David M. Halliday

The Fourier approach to the identification of functional coupling between neuronal spike trains

I. I N T R O D U C T I O N The study of the behaviour of small networks of neurones frequently requires the determination of measures of the strength of association between component neurones, an assessment of their timing relations, and the identification of which neurones may interact directly or are influenced by common inputs. In many of these studies the principal quantities available for analysis are the sequences of extracellularly recorded action potentials (neuronal spike trains). The subsequent analytical work is then based entirely on the relations between the times of occurrence of the action potentials recorded from different neurones. In these circumstances neuronal spike trains are frequently represented as the mathematical entity known as a stochastic point process. These processes are described by providing a probability law for a set of ordered times

Synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man.

1. Simultaneous recordings of cortical activity, recorded as the magnetoencephalogram (MEG), and the electromyogram (EMG) of the ipsilateral and contralateral first dorsal interosseous muscles (1DI) were made during maintained voluntary contractions. 2. The MEG recorded from a localized region of the sensorimotor cortex of the dominant hemisphere was coherent with the EMG from the contralateral 1DI muscle over a limited band of frequencies. The peak coherence was confined largely within the beta range of cortical activity (13‐35 Hz). Significant cortical activity at 10 Hz and 40‐50 Hz was not correlated with motor output. The MEG and EMG from the ipsilateral 1DI muscle were uncorrelated at all frequencies. 3. Significant coherence between the MEG and the EMG was associated with synchronous behaviour between the MEG and EMG in the time domain. 4. The results demonstrate that synchronized cortical activity contributing to MEG activity within the beta range of frequencies during maintained voluntary contractions is coupled to motor output at frequencies of motor‐unit activity associated with motor‐unit synchronization. This observation provides further evidence for the involvement of cortical neurones in the generation of motor‐unit synchronization. 5. We suggest that the coherence between MEG and contralateral EMG observed during maintained isometric contractions may provide an example of binding within the motor system.

Using electroencephalography to study functional coupling between cortical activity and electromyograms during voluntary contractions in humans

Previous studies of neuronal oscillations in sensorimotor cortex in humans and primates have observed rhythmic 15-30 Hz activity, which is correlated with motor output. In humans, this work has been limited to magnetic recordings. In the present study we investigate if similar results can be obtained using electroencephalography (EEG). EEG recordings were made from over the sensorimotor cortex of five adult subjects who performed repeated periods of maintained wrist extension and flexion. Coherence analysis between EEG and electromyogram (EMG) recordings from these muscles revealed correlation in the 15-30 Hz range, with a synchronous correlation structure which matches that previously observed in humans and in paired cortical recordings from primates. We conclude that EEG is equally efficient at investigating functional aspects of these cortical rhythms during voluntary movement in humans.

A review of recent applications of cross-correlation methodologies to human motor unit recording

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.

Coherence between low-frequency activation of the motor cortex and tremor in patients with essential tremor.

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 Parkinsons 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.

Identification of patterns of neuronal connectivity—partial spectra, partial coherence, and neuronal interactions

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.

Detecting time-dependent coherence between non-stationary electrophysiological signals--a combined statistical and time-frequency approach.

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 .

Changes in EMG coherence between long and short thumb abductor muscles during human development

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 ∼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 χ2 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 ∼20 Hz common oscillatory drive to human motoneurone pools.

The origin of ocular microtremor in man

Abstract 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.

On the Need for Rectification of Surface EMG

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.