European Journal of Anaesthesiology 2006; 23: 391–402
© 2006 Copyright European Society of Anaesthesiology doi: 10.1017/S0265021505001857
Original Article An effective correlation dimension and burst suppression ratio of the EEG in rat. Correlation with sevoflurane induced anaesthetic depth P. L. C. van den Broek*†, C. M. van Rijn*, J. van Egmond†, A. M. L. Coenen*, L. H. D. J. Booij† Radboud University Nijmegen, *NICI Department of Psychology, Nijmegen; †Department of Anaesthesiology, Nijmegen, The Netherlands
Summary Background and objective: Anaesthesiologists need parameters that measure the depth of anaesthesia. In the context of this need, the present study investigated in rats how two variables from the electroencephalogram, the burst suppression ratio and effective correlation dimension correlated with a measure of anaesthetic depth as measured in the strength of a noxious withdrawal reflex. Methods: Eight rats were exposed to different inspiratory concentrations of sevoflurane, each rat in two separate experiments. In the first experiment, spontaneously breathing animals could move freely and no painful stimuli were applied. In the second experiment, in mechanically ventilated restrained anaesthetized rats, the withdrawal reflex was measured every 80 s. In both experiments the electroencephalogram was continuously recorded. The concentration in the effector compartment was estimated using a first order two compartment model. Correlation dimension was computed following the Grassberger/Procaccia/Takens approach with optimized parameter settings to achieve maximum sensitivity to anaesthetic drug effects and enable real-time computation. The Hill, equation was fitted to the data, describing the effect as a function of sevoflurane concentration. Results: Good correlations of Depth of Anaesthesia with correlation dimension as well as burst suppression ratio were established in both types of experiments. Arousal by noxious stimuli decreased burst suppression ratio and increased correlation dimension. The effective sevoflurane concentration associated with 50% of the maximum effect (C50) was higher in experiment II (stimulation) than in experiment I (no stimulation): i.e. for correlation dimension 2.18% vs. 0.60% and for burst suppression ratio 3.07% vs. 1.73%. The slope factors were: gCD 4.15 vs. gCD 1.73 and gBSR 5.2 vs. gBSR 5.4. Correlation dimension and burst suppression ratio both correlated with the strength of the withdrawal reflex with correlation coefficients of 0.46 and 0.66 respectively (P 0.001). Conclusions: Both correlation dimension and burst suppression ratio are related to anaesthetic depth and are affected by noxious stimuli. The relationship between anaesthetic depth and burst suppression ratio is confirmed and the potential of correlation dimension is demonstrated. Keywords: ANAESTHETICS, INHALATION, sevoflurane; ELECTROENCEPHALOGRAPHY, methods; NON-LINEAR DYNAMICS; RAT; ANAESTHESIA GENERAL, measurement of depth of anaesthesia.
Correspondence to: P. L. C. van den Broek, NICI Department of Psychology, Radboud University Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, The Netherlands. E-mail:
[email protected]; Tel: 31 24 3612544; Fax: 31 24 3616066 Accepted for publication 10 June 2005 EJA 3045 First published online 10 February 2006
P. L. C. van den Broek et al
Introduction Anaesthetic drugs have been developed that more or less specifically interact with the subsystems of anaesthesia: level of consciousness, analgesia, suppression of autonomic reflexes and muscle relaxation. Although these subsystems are well-distinguished, their mutual interaction is commonly recognized. Despite the mutual interaction of these subsystems it is desirable to monitor each subsystem individually. For the estimation of the anaesthetic state of a patient, up to recently, anaesthesiologists were guided by variables reflecting this state only indirectly: heart rate (HR), blood pressure (BP), oxygen saturation, respiration, perspiration, CO2 production etc. To evaluate the level of consciousness (Depth of Anaesthesia) more specifically, numerous variables deduced from the electroencephalogram (EEG) have been investigated in the past few decades. It is commonly accepted that the effect of in particular hypnotics is expected to be observed first in the EEG. The EEG is a well-known, electrically measurable signal that reflects the overall activity of the central nervous system (CNS). If the anaesthesiologist can obtain relevant information about the depth of anaesthesia from the EEG, a close direct measurement of the effects of anaesthetic agents might be possible. The