Parameter selection in permutation entropy for an electroencephalographic measure of isoflurane anesthetic drug effect

Abstract

The permutation entropy (PE) of the electroencephalographic (EEG) signals has been proposed as a robust measure of anesthetic drug effect. The calculation of PE involves the somewhat arbitrary selection of embedding dimension (m) and lag (τ) parameters. Previous studies of PE include the analysis of EEG signals under sevoflurane or propofol anesthesia, where different parameter settings were determined using a number of different criteria. In this study we choose parameter values based on the quantitative performance, to quantify the effect of a wide range of concentrations of isoflurane on the EEG. We analyzed a set of previously published EEG data, obtained from 29 patients who underwent elective abdominal surgery under isoflurane general anesthesia combined with epidural anesthesia. PE indices using a range of different parameter settings (m = 3–7, τ = 1–5) were calculated. These indices were evaluated as regards: the correlation coefficient (r) with isoflurane end-tidal concentration, the relationship with isoflurane effect-site concentration assessed by the coefficient of determination (R ²) of the pharmacokinetic–pharmacodynamic models, and the prediction probability (P_K). The embedding dimension (m) and lag (τ) have significant effect on the r values (Two-way repeated-measures ANOVA, p < 0.001). The proposed new permutation entropy index (NPEI) [a combination of PE(m = 3, τ = 2) and PE(m = 3, τ = 3)] performed best among all the parameter combinations, with r = 0.89(0.83–0.94), R ² = 0.82(0.76–0.87), and P_K = 0.80 (0.76–0.85). Further comparison with previously suggested PE measures, as well as other unrelated EEG measures, indicates the superiority of the NPEI. The PE can be utilized to indicate the dynamical changes of EEG signals under isoflurane anesthesia. In this study, the NPEI measure that combines the PE with m = 3, τ = 2 and that with m = 3, τ = 3 is optimal.

Appendix

1.1 Calculation of existing EEG measures of DoA

The approximate entropy (AE) is a statistical parameter that quantifies the predictability of subsequent amplitude values of the EEG based on the knowledge of the previous values. The AE looks at previous sequences of length m and then establishes the negative logarithmic probability that these sequences predict a new sequence of m + 1 points to within an error range of r. The value of the AE depends on the values chosen for the parameters: m (embedding dimension), and r (noise threshold) [10]. In this study, m = 2 and r = 0.2 SD were selected in the light of previous work [10].

SEF95 quantifies the frequency below which 95 % of the power in the power spectrum resides [3]. Two sub-parameters in the BIS monitor, BetaRatio and SynchFastSlow, were calculated. The former is a ratio between empirically determined frequency bands (30–47 and 11–20 Hz), and the latter is defined as the ratio of the sum of all bispectrum peaks in the area 0.5–47 Hz over the sum of the bispectrum in the area 40–47 Hz [3, 28]. To calculate these measures, a segment-averaging approach was used, similar to that used in the BIS monitor: 1 min of EEG signals were divided into a series of 2-s epochs, with each epoch overlapping by 75 %, and the Fourier transform was applied to each epoch after windowed by a Blackman function [3, 29].

The spectral entropy was calculated according to the algorithm in the Datex-Ohmeda S/5™ Entropy Module (Datex-Ohmeda Division, Instrumentarium Corp., Helsinki, Finland), where two separate entropy values are calculated using different frequency bands in the time–frequency balanced spectrum: State entropy (SE) (0.8–32 Hz) and Response entropy (RE) (0.8–47 Hz) [4].