BJA Advance Access originally published online on June 24, 2005
British Journal of Anaesthesia 2005 95(2):197-206; doi:10.1093/bja/aei113
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NEUROSCIENCES AND NEUROANAESTHESIA |
Concurrent recording of AEP, SSEP and EEG parameters during anaesthesia: a factor analysis
1 Department of Anaesthesiology, Universität Erlangen-Nürnberg, Germany. 2 Department of Anaesthesiology, Technische Universität München, Germany. 3 Department of Anaesthesiology, Universität München, Germany. 4 Department of Information Technology, Universität Duisburg-Essen, Germany. 5 Department of Medical Psychology, Universität München, Germany
* Corresponding author. Klinik für Anästhesiologie, Krankenhausstraße 12, D-91054 Erlangen, Germany. E-mail: schwilden{at}kfa.imed.uni-erlangen.de
Accepted for publication December 22, 2004.
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Abstract |
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Background. Spontaneous EEG, mid-latency auditory evoked potentials (AEP) and somatosensory evoked potentials (SSEP) have been used to monitor anaesthesia. This poses the question as to whether or not EEG, AEP and SSEP vary in parallel with varying conditions during surgical anaesthesia.
Methods. A total of 81 variables (31 EEG, 22 SSEP, 28 AEP) were simultaneously recorded in 48 surgical patients during anaesthesia. A total of 307 cases of the 81 variables in stable anaesthetic states were recorded. A factor analysis was performed for this data set.
Results. Sixteen variables were excluded because of multicollinearity. We extracted 13 factors with eigenvalues >1, representing 78.3% of the total variance, from the remaining 65 x 307 matrix. The first three factors represented 12%, 11% and 10% of the total variance. Factor 1 had only significant loadings from EEG variables, factor 2 only significant loadings from AEP variables and factor 3 only significant loadings from SSEP variables.
Conclusion. EEG, AEP and SSEP measure different aspects of neural processing during anaesthesia. This gives rise to the hypothesis that simultaneous monitoring of these quantities may give additional information compared with the monitoring of each quantity alone.
Keywords: factor analysis; monitoring, auditory evoked potentials; monitoring, EEG; monitoring, somatosensory evoked potentials
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Introduction |
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General anaesthesia may be understood as the deliberate induction and maintenance of reversible unconsciousness and painlessness. Anaesthetics are able to produce dose- dependent suppression of cognitive processing. The use of neuromuscular blocking agents and the side effects of the anaesthetics themselves on the cardiovascular system may suppress clinical signs of inadequate anaesthesia,1 such as spontaneous movement or increase of blood pressure with surgical stimulation. Therefore methods for the reliable detection of states of inadequate anaesthesia are highly desirable and have been described for a variety of effects such as lowered oesophageal contractility,2 heart rate variability3 and various other electrophysiological methods related to the electroencephalogram (EEG).
During the past decade it has become evident that anaesthesia can be caused by different mechanisms4 5 and that the anaesthetic state itself should be described in a multi- dimensional rather than one-dimensional state-space.6 Monitoring the anaesthetic effect by a number between 0 and 100 has the attraction of being simple but it may be too simplistic. Within the framework of electrophysiological approaches, electrical brain activity such as spontaneous EEG, auditory evoked potentials (AEP)7 8 or somatosensory evoked potentials (SSEP)9 10 have been advocated for the monitoring of anaesthesia. Monitoring derivations of the spontaneous EEG have the longest tradition.11 12 This poses the question of whether the addition of descriptors of AEP and SSEP to this monitoring procedure adds substantial information to the monitoring of the anaesthetic effect by the spontaneous EEG alone.
The aim of this study was to perform a factor analysis for a number of derivations taken from the spontaneous EEG, AEP and SSEP under surgical conditions in anaesthetized patients and to determine whether, and to what degree, AEP and SSEP variables make a relevant contribution to the loadings of the extracted factors.
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Methods |
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This multi-centre study was performed in three university departments of anaesthesia. After approval by the appropriate ethics committees and following informed written consent, 59 adult patients scheduled for elective surgery under general anaesthesia were enrolled in this prospective study. Patients with ASA >II, indication for rapid sequence induction, pregnancy, recent administration of drugs affecting the central nervous system and psychiatric or neurological diseases were excluded from the study. Patients scheduled for intracranial neurosurgery or heart surgery were also excluded.
