Biomedical signal processing (in four parts). Part 3. The power spectrum and coherence function

Rhinal-hippocampal theta coherence during declarative memory formation: interaction with gamma synchronization?

The hippocampus and the rhinal cortex, two substructures of the medial temporal lobe, together play a crucial role in human declarative memory formation. To investigate in detail the mechanism connecting these two structures transiently during memory formation we recorded depth EEG in epilepsy patients from within the hippocampus and the rhinal cortex. During this recording, patients performed a single-trial word list-learning paradigm with a free recall memory test following a distraction task. Rhinal-hippocampal EEG coherence and spectral power at both locations in the time interval up to 2 s after onset of word presentation were analysed in the frequency range 1-19 Hz. Successful as opposed to unsuccessful memory formation was associated with a general rhinal-hippocampal coherence enhancement, but without alterations in spectral power. Coherence increases in the theta range were correlated with the previously reported memory-related changes in rhinal-hippocampal gamma phase synchronization. This correlation may suggest an interaction of the two mechanisms during declarative memory formation. While theta coherence might be associated with slowly modulated coupling related to an encoding state, rhinal-hippocampal gamma synchronization may be more closely related to actual memory processes by enabling fast coupling and decoupling of the two structures.

[Autonomic hyperreflexia induced by sacral root stimulation is detected by spectral analysis of the EEG]

PURPOSE

To compare spectral analysis of the electrocardiogram (ECG) with mean arterial pressure (MAP) and heart rate (HR) monitoring in the detection of autonomic hyperreflexia (AHR) induced by sacral root stimulation.

METHODS

Ten spinal cord injured patients scheduled for implantation of a sacral root stimulator for bladder retention were included. Under target controlled anesthesia with propofol 4 micro g*mL(-1) and remifentanil 4 ng*mL(-1), the patients were placed in the knee chest position. The sacral roots were exposed by laminectomy (L2-S1) and their function assessed by electrostimulation under urodynamic and cardiovascular monitoring. Online power spectrum densities were calculated from the ECG R-R interval by the MemCalc(TM) software using the maximum entropy method. Low frequency (LF: 0.04-0.15 Hz) and high frequency (HF: 0.15-0.4 Hz) spectra were associated with sympathetic and parasympathetic activities respectively. The most extreme value of each variable was noted before and during each stimulation. A difference ( triangle up ) of more than 10% signified AHR. The comparison ( triangle up LF vs triangle up MAP and triangle up HF vs triangle up HR) was done by a concordance test with a kappa coefficient (k): -1 = total discordance to 1 = total concordance.

RESULTS

AHR was detected in six patients as an increase in LF and MAP (n = 4); an increase in LF, HF, MAP with a decrease in HR (n = 2). The detection delay was 5.3 +/- 1 sec (LF, HF) and 10.4 +/- 1.2 sec (MAP and HR). Concordance was 85% (LF vs MAP: k = 0.7) and 90% (HF vs HR: k = 0.8).

CONCLUSION

AHR induced by sacral root stimulation is detected by spectral analysis of the ECG earlier than MAP and HR. Other studies are needed to confirm these results.

Experimental approach for testing the uncoupling between cardiovascular variability series

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parametric autoregressive (AR) method (model order M= 4, 8, 12, 16), on time series with length L = 180, 300, 420, 540 s. Te decreased with increasing B and L and with decreasing M (range: 0.11-0.54 for WC estimator, 0.06-0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B = 0.025 Hz; M = 8; L = 300 s) were, respectively, 0.24 and 0.17. Moreover, Tt was always higher (range: 0.12-0.65) and the results were less dependable than those for Te in defining the zero level of MSC. Thus, with the proposed method, the hypothesis of uncoupling is rejected by accounting for the parameters that affect the confidence of spectral and cross-spectral estimates. The broad applicability of this approach should favour its introduction for assessing the significance of the coupling between cardiovascular variability series.

Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence

This paper introduces the use of wavelet analysis to follow the temporal variations in the coupling between oscillatory neural signals. Coherence, based on Fourier analysis, has been commonly used as a first approximation to track such coupling under the assumption that neural signals are stationary. Yet, stationary neural processing may be the exception rather than the rule. In this context, the recent application to physical systems of a wavelet-based coherence, which does not depend on the stationarity of the signals, is highly relevant. This paper fully develops the method of wavelet coherence and its statistical properties so that it can be practically applied to continuous neural signals. In realistic simulations, we show that, in contrast to Fourier coherence, wavelet coherence can detect short, significant episodes of coherence between non-stationary neural signals. This method can be directly applied for an 'online' quantification of the instantaneous coherence between two signals.

