Age-Dependent Entropic Features During Propofol Anesthesia in Developing Brain

Abstract

BACKGROUND:

Precise monitoring of anesthetic depth in children receiving propofol anesthesia is crucial. Commercial depth of anesthesia monitoring devices do not account for age-related changes in brain states and provide misleading information regarding the actual depth in young children. Entropy analysis, a typical complexity methodology, has been demonstrated to be a simple and robust tool for monitoring consciousness levels during anesthesia in adults. The validity of entropic measures for depth of anesthesia monitoring in children receiving general anesthesia remains largely unexplored. The age-related entropic feature dynamics during propofol anesthesia are still not clear.

METHODS:

We prospectively studied frontal electroencephalogram (EEG) recordings from subjects aged 1 to 18 years receiving propofol anesthesia. We calculated spectral power, permutation entropy (PeEn), sample entropy (SampEn), beta ratio, and bispectral index (BIS) from EEG segments obtained during wakefulness, maintenance, and recovery. PeEn quantifies the randomness of a time series and SampEn quantifies its unpredictability. Both measures convey complexity information on local connectivity within neural circuits for an EEG signal. The accuracy of these EEG measures to distinguish between propofol-induced unresponsiveness and clinical recovery was assessed. The changes in entropic feature dynamics with age during propofol anesthesia were investigated.

RESULTS:

Seventy-seven subjects were included for analysis. Propofol induced a significant decrease in frontal PeEn (from a median [interquartile range] of 0.75 [0.71–0.78] during wakefulness to 0.61 [0.57–0.63] during maintenance, P < .001), which returned to wakefulness levels during recovery (0.75 [0.71–0.79]), contrasting with BIS, which remained lower. A significant increase in SampEn was noted from wakefulness to maintenance (0.04 [0.04–0.06] vs 0.25 [0.20–0.28], P < .001). PeEn provided excellent performance for distinguishing between unresponsiveness and clinical recovery at an optimal classification threshold of 0.67 with the accuracy of 96.6%. The distinguishing capability of PeEn appeared superior in toddlers compared to BIS (accuracy: 94.7% vs 88.9%). SampEn also exhibited good distinguishing accuracy of 81.1% at an optimal threshold of 0.18. Frontal PeEn and SampEn, indicating information amount of intracortical neural circuits connectivity, decreased with age during propofol maintenance (P = .017 and .026, respectively). The adolescents exhibited significantly lower frontal power, PeEn, and SampEn values during propofol administration.

CONCLUSIONS:

The frontal PeEn served as an excellent indicator for distinguishing propofol-induced unresponsiveness from recovery in children. Frontal complexity, represented by PeEn and SampEn, decreased with age during propofol maintenance, which was hypothesized to reflect sequential neurophysiological development in frontal cortex, particularly its maturation during adolescence.

KEY POINTS.

• Question: Is entropic analysis, a nonlinear complexity approach, valuable for depth of anesthesia monitoring in children receiving propofol anesthesia?

• Findings: Frontal permutation entropy served as an excellent indicator for distinguishing propofol-induced unresponsiveness from clinical recovery in children.

• Meaning: Frontal permutation entropy, a simple and robust indicator, is a promising alternative to current depth of anesthesia indices for pediatric propofol anesthesia.

BACKGROUND

Propofol has been increasingly utilized for delivering general anesthesia (GA) in children due to its advantages over inhalational anesthetics.^1,2 Precise monitoring of the depth of anesthesia (DOA) in children receiving propofol anesthesia is crucial, given the heightened risk of intraoperative awakening and sudden movements.³ Most commercial DOA indices currently used in children are developed based on adult electroencephalogram (EEG) frontal power spectra data and do not take into account distinct brain state dynamics under GA in developing brain.^4,5 Significant age-dependent EEG signatures changes exist with brain development from childhood to adulthood.^3,6,7 During propofol anesthesia, total EEG power peaked at approximately 8 years old (y) and subsequently declined with increasing age. Frontal alpha oscillations, essential elements utilized to derive current DOA indices, were not coherent in infants.^6,7 Although several studies have suggested that bispectral index (BIS) values generally correlated with increasing propofol and sevoflurane doses or hypnotic depth in children aged >1 year, they have been shown to be unreliable and provide misleading information about the actual DOA in young children.^6,8,9 The minimum alveolar concentration of sevoflurane for maintaining the BIS index below 50 was significantly higher in children aged 2 to 4 years.⁸ Toddlers displayed highest BIS values during sevoflurane maintenance compared with other children.⁹