Anaesthetic procedure
The anaesthetic procedure was left to the discretion of the attending anaesthetist and performed according to the daily clinical practice of the institution. In all cases, the following procedures were undertaken. An intravenous cannula was placed and infusion of lactated Ringer's solution started prior to administration of anaesthesia. After preoxygenation via a facemask, opioid was administered and anaesthesia was induced with either propofol or thiopental; muscle relaxation was achieved with atracurium. The trachea was intubated and the lungs were ventilated mechanically to maintain normocapnia with a mixture of oxygen in air appropriate to maintain normoxaemia. Drug dosing was maintained according to clinical observation of the patient. Repetitive doses of opioid were administered whenever inadequate analgesia was assumed. The administration of propofol or volatile anaesthetics was increased in the case of undesired patient movements. No further doses of muscle relaxants were administered after induction. At the end of surgery, anaesthetic agents were discontinued. When the patient regained apparent consciousness, the endotracheal tube was removed, the monitors were disconnected and the patient was transferred to the postanaesthesia care unit.
Signal acquisition and data selection
A specially adapted four-channel electrophysiological recording system (Neuroscreen, Viasys Healthcare, Hoechberg, Germany; EEG ‘Infinity POD’, Siemens, Erlangen, Germany) was used for signal acquisition. Before placement of Ag/AgCl EEG electrodes at F1, F2, C3', M2, Fz (reference) and Fp1 (ground) (electrode positions according to the international 10–20 system), the skin was prepared with alcohol to keep impedances <5 k
. The raw signal was digitized at a rate of 4 kHz per channel and stored on hard disk. SSEP stimuli were applied to the right median nerve via an electrode on the right wrist. The appropriate stimulus site and threshold were determined before induction of anaesthesia. Stimulus intensity was chosen 20% above threshold for motor twitch, and stimuli of duration 100 µs were applied with a frequency between 3 and 3.098 Hz. AEP stimulation used rarefraction clicks with a duration of 100 µs, 90 dB (SPL) and a repetition rate of 9.3 Hz, which were presented binaurally via shielded earphones (Viasys Healthcare, Hoechberg, Germany). Each AEP epoch consisted of 1000 stimuli, and each SSEP epoch consisted of 306 stimuli. EEG (i.e. no stimulus), AEP and SSEP stimuli were sequentially applied and evenly distributed. Each modality was measured for 1.7 min. In each patient, the order of stimulus modalities was randomly chosen for nine intervals, and these intervals were constantly repeated during anaesthesia.
We extracted 31 variables from the spontaneous EEG, 22 from the SSEP and 28 from the AEP for factor analysis. A detailed description of all variables is given in the Appendix. Ideally, the spontaneous EEG, SSEP and AEP should be measured simultaneously. As this is not possible, we defined parameter triplets as tightened values of variables from the spontaneous EEG, SSEP and AEP if the following criteria were satisfied: (i) the epoch proved to be artifact free on application of an artificial neuronal net for EEG artifact recognition, (ii) the epochs were recorded in close temporal succession and (iii) the clinical state of anaesthetic depth was constant within the epochs. Therefore no bolus doses of anaesthetic were given for up to 2.5 min before the period, constant anaesthetic infusions or concentrations of volatile anaesthetics were maintained for at least 2.5 min before the period, no prominent surgical stimuli were applied and patients were haemodynamically stable. Thus a parameter triplet is a collection of 81 parameters recorded during such a period (stable anaesthetic period) consisting of 31 parameters from the EEG, 22 from the SSEP and 28 from the AEP.
Factor analysis
Before extraction of the principal factors, the data matrix was screened for the presence of outliers, absence of multicollinearity and factorability of the correlation matrices. The criterion for multivariate outliers was a Mahalanobis distance at P<0.001, evaluated as 
2 with the number of degrees of freedom equal to the number of variables,13 i.e. 81 for this investigation. Multicollinearity and singularity in the data matrix were identified by computing the squared multiple correlations (SMCs) for the variables, where each variable serves as the dependent variable, with the remaining variables as independent variables, in a multiple correlation. Variables with SMCs >0.99 were excluded from further analysis. Factorability of the correlation matrix was considered if there were several correlations >0.30.
