Checkpoint decomposition algorithm to predict brain sensitivity from EEG signals

1 Introduction

Intelligent machines and classification algorithms are increasingly entering clinical fields, so what will their role be in predicting brain activity from electroencephalogram (EEG)? We address this question by developing an EEG segmentation method and proposing an index to estimate the performance of an algorithm (Sun and Holcman, 2022) relative to the classical Bispectral Index™ (BIS™), which is routinely used for EEG interpretation. Real-time brain monitoring based on frontal cortical EEG evaluates neuronal activity with a few seconds’ delay but at high temporal resolution to estimate the depth of general anesthesia (GA).

In the past 20 years, the BIS™, an EEG-based monitor developed by Aspect Medical Systems and now commercialized by Medtronic, has been referred to as the gold standard for assessing depth of anesthesia (DoA). It provides an index (the “bispectral index”), which ranges from 0 (brain death) to 100 (awake). The BIS curve mirrors the phases of general anesthesia and is highly correlated with hypnotic concentration in both children and adults. The induction phase is typically characterized by a decrease in the BIS as the hypnotic dose increases. During the maintenance phase, an admissible target of the BIS is set in the range 40−60. Ideally, maintaining the BIS at a constant target of 50 has been shown to reduce the incidence of intraoperative awareness (Myles et al., 2004). Exiting this range could lead to under- or overdosing and provoke deleterious side effects, such as peri-operative awareness or hemodynamic depression. When the BIS decreases below 40, this event correlates with the proportion of iso-electric suppressions (flat EEG activity periods)—a signature of deep anesthesia (Bruhn et al., 2000a; Rigouzzo et al., 2008) and suspected to be associated with postoperative cognitive dysfunctions such as delirium (Fritz et al., 2016; Wildes et al., 2019). Despite identified imperfections (Bruhn et al., 2000b; Rigouzzo et al., 2019), the BIS remains a useful indicator of the sedation level induced by most hypnotic agents. However, we decided to investigate whether the BIS possesses predictive information during the induction phase when the initial dosage is not known, which could be used to prevent hypnotic drug overdose.

Several signal processing methods are available for analyzing and correcting the EEG signal in real-time (Le Van Quyen and Bragin, 2007; Chui et al., 2016; Chavez et al., 2018; Dora and Holcman, 2022; Dora et al., 2024). These methods are mainly based on wavelet transforms (Averbuch et al., 1996; Mallat, 2009; Jaffard et al., 2001; Flandrin et al., 2013; Daubechies, 1992), independent and principal component analysis, or diffusion-based classification (Turnip et al., 2011; Subasi and Gursoy, 2010; Yuan et al., 2018).

We previously reported a causal relationship between the proportion of α-rhythm suppressions and IES, and this robust temporal correlation can be used as a predictor of brain fragility during GA (Cartailler et al., 2019; Shao et al., 2020). Recently, we combined several parameters, such as the first occurrence time of an iso-electric suppression and the transient suppression of the α-rhythms (8–12 Hz), to predict brain sensitivity to hypnotic drugs during GA (Sun and Holcman, 2022). By combining these parameters, we have proposed an algorithm called the “checkpoint decomposition algorithm” (CDA). During the induction phase, this algorithm was able to detect patient sensitivity to hypnotic drugs, defined as the propensity to develop iso-electric suppressions. In practice, using a cohort of past patients and classification methods based on the first IES and αS occurrences and the increased rate of the αS proportions, the algorithm can infer a sensitivity probability for a new patient (Sun and Holcman, 2022) based on a pre-existing trained model. Additionally, these features were used to show that induction, maintenance, and recovery phases were not statistically correlated (Shortal et al., 2019; Sun et al., 2023).

The aim of this study is to present an EEG segmentation method and a correlation analysis between the CDA and BIS values using a previously acquired database (Rigouzzo et al., 2019). We first directly extract three parameters from the BIS values recorded during the induction of anesthesia with propofol (Rigouzzo et al., 2008). These parameters are the minimum value or “nadir” of the BIS, the time to the minimum, and the time spent below 40. Based on logistic regression classifiers, we then compare these parameters with the output provided by the CDA. In the second part, we describe the correlation between BIS value ranges and EEG behavior and frequency-band power. Finally, we show how the CDA provides complementary information to the BIS, especially during the early phase of GA, and could, therefore, be used in parallel to reveal patient sensitivity from EEG features collected during induction.