From the methodological perspective, the BIS and potentially other commercially available DOA indices are almost exclusively based on EEG spectral analysis, which are suitable for linear and stationary signals.^10,11 However, as electrical activity in the brain exhibits complex, nonlinear dynamic properties,¹² interpretation of EEG data with nonlinear approaches could be an optimal choice.^13–15 Entropy analysis, a typical nonlinear methodology, quantifies the complexity of a time series, essentially assessing the information amount it contains. A time series with repeating patterns indicates an ordered system and would have a low value of entropy. The permutation entropy (PeEn) and sample entropy (SampEn) garner more attention in DOA monitoring.^16–20 The PeEn has been proven to perform outstandingly as a DOA indicator in terms of excellent prediction accuracy, resistance to artifacts, computational efficiency, and less baseline variability compared to other DOA indices in adults.¹⁶ It has also been shown to be valuable for assessing DOA in 15 children receiving sevoflurane anesthesia.¹⁸ The SampEn has demonstrated strong noise resistance and the ability to effectively differentiate various levels of DOA in adults when estimating the effects of sevoflurane.^17,19,20 Both PeEn and SampEn have been integrated into multiple machine learning models as key EEG-based features for assessing hypnotic depth.^21–23

The validity of PeEn and SampEn for DOA monitoring in children receiving GA remains largely unexplored. The effect of age on PeEn and SampEn during propofol-induced unconsciousness in developing brain has not been thoroughly delineated. Characterizing entropic measures in relation to age during propofol-induced brain state alterations could lay the groundwork for developing age-specific entropy-based anesthesia monitoring tools for children. This approach could also enhance our comprehension of developmental neurophysiological trajectories in the brain, focusing on EEG complexity. Hence, the primary aim of this study was to examine the accuracy of frontal PeEn and SampEn in distinguishing propofol-induced unresponsiveness from clinical recovery in children, especially in toddlers, in comparison to BIS measures (the BIS and beta ratio). The secondary aim was to characterize the age-dependent changes in frontal PeEn and SampEn during propofol maintenance.

METHODS

This was a prospective, single-center, observational study conducted at Children’s Health Center of Peking University First Hospital in Beijing, China. Ethical approval was granted by the Ethical Committee of Peking University First Hospital (Approval number: 2022-005), and the study was registered with ClinicalTrials.gov (Identifier: NCT05210764, registered on January 8, 2022; principal investigator: L.-L. Song) before the enrollment of subjects. This manuscript adheres to the applicable Consolidated Standards of Reporting Trials (CONSORT) guidelines.

Study Population

This study included subjects aged between 1 and 18 years, with American Society of Anesthesiologists (ASA) physical status I or II, who received GA for elective surgery lasting 20 minutes and more. Subjects were excluded if they were born preterm, had congenital anomalies or hereditary diseases, or suffered from muscular, neurologic, psychiatric, cardiovascular, or pulmonary disorders. Written informed consent was obtained from the parents or legal guardians. The enrolled Subjects were categorized into 4 age groups: 1 to 3 years, 3 to 6 years, 6 to 12 years, and 12 to 18 years according to international age grouping standards.²⁴ Subjects were sequentially enrolled ensuring a relatively equal distribution across chronological ages.

Anesthesia and Perioperative Management

Subjects were not premedicated. GA was induced and maintained using a continuous infusion of propofol combined with remifentanil throughout the duration of surgery (Supplemental Description 1 in Supplemental Data 1, https://links.lww.com/AA/F348). The management of anesthesia during surgery was left to the discretion of the attending anesthetist based on established clinical parameters. The care team was kept unaware of the EEG data to eliminate any potential sources of bias.

EEG Recording and Analysis

The unilateral BIS sensor (BIS Quatro, Covidien, Norwood) was applied on the subject’s forehead in accordance with the manufacturer’s recommendation. Impedance values <5 KΩ for each channel were considered acceptable. Raw EEG data were recorded continuously using a BIS VISTA monitoring system (BIS VISTA, Covidien, Norwood) for subsequent analysis. The data was sampled at a rate of 128 Hz.

EEG Preprocessing and Segment Selection

MATLAB (version R2022b, MathWorks) was utilized for the preprocessing of the initial EEG recordings to eliminate power line interference and artifacts from body movement, muscular, and ocular signals (Supplemental Description 2 in Supplemental Data 1, https://links.lww.com/AA/F348).