interpretation of the EEG, however, is complex because it is a reflection of the state of the brain, the effects of the surgical procedure (arousing stimuli) and the influence of anaesthetic drugs. Anaesthetic agents (even if belonging to the same group, i.e. hypnotics) have different effects on the EEG and do not present a straightforward solution concerning the monitoring of depth of anaesthesia [1]. Processing of EEG with linear methods as applied so far (power of frequency bands, spectral edge frequency etc.) did not solve this problem; both positive results [2–6], as well as negative ones were reported [7–9]. Nevertheless, the idea that the EEG informs the anaesthesiologist directly about depth of anaesthesia and the inadequacy of linear measures so far to assess this depth under different circumstances were the main reasons for groups to investigate the application of non-linear mathematics to the EEG. A quantitative measure that has been developed to characterize non-linear dynamics is D2, the correlation dimension (CD) [10,11]. In 1987, Mayer–Kress and Layne published one of the first articles that describe the application of D2 to determine anaesthetic drug effect [12]. One year later, Watt and Hameroff demonstrated changes of phase space trajectories and dimensionality as a result of changed depth of anaesthesia [13]. Later, Widman and colleagues investigated a modified version of D2, the non-linear correlation index D*, as a measure of depth of sevoflurane anaesthesia [14]. Lee
and colleagues. found D2 to serve as a better index for the depth of halothane anaesthesia in the rat compared to b-power and median power frequency [15–19]. All these articles showed the potency of D2 or derived measures to inform us about depth of anaesthesia and supported the presumption that going from full consciousness to unconsciousness results in more and more autonomic processes dropping out. Many of the brain-directed processes involve the cortex; the EEG obtained from surface electrodes represents mostly cortical activity. So it is expected that more and more processes disappear from the cortical activity with deeper anaesthesia. The CD, expressing this complexity in a single number, looks very attractive for the purpose of an indicator of anaesthetic depth. At the deepest anaesthetic levels, the EEG pattern changes, i.e. EEG epochs characterized by high frequencies and low amplitudes (suppression) alternate with epochs characterized by low frequencies and high amplitudes (bursts), see Figure 1. The burst suppression ratio (BSR) is defined as the ratio of the summation of the duration of the suppression parts in an epoch of arbitrary length and the epoch time length [20,21], i.e. without any presence of suppression parts BSR 0. The more this epoch is filled with suppressed parts the higher BSR will be, up to a maximum of one in case the whole epoch is filled with suppressed EEG. Several studies evaluated the BSR, the burst suppression pattern (BSP), and the onset of BSP as possible informative of anaesthesia related phenomena [22–26]. The objective of the present study was to investigate how BSR and CD [27] are influenced by changing sevoflurane concentrations and how they are related to depth of anaesthesia in rats. Because EEG is available without any invasive procedure, it has been explored extensively in the search for variables to help control anaesthetic depth, directly in human experiments. But for ethical reasons, no one designs experimental procedures on volunteers under anaesthesia. Burst suppression pattern 0 EEG
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© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
Correlation dimension and anaesthesia Recording of EEG on patients, however, is always accompanied by disturbances during surgical procedures including interaction with diathermy and coagulation, interactions of other drugs on the EEG and mutual interactions of the various drugs. In animal experiments, one is able to study the effects of a single drug (such as sevoflurane) on the EEG. We show in the present study that there is a clear interaction of the EEG under sevoflurane with noxious stimulation. In an animal experiment this can be performed in a pure form: study EEG under sevoflurane at a certain concentration in the presence and in the absence of the stimulus. Therefore, the study was separated into an experiment measuring the transition from awake to a state of anaesthesia in a non-stimulated freely moving rat (I), and a second experiment with measurements only in the anaesthetic range while painful stimuli were applied to the restrained rat (II).