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Results |
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Thirty-six of the 59 patients received midazolam as premedication; the remaining patients did not receive any drugs prior to induction of anaesthesia. Twenty-five patients received total intravenous anaesthesia and 34 patients received balanced anaesthesia with a combination of an opioid and a volatile anaesthetic agent. More than 90% of the patients underwent general or orthopaedic surgery, with 20% of patients undergoing abdominal surgery. Figure 1 gives a synopsis of the original signals (AEP, EEG, SSEP) for a representative patient at various clinical stages.
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Approximately 80% of the variance of the original 81 variables from the AEP, SSEP and EEG could be represented by only 13 factors. The first three factors together represented up to 33% of the total variance. Each of these three factors has significant contributions only from variables of the EEG (factor 1), the AEP (factor 2) or the SSEP (factor 3) and insignificant contributions from the other variables. As the factors are independent of each other by construction, their correlation coefficient is zero. Hence the correlation between each pair of factors is zero, indicating that, to a first approximation, the EEG, the AEP and the SSEP vary independently of each other.
Detailed factor analysis results
A total of 377 parameter triplets during stable anaesthesia periods were recorded for 48 of the 59 patients enrolled in the study. Seventy of the 377 parameter triplets were identified as multivariate outliers at a cut-off level of 
=0.001. These cases were deleted before extraction of the principal factors. Sixteen of the 81 variables were identified as multicollinear at a tolerance level of 0.01 (1-SMC) and were excluded from further analysis (Table 1).
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Extraction of principal factors with varimax rotation was performed using SPSS FACTOR (Version 11.5.1, SPSS Inc., Chicago, IL) on 65 variables for a sample of 307 cases. Thirteen factors with eigenvalues >1, which were internally consistent and well defined by the variables (the lowest of the SMCs for factors from variables was 0.90, where factors serve as dependent variables and variables as independent variables), were extracted. The scree output for factor extraction together with cumulative proportions of variance explained by the rotated factors are presented in Figure 2. The rotated factors account for almost 80% (78.3%) of variance in the data set. Six factors, representing 34.5% of the total variance, had their main loadings from EEG variables, four factors, representing 28.6% of the total variance, had loadings from AEP variables and three factors, representing 15.2% of total variance, were related to SSEP variables. The reverse, i.e. a high proportion of variance in variables that is predictable from the factors underlying them, was also true for this factor solution. Final estimates of communality values (Fig. 3) achieve 0.78 on average. Only 4% of the residual correlation matrix showed values >0.05 and suggest poor probability for the presence of another factor.
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With a cut for factor loadings of 0.45 for inclusion of a variable (corresponding to an overlapping variance of 0.2) all of the 65 variables load on factors. Sixteen of the variables load on two factors. Table 2 shows the variables of the 13 extracted factors having loadings >0.45.
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Discussion |
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In applying factor analysis to the given data set it should be borne in mind that there might be intrinsic non-linear relations among variables which make them appear as independent even though they are entirely dependent on each other. However, this caveat applies to many other situations where linear methods are applied to non-linear phenomena. For our data set we have two apparent dependences: the total power of the power spectrum (i.e. the sum of variables V11,...,V17) is proportional to the mean square amplitude, and the relative power (i.e. the sum of variables V18,...,V24) is equal to unity. Both relations are well handled by the test for multicollinearity although the first relation is not a linear restriction. The multicollinearity test successfully removed variables V2 and V3, which are measures of mean amplitude from the analysis, thus resolving the first restriction, and also removed variable V18 (the relative power between 0.5 and 2 Hz), thus resolving the second restriction.
As shown in Table 2, the extracted principal factors are mainly determined by subsets of variables calculated from different EEG recordings: six factors by spontaneous EEG variables, four factors by AEP variables and three factors by SSEP variables. None of the variables included in the factor interpretation overlapped on factors determined by variables of different sets. The first four extracted principal factors are determined by unique subsets of variables calculated from spontaneous or evoked EEGs and account for 42.4% of the variance in the data set in almost equal proportions (approximately 10% each). Taking into consideration the fact that the extracted principal factors are linearly independent of each other (orthogonality for vectors of factor loadings) and assuming the absence of a non-linear relationship between variables loading on at least the first four principal factors, we can assume that information extracted in each case from spontaneous and evoked EEGs represents different underlying processes.
