The application of independent component analysis to the multi-channel surface electromyographic signals for separation of motor unit action potential trains: part II-modelling interpretation.

The purpose of this article was to investigate whether or not FastICA can separate identical motor unit action potential trains (MUAPTs) of the 8-channel surface electromyographic (sEMG) signals constructed by an sEMG model into the independent components. Firstly, we have examined how much the increase of motor units (MUs) in the simulated sEMG signals influenced the performance on the separation of MUAPTs by kurtosis. The decreased trend of mean kurtosis on both sEMG signals and their independent components were observed as MUs were increased. These data suggested that the separation performance decayed when MUs were increased. Secondary, the differences between the independent components and the principal components have been also applied to the simulated sEMG signals with or without time delay between the sEMG channels. FastICA could successfully separate identical MUAPTs with no time delay but principal component analysis (PCA) could not do so. Against it, both FastICA and PCA could not separate MUAPTs with some time delay. In conclusion, our results suggested that FastICA could separate identical MUAPTs with no time delay into the independent components by FastICA, which might offer a new technique for the separation of interfered MUAP waveforms based on statistical properties of sEMG signal distributions.     

Review and classification of variability analysis techniques with clinical applications

Background

Representation of independent biophysical sources using Fourier analysis can be inefficient because the basis is sinusoidal and general. When complex fractionated atrial electrograms (CFAE) are acquired during atrial fibrillation (AF), the electrogram morphology depends on the mix of distinct nonsinusoidal generators. Identification of these generators using efficient methods of representation and comparison would be useful for targeting catheter ablation sites to prevent arrhythmia reinduction.

Method

A data-driven basis and transform is described which utilizes the ensemble average of signal segments to identify and distinguish CFAE morphologic components and frequencies. Calculation of the dominant frequency (DF) of actual CFAE, and identification of simulated independent generator frequencies and morphologies embedded in CFAE, is done using a total of 216 recordings from 10 paroxysmal and 10 persistent AF patients. The transform is tested versus Fourier analysis to detect spectral components in the presence of phase noise and interference. Correspondence is shown between ensemble basis vectors of highest power and corresponding synthetic drivers embedded in CFAE.

Results

The ensemble basis is orthogonal, and efficient for representation of CFAE components as compared with Fourier analysis (p ≤ 0.002). When three synthetic drivers with additive phase noise and interference were decomposed, the top three peaks in the ensemble power spectrum corresponded to the driver frequencies more closely as compared with top Fourier power spectrum peaks (p ≤ 0.005). The synthesized drivers with phase noise and interference were extractable from their corresponding ensemble basis with a mean error of less than 10%.

Conclusions

The new transform is able to efficiently identify CFAE features using DF calculation and by discerning morphologic differences. Unlike the Fourier transform method, it does not distort CFAE signals prior to analysis, and is relatively robust to jitter in periodic events. Thus the ensemble method can provide a useful alternative for quantitative characterization of CFAE during clinical study.     

Fluctuation and linear analysis of Na-current kinetics in squid axon

The power spectrum of current fluctuations and the complex admittance of squid axon were determined in the frequency range 12.5 to 5,000 Hx during membrane voltage clamps to the same potentials in the same axon during internal perfusion with cesium. The complex admittance was determined rapidly and with high resolution by a fast Fourier transform computation of the current response, acquired after a steady state was attained, to a synthesized signal with predetermined spectral characteristics superposed as a continuous, repetitive, small perturbation on step voltage clamps. Linear conduction parameters were estimated directly from admittance data by fitting an admittance model, derived from the linearized Hodgkin-Huxley equations modified by replacing the membrane capacitance with a "constant-phase-angle" capacitance, to the data. The constant phase angle obtained was approximately 80 degrees. At depolarizations the phase of the admittance was 180 degrees, and the real part of the impedance locus was in the left-half complex plane for frequencies below 1 kHz, which indicates a steady-state negative Na conductance. The fits also yielded estimates of the natural frequencies of Na "activation" and "inactivation" processes. By fitting Na-current noise spectra with a double Lorentzian function, a lower and an upper corner frequency were obtained; these were compared with the two natural frequencies determined from admittance analysis at the corresponding potentials. The frequencies from fluctuation analyses ranged from 1.0 to 10.3 times higher than those from linear (admittance) analysis. This discrepancy is consistent with the concept that the fluctuations reflect a nonlinear rate process that cannot be fully characterized by linear perturbation analysis. Comparison of the real part of the admittance and the current noise spectrum shows that the Nyquist relation, which generally applies to equilibrium conductors, does not hold for the Na process in squid axon. The Na-channel conductance, gamma Na, was found to increase monotonically from 0.1 to 4.8 pS for depolarizations up to 50 mV from a holding potential of -60 mV, with no indication of a maximum value.     