Two-min segments of preprocessed EEG data were selected from 3 distinct states: wakefulness, maintenance, and recovery, and were processed offline. The wakefulness segment was extracted closely before the induction of GA. The maintenance segment was identified during the stable maintenance phase of GA, approximately halfway between the surgical incision and cessation of the anesthetics. This segment was chosen based on a constant infusion of propofol and remifentanil for at least 10 minutes (stable propofol and remifentanil effect-site concentrations) preceding the EEG segment without other anesthetics along with alterations of heart rate and blood pressure of <5%. The recovery segment was recorded in a postoperative, eye-closed resting state closely after clinical recovery, as indicated by a University of Michigan Sedation Scale score of 0 to 1.

Spectral Analysis

The multitaper spectral analysis was performed using the Chronux toolbox (version 2.11; https://chronux.org/) to estimate power spectra and spectrograms of frontal EEG data within the frequency range of 0.1 to 45 Hz. The frontal EEG spectrograms were derived from the short-time Fourier transform. The logarithmic power of the EEG was analyzed across predefined frequency bands: slow oscillation (SO, 0.1–1 Hz), delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–25 Hz), and gamma (25–45 Hz). Group-averaged spectrograms were constructed by ascertaining the median power across all subjects for each temporal and frequency band.

Entropy Analysis

• (1) PeEn

PeEn, initially introduced by Bandt and Pompe,²⁵ serves as a classical complexity measure that quantifies the randomness of a time series. A time series with evenly occurring all oscillation patterns (maximally disordered) is characterized by the highest PeEn of 1, while that dominated by only 1 pattern has the lowest of 0. The calculation of PeEn involves transforming a time series into a sequence of ordinal amplitude patterns at a preset vector length of m and a time delay (overlap) of τ, followed by an analysis of their probability distribution (Figure 1 and Supplemental Description 3 in Supplemental Data 1, https://links.lww.com/AA/F348). The PeEn value was obtained by using Shannon entropy to these distributions and normalized to a range between 0 and 1. We chose an m = 6 and a τ = 1 for PeEn calculation.²⁶ Each 2-minute EEG segment extracted was divided into 10-second epochs with a 50% overlap. The PeEn values were averaged across all 10-second epochs for each segment studied in each patient.

Figure 1.

Schematic calculations of permutation entropy and sample entropy. A, Permutation entropy. B, Sample entropy. EEG indicates electroencephalogram; m, embedding dimension; r, noise filter; SD, standard deviation; τ, time delay.

• (2) SampEn

SampEn, proposed by Richman and Moorman,²⁷ is a refined algorithm of approximate entropy that eliminates the biases present in the latter. It quantifies the unpredictability of a time series by assessing its probability of generating new amplitude patterns. A higher SampEn indicates a greater probability of generating new amplitude patterns and increased unpredictability. To calculate SampEn, an m-length amplitude pattern (template) is selected from the time series, and other m-length vectors with similar patterns (template matching) are identified. The total number of these similar m-length vectors occurring is then calculated. Next, this m-length pattern is extended to an (m+1)-length pattern, and the above step is repeated. SampEn is ultimately calculated as the negative natural logarithm of the ratio between the total number of similar (m+1)-length vectors and that of similar m-length vectors. The term “similar” refers to the differences between amplitude values of these vectors that are within a defined threshold, r, which serves as the noise filter (Figure 1 and Supplemental Description 4 in Supplemental Data 1, https://links.lww.com/AA/F348). We chose an m = 6 and an r = 1 for SampEn calculation.²⁶ Each EEG segment was divided into 10-second epochs with a 50% overlap. The data were then averaged across all 10-second epochs for each patient’s studied segment.

BIS Measures

• (1) Beta ratio

The beta ratio is a key subparameter incorporated within the BIS system. The BIS heavily weights the beta ratio, especially when the EEG exhibits characteristics of light sedation.²⁸ Beta ratio is calculated as $\log (\mathrm{s}\mathrm{u}\mathrm{m}[\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}{\mathrm{y}}_{30-47\mathrm{H}\mathrm{z}}]$$/\mathrm{s}\mathrm{u}\mathrm{m}[\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}{\mathrm{y}}_{11-20\mathrm{H}\mathrm{z}}])$. The averaged beta ratio within the EEG segments for spectral and entropy analysis were used for comparison.

• (2) BIS

The BIS values were directly extracted from the BIS monitor and then averaged over the same sampling segments as those used for spectral and entropy analyses.