The subset of spontaneous EEG variables which load on factor 1 is mainly engaged by power spectrum and entropy measures. The bicoherence variable Bic contributes only 3% to the total variance of this factor. As can be seen in the ordered variable sequence of Table 2, the naïve approximate entropy obtained using the Pincus algorithm, the 95th and 90th power quantiles and the relative power between 20 and 32 Hz load higher on this factor than on the rest (loadings >0.80 compared with loadings <0.70). Factors 5, 6 and 10 are mainly determined by different combinations of power spectrum measures from the spontaneous EEG. Factor 11 represents primarily the proportion of variance in the data set explained by the volume under the bispectrum (V29=BispV) which correlates positively with the skewness of amplitude histogram. This is plausible as the bispectrum is in essence the spectral decomposition of the skewness of the corresponding amplitude histogram. Factor 12 is loaded by the kurtosis of amplitude histogram, the EEG suppression ratio and the approximate entropy apEnt2. As the kurtosis of the amplitude histogram is related to the trispectrum, we can speculate that certain EEG patterns might cause a non-trivial trispectrum.
Without exemption, factor analysis separated the EEG variables discussed above from those derived from AEP and SSEP. Factor 2 is exclusively loaded by variables representing relative energies within level 5 of the wavelet decomposition. With high loadings (>0.7), in particular, the high and highest frequency contents load to this factor; the parameter representing a comparable low frequency band (V54=rL5P1) has the lowest factor loading (0.61).
Unlike factor 2, factor 4, although explaining a comparable amount of variance of all signals, is only loaded by variables representing absolute energies within the different levels of AEP wavelet decomposition. With one exception (V65=L5P0), the variables representing high and highest frequency contents load to this factor. Factor 7 is loaded both by variables of relative and absolute energies, representing a medium frequency band within the AEP. Factor 9, although only accounting for 
3% of overall variance, contains only variables of the last two frequency bands below the lowpass of the filtering, representing both relative and absolute energies, while those of absolute energies yield higher factor loadings. This suggests that the high frequency contents may be altered differently from the rest of the AEP components.
Surprisingly, the variables representing the lowest frequency contents reveal only low threshold (V54=rL5P1 with 0.61 onto factor 2) or even subthreshold loadings on the factors. As substantial alterations of the low frequency contents of the AEP during anaesthesia are already known,14 this might be an indicator that possible variance of the signal was grouped within this parameter, consequently not leading to an independent factor with considerable factor loadings of these variables.
The SSEP variables load onto two distinct factors. Factor 3 is the major factor of the SSEP. Variables representing the medium frequency range are loading highest onto the factor. The highest frequency components also have high loadings on the factor. As a broad frequency range is included, the level of wavelet decomposition does not play the most important role in this parameter. Variables from level 2 decomposition yield similar loadings to variables in the corresponding level 5 decomposition subtrees. Factor 8 is only loaded by variables from level 5 decomposition. The two lowest frequency bands load highest to the factor. Surprisingly, the parameter representing the highest frequency range not cut off by the filters (V75=L5P11) also loads onto this factor, but only with a low loading just above threshold.
One should be careful when discussing the results in the context of possible clinical implications. Our results do not suggest that we should use an artificial construct like factor 1 as a variable to monitor anaesthesia; its usefulness would have to be tested in an appropriate clinical setting. However, our results indicate that the search for the best unique evoked or spontaneous EEG parameter is a search for a chimera. There exist numerous studies comparing, for instance, variables of the spontaneous EEG with variables from mid-latency AEP,15 16 ranking their usefulness and suggesting the use of one or other parameter. Our data support the view that EEG, AEP and SSEP measure different aspects of neural processing during anaesthesia, giving rise to the hypothesis that the simultaneous monitoring of these quantities may provide additional information compared with the monitoring of each quantity alone.