Cortical network resonance and motor activity in humans

Large areas of the human motor cortex are devoted to the control of the contralateral hand and forearm. Just how activities scattered across these motor areas may be brought together in the execution of a given movement remains unclear. There is increasing evidence, largely from animal studies, suggesting that sensory integration involves the synchronization of activity between spatially distributed cortical sites. Here we review recent evidence that cortical activity becomes oscillatory and synchronized between spatially distributed sites during performance of a movement in humans. Cortico-cortical synchronization may occur with a precision in the millisecond range, is essentially limited to those cortical elements active in a given task, and changes in both its distribution and frequency in a task-related manner. Synchronization at specific frequencies may therefore link disparate cortical activities into the functional ensembles underlying voluntary movement in humans.

Blood pressure and heart rate variability and baroreflex sensitivity before and after brain death

OBJECTIVES

To evaluate spontaneous blood pressure and heart rate variability and spontaneous baroreflex sensitivity before and after brain death.

METHODS

Spontaneous variability of arterial blood pressure and heart rate-estimated by power spectra of systolic (SBP) and diastolic blood pressure (DBP) and pulse interval (PI)-and spontaneous baroreflex sensitivity (BRS)-estimated by the alpha index and the sequence technique-were evaluated in 11 patients twice: shortly before and 1 hour after the onset of brain death.

RESULTS

Significant spectral changes occurred after brain death: a general power reduction in PI spectra; a shift of SBP, DBP and PI powers toward the lower frequencies, resulting in a greater slope of the "1/f" spectral trends; and a marked reduction of SBP and DBP powers (-93%) and of SBP-PI coherence (-63%) at 0.1 Hz. The estimated average BRS was relatively high before brain death (around 11 ms/mm Hg), and fell close to 0 or even was not detectable at all after brain death.

CONCLUSIONS

Parameters describing spontaneous blood pressure and heart rate variability and indexes reflecting the baroreflex function, which were relatively normal up to a few hours before brain death, underwent marked changes with the onset of brain death. All the changes found are likely to reflect the cessation of activity of the cardiovascular brain stem centres. These findings indicate that techniques of blood pressure and heart rate spectral analysis and of dynamic assessment of baroreflex sensitivity may be useful to complement the diagnosis of brain stem death.

Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats

Techniques for examining signals in the time and frequency domains are well-established tools. These tools have their limitations; they tell us in a broad sense where the signal component exists in the frequency domain, but they do not tell us how its frequency characteristics change over time. The time-frequency has become a powerful alternative for the analysis of signals. Among various time-frequency distribution methods, one of the most studied is the Wigner-Ville distribution. The aim of this study was to evaluate in conscious rats smoothed pseudo Wigner--Ville distribution (SPWVD) as an alternative to the fast Fourier transform (FFT) in RR intervals and in systolic blood pressure (SBP), before and after adrenergic and cholinergic receptor blockade. Fourteen Wistar rats equipped with telemetry probe were evaluated: (1) under control conditions; (2) after injection of saline (100 microl kg(-1) i.v.); (3) after atenolol (1 mg kg(-1) i.v.); (4) after atropine methyl nitrate (0.5 mg kg(-1) i.v.); and (5) after phentolamine (5 mg kg(-1) i.v.). FFT and SPWVD were applied to RR intervals and SBP time series. Six-minute time series of RR intervals, systolic and diastolic pressures were analysed. The bias and distribution of differences between FFT and SPWVD methods in RR intervals under base conditions were 1.4+/-0.4% (r2=0.94; P<0.01) in LF/LF+HF: 1.5+/-0.5% ( r2=0.92; P<0.01) in HF/LF+HF and 4.8+/-1.9% (r2=0.92; P<0.01) in LF/HF. In SBP the bias and distribution were 1.5+/-0.8% (r2=0.90) P<0.05) in LF/LF+HF and 1.7+/-0.6% (r2=-0.92; P<0.01) in HF/LF+HF. In the frequency domain analysis of RR intervals and SBP there was no difference between FFT and SPWVD. The agreement between the methods demonstrates that in stationary signals both methods can be used interchangeably. SPWVD may be an interesting tool to analyse biomedical signals; it provides a good resolution at high frequency and a good frequency resolution at low frequencies independently if signals remain stationary.

Flash-related synchronization and desynchronization revealed by a multiple band frequency analysis

The fast Fourier transform (FFT) is a good method to estimate power spectral density (PSD), but the frequency resolution is limited to the sampling window, and thus the precise characteristics of PSD for short signals are not clear. To relax the limitation, a multiple band-pass filter was introduced to estimate the precise course of PSDs for flash visual evoked potentials (VEPs). Signals were recorded during -200 and 600 ms using balanced noncephalic electrodes, and sampled at 1,000 Hz in 12 bits. With 1 Hz and 10 ms resolutions, PSDs were estimated between 10 and 100 Hz. Background powers at the alpha- and beta-bands were high over the posterior scalp, and powers around 200 ms were evoked at the same bands over the same region, corresponding to P110 and N165 of VEPs. Normalized PSDs showed evoked powers around 200 ms and suppressed powers following the evoked powers over the posterior scalp. The evoked powers above the 20 Hz band were not statistically significant, however, the gamma band was significantly evoked intra-individually; details in the gamma bands were varied among the subjects. Details of PSDs were complicated even for a simple task such as watching flashes; both synchronization and desynchronization occurred with different distributions and different time courses.

