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The Journal of Physiology logoLink to The Journal of Physiology
. 2007 Jan 18;580(Pt 1):315–326. doi: 10.1113/jphysiol.2006.126748

Interactions between cardiac, respiratory and EEG-δ oscillations in rats during anaesthesia

Bojan Musizza 1,2, Aneta Stefanovska 2,3, Peter V E McClintock 2, Milan Paluš 4, Janko Petrovčič 1, Samo Ribarič 5, Fajko F Bajrović 5,6
PMCID: PMC2075429  PMID: 17234691

Abstract

We hypothesized that, associated with the state of anaesthesia, characteristic changes exist in both cardio-respiratory and cerebral oscillator parameters and couplings, perhaps varying with depth of anaesthesia. Electrocardiograms (ECGs), respiration and electroencephalograms (EEGs) were recorded from two groups of 10 rats during the entire course of anaesthesia following the administration of a single bolus of ketamine–xylazine (KX group) or pentobarbital (PB group). The phase dynamics approach was then used to extract the instantaneous frequencies of heart beat, respiration and slow δ-waves (within 0.5–3.5 Hz). The amplitudes of δ- and θ-waves were analysed by use of a time–frequency representation of the EEG signal within 0.5–7.5 Hz obtained by wavelet transformation, using the Morlet mother wavelet. For the KX group, where slow δ-waves constituted the dominant spectral component, the Hilbert transform was applied to obtain the instantaneous δ-frequency. The θ-activity was spread over too wide a spectral range for its phase to be meaningfully defined. For both agents, we observed two distinct phases of anaesthesia, with a marked increase in θ-wave activity occurring on passage from a deeper phase of anaesthesia to a shallower one. In other respects, the effects of the two anaesthetics were very different. For KX anaesthesia, the two phases were separated by a marked change in all three instantaneous frequencies: stable, deep, anaesthesia with small frequency variability was followed by a sharp transition to shallow anaesthesia with large frequency variability, lasting until the animal awoke. The transition occurred 16–76 min after injection of the anaesthetic, with simultaneous reduction in the δ-wave amplitude. For PB anaesthesia, the two epochs were separated by the return of a positive response to the pinch test at 53–94 min, following which it took a further period of 45–70 min for the animal to awaken. δ-Waves were not apparent at any stage of PB anaesthesia. We applied non-linear dynamics and information theory to seek evidence of causal relationships between the cardiac, respiratory and slow δ-oscillations. We demonstrate that, for both groups, respiration drives the cardiac oscillator during deep anaesthesia. During shallow KX anaesthesia the direction either reverses, or the cardio-respiratory interaction becomes insignificant; in the deep phase, there is a unidirectional deterministic interaction of respiration with slow δ-oscillations. For PB anaesthesia, the cardio-respiratory interaction weakens during the second phase but, otherwise, there is no observable change in the interactions. We conclude that non-linear dynamics and information theory can be used to identify different stages of anaesthesia and the effects of different anaesthetics.

Cardiac and respiratory oscillations have long been known to interact with each other, the resultant respiratory modulation of cardiac frequency, respiratory sinus arrythmia, having first been observed in the eighteenth century (Hales, 1773). Synchronization of the cardiac and respiratory oscillations provides another manifestation of their interaction. Several recent studies have demonstrated the existence of such synchronization (Pikovsky et al. 2001), which was shown to be stronger in young athletes (Schäfer et al. 1998) than in young healthy non-athletes (Lotrič & Stefanovska, 2000). However, the precise physiological basis of the cardio-respiratory interaction is still emerging (Eckberg, 2003). Galletly & Larsen (1997) have shown that the cardio-respiratory interaction is changed during anaesthesia. It was further demonstrated by application of the phase dynamics approach that phase-transition-like phenomena in synchronization occur sequentially in rats as their anaesthesia is made deeper or lighter (Stefanovska et al. 2000), paving the way to an improved understanding of the physiology of anaesthesia.

Studies of neuronal oscillations have been undertaken since the first human electroencephalographic (EEG) recordings by Berger (1929). The recent resurgence of interest in such oscillations has led to an enhanced appreciation of their likely importance and to the tantalizing conjecture that perception, memory and even consciousness could result from the synchronization of neuronal networks (Buzsáki & Draguhn, 2004). Anaesthesia is another state where neuronal oscillations synchronize and desynchronize. Based on a large number of studies, John (2002) and John & Prichep (2005) have proposed a neurophysiological theory of the action of anaesthetics in suppressing awareness. They distinguish six steps leading to decreased γ-coherence and increased frontal δ- and θ-oscillations as a result of the depression of the prefrontal cortex reducing awareness.

We hypothesized that interactions occur between cardio-respiratory and neuronal oscillations. To test this idea, we have applied stochastic non-linear dynamics techniques (Stefanovska & Bračič, 1999; Pikovsky et al. 2001) to the analysis of time-varying physiological oscillations recorded from rats under anaesthesia. The agents chosen were ketamine–xylazine (KX) and pentobarbital (PB), which are commonly used (Destexhe et al. 2003; Rudolph & Antkowiak, 2004) in neuroscience research. The cardiac and respiratory oscillations were extracted from ECG and respiration signals (Stefanovska & Bračič, 1999; McClintock & Stefanovska, 2002). The time evolutions of individual neuronal oscillations were extracted from the EEG by means of the wavelet transform (Bračič & Stefanovska, 1998; Le Van Quyen et al. 2001; Harrop et al. 2002), with particular attention being paid to δ- and θ-waves. The instantaneous frequency of δ-oscillations was traced during the deep phase of KX anaesthesia when they were strongly pronounced (see below). The analyses were based on the phase dynamics technique introduced by Kuramoto (1984) and its subsequent applications to synchronization analysis (Tass et al. 1998; Schäfer et al. 1998; Lotrič & Stefanovska, 2000; Glass, 2001; Pikovsky et al. 2001) and to the detection of causal relationships among coupled oscillators (Schreiber, 2000; Paluš et al. 2001a; Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002; Paluš & Stefanovska, 2003). The phase dynamics approach is a particularly useful tool for the investigation of physiological oscillations because it can cope with their time-variable nature, and because it allows us to study their amplitudes and phases separately. It can reveal the underlying rules that contribute to the deterministic part of the variability, thus yielding evidence about its physiological origins. It also illuminates the question of whether causal relationships exist between the oscillations, and whether some or all of the time variability results from a unidirectional interaction.