The application of independent component analysis to the multi-channel surface electromyographic signals for separation of motor unit action potential trains: part I-measuring techniques.

The purpose of this study is to examine whether or not the application of independent component analysis (ICA) is useful for separation of motor unit action potential trains (MUAPTs) from the multi-channel surface EMG (sEMG) signals. In this study, the eight-channel sEMG signals were recorded from tibialis anterior muscles during isometric dorsi-flexions at 5%, 10%, 15% and 20% maximal voluntary contraction. Recording MUAP waveforms with little time delay mounted between the channels were obtained by vertical sEMG channel arrangements to muscle fibers. The independent components estimated by FastICA were compared with the sEMG signals and the principal components calculated by principal component analysis (PCA). From our results, it was shown that FastICA could separate groups of similar MUAP waveforms of the sEMG signals separated into each independent component while PCA could not sufficiently separate the groups into the principal components. A greater reduction of interferences between different MUAP waveforms was demonstrated by the use of FastICA. Therefore, it is suggested that FastICA could provide much better discrimination of the properties of MUAPTs for sEMG signal decomposition, i.e. waveforms, discharge intervals, etc., than not only PCA but also the original sEMG signals.     

The effect of electrical gradients on current fluctuations and impedance recorded fromNecturus gallbladder

Summary Transepithelial current fluctuations were recorded inNecturus gallbladder, clamped at negative as well as positive potentials up to 64 mV. With NaCl-Ringer's (+10mm TAP) on both sides a mucosa-negative potential enhanced the relaxation noise component, present at zero potential, and produced peaking in the power spectrum at potentials above –36mV. Concomitantly at these potentials an inductive as well as a capacitive low-frequency feature appeared in the impedance locus. Clamping at positive potentials of 18 mV suppressed the relaxation noise component. At potentials above 51mV the spectral values increased predominantly at low frequencies. In this case the power spectrum showed only a 1/f noise component. The experiments confirm the previous finding that a K⁺ efflux through fluctuating apical K⁺ channels exists under normal conditions. With serosal KCl-Ringer's the initial Lorentzian component was enhanced at negative but suppressed at positive potentials. The increase at negative potentials was less pronounced than in experiments with NaCl-Ringer's on both sides, indicating saturation of the fluctuating K⁺ current component. With mucosal KCl-Ringer's a negative potential depressed the initial relaxation noise component, whereas it was enhanced at +18 mV clamp potential. In the latter case an additional Lorentzian component became apparent at higher frequencies. At potentials of 36 mV and above the low-frequency Lorentzian disappeared whereas the corner frequency of the high-frequency component increased. The latter experiments demonstrate that the relaxation noise component inNecturus gallbladder consists of two superimposed Lorentzians. As the relaxation times of these two components behave differently under an electrical field, there may exist two different types of K⁺ channels. It is demonstrated that peaking in the plateau of power spectra can be explained by frequency-dependent attenuation effects, caused by a polarization impedance.     