Event-Related changes of band power and coherence: methodology and interpretation

Event-related calculation of band power changes can be used to quantify event-related desynchronization, event-related synchronization, and event-related coherence (ERCoh). It is shown that in the case of a motor task especially, the ERCoh time course depends on the type of EEG derivation used, whereby referenced EEG data can result in a bilateral coherence increase, although both hemispheres generate independent sensorimotor rhythms. It is further shown that not only Rolandic mu rhythms but also central beta rhythms display a lack of interhemispheric linear phase coupling.

Oscillations in cerebral blood flow detected with a transcranial Doppler index

Although transcranial Doppler ultrasound (TCD) has been used to detect oscillations in CBF, interpretation is severely limited, since only blood velocity and not flow is measured. Oscillations in vessel diameter could, therefore, mask or alter the detection of those in flow by TCD velocities. In this report, the authors use a TCD-derived index of flow to detect and quantify oscillations of CBF in humans at rest. A flow index (FI) was calculated from TCD spectra by averaging the intensity weighted mean in a beat-by-beat manner over 10 seconds. Both FI and TCD velocity were measured in 16 studies of eight normal subjects at rest every 10 seconds for 20 minutes. End tidal CO2 and blood pressure were obtained simultaneously in six of these studies. The TCD probe position was meticulously held constant. An index of vessel area was calculated by dividing FI by velocity. Spectral estimations were obtained using the Welch method. Spectral peaks were defined as peaks greater than 2 dB above background. The frequencies and magnitudes of spectral peaks of FI, velocity, blood pressure, and CO2 were compared with t tests. The Kolmogorov-Smirnov test was used to further confirm that the data were not white noise. In most cases, three spectral peaks (a, b, c) could be identified, corresponding to periods of 208+/-93, 59+/-31, and 28+/-4 (SD) seconds for FI, and 196+/-83, 57+/-20, and 28+/-6, (SD) seconds for velocity. The magnitudes of the spectral peaks for FI were significantly greater (P<0.02) than those for velocity. These magnitudes corresponded to variations of at least 15.6%, 9.8%, and 6.8% for FI, and 4.8%, 4.2%, and 2.8% for velocity. The frequencies of the spectral peaks of CO2 were similar to those of FI with periods of 213+/-100, 60+/-46, and 28+/-3.6 (SD) seconds. However, the CO2 spectral peak magnitudes were small, with an estimated maximal effect on CBF of (+/-) 2.5+/-0.98, 1.5+/-0.54, and 1.1+/-0.31 (SD) percent. The frequencies of the blood pressure spectral peaks also were similar, with periods of 173+/-81, 44+/-8, and 26+/-2.5 (SD) seconds. Their magnitudes were small, corresponding to variations in blood pressure of (+/-) 2.1+/-0.55, 0.97+/-0.25, and 0.72+/-0.19 (SD) percent. Furthermore, coherence analysis showed no correlation between CO2 and FI, and only weak correlations at isolated frequencies between CO2 and velocity, blood pressure and velocity, or blood pressure and FI. The Kolmogorov-Smirnov test distinguished our data from white noise in most cases. Oscillations in vessel flow occur with significant magnitude at three distinct frequencies in normal subjects at rest and can be detected with a TCD-derived index. The presence of oscillations in blood velocity at similar frequencies but at lower magnitudes suggests that the vessel diameters oscillate in synchrony with flow. Observed variations in CO2 and blood pressure do not explain the flow oscillations. Ordinary TCD velocities severely underestimate these oscillations and so are not appropriate when small changes in flow are to be measured.

Event-related dynamics of the gamma-band oscillation in the human brain: information processing during a GO/NOGO hand movement task

To investigate the gamma band activity relating to the discrimination process and motor behavior in the human brain, the event-related dynamics of the EEG spectrum was calculated during the visual GO/NOGO hand movement task and a control task (the visual element of the GO/NOGO task only) in eight subjects. The subjects were instructed to push (GO) or not to push (NOGO) a microswitch according to different visual stimuli and 21-channel scalp EEGs were recorded. The time courses of the power spectra after the stimuli were calculated using the fast Fourier transform for each condition (GO, NOGO and the control task), and were compared statistically between the conditions. The results suggested that a high gamma band oscillation, occurring at the frontal and left parieto-occipital areas at around 90 ms after the stimuli, relates to the discrimination process. Under the GO condition, this oscillation continued until 140 ms, and a subsequent oscillation occurred over the motor areas at around 200 ms, which seemed to be related to the motor action. On the other hand, under the NOGO condition, a low gamma band oscillation occurred in the central area at around 230 ms, which seemed to be related to the inhibition process.