We further hypothesized that cardio-respiratory–neuronal interactions would be detectable through causality analyses; and that the oscillation amplitudes, and the strength and directionality of the coupling, would undergo characteristic changes according to depth of anaesthesia and would be specific for each of the anaesthetics used.

Methods

Experimental procedure

The experiments were performed on two groups of adult, male Wistar rats weighing 250–300 g. Ten animals in the first group were anaesthetized with a single intraperitoneal injection of ketamine hydrocholride (45 mg (kg body wt)−1) and xylazine hydrochloride (7 mg (kg body wt)−1) (KX group). Ten animals in the second group were anaesthetized with a single intraperitoneal bolus of pentobarbital (60 mg (kg body wt)−1) (PB group). As soon as the rat could no longer hold its upright posture (10–15 min after administration of the drug), it was placed in a darkened Faraday cage where sensors were mounted and recording started immediately. The experiments took place in the Institute of Pathophysiology in Ljubljana in accordance with: State Guidelines for granting Licenses for Animal Experiments for Research Purposes, published in the Official Gazette of the Republic of Slovenia 40/85, 22/87; the Protection of Animals Act, ibid 98/99; EU regulations and recommendations, Council Directive 86/609/EEC; European Parliament resolution 2001/2259(INI); and the European Science Foundation Policy Briefing Use of Animals in Research, August 2001, Second Edition.

In both groups, simultaneous recordings were made of EEG over the left and right parietal cortex, electrical activity of the heart (ECG) and respiration. Three hypodermic needles, which served as EEG electrodes, were inserted under the animal's scalp. The EEG was differentially amplified (A = 10 000) and filtered (low-pass filter with cut-off frequency 300 Hz). The ECG was measured differentially (A = 20) with three electrodes placed on the animal's tail and front paws. Respiration was monitored by recording chest wall movement using a piezoelectric probe attached over the animal's thorax. All three signals were then fed through a signal conditioning system (CardioSignals, developed by the Jožef Stefan Institute and the Faculty of Electical Engineering, Ljubljana, Slovenia). They were each digitized at 1 kHz with 16-bit resolution (using a National Instruments multifunction I/O data acquisition board) and stored on the hard disk of a laptop computer.

Depth of anaesthesia was assessed at 5 min intervals by a nociceptive stimulus, the skin-pinch test, applied to the sole of the animal's front paw (Bajrović & Sketelj, 1998). The recording started with a negative test response, i.e. when the rat stopped responding with a reflex withdrawal of the limb.

In the KX group, monitoring was terminated on the reappearance of a positive pinch-test response, as the animal immediately started to move thereby terminating reliable data recording. The duration of recording varied from rat to rat (see Table 1) and was on average 87 min. Monitoring of the PB group continued for a limited period after the reappearance of a positive pinch test, while the rat was still not fully awake. It was stopped 45–70 min after the reappearance of the positive pinch test, thus allowing for recording during an interval of the waking state. Again, the duration of recording varied from rat to rat and was on average 92 min.

Table 1.

Anaesthesia data for the 20 rats, summarizing the times of characterstic events relative to the initiation of anaesthesia

Time of event (minutes from start of anaesthesia) for each rat
Event with KX 1 2 3 4 5 6 7 8 9 10
Duration of recording 62 57 168 72 73 73 100 71 71 122
Increase in fr 18 36 59 52 43 43 47 33 38 73
Decrease in the amplitude of δ 17 ± 4 36 ± 5 60 ± 2 52 ± 4 46 ± 2 43 ± 3 45 ± 3 34 ± 5 38 ± 5 76 ± 4
Interval before the transition 0–17 0–36 0–54 8–42 0–38 4–38 0–33 0–33 0–33 0–33
Interval after the transition 25–50 38–58 63–167 54–71 46–71 46–71 54–83 36–70 43–71 83–117
Event with PB 1 2 3 4 5 6 7 8 9 10
Duration of recording 135 67 31 80 68 75 87 80 109 87
Increase in the amplitude of θ 60 ± 3 16 ± 4 2 ± 1 20 ± 3 14 ± 5 30 ± 5 27 ± 5 28 ± 4 30 ± 4 35 ± 3
Interval before the transition 0–55 0–10 — 0–15 — 0–25 0–20 0–24 0–35 0–30
Interval after the transition 65–135 20–67 5–31 25–80 12–68 35–75 35–87 35–80 35–109 40–87
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Ten rats received ketamine–xylazine (KX group) and 10 received pentobarbital (PB). In the KX group the recording ended with the first positive pinch test. The time of the transition from deep to shallow anaesthesia was based on the changes in fr (Fig. 3, left) and on the amplitude of the δ-wave (see Fig. 2, left). The increase in fr is always clearly defined to within a few seconds. The decrease in amplitude of the δ-wave, although dramatic, cannot be localized precisely in time, so an interval is specified during which the change occurred. In the PB group, the transition from deep to shallow anaesthesia was based on the pinch test and the time at which the θ-wave amplitude increased (Fig. 2, right). Again, the latter cannot be localized precisely in time, so an interval is specified. The pinch test was negative during the deep phase and positive during the shallow phase. The intervals within which the spectral amplitudes of δ- and θ-waves were calculated and the coupling asymmetry tested with surrogate data, before/after the transition from deep to light anaesthesia, are also provided. All values are in minutes.