Methods After approval of the University Committee on Ethics in Animal Research eight adult male Wistar rats (mean weight: 426 g, SD 36 g) were used. A tripolar electrode (Plastic Products Company, MS 333/2A) was implanted under sodium pentobarbital anaesthesia (Narkovet, 60 mg kg1 intraperitoneally) to enable long-term recording of the cortical EEG. The coordinates of the electrodes related to the bregma were: A 2.0, L 3.5; A 6.0, L 4.0. The ground electrode was placed above the cerebellum. Experiments were performed after a recovery period of at least 2 weeks. Experiment I Spontaneous sleep was prevented by swinging the experimental housing: the rats were placed in a box with heated bottom to prevent a cooling down of the rat and a ventilator contributed to even mixing of the sevoflurane in the box. The box was placed on a swing that moved with a period of 40 s and an angle deviation of 20 degrees (both directions). The swinging prevented spontaneous sleep enabling the measurement of the transition from the awake state to the anaesthetic state. Sevoflurane was delivered to the box by a mixed gas flow of 300 mL min1 oxygen and 900 mL min1 air, passing through a sevoflurane vaporizer. Four sevoflurane concentrations (manually adjusted with the vaporizer) were delivered to the box: 0.0% (at least 10 min), 3.0% (10 min), 5.5% (10 min), 8.0% (15 min) and finally again 0.0% until awakening of the rat and thereafter at least 15 min more. Prior to the start of the experiments, the sevoflurane concentration as a function of time (without rat), was measured three times in separate experiments (Mass
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Spectrometer: QP 9000; CaSE Scientific Instruments, Biggin Hill, England). The mean of these three measurements was taken as the reference sevoflurane curve in all experiments. During the experiments the rats were isolated in the box and a video camera allowed observation of the rat’s behaviour with the observer in another room. The vaporizer delivering sevoflurane was placed outside the box enabling adjustments without disturbing the rat. Rats were individually exposed to varying sevoflurane concentrations, as described above, such that the level of vigilance of the rats changed from awake to deep anaesthesia and vice versa. During this forced awake-anaesthesia-awake sequence the EEG of the rat was continuously recorded and afterwards the CD and BSR of the EEG were calculated and related to the applied sevoflurane concentration. The assumption was made that anaesthetic depth was related to the sevoflurane concentration, without knowing the exact relationship.
Experiment II There was an additional resting period of at least 2 weeks between the two experiments. Just before the start of the second experiment the rat was prepared for the measurement of the noxious induced withdrawal response (NIWR) as described in [28]. In short: the animals were anaesthetized with sevoflurane and supplied with a right carotid arterial line, jugular vein infusion line (Ringers/glucose, 2 mL h1) and trachea cannula. The right hind paw was mounted in a shoe that contained two electrodes allowing transcutaneous bipolar stimulation (Grass stimulator S11; Astro-Med Industrial Park, West Warwick, USA). The noxious stimulus consisted of a 500 ms pulse train duration, 4 ms pulse width, 100 Hz pulse frequency and 7.5 mA pulse amplitude and a repetition rate of 0.75 min1 (i.e. every 80 s a stimulus train). The hind paw was connected to a force– displacement transducer (TB-611T; Nihon Kohden Corporation, Japan). The force–displacement transducer allows the measurement of the force of the withdrawal response to the electrical stimulus, expressed in g (force). At the start of the experiment the administered sevoflurane concentration to the rat was maintained at 4% to assure a sufficient level of anaesthesia for the toleration of the lines and the trachea cannula. By changing the amount of administered sevoflurane to the rat the level of anaesthesia was regulated (manually) in such a way that NIWR varied several times between 0 and 125 g. The total recording time for each experiment was approximately 3 h. EEG recording and analysis The EEG and NIWR (force) were continuously recorded. The raw signal was filtered between 1 and
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
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100 Hz (elliptic filter, order 7), digitized at a rate of 256 Hz (sampling interval t 3.9 ms) and stored to disk for ‘off-line’ analysis. For calculating the BSR, suppression periods were defined as follows: as soon as EEG amplitudes within the next period of minimal 0.3 s remain below the threshold amplitude value, the start of a suppression period is detected, i.e. transition from burst to suppression mode. The suppression period is extended as long as amplitudes remain below the threshold value. The position where the amplitude for the first time rose above this threshold defined the end of the suppression period, i.e. transition from suppression to burst mode. The threshold values were manually estimated for each of the eight rats individually and were 0.2 or 0.3 mV. The threshold values were chosen such that after visual examination all or almost all parts with ‘silence EEG’ were allocated as suppression parts. The ratio of the total duration of the suppression parts and the time length of the total observed EEG fragment that was needed to acquire a 64s non-suppression EEG epoch (by concatenating the single burst sub-segments) defined the BSR. The CD of the EEG of the rat was computed for epochs of 64s and repeated every 8s, thus with a 7/8 overlap with previous estimate. The CD was computed following the Grassberger/Procaccia/Takens algorithm [10,11] with alterations to maximize the sensitivity to anaesthetic effects [27]. Attractor reconstruction was performed with 16 384 samples, embedding dimension 20, delay time t t 7.8 ms, and 1 s Theiler correction [29]. To speed up computation time, the correlation integral C(r) was estimated using a subset of the available attractor point distances using P 3, and S 4. More details can be found in [27]. An effective dimension CD was extracted from C(r) at an intermediate region (rb, re), defined by: log C(rb) 2.9 and log C(re) 1.2 as described in the same reference. Since the BSP was highly non-stationary, the suppression periods were omitted in the calculation of CD. During BSPs the number of EEG-samples was maintained at 16 384 by increasing the epoch length. Transitions from burst epochs to suppression epochs and vice versa, i.e. when passing the threshold value, were avoided within the time span of the reconstruction vectors. Skinner and Molnar used a similar technique for enhancing their dimensional algorithms by concatenation of short epochs of EEG data [30].
