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Bojan Musizza^1,2, Aneta Stefanovska^2,3, Peter V. E. McClintock², Milan Palu⁴, Janko Petrovi¹, Samo Ribari⁵ and Fajko F. Bajrovi^5,6

¹ Department of Systems and Control, Joef Stefan Institute, Jamova 39, Ljubljana, Slovenia
² Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
³ Nonlinear Dynamics and Synergetics Group, Faculty of Electrical Engineering, University of Ljubljana, Traka 25, Ljubljana, Slovenia
⁴ Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou ví 2, 182 07 Prague 8, Czech Republic
⁵ Institute of Pathophysiology, Faculty of Medicine, University of Ljubljana, Zaloka 7, Ljubljana, Slovenia
⁶ Department of Neurology, Clinical Centre Ljubljana, Zaloka 7, Ljubljana, Slovenia

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 -waves (within 0.5–3.5 Hz). The amplitudes of - and -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 -waves constituted the dominant spectral component, the Hilbert transform was applied to obtain the instantaneous -frequency. The -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 -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 -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. -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 -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 -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.

(Received 15 December 2006; accepted after revision 10 January 2007; first published online 18 January 2007)
Corresponding author A. Stefanovska: Department of Physics, Lancaster University, LA1 4YB Lancaster, UK. Email: aneta{at}lancaster.ac.uk

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