All measurements were at constant room temperature (24 ± 1°C). At the end of the recordings the animals were killed by administration of an overdose of the same anaesthetic.

Signal preprocessing

To reduce the effects of noise and artifacts, the recorded signals were preprocessed prior to analysis. The ECG and respiratory signals were bandpass filtered in the 4–6 and 1–2 Hz intervals, respectively (the characteristic frequencies in rats being ∼4 times higher than in humans), with care taken to avoid any introduction of phase lags. The EEG signal was also bandpass filtered, but only after extensive investigation of its time–frequency content by wavelet analysis. Short samples of time series after preprocessing are shown in Fig. 1.

Figure 1. Extracts from the preprocessed time series.

Figure 1

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EEG (top panel); respiratory signal (middle); and ECG (bottom).

Wavelet transform

The EEG power spectrum is conventionally divided (John, 2002) into the frequency bands: δ (0.5–3.5 Hz); θ (3.5–7.5 Hz); α (7.5–12.5 Hz); β (12.5–25 Hz); γ1 (25–35 Hz); γ2 (35–50 Hz); and γ3 (50–100 Hz). We calculated the time evolution within each band by application of the continuous wavelet transform (Stefanovska & Bračič, 1999). Wavelet analysis overcomes an inherent problem of the windowed Fourier transform for which time and frequency resolution cannot be optimal for all frequencies. It uses a window function of variable width – the mother wavelet Ψ(u) – which is shifted in time so that a family of generally non-orthogonal basis functions

graphic file with name tjp0580-0315-m1.jpg (1)

is obtained. Here s is the scale of the wavelet and t is the shift in time; p is an arbitrary non-negative number (usually set to 0.5). The wavelet transform of a signal g(t) is defined as:

graphic file with name tjp0580-0315-m2.jpg (2)

The Morlet mother wavelet was used because it allows direct connection between scale and frequency. To accelerate computation, the signal was first downsampled to 40 Hz. The wavelet transform was then segmented into the conventional EEG frequency intervals (see above).

Figure 2 shows typical time–frequency plots for the two groups. For the KX group, activity occurred mainly in the 0.5–3.5 Hz and 3.5–7.5 Hz bands, in agreement with earlier work (Amzica & Steriade, 1998). For the PB group, activity was observed only within 3.5–7.5 Hz, and only during the second part of the experiment. For further analysis each signal was divided into two intervals: (i) before and (ii) after the transition. The latter was defined by the diminution of the δ-band signal for the KX group, and by the appearance of θ-activity for the PB group, which usually coincided with the first positive pinch test. The time for each rat is given in Table 1.

Figure 2. Evolution with time of the characteristic frequencies of EEG δ- and θ-oscillations during KX (left) and PB (right) anaesthesia, analysed by wavelet transform.

Figure 2

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For KX, two separate analyses using different frequency windows were needed to reveal the θ-activity, because of the dominance of the δ-waves. Note that the δ-oscillations occur only with KX and dramatically diminish at ∼40 min, which is when the θ-oscillations emerge. The latter also appear for PB, almost simultaneously with positivity of the pinch test; the sharp spectral peak near 1 Hz is spurious: it corresponds to the respiratory frequency and results from movement artefacts due to respiration. Its second harmonic can also be seen.

Quantitative analysis of wavelet transform

Values of average wavelet amplitudes, as previously defined for the blood flow signal (Bračič & Stefanovska, 1998)

graphic file with name tjp0580-0315-m3.jpg (3)

were compared statistically for the δ- and θ-bands separately for the first and second parts of the recording by use of the Matlab (MathWorks Inc., Natick, MA, USA) Statistical Toolbox. The data are presented in each case as a boxplot of the paired group differences, thus providing a graphical representation of the data distribution, with box lines at the lower quartile, median and upper quartile values. The spread of the data is shown by lines extending from each end of the box. A paired Wilcoxon signed rank statistical test was used to test the hypothesis that the differences between the matched samples come from a distribution whose median is zero; P ≤ 0.05 was considered as statistically significant.

Instantaneous phases

In estimating an instantaneous phase we suppose that the studied processes, {X(t)} and {Y(t)}, can be modelled by weakly coupled oscillators (Linkens et al. 1982; Stefanovska & Bračič, 1999) and that their interactions can be inferred by analysis of the dynamics of their instantaneous phases (Kuramoto, 1984), φ1(t) and φ2(t), confined within [0,2π) or [−π,π). The latter can be estimated from the measured time series {x(t)} and {y(t)}, e.g. by the marked events method, or by application of the discrete Hilbert transform (Pikovsky et al. 2001), or by wavelet transform (Bračič & Stefanovska, 1998; Le Van Quyen et al. 2001; Harrop et al. 2002; Quiroga et al. 2002).