The method of linear transformation in revealing EEG polyharmonic components in comparison to the Fourier analysis

The method of linear transformation (LT) in the modification known as method of Buys Ballot was examined in its ability to reveal polyharmonic periodicities in EEG signals. Applying this method to simulated signals-additive mixtures of sinusoids, periodic squared waves and Gaussian noise some rules were found, which can be used in analyzing of EEG signals. The results were compared to that of Discrete Fourier analysis. The conclusion was made that in contrast to the method of Fourier giving the frequency contents, LT method is able to reveal not only the mono- but also polyharmonic components with their waveshape (the reconstruction) even if their frequency bands are overlapping.

Spectral modulation of cortical connections measured by EEG coherence in humans

OBJECTIVE

Description of coherence patterns of cortical EEG.

METHODS

EEG recordings were collected from 9 subdural electrode grids implanted in 6 patients undergoing EEG monitoring for refractory epilepsy.

RESULTS

Coherence decreased with increasing inter-electrode distance and exhibited considerable variability at the same inter-electrode distances. Analysis of variance demonstrated that both spatial and temporal factors contributed significantly (P < 0.01) to this variability. The spatial factor contributed the largest portion (up to 90%) of the variability, and was modulated by frequency and inter-electrode distance.

CONCLUSION

The finding that the mean frequency modulation was consistent over time for the same pair of electrodes and was different between different pairs of electrodes indicated a spatial-spectral pattern of cortical synchrony. The connections (pairs of electrodes) could be accordingly predicted from their spatial-spectral pattern, which suggested that the spatial heterogeneity of neuronal synchrony was expressed not only by the degree of synchrony, but also by distinct spectral channels of synchrony. A model based on neuronal connection and activation is proposed to account for the observations.

Autonomic instability during relaxation in panic disorder

The ability to relax was assessed in 14 patients with panic disorder (PD) and 15 non-anxious control subjects for 10 min. Before and after relaxation, subjects performed a standardized activating task of talking continuously for 4 min. The fractional decline in reported anxiety, tension, and alertness between the first talking period and the relaxation minimum did not differ between groups, although absolute levels of anxiety and tension were higher for PD patients. The fractional decline in skin conductance between the first talking period and the last minute of relaxation was less for PD patients than control subjects, while their increase in skin temperature was greater. Skin conductance showed a linear decline over the logarithm of relaxation time, the slope of which was less steep for PD patients. Goodness of fit of skin conductance over log time was also significantly poorer for PD patients. Heart rate levels or slopes did not differ between groups. Autonomic differences between PD and control subjects were largely due to six patients who reported having panic attacks during the test and higher pretest anxiety levels. In conclusion, indicators of relaxation were inconsistent. Skin conductance suggested autonomic instability during quiet sitting in patients who panic or who are prone to panic.

The synchronization between brain areas under motor inhibition process in humans estimated by event-related EEG coherence

To investigate the functional connection of brain areas under motor inhibition, the event-related coherence (ERCoh) of the electroencephalogram (EEG) was calculated for 10 subjects who were asked to perform a visual discrimination (GO/NO-GO) task. The subjects were instructed to push (GO) or not to push (NO-GO) a micro-switch according to different visual stimuli. Twenty-one-channel scalp EEGs were recorded and the surface Laplacians were calculated at F3, F4, C3, C4, P3 and P4 using the source derivation method. The time-courses of the inter- and intra-hemispheric coherence were calculated using the fast Fourier transform for each condition (GO or NO-GO), and were compared statistically between the two conditions. The results suggest that the ERCoh under the NO-GO condition consisted of two components; alpha band synchronization between bilateral frontal areas and theta band synchronization among bilateral frontal, central and parietal areas. It is likely that the former is related directly to the decision not to move, and the latter is related to the motor inhibition process.

Synchronization between prefrontal and posterior association cortex during human working memory

We measured coherence between the electroencephalogram at different scalp sites while human subjects performed delayed response tasks. The tasks required the retention of either verbalizable strings of characters or abstract line drawings. In both types of tasks, a significant enhancement in coherence in the theta range (4-7 Hz) was found between prefrontal and posterior electrodes during 4-s retention intervals. During 6-s perception intervals, far fewer increases in theta coherence were found. Also in other frequency bands, coherence increased; however, the patterns of enhancement made a relevance for working memory processes seem unlikely. Our results suggest that working memory involves synchronization between prefrontal and posterior association cortex by phase-locked, low frequency (4-7 Hz) brain activity.

The dose-response effects of terbutaline on the variability, approximate entropy and fractal dimension of heart rate and blood pressure

AIMS

To study the dose-response effects of intravenous terbutaline on the cardiovascular and respiratory autonomic nervous regulation.

METHODS

The study followed a randomized, placebo-controlled crossover design in six healthy adult volunteers. The terbutaline dose ranged from 10 to 30 microg min(-1) We continuously measured electrocardiogram, finger systolic arterial pressure (SAP) and flow-volume spirometry in supine and upright positions at baseline and during 3 h drug infusion. The periodic variability components of R-R intervals (time between successive heart beats) and SAP in relation to respiration were assessed using spectral analysis techniques. The regularity of the time series was assessed by approximate entropy (ApEn) and the convolutedness by fractal dimension (FD).