Clinical Data Collection

Anesthetic administration was reliably tracked in real-time through electronic medical records. The propofol effect-site concentrations were estimated using the Eleveld and Paedfusor pharmacokinetic models for pediatric use.^29,30

Outcomes

Primary Outcomes

The primary outcomes were the accuracy of frontal PeEn and SampEn to distinguish between propofol-induced unresponsiveness and clinical recovery from anesthesia across the cohort, in comparison to BIS measures (the BIS and beta ratio).

Secondary Outcomes

1. Frontal EEG total power and spectral power at predefined frequency bands for the cohort and age groups across anesthetic states were calculated using MATLAB.

2. Frontal EEG measure (PeEn, SampEn, BIS, and beta ratio) values across anesthetic states for the cohort and age groups were averaged using MATLAB.

3. The areas under the curves (AUCs) of frontal EEG measures to differentiate between unresponsiveness and clinical recovery for the cohort and age groups were estimated using MATLAB.

4. Accuracy of frontal EEG measures in predicting clinical recovery from maintenance among age groups was estimated using MATLAB.

5. The Correlation coefficients among frontal EEG measures for the cohort and age groups across anesthetic states were evaluated to reflect their similarities.

6. The Within-individual and interindividual coefficients of variation (CVs) of frontal EEG measures across anesthetic states were assessed using the quartile CV and the ratio of SD to mean, respectively, to determine their abilities to resist within-individual interference and variations between individuals.

Statistical Analysis

The accuracy for the BIS to separate propofol-induced unresponsiveness from clinical recovery in children was reported of 80%.³¹ With a sample size of 74, this study had 80% power to detect a noninferiority difference of 10% for 90% accuracy, setting a significance level at 0.05. Eighty-one subjects were enrolled to account for potential dropouts. The minimum sample size required for each of 4 age groups was 21 to detect the above noninferiority difference for the clustered matched-pair design.³²

Subject characteristics were summarized using medians (interquartile range) for continuous variables. The MATLAB-based MES toolbox was utilized to determine accuracy, sensitivity, specificity, AUCs, and 95% confidence intervals (CIs) of EEG measures. The distinguishing accuracy of EEG measures at the optimal threshold was compared using the McNemar test in the R-based “exact 2×2” package (mcnemar.test and mcnemarExactDP). Linear mixed models with Satterthwaite’s approximation were used to assess the impact of age groups and anesthetic states on spectral estimates and EEG measures using MATLAB (fitlme), with age groups and anesthetic states as fixed effects and individual subjects as a random effect. Linear mixed models are particular suitable for multilevel sampling and repeated measures designs.³³ Post hoc multiple comparisons among age groups were conducted using the Tukey test to explore the differences in spectral estimates and EEG measures across age groups and anesthetic states. Total power and entropic measures were modeled as nonlinear polynomial functions of age using MATLAB (polyfit). The index R-squared (R²) was used for selecting the nonlinear functions, defined as the ratio of the regression sum of squares to the total sum of squares. All the statistical tests were 2-sided. A P value of < .05 was considered significant.

RESULTS

A total of 77 subjects completed the study and were included in the final analysis (Figure 2). Among them, the 1 to 3 years and 6 to 12 years subjects had a higher percentage of males, while the 12–18 years subjects were primarily female. The averaged propofol infusion rate at chosen EEG segments was 7.8 (6.7–9.5) (median [interquartile range]) mg kg^–1 h^–1 and the averaged propofol effect-site concentration, as estimated using the Eleveld pediatric model, was 2.90 (2.51–3.15) μg mL^–1, which significantly decreased with age (P < .001 and 0.002, respectively; Table). The available numbers of subjects with viable EEG segments across anesthetic states and the detailed surgery types are presented in Supplemental Tables 1 and 2 (Supplemental Data 2, https://links.lww.com/AA/F349).

Figure 2.

The enrollment flowchart for subjects.

Table.

Subject Characteristics and Clinical Data (n = 77)