Pharmacokinetic/dynamic analysis A first order model, as introduced by Sheiner and colleagues. (Equation 1), was used to describe the relation between inspiratory concentration and effectcompartment concentration [31]. The relation between
effect compartment sevoflurane concentration and effect (i.e. BSR or CD) was described by the Hill equation [32], Equation 2: dCeff (Cin Ceff ) ke 0 dt
(1)
Cg E Ebegin (Eend Ebegin ) g eff g C50 Ceff
(2)
Ceff concentration in the effect compartment, Cin inspiratory concentration of sevoflurane, and ke0 rate constant determining the transport delay between the effector and the central compartment and vice versa. Ebegin baseline value of the variable at awake condition, Eend end value at infinite sevoflurane concentration, C50 concentration associated with 50% of the maximum change in the value of the variable, g steepness factor determining the slope of the concentration–response relation. The parameters were determined for each rat individually. The parameters were optimized using the Solver tool within Excel (Microsoft, Redmond, WA) using nonlinear regression with least-squares (Prism 4.01 for Windows, GraphPad Software Inc., San Diego, CA, USA). The total model, (Equation 1 combined with Equation 2) was used to determine the relation between sevoflurane concentration and CD. The resulting effectcompartment concentrations (Ceff) were utilized to determine the relation between sevoflurane concentration and BSR with Equation 2.
Results Experiment I The BSR and CD of the EEG of all eight subjects are displayed in Figure 2. At time point zero the delivery of the sevoflurane was started. All subjects show a decrement of CD in response to the increased sevoflurane concentration. When the sevoflurane concentration in the box decreases, CD increases and returns to its baseline values. Some peaks emerged in the CD curve some minutes after the start of sevoflurane delivery. These increments coincided with an excitation period in the behaviour of the animals, characterized by attempts of the rats to stand up and by ataxic walking. The awakening of the rats approximately 25 min after stopping the sevoflurane coincides in most cases with a sudden return of CD to baseline values. The BSR starts to increase at the higher sevoflurane concentrations and reaches its maximum at the highest sevoflurane concentration. During wash out of the sevoflurane, BSR decreases towards zero. In awake conditions no BSPs is supposed
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
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Figure 2. Results of CD (䊊) and BSR ( ) as a function of time of all eight subjects. At time point zero the delivery of the sevoflurane was started. At time point 35 min, the delivery of sevoflurane was stopped.