The instantaneous frequencies of the cardiac (i.e. HRV) and respiratory oscillations were obtained by the marked events method, Inline graphic where tk and tk+1 are the times of consecutive peaks. The instantaneous phases Inline graphic were then obtained, linearly interpolated, and resampled with Δt = 0.05 s. To obtain the instantaneous frequency corresponding to the δ-oscillations in the EEG, an analytic signal ζ(t) was constructed from the original time series. This is a complex function of time defined as ξ (t) = s(t) + isH (t) = A(t) eιφ(t), where A(t) is the amplitude and φ(t) is the phase of the signal s(t), and sH(t) is its Hilbert transform. The instantaneous phase is given by Inline graphic. For comparison we also computed the phases using the complex continuous Morlet wavelet (Torrence & Compo, 1998) for the scale 0.64, which gave a period of 0.66 s, i.e. a main central frequency of 1.5 Hz. The instantaneous phase φ(t) of the cortical δ-oscillations was then found by substitution of the real and imaginary parts of the wavelet coefficient for those of the analytic signal.

We had hoped to extract the instantaneous phases of cardiac, respiratory, δ- and θ-oscillations for both groups. In the event, only the phases of the cardiac and respiratory oscillations could be determined reliably throughout the anaesthesia. The instantaneous phase of the δ-oscillations could be calculated only for the KX group, and then only during the first section of the recording; in the second section, their amplitude became too small. The phase of δ-oscillations for the PB group was undetectable throughout. Note in Fig. 2 that, for most rats in the PB group, a sharp peak (with associated harmonics) appears at the frequency where δ-waves are to be expected in the EEG. However, a very strong coherence (near unity) was found with the instantaneous phase of respiration, showing that the peak is attributable to movement artefacts.

For both groups, the amplitude of θ-oscillations was significant only during the second part of the recordings. Under both anaesthetics, they spanned a large frequency interval (see Fig. 2) so that the notion of an instantaneous phase could not be defined unambiguously. Figure 3 shows examples of cardiac, respiratory and δ instantaneous phases for one rat during KX (left) and PB (right) anaesthesia. We now explain in detail how the interactions were evaluated.

Figure 3. Left: evolution with time of the EEG δ-wave fδ (bottom), respiratory fr (middle) and cardiac fc (top) characteristic frequencies during KX anaesthesia. Right: evolution of fr (bottom) and fc (top) for PB.

Figure 3

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The patterns of activity for both cardiac and respiratory frequencies differ substantially between the two groups. For the KX group, the phase of the fδ wave could be detected reliably only during the deep phase of anaesthesia; for the PB group it could not be detected reliably in either phase. Left: evolution of the respiratory fr (bottom), EEG δ-wave fδ (middle) and cardiac fc (top) characteristic frequencies with time during KX anaesthesia. Right: evolution of fr (bottom) and fc (top) for PB. The dashed vertical lines indicate the separation of the two phases of anaesthesia in each case. The patterns of activity for both cardiac and respiratory frequencies differ substantially between the two groups. For the KX group, the phase of the fδ wave could be detected reliably only during the deep phase of anaesthesia; for the PB group it could not be detected reliably in either phase.

Detection of interactions among coupled oscillators

We inferred the directionality of coupling using two independent methods, based on: (i) phase dynamics (Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002); and (ii) information theory (Paluš et al. 2001a; Paluš & Stefanovska, 2003). For studying the coupling and its asymmetry in more detail, we use method (ii). Generally, the mutual information I(X; Y) of two random variables X and Y is given as I(X; Y) = H(X) + H(Y) − H(X,Y). Here the entropies H(X), H(Y), H(X,Y) are given in the usual Shannonian sense (Cover & Thomas, 1991; Paluš et al. 2001a). The entropy and information are usually measured in bits if logarithm to base 2 is used; here we use the natural logarithm for which they are in nats. The conditional mutual information I(X; Y | Z) of the variables X, Y given the variable Z is then defined using the conditional entropies (Cover & Thomas, 1991; Paluš et al. 2001a) as

graphic file with name tjp0580-0315-m4.jpg (4)

Consider two time series {x(t)} and {y(t)} regarded as realizations of two stationary ergodic stochastic processes {X(t)} and {Y(t)} representing observables of two possibly coupled systems. Dependence structures between the two processes (time series) can be studied using the simple mutual information I(y; xτ), where we use y for y(t) and xτ for x(t + τ). I(y; xτ) measures the average amount of information contained in the process {Y} about the process {X} in the future, τ time units ahead (referred to hereafter as the τ-future). Note that, if processes {X} and {Y} are not independent, i.e. if I(x; y) > 0, this measure could also contain information about the τ-future of the process {X} contained in this process itself; so also could other dependence and predictability measures.

Causal relationships

For inferring causal relationships, i.e. the directionality of coupling between the processes {X(t)} and {Y(t)}, we need to estimate the ‘net’ information about the τ-future of the process {X} contained in the process {Y} using an appropriate tool – the conditional mutual information (CMI) I(y; xτ| x). It has been shown (Paluš et al. 2001a,b) that, using I(y; xτ| x) and I(x; yτ| y), the coupling directionality can be inferred from time series measured in coupled, but not yet fully synchronized, systems.