clinical data	1–3 y (n = 10)	3–6 y (n = 18)	6–12 y (n = 28)	12–18 y (n = 21)	P value
Age	24 (18–30) mo	4 (3–5) y	8 (7–9) y	15 (13–16) y	<.001a
Male, n (%)	8 (80)	10 (56)	22 (79)	7 (33)	.007a
Weight, kg	12.9 (11.0–13.9)	18.0 (15.0–21.0)	32.8 (26.3–42.0)	62.0 (52.7–67.0)	<.001a
BMI	16.1 (14.9–16.9)	15.3 (14.1–16.4)	18.3 (15.0–21.6)	21.5 (20.2–23.7)	<.001a
ASA physical status I/II, n	9/1	16/2	27/1	19/2	.771
Airway device  Laryngeal mask airway/endotracheal tube, n	1/9	15/3	22/6	5/16	<.001a
BIS, L/R	6/4	7/11	17/11	15/6	.232
Mean propofol infusion rate during anesthesia, mg kg–1 h–1	14.9 (12.5–16.0)	12.8 (11.1–15.3)	11.1 (9.3–12.4)	8.2 (7.2–8.8)	<.001a
Propofol infusion rate during maintenance EEG segments, mg kg–1 h–1	10.0 (8.4–10.9)	9.8 (7.8–10.0)	8.0 (7.2–8.9)	6.3 (5.7–6.7)	<.001a
Estimated propofol effect-site concentration (Eleveld), μg mL–1	3.20 (2.75–3.47)	2.99 (2.53–3.19)	2.96 (2.69–3.17)	2.55 (2.43–2.82)	.002a
Estimated propofol effect-site concentration (Paedfusor), μg mL–1	2.92 (2.51–3.31)	2.90 (2.48–3.23)	2.63 (2.42–2.85)	2.50 (2.13–2.72)	.013a
Remifentanil infusion rate during anesthesia, μg kg–1 min–1	0.21 (0.20–0.23)	0.22 (0.19–0.23)	0.19 (0.16–0.21)	0.14 (0.13–0.15)	<.001a
Remifentanil infusion rate during maintenance EEG segments, μg kg–1 min–1	0.19 (0.18–0.20)	0.20 (0.19–0.21)	0.20 (0.16–0.21)	0.15 (0.14–0.16)	<.001a
Sufentanil, μg kg–1	0.14 (0.10–0.15)	0.15 (0.12–0.20)	0.14 (0.12–0.15)	0.15 (0.10–0.25)	.344
Cisatracurium, mg kg–1	0.11 (0.09–0.14)	0.10 (0.09–0.11)	0.10 (0.10–0.11)	0.09 (0.08–0.10)	.024a
Surgery type, n (%)
General	9	2	2	4
Otolaryngology	1	14	19	2
Gynecology	0	0	0	9
Eye surgery	0	1	6	4
Others	0	1	1	2

Presented as number (percentage) or median (interquartile range).

Abbreviations: BIS, bispectral index; BMI, body mass index; EEG, electroencephalogram.

^aP < .05.

Age-Dependent Frontal EEG Spectral Features in Propofol-Induced Anesthetic States

Propofol-Induced Frontal Spectral Dynamics

Propofol administration did not induce a significant change in frontal total power from wakefulness to maintenance; however, total power hit its lowest point during recovery (wakefulness, 1.66 (−3.76 to 7.16) dB; maintenance, 0.40 (−2.49 to 4.02) dB; recovery, −5.74 (−11.49 to 0.80) dB, P < .001) (Supplemental Table 3 in Supplemental Data 2, https://links.lww.com/AA/F349). Absolute alpha and beta power increased from baseline to maintenance, except for beta power in the 1 to 3 years subjects; in contrast, the power in other frequency bands showed consistent decrease (Figure 3).

Figure 3.

Group-level frontal spectrograms and power spectra from 0.1 to 45 Hz across predefined frequency bands in propofol-induced anesthetic states. A, Age-related change in frontal spectrograms. B, Power spectra across age groups during propofol maintenance, with the median power and bootstrapped 95% confidence interval shown. C, The comparisons of group-level spectral power within frequency bands in propofol-induced anesthetic states. The central mark in each box represents the median, with the edges indicating the 25th and 75th percentiles. The extending whiskers are the most extreme nonoutlier data points as determined by MATLAB, and red cross denotes outlier. The detailed absolute power values for each frequency band across age groups are available in Supplemental Table 4 (Supplemental Data 2, https://links.lww.com/AA/F349). *P < .05, **P < .01, ***P < .001. SO indicates slow oscillation.

Age-Dependence of Frontal EEG Spectral Features

During wakefulness, all age groups exhibited grossly similar frontal EEG spectral structures. Overall, the absolute power across each frequency band remained consistent with age, with the exception that toddlers displayed the highest levels of beta and gamma power compared to other age groups (Figure 3). During maintenance, power spectra consistently exhibited a pattern dominated by alpha and SO waves across age groups. Frontal spectra indicated reduced alpha, beta, and gamma power in adolescents (>12 years) compared to children <12 years after propofol administration (Figure 3, Supplemental Table 4, and Supplemental Figure 1 in Supplemental Data 2, https://links.lww.com/AA/F349). During recovery, the 12- to 18-year-old subjects maintained relatively lower power values in delta and theta bands compared to other age groups.