RESULTS

Terbutaline dose-dependently decreased total variability of R-R intervals, low frequency (LF) variability of R-R intervals (10 s waves), high frequency (HF) variability of R-R intervals (respiratory variability), total variability of SAP, HF variability of SAP, baroreflex sensitivity, plasma potassium concentration, approximate entropy of R-R interval and of SAP as well as fractal dimension of R-R interval. Terbutaline dose-dependently increased heart rate, LF/HF ratios of R-R intervals and of SAP, LF variability of SAP, minute ventilation and plasma terbutaline concentration.

CONCLUSIONS

Terbutaline infusion decreases parasympathetic cardiovascular reactivity, baroreflex sensitivity, dimensionality of heart rate and plasma potassium concentration; it increases sympathetic dominance in cardiovascular autonomic balance, minute ventilation, and the regularity of heart rate and blood pressure time series.

The time course of interhemispheric EEG coherence during a GO/NO-GO task in humans

Event-related coherence of the EEG was calculated for 10 subjects performing a visual discrimination GO/NO-GO task. The subjects were instructed to push (GO) or not to push (NO-GO) a button according to visual stimuli. Twenty-one-channel scalp EEGs were recorded and the surface Laplacian was calculated using the source derivation method. The time courses of the coherence between F3 and F4, C3 and C4, and P3 and P4 were calculated using the fast Fourier transform for each task and were compared between conditions. Statistical analysis showed that coherence in the NO-GO condition became significantly higher than that in the GO condition between F3 and F4. The synchronization between bilateral dorsolateral frontal areas might therefore play an important role in the motor inhibition process.

Abnormal awake respiratory patterns are common in chronic heart failure and may prevent evaluation of autonomic tone by measures of heart rate variability

BACKGROUND

Reduced heart rate variability, particularly in the Very-low-frequency (VLF) spectral band, has been found to be a marker for poor prognosis in patients after myocardial infarction, but the origin of the VLF oscillations is unclear. In this study, we demonstrate that the power of cardiovascular oscillations in the VLF band in awake patients with mild to severe chronic heart failure is greatly increased by the common occurrence of unrecognized irregularity of breathing, which may confound the use of heart rate variability measures as indexes of autonomic tone or prognosis.

METHODS AND RESULTS

Among 110 consecutive patients referred for consideration of transplantation, 90 were in sinus rhythm, of whom 10 were excluded as unstable. The remaining 80 patients underwent recordings of ECG, beat-to-beat arterial oxygen saturation (SaO2), and respiration during both spontaneous and controlled breathing. During spontaneous awake breathing, 64% showed periodic breathing or Cheyne-Stokes respiration (CSR), which was associated with dominant power in the VLF band of all signals. This VLF power accounted for 55%, 77%, and 87% of heart rate variability, respectively, in patients with normal breathing, periodic breathing, and CSR. It was reduced by 48% and 62%, respectively, during controlled breathing in patients with periodic breathing or CSR. Controlled ventilation also improved oxygen saturation and markedly reduced its variability.

CONCLUSIONS

Breathing disorders are surprisingly common in awake patients with poor left ventricular function and produce large VLF oscillations in heart rate variability. If measures of heart rate variability are used for prognostic purposes during both short-term and long-term recordings, the confounding effects of variable respiratory patterns should be excluded. Respiratory rehabilitation might help control potentially hazardous surges in sympathetic tone.

Power spectra accuracy improvement by a method for leakage effect reduction

A method for leakage effect reduction by a modification of the classical spectra obtained Discrete Fourier Transform is proposed. The properties of the new method are investigated analytically and validated through synthesized signals, processed by the developed complete computational procedure. This combines the proposed method for leakage reduction and our previous approach for optimal epoch selection, enabling more accurate spectral analysis of relatively short epochs of various biomedical and other signals. An application of heart rate variability to power spectra is presented.

Power spectra accuracy improvement by optimal signal epoch selection: an heuristic approach

The problem of epoch selection in frequency analysis of biomedical signals often involves tradeoffs between the physiological system studied stationarity, the spectral resolution required, the need for dynamic investigations implying shorter epochs, etc. The accuracy of the spectra strongly depends on the epoch length. We propose a method for optimal epoch selection introducing the notion of 'quality of power spectra'. Two criteria for quantitative estimation of spectral quality are defined, considering a quality to be high when more power is concentrated in narrow frequency bands. A synthesized signal is used for describing the procedure developed and evaluating the accuracy. Noise sensitivity is assessed by adding intensive noise to the signal. Hundreds of synthesized signals are used for validation of the method and some initial experiments with heart rate variation data are presented.