to be present in the EEG and therefore BSR should be zero. The BSR results higher than zero at awake conditions of the rat are therefore ascribed to methodological artifacts in the BSR algorithm (EEG-patterns during awake conditions were confused with burstsuppression patterns). The pharmacokinetic/dynamic parameters were determined for each rat individually. While fitting the model to the data, the periods of behavioural excitation at the start of the sevoflurane delivery were omitted. One rat (rat 3, see Fig. 3 bottom) was excluded because the fit did not converge. The means of the estimated parameters are given in Table 1. Plots of BSR and CD vs. the inspired sevoflurane concentration are presented in the left top panel of Figure 3. Variation of CD and BSR during the induction and wash-out of sevoflurane takes place at different sevoflurane concentration ranges. This hysteresis is eliminated by the introduction of a rate constant ke0 (see Table 1), describing the delay due to the sevoflurane transport from the lungs to the brain and vice versa. In experiment II, Ceff was estimated with the rate constant values ke0 as determined for each rat individually in experiment I. Plots of the BSR and the CD of all subjects vs. the effective sevoflurane concentration are presented in Figure 6 (solid lines). The Hill equation describes the relation between the BSR or CD and effect-compartment concentration Ceff [32], see Equation 2. In Figure 6 the average values and fits are plotted. In order to combine the results of all the rats in one plot, the BSR and CD
values were per animal pooled over 0.1 divisions on a logarithmic sevoflurane concentration scale and averaged over rats. The absolute value of the BSR varied between 0 and 0.9 and that of the CD varied between 9 and 4 for the lowest and highest administered sevoflurane concentrations, respectively. The C50, determining the concentration associated with 50% of the effect, was nearly a factor 3 higher for the BSR than for the CD. The steepness factor, determining the slope of the concentration-response relation was higher for the BSR than for the CD.
Experiment II Figure 4, a typical example of a time tracing of one rat, shows the reactions of the variables NIWR, CD and BSR in response to an increase or decrease of the inspired sevoflurane concentration. With an increase of the concentration, a decrease of the NIWR is observed and vice versa. A correlation between CD, BSR and NIWR is demonstrated by the coincidence of a decrease of CD and an increase of BSR and NIWR and vice versa. Figure 5 (left panel) shows the dose-response curves of NIWR, CD and BSR vs. Ceff. Averaged results of the eight rats (for each variable) were obtained per 0.2 division on a logarithmic sevoflurane concentration scale. Ceff must be higher than approximately 2.5% to maintain a sufficient level of anaesthesia during the NIWR measurements. If Ceff increases beyond 4.5% NIWR reaches its measurable minimum.
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
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At this percentage sevoflurane: however, the results of CD and BSR suggest that these variables did not yet reach their measurable endpoint. The start value of CD around 6 (the rat is already in an anaesthetic
condition) is conceivable as experiment I revealed values of approximately 9 for CD in an awake condition. A Hill equation [32], see Equation 2, describes the relation between CD, BSR, NIWR and Ceff. Table 1 BSR
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Figure 3. Relation between both CD ( ), BSR (-----), and inspired sevoflurane concentrations (top-left subplot) or estimated effect-compartment sevoflurane concentrations (top-right subplot) as obtained by the Sheiner algorithm [31]. Time course is indicated by arrows. The bottom figure shows estimated effect-compartment sevoflurane concentrations for all subjects. Table 1. Averaged results (eight subjects) of the pharmacodynamic parameters that describe the relation between NIWR, CD, BSR and the effect-compartment concentration Ceff, see Equation 2. The parameters of the CD and the BSR in the absence (experiment I) and those in the presence of the noxious stimuli eliciting the NIWR are given. CD mean (95% CI)
Ebegin Eend C50 (%) g
NIWR mean (95% CI) (g)
Without noxious stimuli
190 (constant) 0.0 (constant) 2.13 (1.92/2.37) 3.11 (3.92/2.31)
9.5 (9.2/9.8) 4.0 (3.5/ 4.5) 0.61 (0.51/0.73) 1.73 (2.23/1.23)
BSR mean (95% CI) In presence of noxious stimuli
Without noxious stimuli
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2.18 (2.04/2.34)* 4.15 (5.20/3.09)*
0.0 (constant) 0.91 (0.87/0.96) 1.73 (1.69/1.78) 5.36 (4.38/6.35)
3.07 (3.00/3.15)* 5.20 (4.38/6.02)
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Significant differences from the value in the absence of the stimuli. In the fit procedure for the estimation of the parameters describing the CD, the Ebegin and Eend values were shared. For the BSR the begin value was fixed to zero, the end value was shared in the fit and g was not significantly different between the two conditions.