During wakefulness, total frontal EEG power peaked at 1 year and then decreased with age by 6 years (P < .001, R²=0.334) (Supplemental Figure 2 in Supplemental Data 2, https://links.lww.com/AA/F349). In contrast, total frontal power during maintenance exhibited an increase from toddlers, reaching a peak around 9 years, after which it declined and plateaued at the adolescent years (R² = 0.473, P < .001).

Age-Dependent Frontal Entropy Dynamics in Propofol-Induced Anesthetic States

Propofol-Induced Frontal Entropy Dynamics

The frontal PeEn values decreased significantly from wakefulness to maintenance (0.75 [0.71–0.78] vs 0.61 [0.57–0.63], P < .001) with distinct nonoverlapping ranges. These values then returned to wakefulness levels during recovery across age groups (0.75 [0.71–0.79]) (Figure 4 and Supplemental Table 5 in Supplemental Data 2, https://links.lww.com/AA/F349). In contrast, a significant increase in SampEn was noted from wakefulness to maintenance (0.04 [0.04–0.06] vs 0.25 [0.20–0.28], P < .001). During recovery, the trajectories of PeEn and BIS diverged; while PeEn returned to baseline, the BIS values remained consistently lower than those during wakefulness.

Figure 4.

Age-dependent changes in entropic and BIS measures in propofol-induced anesthetic states. A, Averaged entropic and BIS measures within the cohort in propofol-induced anesthetic states, with solid lines representing the means and shaded area representing standard deviations. The adjusted BIS was calculated by dividing BIS by 100. B, Averaged entropic and BIS measures across age groups during wakefulness, maintenance, and recovery. The central mark in each box represents the median, with the edges indicating the 25th and 75th percentiles. The extending whiskers are the most extreme nonoutlier data points as determined by MATLAB, and red cross denotes outlier. Detailed entropic and BIS measure values across age groups are available in Supplemental Table 5 (Supplemental Data 2, https://links.lww.com/AA/F349). *P < .05, **P < .01. BIS indicates bispectral index; PeEn, permutation entropy; SampEn, sample entropy.

Age-Dependence of Frontal Entropy Dynamics

The frontal PeEn was capable of detecting differences in the EEG oscillatory patterns across age groups, mirroring the ability observed with the beta ratio (Figure 5 and Supplemental Table 5 in Supplemental Data 2, https://links.lww.com/AA/F349). During wakefulness, the PeEn was the sole measure to exhibit higher values in 1- to 3-year-old subjects. During maintenance, the 12- to 18-year-old subjects displayed significantly lower PeEn values in comparison to the 1- to 3-year-old subjects, even with the lowest averaged propofol effect-site concentration across age groups. During recovery, the PeEn values in the 12- to 18-year-old subjects rapidly restored and exceeded those observed in the 3- to 6-year-old and 6- to 12-year-old subjects, revealing the significant impact of age. The SampEn evaluation during maintenance also indicated an age-induced effect, with the 12- to 18-year-old subjects showing significantly lower SampEn values compared to the 6- to 12-year-old subjects.

Figure 5.

Trajectories of entropic and BIS measures with age in propofol-induced anesthetic states, modeled using linear regression. Straight line represents linear regression for each EEG measure with the line equation displayed. *P < .05, ***P < .001. BIS indicates bispectral index; PeEn, permutation entropy; SampEn, sample entropy.

During maintenance, age was significantly correlated with both frontal PeEn and SampEn (PeEn, slope=-0.002, P = .017; SampEn, slope=-0.003, P = .026), with PeEn’s age-dependent characteristics closely resembling beta ratio (Figure 5).

During wakefulness, both frontal PeEn and SampEn peaked around 1 year, subsequently declined, and bottomed around 6 years. From this point, they remained stable until adolescence (Supplemental Figure 2 in Supplemental Data 2, https://links.lww.com/AA/F349). During maintenance, PeEn peaked again around 1 year and then gradually decreased until 18 years while SampEn exhibited an age-related change that resembled frontal total power.

