibres. However the direct observations of dynamic bag1 fibre behaviour during stretching were made on damaged fibres and during very slow stretches. Preliminary results of experiments employing faster stretches of intact muscle spindles are reported here. An image processing system is being developed to automate and facilitate analysis of sarcomere movements during stretch, release and activation of intrafusal fibres. Unequivocal evidence confirming the development of stretch activation has not yet been found. Boyd (1986a) believed that static bag2 and chain fibres are controlled by separate populations of static gamma motoneurones, while accepting that there is some degree of common innervation. His evidence and the functional implications are discussed.

When an isolated cat muscle spindle is subjected to a ramp and hold stretch the primary sensory annulo-spiral round the dynamic bag1 (Db1) fibre is extended and then creeps back part way towards its original state over several seconds since the poles of the fibre give way (Boyd, 1976). This ‘creep’ at the final length is small, or absent, when the fibre is inactive, and is greatly enhanced by activation of the fibre (Fig. 1; Boyd, Gladden & Ward, 1981). The length sensitivity of the primary sensory ending is greatly increased during the dynamic phase of stretching, but the static length sensitivity is little increased because the creep causes pronounced slow adaptation of the Ia discharge (Fig. 2).

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 interactions 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.

The work presented in this report forms part of a larger research programme in which the behaviour of the muscle spindle is described under conditions when several fusimotor inputs, and length changes are applied simultaneously to the spindle while recording simultaneously from its primary (Ia) and secondary (II) sensory endings. We restrict the current presentation to a discussion of the strength of coupling or association and time delay between the responses of primary and secondary endings from the same tenuissimus muscle spindle during activation of single and multiple fusimotor inputs. A description of this interaction is particularly interesting in the light of a recent study by Edgley and Jankowska (1987) which demonstrated the convergence of group Ia and II afferent axons onto the same interneurones in the midlumbar segment of the spinal cord.

This study describes two load-independent rhythmic contributions from motor-unit synchronization to normal physiological tremor, which occur in the frequency ranges 1–12 Hz and 15–30 Hz. In common with previous studies, we use increased inertial loading to identify load-independent components of physiological tremor. The data consist of simultaneous recordings of tremor acceleration from the third finger, a surface electromyogram (EMG), and the discharges of pairs of single motor units from the extensor digitorum communis (EDC) muscle, collected from 13 subjects, and divided into 2 data sets: 106 records with the finger unloaded and 84 records with added mass from 5 to 40 g. Frequency domain analysis of motor-unit data from individual subjects reveals the presence of two distinct frequency bands in motor-unit synchronization, 1–12 Hz and 15–30 Hz. A novel Fourier-based population analysis demonstrates that the same two rhythmic components are present in motor-unit synchronization across both data sets. These frequency components are not related to motor-unit firing rates. The same frequency bands are present in the correlation between motor-unit activity and tremor and between surface EMG activity and tremor, despite a significant alteration in the characteristics of the tremor with increased inertial loading. A multivariate analysis demonstrates conclusively that motor-unit synchronization is the source of these contributions to normal physiological tremor. The population analysis suggests that single motor-unit discharges can predict an average of 10% of the total tremor signal in these two frequency bands. Rectified surface EMG can predict an average of 20% of the tremor; therefore within our population of recordings, the two components of motor-unit synchronization account for an average of 20% of the total tremor signal, in the frequency ranges 1–12 Hz and 15–30 Hz. Our results demonstrate that normal physiological tremor is a complex signal containing information relating to motor-unit synchronization in different frequency bands, and lead to a revised definition of normal physiological tremor during low force postural contractions, which is based on using both the tremor spectra and the correlation between motor-unit activity and tremor to characterize the load-dependent and the load-independent components of tremor. In addition, both physiological tremor and rectified EMG emerge as powerful predictors of the frequency components of motor-unit synchronization.