Depth of anaesthesia can be assessed clinically, and a number of monitors also provide useful information. This is an important concept as it forms the basis of the prevention of awareness as well as the avoidance of unnecessarily deep anaesthesia.
The raw scalp EEG signal changes dramatically with general anaesthesia. There have been many attempts to quantify the observed changes in a way that provided a simple, universally applicable monitor of anaesthetic depth, but this apparently straightforward goal has proved elusive.Researchers had to deal with agent-specific changes, as well as changes which significantly lagged behind clinically obvious depth-of-anaesthesia. Despite these difficulties, considerable strides have been made.
The EEG can be used unstimulated, or stimulated (somato-sensory, auditory, visual). The mathematical techniques used for these two groups are fundamentally different - so will be described separately.
The earliest attempts to quantify the observed EEG changes associated with anaesthesia used the unstimulated EEG. A number of techniques were explored - most of which involved an initial Fourier transform, and a measure of "slowing" (an overall shift toward lower frequencies) taken from the frequency power spectrum. These spectral-based measures included:
Median Power
SEF 95 (Spectral Edge Frequency = the frequency below which 95% of the power is contained)
SEF 95 modified for Burst Suppression
All of these methods were superceded clinically by the Bispectral Index Scale (BIS). This proprietary measure built on the foundation of the above techniques - essentially a SEF95 modified for burst suppression, with an additional variable representing bicoherence. The variables were weighted mathematically using multivariate analysis based on a large clinical dataset.
An alternative approach to spectral measures is complexity measures. After sporadic reports, there was recent work on Entropy Rate Estimation from the EEG waveform culminating in a clnical monitor.
Entropy Rate Estimation (usually referred to as Entropy) is a complexity measure which has been assessed as a depth of anaesthesia measure when applied to the unstimulated EEG.
The term Entropy was borrowed from thermodynamics by a branch of mathematics: non-linear dynamics. Kolmogorov-Sinai Entropy (KSE) is a theoretical measure of the predictability of a time-series. Entropy Rates are a measure of how unpredictable a single value is based on the values which preceded it. Truly random processes have high entropy rates conversely periodic processes have low entropy rates.
A number of techniques for estimating entropy rates have been published. Some of these specifically apply corrections for limited or noisy data ... the sort of EEG data available in a clinical setting.
These techniques include Conditional Entropy (CEn); Corrected Conditional Entropy (CCEn); Approximate Entropy (ApEn); Coarse-grained Entropy rates (CGEn); and Gaussian Process Entropy rates (GPEn). There is, as you would expect, considerable correllation between these, differences being mainly due to the way they handle imperfect data.
A related entropic measure, Spectral Entropy (SpEn) is defined as the Shannon entropy computed over the normalized power spectral density function. Shannon entropy is computed from a number of values, rather than from a time-series. SpEn is an entropic measure which can be used as a measure of system complexity and is therefore included here. However, the complexity of the system in SpEn is understood as the number of different processes making up the time series rather than the sense of regularity as in the case of the above listed entropy rates measures.
Of these methods (Spectral Entropy) has been introduced as the basis of a commercial depth-of-anaesthesia monitor (Datex-Ohmeda).
Comparison with Bispectral Index Scale (BIS). BIS is an established proprietary measure of depth of anaesthesia which is a development of earlier measures of EEG slowing. It incorporates a measure of phase alignment, and of burst suppression, and has been refined mathematically against a large clinical database. Entropy Rate Estimation, unrefined, correlates well with BIS in the clinical setting, and it will be interesting to see how this newer technology fares as different algorithms are trialled and the results refined.