The Performance of Entropic Measures As a DOA Indicator

Distinguishing Unresponsiveness From Clinical Recovery

The frontal PeEn showed excellent reliability for distinguishing unresponsiveness from clinical recovery, with an AUC of 0.99 (95% CI, 0.96–1.00, P < .001), a performance that rivaled both beta ratio and BIS (Supplemental Figure 3 in Supplemental Data 2, https://links.lww.com/AA/F349). The optimal classification threshold for PeEn was 0.67 (95% CI, 0.65–0.69) with the sensitivity of 96.1%, the specificity of 95.8%, and the accuracy of 96.6% (95% CI, 92.3%–98.9%) (Figure 6). The differences in accuracy were 5.0% (95% CI, −0.6%–11.0%, P = .070) between PeEn and BIS, and 0.7% (95% CI, −4.1%–5.6%, P = .752) between PeEn and beta ratio. The SampEn was also a reliable discriminator, with an AUC of 0.83 (95% CI, 0.78–0.90, P < .001). It achieved the optimal classification threshold at 0.18 (95% CI, 0.17–0.23), along with sensitivity of 83.1%, specificity of 78.9%, and accuracy of 81.1% (95% CI, 73.8%–87.0%). SampEn was less reliable compared to BIS, with a difference in accuracy of 10.5% (95% CI, 2.6%–18.4%, P = .009). Notably, in 1 to 3 years subjects, PeEn and beta ratio were more accurate in separating unresponsiveness from recovery than BIS and SampEn (Figure 6 and Supplemental Figure 3 in Supplemental Data 2, https://links.lww.com/AA/F349), with respective accuracy of 94.7%, 94.7%, 88.9%, and 84.2%.

Figure 6.

The accuracy of entropic and BIS measures to distinguish between propofol-induced unresponsiveness and clinical recovery across all subjects and subjects of each chronological age. Data are presented as accuracy (95% confidence interval). Round dot indicates the accuracy and straight line indicates 95% confidence interval. BIS indicates bispectral index; PeEn, permutation entropy; SampEn, sample entropy.

Correlations Among Entropic and BIS Measures

The frontal entropic measures correlated significantly with the BIS measures during propofol-induced anesthetic states, with greatest correlation noted between PeEn and beta ratio (r=0.919) and the least between PeEn and SampEn (r=-0.573) (Supplemental Table 6 in Supplemental Data 2, https://links.lww.com/AA/F349). Additionally, the correlations between SampEn and other EEG measures exhibited significant age-dependent characteristics (Supplemental Figure 4 in Supplemental Data 2, https://links.lww.com/AA/F349).

CVs of Entropic and BIS Measures

The within-individual CVs for the frontal PeEn during wakefulness and maintenance were 2.3% and 1.7%, respectively, compared to the beta ratio and BIS (wakefulness: 22.4% and 2.1%; maintenance: 4.8% and 2.9%, respectively), which underscored its robustness against interference (Supplemental Table 7 in Supplemental Data 2, https://links.lww.com/AA/F349). Furthermore, the PeEn values demonstrated remarkable consistency across individuals during both wakefulness and maintenance (6.1% and 6.6%, respectively), indicating its robustness to individual variability.

DISCUSSION

In this observational cohort study, we demonstrated that frontal spectral features and entropic measures changed significantly with age during propofol anesthesia, from toddlers to adolescents. It also pointed to the necessity for age-adjusted strategies to track brain states of children receiving propofol anesthesia. The PeEn was validated as an excellent measure for discriminating changes in brain state induced by propofol in children, comparable to BIS measures. Additionally, SampEn demonstrated good discriminating performance.

Age-Dependent Spectral Features During Propofol-Induced Unconsciousness

The propofol-induced frontal EEG spectral features from toddlers to adolescents in our cohort aligned with those reported in previous studies.^3,34,35 The body of knowledge we can add to previous findings was that the EEG oscillations showed increased frontal beta power in children <12 years compared with those in adolescents during maintenance, despite increased estimated propofol brain concentrations in these children. In adults, an increase in beta power is a notable indicator of lighter anesthesia levels. This age-related variation in beta power could result in the misestimation of DOA in young children if adult-derived EEG indices are applied. The beta band was reported to be linked to intracortical and corticocortical processing of sensory and motor activities.^36,37 Increased beta oscillations during anesthesia in children younger than 12 years could be indicative of immature interneuron networks and thalamocortical connectivity, further less proficient inhibitory or synchronized activities. This finding thereby underscored a critical transition in brain development around the age of 12.