Now suppose that the processes {X} and {Y} can be modelled by weakly coupled oscillators and that their interactions can be inferred by analysis of the dynamics of their instantaneous phases φ1(t) and φ2(t) (Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002), as stated above. Rather than simply replacing the series {x(t)} and {y(t)} with the phases φ1(t) and φ2(t) (which are confined within the interval [0,2π) or [−π,π)), we consider phase increments

graphic file with name tjp0580-0315-m5.jpg

and the CMI I(φ1 (t), Δτ φ2 | φ2 (t)) and I(φ2 (t), Δτ φ1 | φ1 (t)) or, in a shorter notation, I(φ1;Δτ φ2 | φ2) and I(φ2;Δτ φ1 | φ1). Next, in analogy with Rosenblum et al. (Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002) we define a directionality index

graphic file with name tjp0580-0315-m6.jpg (5)

where the measure i(1 → 2) of how the system 1 drives the system 2 is either equal to the CMI I(φ1;Δτ φ2 | φ2) for a chosen time lag τ, or to an average of I(φ1;Δτφ2 | φ2) over a selected range of lags τ. In full analogy we define i(2 → 1) using I(φ2;Δτ φ1 | φ1); d(1,2) is positive if the driving from system 1 to system 2 prevails, and negative for the opposite case.

Note that, if each observed system were responding separately to an unseen third system, they could exhibit correlations without causal connections. Although we cannot rigorously exclude this possibility, our model studies with three variables show that the CMI, evaluated over a range of time lags, should not be significantly changed by such a third variable influencing the other two variables with different delay times.

Statistical analyses with surrogate data

The reliability of the measures was checked through the use of surrogate data (Paluš et al. 2007). These are artificially generated time series that preserve the statistical properties of the original data but are randomized such that any possible coupling is removed (Theiler et al. 1992; Schreiber & Schmitz, 2000). They were constructed by random permutation of the RR intervals, and of the intervals between respiration and δ-wave maxima; and phases were computed using these randomized intervals as described above. This approach should have destroyed any dependence or causal relationship, if present in the original data, while preserving the basic statistical properties (i.e. distributions of cardiac, respiratory and δ-wave frequencies) of the original data which can be sources of bias and variance in estimation of the CMI. Testing of significance was based on the CMI, which quantifies the coupling in each direction. The CMI itself is more reliable than the directionality index (5) given by the normalized difference of two CMIs. Note that, for establishing the significance of the results, the absolute value of the CMI is irrelevant. Rather, it is its difference from the surrogate range that counts. The reason is that a particular data distribution and frequency content lead to a particular bias, and this bias is also preserved in the surrogate data. Consequently, only values that are significantly greater than those from the surrogate data can be taken as reliable evidence of interaction.

Results

The two phases of anaesthesia were defined under Methods. The effect of each anaesthetic was distinctively different. With KX, the rats were fully awake as soon as the pinch test was positive, and the recording was stopped immediately. With PB, even after the rats started reacting to the pinch test, they were not fully awake and recording remained possible for a further period. Thus, the PB light phase was easy to determine reliably and served as a control. Cardiac and respiratory frequency data for all rats are summarized in Table 2.

Table 2.

Cardiac and respiratory frequency data for the 20 rats

KX 1 2 3 4 5 6 7 8 9 10
fc before 4.2 4.4 5.8 4.0 4.3 5.1 3.9 4.0 4.3 4.9
fc after 4.3 4.2 5.3 3.7 3.7 4.7 3.6 5.2 6.2 6.5
fr before 0.8 1.3 1.4 0.8 1.3 1.1 0.8 1.0 1.1 1.0
fr after 1.8 1.9 1.9 0.8 2.1 3.1 1.4 2.7 3.0 1.9
PB 1 2 3 4 5 6 7 8 9 10
fc before 5.7 5.3 6.3 6.8 6.4 6.1 5.5 5.9 4.9 5.3
fc after 5.3 4.5 6.0 6.5 6.2 5.6 5.2 4.8 5.0 4.7
fr before 1.0 0.7 2.2 1.0 1.2 0.8 0.8 1.0 0.8 0.7
fr after 0.6 0.5 1.3 1.0 1.1 0.8 0.8 0.9 0.7 0.6
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The intervals before and after the transition from deep to shallow anaesthesia, as specified in Table 1, are used to calculate average heart rate (fc) and respiratory frequency (fr) for each rat. All values are in Hz.

Instantaneous frequencies

The δ-wave frequency in the EEG of the KX group increased slightly during the initial deep phase of anaesthesia. It underwent a dramatic decrease in amplitude at the transition from deep to light anaesthesia. The θ-oscillations also underwent changes at the transition (left and right panels of Fig. 2), with a noticeable increase in the amplitude of the latter. In agreement with the earlier study (Stefanovska et al. 2000), the respiration frequency increased and became erratic at the transition, and the cardiac frequency increased (Fig. 3). The instantaneous frequencies of cardiac and respiratory oscillations did not undergo any particular changes during the transition from deep to light PB anaesthesia. The only dramatic change during PB anaesthesia was in the phase dynamics of the θ-oscillations, which was similar to that observed in the KX group.

Time–frequency analysis of EEG

Figure 4 presents box plots with group median values and distributions of spectral amplitudes within the δ and θ frequency intervals for deep and light KX and PB anaesthesia. Again, the δ-waves are characteristic of KX deep phase anaesthesia and significantly decrease during the light phase. For PB, their amplitudes are low and do not differ significantly between the two phases of anaesthesia. The θ-waves are similar for both anaesthetics, being weak during the deep phase and increasing significantly as the light phase is entered.

Figure 4. Group median values and the distribution of wavelet amplitudes for deep and light anaesthesia.

Figure 4

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Box plots presenting group median values and the distribution of wavelet transform amplitudes for deep and light anaesthesia within the δ (left) and θ (right) EEG frequency intervals for KX (top panels) and PB (bottom).

