Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized EMG

We investigate the relationship between the extensor electromyogram (EMG) and tremor time series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand.Comment: 9 pages, 6 figures, to appear in Biological Cybernetic

Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica

Motor Unit-Driven Identification of Pathological Tremor in Electroencephalograms.

Background: Traditional studies on the neural mechanisms of tremor use coherence analysis to investigate the relationship between cortical and muscle activity, measured by electroencephalograms (EEG) and electromyograms (EMG). This methodology is limited by the need of relatively long signal recordings, and it is sensitive to EEG artifacts. Here, we analytically derive and experimentally validate a new method for automatic extraction of the tremor-related EEG component in pathological tremor patients that aims to overcome these limitations. Methods: We exploit the coupling between the tremor-related cortical activity andmotor unit population firings to build a linearminimummean square error estimator of the tremor component in EEG. We estimated the motor unit population activity by decomposing surface EMG signals into constituent motor unit spike trains, which we summed up into a cumulative spike train (CST). We used this CST to initialize our tremor-related EEG component estimate, which we optimized using a novel approach proposed here. Results: Tests on simulated signals demonstrate that our new method is robust to both noise and motor unit firing variability, and that it performs well across a wide range of spectral characteristics of the tremor. Results on 9 essential (ET) and 9 Parkinson’s disease (PD) patients show a ∼2-fold increase in amplitude of the coherence between the estimated EEG component and the CST, compared to the classical EEG-EMG coherence analysis. Conclusions: We have developed a novel method that allows for more precise and robust estimation of the tremor-related EEG component. This method does not require artifact removal, provides reliable results in relatively short datasets, and tracks changes in the tremor-related cortical activity over time.post-print2672 K

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

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 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°). 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 - 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 Ia afferent signal from the imposed movement being the most likely candidate to provide the entraining signal for the central oscillator(s)

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 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°). 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 - 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 Ia afferent signal from the imposed movement being the most likely candidate to provide the entraining signal for the central oscillator(s)

One central oscillatory drive is compatible with experimental motor unit behaviour in essential and Parkinsonian tremor

Pathological tremors are symptomatic to several neurological disorders that are difficult to differentiate and the way by which central oscillatory networks entrain tremorogenic contractions is unknown. We considered the alternative hypotheses that tremor arises from one oscillator (at the tremor frequency) or, as suggested by recent findings from the superimposition of two separate inputs (at the tremor frequency and twice that frequency). Approach. Assuming one central oscillatory network we estimated analytically the relative amplitude of the harmonics of the tremor frequency in the motor neuron output for different temporal behaviors of the oscillator. Next, we analyzed the bias in the relative harmonics amplitude introduced by superimposing oscillations at twice the tremor frequency. These findings were validated using experimental measurements of wrist angular velocity and surface electromyography (EMG) from 22 patients (11 essential tremor, 11 Parkinson’s disease). The ensemble motor unit action potential trains identified from the EMG represented the neural drive to the muscles. Main results. The analytical results showed that the relative power of the tremor harmonics in the analytical models of the neural drive was determined by the variability and duration of the tremor bursts and the presence of the second oscillator biased this power towards higher values. The experimental findings accurately matched the analytical model assuming one oscillator, indicating a negligible functional role of secondary oscillatory inputs. Furthermore, a significant difference in the relative power of harmonics in the neural drive was found across the patient groups, suggesting a diagnostic value of this measure (classification accuracy: 86%). This diagnostic power decreased substantially when estimated from limb acceleration or the EMG. Signficance. The results indicate that the neural drive in pathological tremor is compatible with one central network providing neural oscillations at the tremor frequency. Moreover, the regularity of this neural oscillation varies across tremor pathologies, making the relative amplitude of tremor harmonics a potential biomarker for diagnostic use

Online tracking of the phase difference between neural drives to antagonist muscle pairs in essential tremor patients

Transcutaneous electrical stimulation has been applied in tremor suppression applications. Out-of-phase stimulation strategies applied above or below motor threshold result in a significant attenuation of pathological tremor. For stimulation to be properly timed, the varying phase relationship between agonist-antagonist muscle activity during tremor needs to be accurately estimated in real-time. Here we propose an online tremor phase and frequency tracking technique for the customized control of electrical stimulation, based on a phase-locked loop (PLL) system applied to the estimated neural drive to muscles. Surface electromyography signals were recorded from the wrist extensor and flexor muscle groups of 13 essential tremor patients during postural tremor. The EMG signals were pre-processed and decomposed online and offline via the convolution kernel compensation algorithm to discriminate motor unit spike trains. The summation of motor unit spike trains detected for each muscle was bandpass filtered between 3 to 10 Hz to isolate the tremor related components of the neural drive to muscles. The estimated tremorogenic neural drive was used as input to a PLL that tracked the phase differences between the two muscle groups. The online estimated phase difference was compared with the phase calculated offline using a Hilbert Transform as a ground truth. The results showed a rate of agreement of 0.88 ± 0.22 between offline and online EMG decomposition. The PLL tracked the phase difference of tremor signals in real-time with an average correlation of 0.86 ± 0.16 with the ground truth (average error of 6.40° ± 3.49°). Finally, the online decomposition and phase estimation components were integrated with an electrical stimulator and applied in closed-loop on one patient, to representatively demonstrate the working principle of the full tremor suppression system. The results of this study support the feasibility of real-time estimation of the phase of tremorogenic neural drive to muscles, providing a methodology for future tremor-suppression neuroprostheses

The phase difference between neural drives to antagonist muscles in essential tremor is associated with the relative strength of supraspinal and afferent input

The pathophysiology of essential tremor (ET), the most common movement disorder, is not fully understood. We investigated which factors determine the variability in the phase difference between neural drives to antagonist muscles, a long-standing observation yet unexplained. We used a computational model to simulate the effects of different levels of voluntary and tremulous synaptic input to antagonistic motoneuron pools on the tremor. We compared these simulations to data from 11 human ET patients. In both analyses, the neural drive to muscle was represented as the pooled spike trains of several motor units, which provides an accurate representation of the common synaptic input to motoneurons. The simulations showed that, for each voluntary input level, the phase difference between neural drives to antagonist muscles is determined by the relative strength of the supraspinal tremor input to the motoneuron pools. In addition, when the supraspinal tremor input to one muscle was weak or absent, Ia afferents provided significant common tremor input due to passive stretch. The simulations predicted that without a voluntary drive (rest tremor) the neural drives would be more likely in phase, while a concurrent voluntary input (postural tremor) would lead more frequently to an out-of-phase pattern. The experimental results matched these predictions, showing a significant change in phase difference between postural and rest tremor. They also indicated that the common tremor input is always shared by the antagonistic motoneuron pools, in agreement with the simulations. Our results highlight that the interplay between supraspinal input and spinal afferents is relevant for tremor generation