Entropy Dynamics in Propofol Anesthesia

Our findings supported Puglia’ whole scalp EEG study in 8- to 16-year-old subjects, revealing a decrease in cortical spatiotemporal Lempel-Ziv complexity after GA.³⁵ PeEn, essentially quantifying the number of the dominating patterns within the signal, represents information amount presented by local functional neural circuit connectivity.^38,39 The reduction in frontal PeEn observed during propofol anesthesia likely reflected reduced intracortical and corticocortical functional connectivity and biologically information processing.^38–40 Propofol-induced hypercoherent alpha oscillations lead to significant functional disconnection of the prefrontal cortex, disrupting corticocortical communication through functional fragmentation.⁴¹ Several studies have indicated that unconsciousness induced by anesthetics correlated with a reduction in connectivity and information transfer within frontal-parietal networks, as assessed by functional magnetic resonance imaging.^39,40,42 SampEn, which measures probability of new patterns due to amplitude changes, characterizes the complexity of the signal from the perspective of amplitude magnitude.^20,26 Given that the power spectra during propofol maintenance were characterized by dominant alpha power, the rise in frontal SampEn after propofol administration indicated an increased amount of information within alpha-dominating neural circuits.

Entropic Measures as a Hypnotic Indicator in Children

Our study reinforced Kim’s study, which highlighted the frontal PeEn’ value for gauging DOA in 3- to 15-year-old children receiving sevoflurane anesthesia.¹⁸ The superior discriminating performance of PeEn in 1- to 3-year-old children is likely due to its sensitivity to changes in the centered faster frequencies,⁴³ which are typical of this age group’s EEG patterns with greater power in the faster frequency bands. Furthermore, the prompt return of PeEn to baseline levels on recovery from anesthesia, in contrast to the hysteresis observed with BIS, underscored PeEn’s exceptional capability to distinguish between responsiveness from unresponsiveness in children. The PeEn offers the advantage of simplicity, requiring only a single-channel frontal EEG for application. It demonstrated excellent timeliness with an average computation time of 0.041 seconds for a 2-minute EEG segment. In comparison, the BIS has an averaging delay of 15 seconds from EEG data acquisition to value display.⁴⁴ Additionally, PeEn is highly resistant to low-frequency blink artifacts and is less prone to outliers compared to SampEn and beta ratio. PeEn, as a potential DOA indicator, requires age adjustment during propofol maintenance to ensure its discriminating accuracy between maintenance and clinical recovery. However, no age adjustments appear to be necessary during wakefulness or recovery in the pediatric population based on the findings of this research. Further work with a large sample size is warranted to validate these results.

Implications of Complexity for Developmental Neurophysiology

Alongside the frontal spectral features, the consistent functional network connectivity information amount (reflected by frontal complexity) during wakefulness regardless of age suggested that key developmental milestones were already achieved by 1 year. The decline in complexity with age during maintenance in our cohort exhibited more uniform oscillation patterns (PeEn) and lower amplitude (SampEn) in adolescents compared to children <12 years. The decreased information amount of frontal neural circuits connectivity during propofol maintenance in adolescents might suggest a decrease in intracortical communication and more involvement of frontal cortex in long-range functional network connections, further mirroring neural pruning fulfillment and the maturation of neural circuits in this critical period.

Future Research

Further complexity-based research in GA infants is necessary to develop reliable DOA monitoring strategies for these very young individuals.

Limitations

First, the study included a relatively small sample size, which might disproportionately affect the outcomes for toddlers. The small sample size per age group restricted the ability to draw firm conclusions regarding performance metrics. Moreover, the limited sample size hindered the feasibility of conducting a multivariable analysis to account for potential confounders and verify the reproducibility of the results. Second, factors such as subject anxiety and ambient noise during initial recordings could introduce variability. Third, the BIS values reported may not precisely correspond to the analyzed EEG segments due to a time delay of at least 15 seconds to apply algorithms by manufacturer’s default.⁴⁴ However, the selected EEG segments were in relatively stable states, exhibiting minimal fluctuations in BIS values. Fourth, the AUC performance metrics are best evaluated using an independent test sample or cross-validation methods. Future research with a larger sample size is warranted.

CONCLUSIONS

The frontal PeEn served as an excellent indicator for distinguishing propofol-induced unresponsiveness from clinical recovery in children, showing particular efficacy in toddlers. Frontal complexity, represented by PeEn and SampEn, decreased with age during propofol maintenance, which was hypothesized to reflect sequential neurophysiological development in the frontal cortex, particularly its maturation during adolescence.

ACKNOWLEDGMENTS

The authors thank pediatric surgeons for their help in facilitating data collection for this study.

DISCLOSURES

Conflicts of Interest: None. Funding: This work was supported by the Scientific and Technological Innovation 2030 (STI2030-Major Projects+2021ZD0204300), the National Natural Science Foundation of China (grant numbers 62073280, 62471428, and 82430040), and the S&T Program of Hebei Province (21372001D; China). This manuscript was handled by: Jiro Kurata, MD, PhD.