The discriminatory value of cardiorespiratory interactions in distinguishing awake from anaesthetised states: a randomised observational study.

Depth of anaesthesia monitors usually analyse cerebral function with or without other physiological signals; non-invasive monitoring of the measured cardiorespiratory signals alone would offer a simple, practical alternative. We aimed to investigate whether such signals, analysed with novel, non-linear dynamic methods, would distinguish between the awake and anaesthetised states. We recorded ECG, respiration, skin temperature, pulse and skin conductivity before and during general anaesthesia in 27 subjects in good cardiovascular health, randomly allocated to receive propofol or sevoflurane. Mean values, variability and dynamic interactions were determined. Respiratory rate (p = 0.0002), skin conductivity (p = 0.03) and skin temperature (p = 0.00006) changed with sevoflurane, and skin temperature (p = 0.0005) with propofol. Pulse transit time increased by 17% with sevoflurane (p = 0.02) and 11% with propofol (p = 0.007). Sevoflurane reduced the wavelet energy of heart (p = 0.0004) and respiratory (p = 0.02) rate variability at all frequencies, whereas propofol decreased only the heart rate variability below 0.021 Hz (p < 0.05). The phase coherence was reduced by both agents at frequencies below 0.145 Hz (p < 0.05), whereas the cardiorespiratory synchronisation time was increased (p < 0.05). A classification analysis based on an optimal set of discriminatory parameters distinguished with 95% success between the awake and anaesthetised states. We suggest that these results can contribute to the design of new monitors of anaesthetic depth based on cardiovascular signals alone.

Characterizing an ensemble of interacting oscillators: the mean-field variability index.

We introduce a way of characterizing an ensemble of interacting oscillators in terms of their mean-field variability index κ, a dimensionless parameter defined as the variance of the oscillators' mean field r divided by the mean square of r. Based on the assumption that the overall mean field is the sum of a very large number of oscillators, each giving a small contribution to the total signal, we show that κ depends on the mutual interactions between the oscillators, independently of their number or spectral properties. For purely random phasors, or a noninteracting ensemble of oscillators, κ converges on 0.215. Interactions push κ in different directions: lower where there is interoscillator phase coherence, tending to zero for complete phase synchronization, or higher for amplitude synchronization or intermittent synchronization. We calculate κ for several different cases to illustrate its utility, using both numerically simulated data and electroencephalograph signals from the brains of human subjects while awake, while anesthetized, and while undergoing an epileptic fit.

Testing for time-localized coherence in bivariate data.

We present a method for the testing of significance when evaluating the coherence of two oscillatory time series that may have variable amplitude and frequency. It is based on evaluating the self-correlations of the time series. We demonstrate our approach by the application of wavelet-based coherence measures to artificial and physiological examples. Because coherence measures of this kind are strongly biased by the spectral characteristics of the time series, we evaluate significance by estimation of the characteristics of the distribution of values that may occur due to chance associations in the data. The expectation value and standard deviation of this distribution are shown to depend on the autocorrelations and higher order statistics of the data. Where the coherence value falls outside this distribution, we may conclude that there is a causal relationship between the signals regardless of their spectral similarities or differences.

Oscillatory dynamics of vasoconstriction and vasodilation identified by time-localized phase coherence.

We apply wavelet-based time-localized phase coherence to investigate the relationship between blood flow and skin temperature, and between blood flow and instantaneous heart rate (IHR), during vasoconstriction and vasodilation provoked by local cooling or heating of the skin. A temperature-controlled metal plate (approximately 10 cm2) placed on the volar side of the left arm was used to provide the heating and cooling. Beneath the plate, the blood flow was measured by laser Doppler flowmetry and the adjacent skin temperature by a thermistor. Two 1 h datasets were collected from each of the ten subjects. In each case a 30 min basal recording was followed by a step change in plate temperature, to either 24 °C or 42 °C. The IHR was derived from simultaneously recorded ECG. We confirm the changes in the energy and frequency of blood flow oscillations during cooling and heating reported earlier. That is, during cooling, there was a significant decrease in the average frequency of myogenic blood flow oscillations (p < 0.05) and the myogenic spectral peak became more prominent. During heating, there was a significant (p < 0.05) general increase in spectral energy, associated with vasodilation, except in the myogenic interval. Weak phase coherence between temperature and blood flow was observed for unperturbed skin, but it increased in all frequency intervals as a result of heating. It was not significantly affected by cooling. We also show that significant (p < 0.05) phase coherence exists between blood flow and IHR in the respiratory and myogenic frequency intervals. Cooling did not affect this phase coherence in any of the frequency intervals, whereas heating enhanced the phase coherence in the respiratory and myogenic intervals. This can be explained by the reduction in vascular resistance produced by heating, a process where myogenic mechanisms play a key role. We conclude that the mechanisms of vasodilation and vasoconstriction, in response to temperature change, are oscillatory in nature and are independent of central sources of variability.

Detecting the harmonics of oscillations with time-variable frequencies.

A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.