The fact that the δ- and θ-oscillations during KX anaesthesia, and the θ-oscillations during PB anaesthesia, undergo changes at the same moment as those in the cardiac and respiratory oscillations suggests the possibility of mutual interactions.

Interactions and causal relationships

Figure 5 presents details of the cardio-respiratory interaction during KX (left) and PB (right) anaesthesia: the temporal evolution of the directionality index dr,c is plotted, as determined by the phase dynamics (Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002) and mutual information (Paluš et al. 2001a; Paluš & Stefanovska, 2003) approaches. Note that the directionality indices in Fig. 5 are calculated using short moving windows to obtain their time evolutions. In each case the interaction during KX is seen to undergo a marked and sudden change at the transition, at the same time as the onset of erratic respiration (Fig. 3, left) and the pronounced decrease in amplitude of the δ-oscillation (Fig. 2, left). Up to that point, the directionality index is positive, i.e. respiration drives cardiac activity as in the waking state. As the anaesthesia becomes shallow, however, this is no longer true and, if anything, it is then the cardiac rhythm that drives respiration. On the contrary, no significant change in cardio-respiratory interactions can be observed during either phase of PB anaesthesia (Fig. 5, right). The results obtained from these two very different methods are clearly in good qualitative agreement.

Figure 5. Direction of the cardio-respiratory interaction dr,c measured during KX (A and B) and PB (C and D) anaesthesia.

Figure 5

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A and C, calculated using the phase dynamics method (Rosenblum & Pikovsky, 2001; Rosenblum et al. 2002). B and D, calculated from the same data using mutual information (Paluš et al. 2001a; Paluš & Stefanovska, 2003). If dr,c > 0 it means that respiration drives cardiac function, and vice versa if dr,c < 0. The dashed lines separate the two phases of anaesthesia in each case.

Causal relationships checked using surrogate data

The analysis was based on the maximum possible window lengths corresponding to each of the two phases of anaesthesia. This means that possible short episodes of interaction will not be observed, but makes for a more reliable estimate of the average interaction during that phase. We now illustrate the surrogate testing using as an example the cardio-respiratory interactions in rat no. 9 from the KX group. In this case, the first segment (before the transition) was 0–33 min, and the second segment (after the transition) was 43–71 min. The surrogate data were constructed from the tested data segment, thus retaining the same frequency distribution. The results are presented in Fig. 6, in which the CMI for the original data is represented by the position of a vertical bar, whereas the range of values given by 2500 realizations of the surrogate data is shown as a 100-bin histogram. If the value of CMI for the original data lies within this distribution, it is considered as statistical significance for accepting the null hypothesis (no coupling). Results are shown for the four different cases, i.e. in each direction, before and after the transition. The statistical tests for all 20 rats are summarized in Table 3.

Figure 6. Use of surrogate data for testing the significance of the conditional mutual information (CMI) calculated from the data.

Figure 6

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The ordinates plot the relative frequencies with which the CMI surrogate realization falls in a particular histogram bin and are in dimensionless units. The CMI characterizes the information flow (influence) from respiratory to cardiac activity (A and C), and in the opposite direction from cardiac to respiratory activity (B and D), for a rat during KX anaesthesia. The top two panels (A and B) refer to a period 0–33 min within the first part of the anaesthesia, and the lower panels (C and D) refer to a period 43–71 min within the second part. CMI values calculated from the rat data under test are shown by the positions of the vertical bars; the distributions of 2500 realizations of surrogate data are shown by their histograms, obtained in each case using 100 bins; nats, bits of information obtained using the natural logarithm.

Table 3.

Statistical tests of directional couplings

CMI Significance level for each rat
KX 1 2 3 4 5 6 7 8 9 10
C→R 0.03/0.45 0.23/0.00 0.14/0.90 0.14/0.60 0.80/0.90 0.90/0.00 0.80/0.00 0.20/0.90 0.20/0.10 0.70/0.90
R→C 0.00/0.70 0.00/0.90 0.34/0.70 0.02/0.60 0.00/0.00 0.00/0.07 0.10/0.40 0.00/0.70 0.03/0.50 0.00/0.50
δ→R 0.50/− 0.25/− 0.33/− 0.70/− 0.08/− 0.40/− 0.05/− 0.50/− 0.07/− 0.22/−
R→δ 0.30/− 0.03/− 0.70/− 0.26/− 0.02/− 0.07/− 0.03/− 0.18/− 0.16/− 0.05/−
δ→C 0.90/− 0.60/− 0.23/− 0.42/− 0.06/− 0.90/− 0.70/− 0.30/− 0.90/− 0.90/−
C→δ 0.10/− 0.90/− 0.90/− 0.64/− 0.60/− 0.50/− 0.26/− 0.90/− 0.90/− 0.50/−
PB 1 2 3 4 5 6 7 8 9 10
C→R 0.00/0.04 0.10/0.00 −/0.09 0.79/0.84 −/0.17 0.02/0.77 0.90/0.18 0.72/0.21 0.41/0.06 0.04/0.28
R→C 0.00/0.48 0.00/0.00 −/0.00 0.00/0.00 −/0.00 0.00/0.00 0.00/0.00 0.00/0.50 0.00/0.00 0.00/0.07
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The couplings from cardiac to respiratory (C→R) and from respiratory to cardiac (R→C) activity are shown for both the KX and PB groups. The couplings from δ to respiratory (δ→R), from respiratory to δ (R→δ), from δ to cardiac (δ→C) and from cardiac to δ (C→δ) activity were calculated only for the KX group and only for the deep phase of anaesthesia. Each pair of numbers refers to measures before/after the deep/light anaesthesia transition. The times of the two intervals within which the directional coupling was calculated for each rat are specified in Table 1. The tests were performed as illustrated in Fig. 6. The ‘significance level’ corresponds to the probability that the obtained CMI value occurred by chance, and was read from the cumulative histograms obtained by summing up the histogram bins from the estimated surrogate histograms such as those in Fig. 6. The result was considered significant for P < 0.05 (indicated by italicised numbers).