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
Correlation dimension and anaesthesia shows the averaged results of the estimated pharmacodynamic parameters. Since no baseline values of the awake situation were available in experiment II, for the NIWR the Ebegin was extrapolated to be 190 g. For the determination of the Ebegin of the CD the data of experiment I were included in the fit procedure,
constrained such that the Ebegin values were shared. The baseline value for the BSR was assumed to be zero and the top values of the first and the second experiment were shared in the fit procedure. In Table 1 the estimates of both experiments are given. Figure 5 (right panel) shows the effect-response curves of CD and BSR vs. NIWR. For a complete visualization of the dependencies between all the variables Ceff is also included in the figure. Averaged results of the eight rats (for each variable) were obtained for every NIWR-subsection of 10 g. Regression lines through the curves of CD (correlation coefficient r 0.46; P 0.001) and BSR (r 0.66; P 0.001) show their relation to NIWR. The results of experiment I (without NIWR) and the second experiment (with NIWR) are combined in one figure (Fig. 6). Examining the results of both experiments at the same sevoflurane concentrations, one can observe that the CD is increased and the BSR is decreased when noxious stimuli were applied.
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Discussion Anaesthesia has been defined as a process of modification of the normal physiological reflex stimuli (provided by surgery), and includes consciousness, analgesia, reflex suppression and muscle relaxation
NIWR (g)
Figure 4. Typical example of the responses of NIWR (top), CD (3rd curve from below) and BSR (bottom) to changes in the administered sevoflurane concentrations (2nd curve from below) to the rat. 80
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Figure 5. Dose-response relationship (left) between NIWR (䉭), CD (䊊), BSR (䊐), and Ceff and effect-response relationship (right) between Ceff (䉱) CD (䊊), BSR (䊐) and NIWR. Error bars represent SEM values.
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
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Figure 6. Relation between CD (left plot), BSR (right plot) and effect-compartment sevoflurane concentration restricted to the non-excited behaviour. The figure displays the combined results of seven subjects. Values were pooled per 0.1 division on a logarithmic sevoflurane concentration scale. Error bars represent SEM values. The accompanying pharmacokinetic/dynamic parameters are displayed in Table 1.
[33]. In the present study, the force of withdrawal
reflexes, elicited by noxious stimulation of the hind paw of a rat (NIWR) and suppressed by sevoflurane, was taken as the measure for depth of anaesthesia [28]. Both CD and BSR correlate with this measure for depth. In the first experiment sevoflurane was fed into a chamber in which rats were allowed to freely move. Higher sevoflurane concentrations may have depressed spontaneous breathing probably resulting in an accumulation of carbon dioxide, which may have had an effect on EEG. In addition, cardiovascular depression may have also been occurred changing cerebral blood flow, metabolism and EEG. In the second experiment we did monitor a number of physiological variables: apart from the EEG and the NIWR we also monitored haemodynamic variables; HR, BP and CO2 concentration. The animals were artificially ventilated with a frequency of 70 min1. With this artificial ventilation, the changes in the named variables were indeed minor: starting at 5% sevoflurane, the HR, with a start value of 350 bpm declined with 6 bpm per % sevoflurane; BP, with mean arterial pressure of 160 mmHg, declined with 10 mmHg per % sevoflurane and expired CO2, with a basal concentration of 6.6%, increased with 0.1% per % sevoflurane, see Table 2. The EEG is a complex measure; it is determined by many factors and we are at present unable to attribute every physiological variable to the relation between the EEG and anaesthesia. The NIWR measurement resembles a somatic motor response of a patient in clinical conditions to a standardized surgical stimulus such as an incision. A motor response has served earlier as the pharmacodynamic endpoint e.g., in the study of total intravenous anaesthesia in humans [34,35]. The