Dynamic aspects for interislet synchronization of oscillatory insulin secretions

How are the oscillatory insulin secretions from numerous islets synchronized to result in an identifiable oscillation? We postulated that a sudden increase in glucose concentration could best account for the interislet synchronization. The perifusion with two parallel chambers each containing 100 islets from the same rat was performed. The glucose concentrations of two chambers were simultaneously increased from 100 to 300 mg/dl in step function to examine the synchronizing efficacy. Synchrony and regularity of insulin oscillation were evaluated by cross-correlation and/or power spectral analysis. Although the insulin had been in stable oscillation, we found that the synchrony between two chambers and the regularity of each chamber were still significantly improved after a sudden increase in glucose level. However, the improved synchrony and regularity were transient. They gradually slid toward a less rigorous condition in a 15-h long-term perifusion. We suggested that the interislet synchronization of oscillatory insulin secretions could be improved by a sudden increase in glucose level. The insulin pulses were therefore enhanced to present their physiological effects.

Renal nerve responses to somatic nerve activation in stroke-prone spontaneously hypertensive rats

In chloralose/urethane anaesthetised stroke-prone spontaneously hypertensive rats, blood pressure and integrated renal nerve activity were higher whereas heart rate was lower than in Wistar rats by 37, 146 and 11%, respectively (all P < 0.001). The renal nerve signal was subjected to fast Fourier transformation to generate power spectra. In the hypertensive rats, total spectral power was 400% (P < 0.01) and power at the heart rate frequency was 50% (P < 0.01) greater while phase and time differences were shorter (both P < 0.001) than in Wistar rats. Brachial nerve stimulation increased total power in Wistar and hypertensive rats (P < 0.05), but importantly, power at the heart rate frequency was decreased by 80% in Wistar whereas there was a 20% (P < 0.05) increase in hypertensive rats, while phase and time differences were raised only in hypertensive rats (P < 0.05). Bilateral cervical vagotomy of the hypertensive rats had minimal actions on most variables but phase and time differences were doubled compared to intact hypertensive animals, but brachial nerve stimulation decreased power at the heart rate frequency (P < 0.05) which was a very different response from intact rats. Resting blood pressure, heart rate, total power and power at the heart rate frequency in the carotid sinus denervated animals were lower than in intact hypertensive rats, between 17 and 71%, respectively, but increased during brachial nerve stimulation. These experiments demonstrated that whereas somatic sensory input can modulate the pattern of sympathetic nerve activity to the kidney under normal conditions, this does not occur in the hypertensive rat. This appears to be related to afferent information carried by the vagus which suppresses the normal response; the carotid sinus baroreceptors are devoted to organising the nerve activity in relation to the blood pressure pulse wave.

Effects of sino-aortic denervation on spectral characteristics of blood pressure and pulse interval variability: a wide-band approach

Sino-aortic denervation (SAD) is employed in cats to evaluate the baroreflex influence on blood pressure (BP) and pulse interval (PI) spectral components from 0.00008 to 0.9 Hz as assessed by FFT wide-band spectra and their 1/f modelling; and the linear coupling between BP and PI and between systolic and diastolic BP as assessed by coherence analysis. Specific procedures have been developed to obtain an effective smoothing of spectra and coherence functions. SAD induced an increase in BP powers from 0.03 to 0.0006 Hz and a power reduction of most of the remaining BP components; a reduction of PI powers at all frequencies; marked deviations of BP spectra from the 1/f trend; a reduction of the coherence between BP and PI from 0.12 to 0.5 Hz and a coherence enhancement at lower frequencies. These findings indicate that the arterial baroreflex modulates both fast and slow spectral components of BP and PI; homogeneously enhances PI fluctuations at all frequencies; produces differentiated effects on BP fluctuations along the frequency axis; and at low frequencies exerts the buffering action on BP through strategies which reduce the BP-PI linear link.

Event-related coherence as a tool for studying dynamic interaction of brain regions

This paper demonstrates a simple approach to calculating time courses of coherence for data recorded during an event-related paradigm. Event-related coherence (ERCoh) was investigated between left and right sensorimotor areas, and between contralateral sensorimotor and SMA during discrete right index finger movements. It is demonstrated that ERCoh can provide information regarding the dynamic interaction of spatially separated brain regions. In the upper alpha band, the mu rhythm of the contralateral sensorimotor area is shown to be linearly phase-coupled to rhythmic activity recorded over the SMA. This synchrony between the rhythms decreases during planning and execution of movement when the respective areas become active. In the gamma band, a short-lasting increase in coherence is found between the contralateral sensorimotor area and the SMA prior to movement, indicating possible functional interaction of these areas during the final stages of movement preparation.

Descriptive multidimensional statistical methods for analysing signals in a multifactorial biomedical database

A methodology is presented to analyse multidimensional signals from several recording periods resulting from an experimental study on human or other living systems. The methodology is divided into two stages: intra-period analysis and inter-period analysis. The purpose of the first stage is to highlight general trends in multidimensional signal changes and the more informative components of the signals. The purpose of the second stage is to assess the influence of environmental or individual difference factors on a given signal component that appears to be discriminant in the first stage. To take into account the multivariable state of the system and the multi-observational aspect, a multidimensional descriptive statistical approach is used. The methods are correspondence analysis and hierarchical clustering. They are illustrated through an occupational medicine application from a study of sedentary posture.