Autonomous function of synaptotagmin 1 in triggering synchronous release independent of asynchronous release

Ca(2+) triggers neurotransmitter release in at least two principal modes, synchronous and asynchronous release. Synaptotagmin 1 functions as a Ca(2+) sensor for synchronous release, but its role in asynchronous release remains unclear. We now show that in cultured cortical neurons stimulated at low frequency (or Hz), deletion of synaptotagmin 1 also alters only synchronous, not asynchronous, release during the stimulus train, but dramatically enhances "delayed asynchronous release" following the stimulus train. Thus synaptotagmin 1 functions as an autonomous Ca(2+) sensor independent of asynchronous release during isolated action potentials and action potential trains, but restricts asynchronous release induced by residual Ca(2+) after action potential trains. We propose that synaptotagmin 1 occupies release "slots" at the active zone, possibly in a Ca(2+)-independent complex with SNARE proteins that are freed when action potential-induced Ca(2+) influx activates synaptotagmin 1.     

Spectral analysis of the surface electromyogram as a tool for studying rate modulation: A comparison between theory,simulation, and experiment

Theoretical work suggests that if the interpulse intervals (IPIs) of motor unit action potential trains (MUAPTs) are independently and normally distributed, then spectral analysis of the electromyogram could be a useful tool for studying rate modulation by virtue of the presence of a peak in the power spectrum at the average firing frequency of all active motor units. It is shown in this paper that IPIs need not be normally distributed, specifically that the results are very much the same if the IPIs are distributed according to a Gamma probability density function (PDF). Simulation of the electromyogram based on this theory proved the applicability of the method. Experimental results obtained for the masseter, biceps brachii and first dorsal interosseus (FDI) muscles, however, were in disagreement with both theory and simulation except for the biceps muscle at force levels up to 20% of the maximal force and for the masseter and FDI muscles in 1 out of 5 subjects. This indicates that the models for MUAPTs hitherto used might not be generally correct. Apart from this discrepancy, our results reveal differences between masseter and FDI muscles on the one hand and the biceps brachii on the other, which indicate that motor unit synchronisation is much more pronounced in the latter muscle.     

Effect of thyrotropin-releasing hormone (TRH) on EEG topography

EEG topography by a microcomputer system (ATAC-3700 Nihon-Kohden) was performed in the rabbit in order to investigate the mechanism of TRH action on the brain wave. Power spectral analysis was carried out using a fast Fourier transform algorithm. The square root of the power spectra was defined as the equivalent potential over each frequency band by Ueno & Matsuoka's method. Potential fields of EEG frequency band were printed out on the topographic maps. The potentials of the electrocortical delta and theta waves were high, while the potentials of the alpha, beta 1 and beta 2 waves were low. Stimulation of the nucleus ventralis anterior (VA) by 3 Hz and 8 Hz resulted in a decrease in these potentials, especially, those of the alpha, beta 1 and beta 2 waves. The potentials of the alpha and fast waves were increased following unilateral destruction of VA. In the rabbit, in which TRH 0.5 mg/kg had been administered beforehand, there was no decrease in the potential of each wave induced by stimulation of VA with frequencies of 3 Hz and 8 Hz. The findings suggest involvement of the diffuse thalamocortical projection system in the activation of EEG by TRH.     

The low-frequency EEG component in the healthy subject and its changes as affected by acutely developing foci at the level of the diencephalon and brain stem structures

The data are given of the analysis of the low-frequency EEG component (LF EEG--0.2--2.0 Hz) of 34 healthy subjects and 36 patients examined in dynamics in the acute period after operations: ablation of a tumour localized at the level of the diencephalon and the level of the brainstem. The LF EEGs were analyzed by a special program: auto- and crosscorrelation functions and power spectra were estimated. In the norm LF EEGs were characterized by mosaics, various frequencies and periodicity in various cortical areas, they appeared with interhemispheric asymmetry, depended on the EEG type--dominance or lack of the alpha-rhythm. In patients in the post-operative period the LF EEGs were changed; in favourable terminations, at first the period of oscillations and the coefficient of correlation increased, then they tended to normalization. In unfavourable terminations, with gross pathological foci in these areas, the LF EEGs acquired a synchronized character, with a higher frequency than in the norm.     