Table 2. Anaesthetic effect on haemodynamic variables. Apart from the EEG and the NIWR were also monitored; HR, BP and CO2 concentration. The animals were artificial ventilated with a frequency of 70 min1. Change/ % sevoflurane HR (min1) BP diastolic (mmHg) BP systolic (mmHg) BP mean (mmHg) Maximal expired CO2 (%) Breathing frequency (min1)
351 5 108 6 186 6 159 7 6.6 0.3 Artificial 70
6 6 10 8 0.1 0.1 Constant
NIWR measures in graded terms the motor responses to sevoflurane. We consider this graded response as a suitable variable that reveals at least certain aspects of depth of anaesthesia [28]. Indeed this type of elicitation of reflexes is used in clinical practice to estimate adequacy of anaesthesia [36]. One can argue about using a force transducer or using Electromyogram (EMG), given that one of the elements of anaesthesia is muscle relaxation, and both disappear with a muscle relaxant drug. In practice, force as an indicator for anaesthetic depth in the combination with muscle relaxation is not applicable. Here, the NIWR is just used as a reference measure of anaesthetic depth. The precise mechanisms of the effect of muscle relaxants on depth of anaesthesia is not completely solved, however, it is clear that both elements (anaesthetics and muscle relaxants) of anaesthesia do affect each other. During muscle relaxation the input to the CNS via the gammamotor system is decreased and thus is there less arousal and anaesthesia is therefore presumably deeper. During deeper anaesthesia the basic tonus of the muscles is
© 2006 Copyright European Society of Anaesthesiology, European Journal of Anaesthesiology 23: 391–402
Correlation dimension and anaesthesia lower and therefore the effect of the muscle relaxants is reduced. It is to be expected that anaesthetics, and especially the inhalation anaesthetics, besides these mentioned central effects also have a direct effect on the muscle and will decrease muscle contraction force. Both effects are described in the literature. It, therefore, is likely that both contraction force and EMG are affected by anaesthesia. Investigators, also in our institution, have found differences between EMG and force displacement when investigating muscle relaxants and have demonstrated a dose and drug related (degree different amongst different anaesthetics and different concentrations) effect of anaesthesia on the effect of muscle relaxants. Eliminating the periods of ‘EEG-silence’ is open to discussion. Perhaps, criticism focuses on some valuable information not being used. From a technical point of view, however, in the CD calculation process the EEG-silence behaves like noise. An explanation for this could be the strong reduction in EEG signal power during a period of ‘EEG-silence’, and hence a very poor signal to noise ratio. Since the analysis should focus on signal and not on noise or noise-like signals, the ‘EEG-silence’ parts were excluded from the analysis. The consequence of this procedure is the neglect of a substantial amount of data, especially during high BSR-levels. More time is then needed in order to collect enough data for the calculation of CD. This is disadvantageous to the time resolution of CD, however, at the same time the ‘EEG-silence’ as reflected in the BSR informs about anaesthetic depth. It very well illustrates how multiple variables above a single variable can improve results. The reason for evaluating the relationship between BSR and anaesthetic depth is the fact that this information by the special design – elimination of ‘EEGsilence’ for reasons of artifact – routinely became available. It also explains the slightly modified definition of BSR. Instead of calculating BSR for fixed epochs, the epochs varied with the amount of suppressed EEG present. Since CD and BSR are then calculated using the same EEG epochs, comparisons are easily made. The only consequence of the modified BSR definition is results being sampled at nonequidistant intervals and decreased time resolution (averaging in time). In experiment I, the relation was investigated between sevoflurane concentration and the EEG variables BSR and CD. Due to the setup of the experiment with the aim to measure transitions from awake to sleep, and vice versa, end-tidal sevoflurane concentrations could not be measured. Animals were allowed to breathe freely and therefore the concentration in the effect compartment (Ceff) was estimated using the inspiratory sevoflurane concentrations (see Equations 1, 2).