Heart rate and respiratory rhythm dynamics on ascent to high altitude

OBJECTIVE

To investigate the alterations in autonomic control of heart rate at high altitude and to test the hypothesis that hypoxaemic stress during exposure to high altitude induces non-linear, periodic heart rate oscillations, similar to those seen in heart failure and the sleep apnoea syndrome.

SUBJECTS

11 healthy subjects aged 24-64.

MAIN OUTCOME MEASURES

24 hour ambulatory electrocardiogram records obtained at baseline (1524 m) and at 4700 m. Simultaneous heart rate and respiratory dynamics during 2.5 hours of sleep by fast Fourier transform analysis of beat to beat heart rate and of an electrocardiographically derived respiration signal.

RESULTS

All subjects had resting hypoxaemia at high altitude, with an average oxyhaemoglobin saturation of 81% (5%). There was no significant change in mean heart rate, but low frequency (0.01-0.05 Hz) spectral power was increased (P < 0.01) at high altitude. Time series analysis showed a complex range of non-linear sinus rhythm dynamics. Striking low frequency (0.04-0.06 Hz) heart rate oscillations were observed during sleep in eight subjects at high altitude. Analysis of the electrocardiographically derived respiration signal indicated that these heart rate oscillations correlated with low frequency respiratory oscillations.

CONCLUSIONS

These data suggest (a) that increased low frequency power during high altitude exposure is not simply attributable to increased sympathetic modulation of heart rate, but relates to distinctive cardiopulmonary oscillations at approximately 0.05 Hz and (b) that the emergence of periodic heart rate oscillations at high altitude is consistent with an unstable cardiopulmonary control system that may develop on acute exposure to hypoxaemic stress.

Heart rate variability: technique and investigational applications in cardiovascular medicine

OBJECTIVE

To describe heart rate variability (HRV) analysis, especially time- and frequency-domain analyses, and some of its investigational applications in clinical cardiovascular medicine.

DESIGN

We provide a brief introduction to the magnitude of sudden cardiac death and the factors that influence life-threatening ventricular arrhythmias as a backdrop to the potential importance of the autonomic nervous system and how this system might be assessed by the analysis of HRV.

MATERIAL AND METHODS

We reviewed the literature from 1973 to 1994 that described beat-to-beat changes in heart rate, heart rate signal recording and processing, and investigational applications of HRV analysis to cardiovascular medicine.

RESULTS

Beat-to-beat changes in heart rate are partly influenced by the autonomic nervous system. Briefly, changes in sympathetic input to the sinoatrial node affect low-frequency HRV, whereas changes in parasympathetic input affect high-frequency HRV. Multiple physiologic and nonphysiologic determinants of HRV exist, and therefore analysis of HRV as a direct "window" to autonomic tone is problematic.

CONCLUSION

In selected patient populations, analysis of HRV yields important information about sinoatrial responsiveness to autonomic input and mortality risk stratification. Routine application of HRV analysis to clinical cardiovascular medicine awaits further investigation, however.

Renal sympathetic nerve responses to somato-sensory nerve stimulation in normotensive rats

Blood pressure, heart rate and renal sympathetic nerve activity were recorded in groups of chloralose/urethane-anaesthetised intact, vagotomised and carotid sinus denervated Wistar rats before and during bilateral somatic afferent nerve stimulation from 0.1 to 3.2 Hz. Renal sympathetic nerve activity was subjected to power spectral and cross correlation analysis. Haemodynamic and integrated renal nerve responses to graded brachial nerve stimulation were not altered by either bilateral vagotomy or carotid sinus denervation and total power of the spectra, from 0-10 Hz, was similar in each group. The percentage power peak at heart rate in intact rats decreased with increasing stimulus frequency, from a control value of 19.2 +/- 1.9% to a minimum of 2.8 +/- 0.7% at 1.6 Hz, while coherence and phase were not altered. Conversely, the peak at the stimulus frequency rose with increasing stimulus frequency reaching 35.3 +/- 2.0% at 3.2 Hz. In the vagotomised group, power at heart rate was significantly lower at each stimulus frequency compared to intact rats although coherence was similar and the phase difference was larger. The peak power at stimulus frequency, coherence and phase difference were similar to those obtained in the intact rats. In the carotid sinus denervated rats, the percentage power at heart rate, coherence and phase difference were significantly smaller than in intact rats. The peak at the stimulus frequency and the phase difference were similar to those obtained in the intact rats whereas coherence was lower. These findings demonstrate that the pattern of renal nerve activity can be changed from one modulated by the baroreceptor to one driven by somatic afferent nerve activity. The vagus appears to play a minor role in the overall pattern of renal nerve activity with the primary controller being the carotid sinus baroreceptors. The data also show that the renal nerve response to somatic afferent nerve stimulation is independent of the afferent nerve input arising from either the atrial or the carotid sinuses.