Auditory evoked responses to amplitude modulated stimuli consisting of multiple envelope components

Steady-state auditory-evoked potentials were recorded noninvasively from alert bottlenosed dolphins, Tursiops truncates, using suction cup electrodes placed on the scalp surface. Responses were elicited using continuous acoustic signals consisting of 2, 3, or 4 tones with lowest frequency at 1000 Hz or 5000 Hz, and having a maximum frequency separation of 171 Hz. Due to the interaction of the stimulus tones, the stimulus waveform was comprised of 1 to 6 dominant temporal envelope components. Evoked responses were averaged in the time domain and Fourier transformed for analysis. The spectrum of the averaged evoked potential contained peaks at Fourier components corresponding to all stimulus envelope frequencies. Thus, scalp potentials, representing the synchronized discharge of large neuronal assemblies, followed the low-frequency temporal envelope of the stimulating waveform whether comprised of 1, 3, or 6 dominant envelope components; this envelope following response (EFR) was the dependent variable in all experiments.     

Intrinsic difference in beat frequency between the two flagella of Chlamydomonas reinhardtii

The flagellar beat frequency of the biflagellated green alga Chlamydomonas reinhardtii was measured by fast Fourier transform analysis of the light intensity fluctuation in microscope images of swimming cells. Live cells had a mean beat frequency of 48-53 Hz at 20 degrees C. However, detergent-extracted "cell models," when reactivated in the presence of 1 mM ATP, appeared to have two different beat frequencies of about 30 and 45 Hz. Measurements in cell models in which only one of the two flagella was beating indicated that the lower and higher frequencies most likely represented the beat frequency of the flagellum nearer to the eyespot (the cis-flagellum) and that of the flagellum farther from it (the trans-flagellum), respectively. In live cells also, the trans-flagellum beat at a frequency about 30% higher than that of the cis-flagellum when the cells were rendered uniflagellated by mechanical treatment, whereas both flagella beat at the frequency of the cis-flagellum under normal conditions. These observations suggest that the two flagella of Chlamydomonas have different intrinsic beat frequencies but that they are somehow synchronized when beating together on a live swimming cell.     

The potential coding utility of intercell cross-correlations in the retina

The action potentials (impulses) produced by pairs of neighboring retinal ganglion cells often show a tendency either to fire in close temporal synchrony or to avoid temporal synchrony. This cross-correlation (a rate of coincidences that differs from that expected by chance) has been exploited as a window into retinal processing, but its possible functional significance has proven elusive. Previous work has failed to show that the coincidences serve as a direct code for visual stimuli. In this analysis it is shown that the coincidences serve neither as a key for reducing variability nor as a key for improving the coding by the individual cells. The residual impulse trains (trains with coincidences deleted) are more variable than the raw impulse trains and provide an inferior coding to that of the raw impulse trains. There is negative correlation between the firing rate of the residual impulse trains and that of the coincidence impulse trains, which is consistent with the lower variance of the raw impulse trains. There is no consistent cross-correlation between the rates of residual impulse trains of cells in pairs showing cross-correlation; however, it is found that this observation does not discriminate among models for generating coincidences.     

Baseline gamma activity EEG and induced responses to facial stimuli of the visual cognitive set

Power spectra of cortical potentials of baseline activity during interstimuli intervals (4 s; Fourier transform in the frequency band of 1-60 Hz) and short-term (0.8 s) induced responses to facial stimuli (wavelet transform in the 15-60 Hz band) were assessed in the study of the visual cognitive set to facial expression. Significant differences between groups of subjects with different set rigidity were observed only at the set-testing stage. Estimation of the short-term (0.8 s) induced responses of the wavelet spectra in the group with plastic set revealed an increase in the power (in comparison with the power of background activity) of the gamma2 band (41-60 Hz) in the left hemisphere of the temporal, central and occipital areas, whereas in the group with rigid set these power spectra decreased. At the same time the power in the gamma1 band (21-40 Hz) was significantly lower (at the same level with the rigid form), indicating a discrete nature and functional selectivity in the gamma frequency band.     