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The induction of sevoflurane induced a period of excitatory behaviour. Coinciding with these periods increased values of the CD were observed. This increased CD seems reasonable since the rat becomes more active. Due to the inserted EEG electrodes (the tips of the electrodes are on the dura), this increase is not attributed to EMG activity. Excitation is also seen in the clinic, when sevoflurane is administered to the patient with slowly increasing concentrations [37]. During the awakening phase, however, when sevoflurane concentrations decrease and no excitatory behaviour was observed, no temporary increased CD values were found. These observations indicate that the CD of the EEG is not only related to Ceff, but also to the brain state. In experiment II we explored this latter relationship; clear relations between CD and BSR with sevoflurane concentration (Ceff) were demonstrated. These relations were confirmed by the observation that forward and reverse trajectories (falling asleep and awakening) overlapped and that BSR and the CD returned to baseline levels at the end of each experiment. The BSR is a simple linear measure that can be implemented easily. However, the relation between BSR and Ceff, was restricted to high sevoflurane concentrations, thus most likely to periods of deep anaesthesia, while the greatest changes in the value of the CD were observed at low sevoflurane concentrations; thus presumably in the transition periods between light and deep anaesthesia. In the clinic instantaneous information about the depth of anaesthesia is needed precisely during these transition periods and during periods of light anaesthesia. At these periods information is needed for controlling purposes. The concentration–response relations of the CD and BSR with sevoflurane were markedly different between experiment I (no stimulation), and experiment II (with stimulation); higher concentrations of sevoflurane correspond to the same CD and BSR when stimuli are present. If the rat is stimulated, it is conceivable that the level of vigilance increases as painful stimuli arouse the rat. The differences in the results (shifted curves) between experiment I (without NIWR) and experiment II (with NIWR) show that the effects of this arousal on the rat are indeed reflected in CD and BSR. This result is an extra indication that CD and BSR are related to depth of anaesthesia. The administration of stimuli in experiment II induced a shift of concentration–response curve to higher concentrations (both BSR and CD). However, for CD not only the magnitude of responses to various concentrations of sevoflurane was markedly different between the experiments in which noxious stimuli were absent or present, but also the concentrationresponse relationships were not parallel. This finding
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has a direct implication for clinical methods that intend using the CD for steering purposes, because the presence of parallel dose–response relationships is imperative when one wishes to compare potencies based on a dose-requirement response in other conditions. In other words, both experiments very well illustrate that dose-based depth of anaesthesia steering is hazardous and confirms that it should be based on variables that reflect the patient’s anaesthetic condition. The application of the non-linear approach to EEG signals considers the EEG to be the output of a deterministic system of relatively simple complexity, but containing non-linearities. This presumption became a single point of interest: is there evidence for the assumption that an EEG signal originates from a deterministic non-linear dynamical system? At present in literature different methods or tests are proposed to give an answer to the non-linearity or determinism question [38,39]. None of these methods were applied here. Kugiumtzis suggests that these tests should be performed numerous times for different parameter combinations, which hinders a practical implementation [40]. Nevertheless, the authors struggled with the question of what is exactly the meaning of the CD results. Although we know that a single neuron in the brain is highly non-linear, this does not imply that the averaged measured neuronal activity at the cortex, i.e. the EEG expresses itself as such to the ‘outside world’. On the other hand, regardless of the outcome of the non-linearity/determinism tests (i.e. the signal is Gaussian or not), the observed relationship between sevoflurane concentrations and CD remains identical. Even if the signal is Gaussian it is still unclear how to obtain the same information from the power spectrum. Therefore, the correlation integral derived statistic CD is regarded as an operational measure strongly related to complexity, just as proposed for D* by Widman and colleagues [14]. The absolute value of the CD varied between 9 and 4. Comparison of absolute values of dimension results among different studies is cumbersome due to the different defined dimensions and due to the large dependency of algorithm parameter settings. Therefore we suggest considering the relative change of CD as a response to the administered anaesthetic. We conclude that CD and BSR can be useful for monitoring depth of anaesthesia. However, CD can be measured from awake vigilance levels to deep levels of anaesthesia where BSR can only be measured starting at the deeper levels of anaesthesia. The monitoring of depth is a very complex matter [1,41]. The present study confirms the previous signs of the potency of the CD to inform us about depth of anaesthesia [12,14] and demonstrates that CD is an extra tool that can be utilized for this purpose. Further study is advised to investigate the role of CD as a possible
predictor of patient movement. At present, Bispectral index (BIS) is widely accepted as a new depthmonitoring variable despite its shortcomings [42–50]. The occasional failures of BIS emphasize the complexity of the assessment of depth of anaesthesia. Therefore, the search for new variables to inform us about depth must be prolonged. This becomes even more evident by the potential enhancements that can be achieved with the multi-methodological approach. At present, some research groups already combine several EEG variables each of which may have some utility in tracking depth of anaesthesia [16–19,51]. Our results support this approach. Both CD and BSR can be added to the list of variables that are capable of providing useful information. A relevant novelty of the utilized CD algorithm is the feasibility of real-time calculation of several EEG channels simultaneously. It remains a challenge to combine the information of these variables into an index that optimally informs the anaesthesiologist about depth of anaesthesia.
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