Measurement of baroreflex gain from heart rate and blood pressure spectra: a comparison of spectral estimation techniques

The baroreflex is the physiological control system linking blood pressure and heart rate. Baroreflex gain, alpha, can be estimated from the ratio of heart rate and blood pressure spectra. The aim of this study was to quantify differences in estimates of alpha incurred by using four different spectral analysis techniques. ECG and blood pressure were recorded from 10 healthy subjects. Spectra were estimated using fast Fourier transform (FFT), zero-padded FFT (FFTZ), FFT of the windowed autocovariance function (ACVF), and maximum-entropy (ME) methods. For each subject a mean value of alpha was calculated in the MF (0.05-0.15 Hz) and HF (0.15-0.35 Hz) bands. Mean alpha MF varied between subjects (range 2-10 ms mmHg-1) as did mean alpha HF (range 4-12 ms mmHg-1). Mean differences in alpha MF and alpha HF estimated with different techniques were small. Differences in alpha MF ranged from 0.074 ms mmHg-1 (FFTZ against ME) to 0.298 ms mmHg-1 (FFT against ACVF) and those in alpha HF ranged from 0.057 ms mmHg-1 (FFT against FFTZ) to 0.342 ms mmHg-1 (ACVF against ME). None of these differences were significant. The use of different spectral analysis techniques does not significantly affect estimates of alpha.

Advances in processing of surface myoelectric signals: Part 1

During sustained voluntary or electrically elicited muscle contractions the surface myoelectric signal is nonstationary and it undergoes progressive changes reflecting the modifications of the motor unit action potentials and their propagation velocity. In particular, during sustained electrical stimulation, the evoked signals show progressive amplitude, time scaling and shape modification. The quantitative evaluation of these changes is important for non-invasive muscle characterisation and may be performed in either the time or frequency domain using parametric and nonparametric spectral analysis as well as alternative methodologies. The paper introduces the detection techniques, reviews and compares the methods of spectral estimation based on FFT and autoregressive models, and discusses their applications and limitations in extracting information from the surface myoelectric signal with particular regard to myoelectric manifestations of localised muscle fatigue during sustained contractions.

Hemodynamic analysis of arterial pressure oscillations in conscious rats

This study examined the contribution of rhythmic fluctuations of regional blood flow and vascular conductance to the genesis of low- (LF, 0.27-0.74 Hz) and high- (HF, 0.76-5 Hz) frequency oscillations of arterial pressure. In conscious 15-week-old male intact (n = 11), guanethidine-sympathectomized (n = 8) and chronically sinoaortic denervated (n = 7) rats, arterial pressure and regional blood flow velocities (pulsed Doppler probes) were simultaneously recorded. Indices of subdiaphragmatic aortic, hindquarters and superior mesenteric conductances were calculated on a beat-to-beat basis over a 60-min period. Spectral power was calculated in the LF and HF bands using a fast Fourier transform algorithm. Transfer function analysis was also performed to calculate coherence and phase between arterial pressure and regional flows and conductances. In the LF band, spectral power of arterial pressure was decreased by approx. 85% in sympathectomized and approx. 54% in sinoaortic denervated rats. In the HF band, spectral power did not differ between the groups. In the three groups of rats, relations between arterial pressure and blood flow were characterized by a significant coherence in the HF band with little or no phase delay (synchronous oscillations). Relations between arterial pressure and vascular conductance were characterized in intact rats by a significant coherence in the LF band and a phase delay tending to pi radians (opposite oscillations), whereas in both sympathectomized and sinoaortic denervated rats, coherence did not reach significance. It is concluded that LF oscillations of arterial pressure are mostly secondary to rhythmic fluctuations in the vasomotor sympathetic tone in several regional circulations. Part of these oscillations originate from the synchronizing influence of the baroreceptor reflex. The study also suggests that the respiratory (HF) oscillations of arterial pressure involve fluctuations in cardiac output of purely mechanical origin.

Respiration-synchronous fluctuations in stroke volume, heart rate and arterial pressure in humans

1. Simultaneous recordings of beat-to-beat left cardiac stroke volume (SV, pulsed ultrasound Doppler), mean arterial pressure (MAP) and heart rate (HR) were obtained in ten healthy young adults during spontaneous respiration at supine rest, before and after cholinergic blockade by atropine (0.035 mg kg-1). 2. Respiration-synchronous fluctuations in SV, HR, cardiac output (CO) and MAP were quantified by spectral analysis of the recordings of each of these variables. 3. Before atropine administration, respiration-synchronous fluctuations in HR and SV were prominent. The changes in HR and SV were inversely related and variation in SV was the main source of respiratory variability in CO. Respiration-synchronous fluctuations in MAP were mainly caused by variations in CO. 4. After cholinergic blockade, respiratory HR variations were eliminated, whereas the respiratory fluctuations in SV persisted. The fluctuations in CO and MAP increased. In this situation, mechanically induced variations in SV were not counteracted by inverse HR fluctuations and the influence on CO thus increased. 5. The main source of respiratory fluctuations in MAP in supine humans is thus variation in SV, while inverse, vagally mediated HR variations tend to reduce the fluctuations in CO and MAP.