Equivalence of two Fourier methods for biological sequences

 Two methods for defining Fourier power spectra for DNA sequences or other biological sequences are compared. The first method uses indicator sequences for each letter. The second method by Silverman and Linsker assigns to each letter a vertex of a regular tetrahedron in space, and this can be generalized to any dimension. While giving different Fourier transforms, it is shown that the power spectra of the two methods are essentially the same. This is also true if one replaces the Fourier transform in both methods with another linear transform, such as the Walsh transform. Received 4 December 1995     

Normal coordinate analysis and vibrational spectra of 9-β-D-arabinofuranosyladenine hydrochloride (ara-A.HCl)

The vibrational spectra of a synthetic purine nucleoside with known antiviral activity, 9--D-arabino-furanosyladenine hydrochloride (ara-A.HCl) are reported. The Fourier transform infrared (FT-IR) and Fourier transform Raman (FT-Raman) spectra were recorded in the 4000-30 cm^–1 spectral region. The harmonic frequencies and potential energy distributions (PED) of the vibrational modes of ara-A.HCI were calculated by two different methods: a classical molecular mechanics method and a semiempirical molecular orbital (MO) method, PM3. The results of both computational methods, based on the Wilson GF method, are compared with observed spectra, and an assignment of the vibrational modes of ara-A.HCl is proposed on the basis of the potential energy distributions (PED). It is found that the wavenumbers can be calculated with remarkable accuracy (1% deviation in most cases), with the classical mechanics method, by transferring a sufficiently large set of available harmonic force constants, thus permitting a reliable assignment. The semiempirical MO method, PM3, is found to be useful for the assignment of experimental frequencies although it is less accurate (10% deviation). IR intensities calculated by this method did not coincide with the experimental values. Certain out-of-plane vibrations in the base, not reported in previous studies, have been observed. The performance of both methods was related to the crystallographic and ab initio data available. Previous normal coordinate calculations for the adenine base and the nucleoside 5-dGMP are compared with our results and discussed, in relation to the crystal structure of Ara-A.HCl. Correspondence to: A. Hernanz     

Identifying cardiovascular neurocircuitry involved in the exercise pressor reflex in humans using functional neurosurgery

Groups III and IV afferents carry sensory information regarding the muscle exercise pressor reflex, although the central integrating circuits of the reflex in humans are still poorly defined. Emerging evidence reports that the periaqueductal gray (PAG) could be a major site for integrating the "central command" component that initiates the cardiovascular response to exercise, since this area is activated during exercise and direct stimulation of the dorsal PAG causes an increase in arterial blood pressure (ABP) in humans. Here we recorded local field potentials (LFPs) from various "deep" brain nuclei during exercise tasks designed to elicit the muscle pressor reflex. The patients studied had undergone neurosurgery for the treatment of movement or pain disorders, thus had electrodes implanted stereotactically either in the PAG, subthalamic nucleus, globus pallidus interna, thalamus, hypothalamus, or anterior cingulate cortex. Fast Fourier transform analysis was applied to the neurograms to identify the power of fundamental spectral frequencies. Our PAG patients showed significant increases in LFP power at frequencies from 4 to 8 Hz (P < 0.01), 8 to 12 Hz (P < 0.001), and 12 to 25 Hz (P < 0.001). These periods were associated with maintained elevated ABP during muscle occlusion following exercise. Further increases in exercise intensity resulted in corresponding increases in PAG activity and ABP. No significant changes were seen in the activity of other nuclei during occlusion. These electrophysiological data provide direct evidence for a role of the PAG in the integrating neurocircuitry of the exercise pressor reflex in humans.     