The results of Fig. 6 confirm those of Fig. 5, left, which were obtained with short time windows. Figure 6A shows strong statistical evidence for respiration driving the heart during deep KX anaesthesia; Fig. 6B and D provide evidence that there may be a change between deep and shallow anaesthesia in the ic→r information transfer under PB, though it is not statistically significant. Figure 6C shows that there is no significant ir→c information transfer in the shallow phase of anaesthesia under KX.

Figure 7 summarizes schematically the main results of the study, based on all 20 rats analysed. It illustrates the existence of causal relationships between cardiac and respiratory oscillations for both KX (Fig. 7A and B) and PB (Fig. 7C and D) anaesthetics. The direction of coupling reverses between the deep and shallow phases of KX anaesthesia. With PB, the direction of driving remains from respiration to cardiac activity throughout the recording but weakens after the transition, while the interaction ic→r in the opposite direction becomes insignificant in the shallow phase.

Figure 7. Schematic diagram illustrating the main results of the study in terms of the 3-oscillator model of respiratory (r), cardiac (c) and cortical (δ) mutual interactions (arrows).

Figure 7

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Inter-oscillator interactions during the period of deep anaesthesia (A and C) are compared with those during shallow anaesthesia (B and D) with KX (A and B) and PB (C and D), respectively. The significances of the calculated CMIs (inter-oscillator couplings) are indicated by the numbers of stars (** for N > 6, * for 3 < N < 6, and 0 for N < 3, where N is number of rats). A ‘?’ is used to indicate cases where an interaction could not be evaluated (the phases of EEG δ-waves were difficult to detect unambiguously during shallow anaesthesia with KX, and throughout the entire period of PB anaesthesia).

For the KX group, interactions with the EEG δ-oscillations in the deep phase of anaesthesia are also summarized. Statistically significant evidence for respiration driving the cortical δ-oscillations is established for half of the rats; for the others, the evidence points in the same direction, but is weaker (not statistically significant). A firm signature of driving in the opposite direction is obtained for only one rat, and P ≤ 0.08 is obtained for an additional two rats (see Table 3). No signature of cardiac–δ interactions is obtained for any of the rats and there is a high probability of there being no driving in either direction.

Discussion

Although the two anaesthetics differ markedly in their effects, they have in common a sudden increase in θ-wave activity as an initial deep phase of anaesthesia gives way to lighter anaesthesia.

For KX, the transition from the first phase of anaesthesia to the second (Table 1) occurred at a time of 18–73 min after the injection. The first period is characterized by the presence of strong δ-oscillations, only, in the EEG. Both the respiratory and cardiac frequencies remain relatively stable. During the second period, δ-oscillations are markedly decreased, either because the underlying activity has lessened, or because it has become spatially desynchronized. Simultaneously, weak activity appears in the θ (3.5–7.5 Hz) interval. At the same time, the cardiac and respiratory instantaneous frequencies increase significantly and their variability becomes very large. We suggest that this may be attributable to the effects of the ketamine wearing off faster that those of xylazine so that during the second phase the effect of xylazine is dominant.

For PB, the mean cardiac frequency decreased slightly during the deep phase of anaesthesia, and its variability remained very small during the whole period of measurement. The mean respiratory frequency stayed virtually constant, with almost no variability. Soon after the onset of θ-activity, 53–94 min after the onset of anaesthesia, the pinch test became positive, but this did not coincide with movements or righting attempts (Devor & Zalkind, 2001). The next 45–70 min, until the animal awakened, represent shallow anaesthesia.

For KX the two stages clearly differ in respect of the causal relationships between δ, cardiac and respiratory oscillations. The cardio-respiratory interaction reverses, with respiration strongly driving the cardiac oscillations during the first period. During the second period, the interaction is much weaker, but is in the opposite direction, with respiration being driven by the cardiac oscillations. We have also demonstrated that the respiratory–δ interaction is probably bidirectional, but further investigation is needed. For PB, the cardio-respiratory interaction during deep anaesthesia is bidirectional, with respiration driving the cardiac oscillator in both phases of anaesthesia, for all rats. Such causal relationships during anaesthesia have not previously been reported. We now discuss their implications.

The observed evolutions of the δ-oscillations for KX, and of θ-oscillations for both KX and PB, are consistent with the results reviewed and the picture proposed by John (2002) and John & Prichep (2005). They concluded from many studies using several different anaesthetics that δ-oscillations are associated with reduced awareness. Using a time–frequency representation of EEG measurements recorded on dogs, Nayak et al. (1994) also demonstrated that the δ and θ frequency bands can be related to depth of anaesthesia. Dossi et al. (1992) have demonstrated that the majority of thalamocortical neurons are endowed with electrophysiological properties, allowing them to oscillate at 0.5–4 Hz. Steriade et al. (1993) have shown that such oscillations are strongly synchronized during sleep, and desynchronized in the waking state. Rhythmic neuronal activity in the frequency range 0.5–4 Hz is now widely accepted (Rudolph & Antkowiak, 2004) as characteristic of stages III and IV of non-rapid-eye-movement sleep (also known as slow-wave sleep). It has been shown (Alkire, 1998) that the transition from a sedated to an unconscious state is accompanied by a decrease in cortical glucose metabolism and, at the same time, a reduction in β, α and θ power, whereas δ power is increased indicating increased thalamic activity. Alkire et al. (2000) have further proposed that thalamocortical cells, which have been identified as the main generators of cortical δ-rhythms, are also involved in producing an anaesthetic-induced δ-activity similar to natural sleep.