In conclusion, factor analysis revealed that the variance of variables automatically extracted from EEG, AEP and SSEP during general anaesthesia cannot be projected onto a single dimension. For the chosen variables, a set of 13 factors best explains the observed variance up to 80% of the total variance of all variables. Interestingly, none of the new derivate factors combines information from AEP, SSEP and EEG. Therefore it might be speculated that each of the three methods represents a different aspect of the changes in electrophysiological action of the central nervous system produced by general anaesthesia.
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Appendix |
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EEG processing
The raw EEG signal, sampled at 4 kHz from acoustic or somatosensoric stimulus free periods, was first low-pass filtered with a finite impulse response (FIR) filter at 32 Hz (preserves phase information needed for bispectral analysis), downsampled to 125 Hz (reduction of redundant data) and subsequently high-pass filtered with an FIR filter at 0.5 Hz (Matlab Signal Processing Toolbox, Release 12.1, MathWorks Inc., Natick, MA). After automatic neural networks based artifact rejection,17 stationary EEG epochs of length 8.192 s length (210 data points) were selected using the non-parametric ‘run’ test18 and included in further analysis.
The 31 univariate EEG descriptors, calculated from each EEG epoch after DC shift subtraction, were as follows.
- From the sequence of voltages: mean, standard deviation, skewness, kurtosis, electroencephalographic suppression ratio, symbolic entropy,19 a parameter also known as approximate entropy,20 using the algorithm described by Pincus21 for complexity estimation of heart rate variability, and approximate entropy using the algorithm described by Kaplan et al.22 for complexity estimation of cardiovascular dynamics.
- From the power distribution between 0.5 and 32.0 Hz: the 25th, 50th, 75th, 90th and 95th quantiles, the spectral entropy23 and the absolute and relative power in the ranges 0.5–2.0 Hz, 2.0–4.0 Hz, 4.0–8.0 Hz, 8.0–13.0 Hz, 13.0–20.0 Hz, 20.0–26.0 Hz and 26.0–32.0 Hz (range from >x to
y).
- Between 0.5 and 32.0 Hz: the volume enclosed by the hyperplane of the bispectrum24 and the zero hyperplane, the magnitude of the volume enclosed by the hyperplane of the bispectrum and the zero hyperplane, and the volume enclosed by the hyperplane of the normalized bispectrum (bicoherence) and zero hyperplane.
In order to obtain robust electroencephalographic estimators, in the final processing step we averaged the calculated descriptors over the available, consecutive electroencephalographic epochs within defined stable anaesthesia periods.
Somatosensory evoked potential (preprocessing, signal extraction and artifact reduction)
One SSEP was extracted from each SSEP stimulus sequence. First, the EEG was filtered with a bandpass of 3–500 Hz (FIR filter with 125 coefficients) and the moving-average technique with seven samples was used to smooth the signal. SSEPs of 100 ms duration were generated from 306 single sweeps, i.e. EEG segments following the trigger. SSEPs without peaks N20 and P25, baseline drifts or signal shifts were excluded by visual inspection. These SSEPs underwent additional artifact filtering based on visual single-sweep analysis.
Auditory evoked potential (preprocessing, signal extraction and artifact reduction)
For extraction of the auditory evoked responses, EEG intervals of 100 ms duration were selected from the raw EEG and filtered with an FIR filter (bandpass 3–500 Hz), starting with the corresponding trigger information. Out of each stimulation block consisting of 1000 single sweeps, signals with amplitudes >90% of the full scale of the amplifier were rejected from further analysis. All other sweeps were averaged within the post-stimulus interval of 100 ms. Averages consisting of less than 500 single sweeps were excluded from further analysis. The resulting averaged auditory evoked responses were subjected to a visual inspection of the signal; averages containing gross artifacts were excluded. As the early auditory evoked potentials within a post-stimulus interval of up 10 ms can also be recorded during deep general anaesthesia, the major peak within these signals, labelled V according to the taxonomy of Picton et al.,25 was detectable in all resulting averages.
Generation of AEP and SSEP parameters based on wavelet analysis
The methodology used to provide parameters characterizing the SSEPs and AEPs comprised the following three steps.