Joint non-uniform sampling of all incremented time delays for quicker acquisition in protein relaxation studies

NMR relaxometry plays crucial role in studies of protein dynamics. The measurement of longitudinal and transverse relaxation rates of \(^{15}\)N is the main source of information on backbone motions. However, even the most basic approach exploiting a series of \(^{15}\)N HSQC spectra can require several hours of measurement time. Standard non-uniform sampling (NUS), i.e. random under-sampling of indirect time domain, typically cannot reduce this by more than 2–4\(\times\) due to relatively low “compressibility” of these spectra. In this paper we propose an extension of NUS to relaxation delays. The two-dimensional space of \(t_1\)/\(t_{relax}\) is sampled in a way similar to NUS of \(t_1\)/\(t_2\) domain in 3D spectra. The signal is also processed in a way similar to that known from 3D NUS spectra i.e. using one of the most popular compressed sensing algorithms, iterative soft thresholding. The 2D Fourier transform matrix is replaced with mixed inverse Laplace-Fourier transform matrix. The peak positions in resulting 3D spectrum are characterized by two frequency coordinates and relaxation rate and thus no additional fitting of exponential curves is required. The method is tested on three globular proteins, providing satisfactory results in a time corresponding to acquisition of two conventional \(^{15}\)N HSQC spectra.     

The response of excitable membrane models to a cyclic input

The response of a space-clamped patch of Hodgkin-Huxley membrane to an applied current density ofA cos(2ft)+BA/cm² is computed for frequencies from 5 to 250 Hz. The train of action potentials generated is phase-locked to the driving cycle,N action potentials occurring at fixed phases inM cycles. For frequencies whereN/M is a simple ratio a describing function for the membrane is computed. The phase-locked behaviour and describing functions are similar to those obtained for a simple leaky integrator neurone model.     

Shifts in frequency tuning of electroreceptors in androgen-treated mormyrid fish

Summary Several species of mormyrid electric fish have a sex difference in the pulse waveform of their electric organ discharge (EOD). Field studies in Gabon, West Africa have shown for one such species,Brienomyrus brachyistius (triphasic), that the sexually mature male EOD differs in shape and is nearly twice the duration of the EODs of females and juveniles. Fourier analysis reveals that differences in EOD duration correlate with those in the EOD power spectrum which has a peak at 0.3 kHz in males and 1.3 kHz in females and juveniles. We find a corresponding sex difference in the frequency tuning of at least one class of electroreceptors known as Knollenorgans. The average best or characteristic frequency of Knollenorgans is lower in males compared to females and juveniles. This correlates with a lower peak in the power spectrum of the male's pulse. When females are treated with gonadal androgens, their EODs increase 2–3 fold in duration, and the power spectra of their pulses are correspondingly lowered to match that of mature males. The average best frequency of Knollenorgans decreases by nearly 1 kHz which matches the downward shift of their EOD's power spectrum.For a second species ofBrienomyrus (sp. 2) which is commercially imported from Nigeria, we have not detected a sex difference in the power spectrum or duration of the EOD. The power spectrum peaks at about 4.2 kHz in males, females, and juveniles. Androgens, however, do cause a coincident downward shift in the average peak of the EOD power spectrum (from 4.2 to 1.3 kHz) and the average best frequency of Knollenorgans (from 2.3 to 1.4 kHz).Specimens ofBrienomyrus (sp. 2) that have been electrically silenced by surgical means are tuned, on the average, only 0.2 kHz higher than control animals. Silenced animals that have been treated with androgens are tuned, on the average, 0.2 kHz below controls. The results suggest that electroreceptor tuning is only partially modifiable during androgen treatment if the electroreceptors arenot being stimulated by an external electrical stimulus, i.e. the animal's own EOD. Since androgen treatment has a dramatic effect on receptor tuningonly in intact fish, it seems likely that retuning isnot due to a direct action of androgens on receptors, but rather due to the action of the principal electrical stimulus upon the receptors, i.e. the EOD. The implications of such results for the development of species and sex differences in electro-receptor tuning is discussed.