A significant implication of our results is the possibility of quantifying depth of anaesthesia. During the first stage of KX anaesthesia, all the elements for loss of awareness discussed by John & Prichep (2005) are fulfilled. Initially, there is an abrupt alteration of the brain state but, as the anaesthetic is metabolized, the changes involved in some of the six steps may be reversed leading to the second stage where δ-oscillations decrease and θ-activity starts to return. This is consistent with the suggestion by John & Prichep (2005) that the three dimensions of anaesthesia – immobility, amnesia and absence of awareness – are mediated by different regions of the central nervous system. Destexhe et al. (2003) have recently reviewed the results of simultaneous intracellular and EEG recording in the waking state and during KX and barbiturate anaesthesia. The fact that we did not observed δ-activity in the PB group is probably attributable to the fact that barbiturates profoundly depress cortical excitability and may well affect thalamocortical cells in a similar way. The fact that we can distinguish deep and shallow phases of anaesthesia for two different agents shows that, although further experiments in animals and humans are needed, the approach presented here can be used to trace the changes that occur during anaesthesia.

A second implication is that causal relationships exist between cardiac, respiratory and brain oscillatory processes. These results are consistent with earlier work demonstrating the existence of the cardio-respiratory interaction, but substantially extend it by inferring the direction of the interaction and through the inclusion of δ-oscillations. Note that Pomfrett et al. (1993) pointed out that significant changes in respiratory sinus arhythmia were associated with changes in the median frequency of the EEG following changes in propofol infusion in humans. A temporal relationship between changes in HRV and EEG activity has also been demonstrated during sleep in both humans (Otzenberger et al. 1997; Yang et al. 2002) and rats (Yang et al. 2003). When recording from the olfactory cortex of rats under similar KX anaesthesia Fontanini et al. (2003) and Fontanini & Bower (2005) observed that most of the slow oscillations concentrated in the 0.7–1.5 Hz band. They also discovered higher frequencies during light anaesthesia. The relationship between respiration and EEG was also analysed in detail in these two papers. The interaction of respiration with EEG waves may, however, be quite different in the olfactory cortex, with more respiration-related sensory inputs than in the parietal cortex. The complex interactions between cardiac, respiratory and brain rhythms are important, not only for anaesthesia, but also for cognitive and functional disturbances (John, 2002). For example, disorders of autonomic cardiovascular control were detected in patients with epilepsy, even in the absence of abnormal findings during EEG monitoring (Massetani et al. 1997). Recent studies have started to elucidate the pathways involved in neurovascular regulation in the brain (Iadecola, 2004), including the effect of brainstem catecholamine neurons on respiration (Li & Nattie, 2006) and the connection between neuronal activity, neuronal oxydative metabolism and astrocytic glycolisis (Kasischke et al. 2004).

A third outcome relates to the possible involvement of glial cells in slow δ-waves. Our analysis of time–frequency spectral content within the classical frequency intervals (John, 2002), revealed non-zero amplitudes within 0.5–3.5 Hz and 3.5–7.5 Hz (Fig. 2). That in 0.5–3.5 Hz was dominant for KX, especially during deep phase anaesthesia. We note that Amzica & Steriade (1998) identified several oscillations, with distinct mechanisms and sites of origin, within the classical δ-band: a slow (< 1 Hz) cortically generated oscillation, a clock-like thalamic oscillation (1–4 Hz) and a cortical oscillation (1–4 Hz). Using the envelope of the power of the higher frequencies or neuronal spikes, Penttonen & Buzsáki (2003) distinguished several slow oscillatory states in rats and, in particular, two components within the classical δ-band 0.5–1.5 and 1.5–4 Hz, named slow-1 and δ, respectively. In the present work, the Hilbert transform was used to determine the instantaneous frequency within the interval 0.5–3.5Hz. The frequency varied with time, but remained between 1 and 2 Hz. We assume that, because we detect the compound activity of the brain, the slow-1 and δ-waves reported by Penttonen & Buzsáki (2003) using highly regional recordings manifest here as a single oscillatory component. The fact that it interacts with respiratory oscillations for KX (Fig. 7) is of particular interest, given the known activity of glial cells in this frequency range (Amzica & Steriade, 1998; Amzica, 2002), and their pivotal role as intermediaries between neurons and brain microcirculation (Zonta et al. 2003; Kasischke et al. 2004). It suggests that causality analyses like those described above have potential for revealing details of glial activity in vivo that cannot be evaluated in other ways.

In summary, for both KX and PB we have identified two distinct phases of anaesthesia. With KX there is a sudden change in the directionality of the cardio-respiratory interaction as deep anaesthesia gives way to light anaesthesia. Marked changes in EEG δ and θ waves also occur at the transition. Evidence is reported for interactions between respiratory and δ-oscillations, with the former driving the latter during deep anaesthesia.

Acknowledgments

This research was supported by ARRS (Slovenia), the CMEYS Programme KONTAKT and the Institutional Research Plan AV0Z10300504 (Czech Republic), the Wellcome Trust, and the FP6 EC NEST-Pathfinder project BRACCIA.

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