- Obtaining a time–frequency characterization of extracted signals using wavelet packet decomposition (WPD), resulting in a binary tree of sets of wavelet coefficients (packets) (Fig. A1).
- Determination of the optimal subtree of WPD coefficients which characterize the analysed signals based on a generalized procedure of grouping the wavelet coefficients or determination of those packets of the last level which are located within the frequency band of the SSEP and AEP (bandpass 3–500 Hz).
- Computation of energy-based parameters.
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Wavelet packet decomposition
Wavelet transform provides a time–frequency-representation of a signal based on an analysis function called a wavelet, which shows a localization in the time and frequency domain. Shifted and dilated versions of this wavelet are used for transformation and provide different frequency resolutions at different locations in time. The orthogonal wavelet transformation,26 27 in the sense of a multiresolution analysis, splits a low frequency component of the signal into a high frequency component and its orthogonal complement, which contains low frequencies at the next level of decomposition. The decomposition is applied to the low frequency components at each level.
Wavelet packet transform can be understood as a generalization of the wavelet transform, such that high frequency components are also split. The iterative procedure results in a binary tree (Fig. A1).
Discrete wavelet analysis is performed by subsequently using filters approximating the wavelet function, also known as wavelet packet decomposition. The coefficients of each separated signal component are arranged in wavelet packets and assigned to a level in the binary tree according to the number of decomposition steps. The wavelet packets are related to disjoint frequency bands, whose width depends on the sampling frequency of the signal, the time and the frequency localization of the shifted and dilated version of the wavelet used. In the case of redundant WPDs, different subsets of packets can be chosen such that they give a complete representation of the signal.
Analysis of the evoked responses (AEP and SSEP) was performed using Matlab (MathWorks Inc., Natick, MA) and the affiliated Wavelet Toolbox. The averaged signals were decomposed up to level 5 by a wavelet package analysis using the Daubechies 4 wavelet.28
Selection of WPD coefficients
Two different selection procedures were used.
- Selection of those packets of the last level, which are located within the frequency band of the SSEP and AEP (bandpass 3500 Hz). Selected packets (level number, packet number) are (5,0), (5,1),..., (5,11).
- Selection of an optimal subtree of packets based on grouping WPD coefficients.
The aim of grouping is to find distinct groups of coefficients at each level of decomposition (and each packet). Each distinct group contains a number of coefficients, placed in successive positions, which have only either large or small absolute values. To discriminate between these two categories of coefficients, a statistical test is applied. Therefore each packet may contain one or more groups of coefficients. Packets with more than one group of coefficients (i.e. packets containing both large and small coefficients) are considered to contain more useful time–frequency information for characterizing the analysed signals.
After applying the clustering procedure separately, a combination of packets is selected using two variants. In the present study, the following subtrees were determined:
- SSEP signals
Variant 1: (5,0), (5,1), (4,1), (3,1), (2,1), (2,2), (2,3)
Variant 2: (5,0), (5,1), (5,2), . . ., (5,14), (5,15), (2,2), (2,3)
- AEP signals:
Variants 1 and 2: (5,0), (5,1), (5,2), (5,3), (4,2), (4,3), (2,1), (2,2), (2,3).
Computation of energy-based wavelet parameters
A number of meaningful parameters are selected for each signal analysed. Each packet consists of several coefficients and can be seen as a packet vector. The Euclidean norm, which is the square root of the energy of wavelet coefficients, is computed as a parameter for each vector. These parameters, which are based on the absolute energy content of the signal, are labelled LlPj, where l is the actual level of decomposition and j is the number of the packet (e.g. L5P3).
We computed the relative energies for the frequency bands corresponding to the wavelet packet vectors 0–11 of level 5, which is the sum of the squared coefficients per wavelet packet vector divided by the sum of all squared coefficients of level 5 (labelled rL5Pj).
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Acknowledgments |
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This work was supported by the Bayerische Forschungsstiftung, München, Germany (grant no. AZ 261/98) and supported by Siemens AG, Erlangen, Germany, and Erich Jäger GmbH/Viasys Healthcare, Höchberg, with non-commercial hardware and software components.
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H. Schwilden and E. Kochs contributed equally to this work. 
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