2 Results

2.1 BIS vs. checkpoint decomposition algorithm parameters

To compare the ability of the CDA and BIS algorithms to predict brain sensitivity, we tested two sets of parameters extracted from EEG and BIS recordings during the induction period (see Table 1 for the list of symbols and their meanings) see also Equations 1–10 for definitions. The first three parameters described by Sun and Holcman (2022) are computed after induction.

• The first occurrence time t α S of an α −band suppression (Figure 1A, yellow segments). An α −band suppression corresponds to an EEG segment that does not contain any power in the alpha band for at least 0.5 s (see mathematical definition in “Materials and Methods”).
• The first occurrence time t IES of an iso-electric suppression (Figure 1A, red segments). An IES is defined as a period of time where the EEG is locally flat (the amplitude of the signal is small; see also the mathematical definition in “Materials and Methods”).
• The slope a of the αS proportion (Figure 1A, blue dashed line), computed at 10 min after the hypnotic injection started T 0 (Figure 1A, blue point).

TABLE 1. Summary of variables and their meanings.

The second set of parameters was drawn from BIS recordings. We determined the following:

• BIS minimum value B I S min to represent the maximum depth of anesthesia;
• time to reach the minimum peak t BISpeak from the initial time T 0 (Figure 1B, green and purple); and
• total duration during which the BIS was below 40 (Figure 1B, black).

2.2 Simultaneous recording of EEG, BIS, and anesthetic agent concentration

To compare the EEG signal with the BIS values and propofol concentrations, we developed a representation that allowed simultaneous monitoring of the temporal evolution of the EEG and spectrogram, which represents the time–frequency evolution of the waveform. The spectrogram is computed using short-time Fourier transform (STFT) (Allen, 1977) (Figures 2A,B). We segmented the EEG waveform amplitude in IES (red) and αS (yellow) (Figure 2C). The proportions of IES ( P IES ), αS ( P α S ), and the remaining EEG ( P EEG ) are computed over a sliding window of 4 min with a 1 s overlap. In parallel, we tracked the BIS values (Figure 2D) and the target propofol C t, the effect site C e, and the plasmatic C m concentrations (Figure 2E).

2.3 Comparing two criteria of sensitivity

We define and compare two criteria for patient sensitivity: the first is based on the total time spent in iso-electric suppression exceeding 12 s, and the second is based on the hypnotic concentration at which the BIS was maintained at a value of 50. We found that the two criteria overlap for 70% of our patient cohort, as shown in the matrix of Figure 3A. Thus, for the remaining 30% of the patients, BIS50 sensitivity is not associated with IES sensitivity. Furthermore, we investigated the correlation between patient age and the total time spent in suppressions for the two sensitivity criteria (Figures 3B and C). For the IES-sensitive patients, we found that the Spearman correlation between age and the total time spent in IES (resp. αS) was ρ = 0.10, p-value= 0.12 (respectively, ρ = − 0.23, p-value= 0.32). Similarly, for BIS50 sensitivity, we found a Spearman correlation of ρ = 0.11, p-value= 0.62 (respectively, ρ = 0.00, p-value= 0.99) between age and the total duration of IES (respectively, αS) duration. We conclude that there was no correlation between patient age and the total time spent in IES (respectively, αS) for either sensitivity criterion.

2.4 BIS parameters do not predict sensitivity to general anesthesia

To evaluate patient sensitivity, we compared several combinations of the three parameters (see “Methods”) using stratified repeated k-fold cross-validation (k = 5 folds, 10 randomized repetitions, 50 iterations in total) and plotted the AUC distribution from these 50 samplings in Figure 4A.

For the IES-duration criterion, among BIS parameters, BIS_min achieved the highest AUC (0.54\pm 0.17), with the remaining two BIS parameters below chance level (AUC < 0.50). In contrast, t_IES achieved the highest AUC (0.82\pm 0.13; Figure 4B) and led on all remaining metrics (sensitivity, specificity, precision, F1; see Table 2) among univariate CDA parameters. For multivariate combinations, slope + t_IES achieved the highest overall AUC (0.83\pm 0.13), with a 0.29 AUC improvement over the best BIS parameter; performance across the remaining metrics was comparable among the multivariate combinations.

TABLE 2. Classification performance (see Supp. Info.) for all univariate and multivariate predictors under IES-duration and concentration (CC) sensitivity criteria. AUC is reported as the mean ± std over 50 random sub-sampling folds. Sensitivity, specificity, precision, and F1-score are computed at the Youden-optimal threshold and averaged across folds. CDA parameters are shown above the mid-rule and BIS parameters below.

Bolded values indicate the maximum value achieved for each performance metric within each sensitivity criterion (IES vs. CC).

For the concentration criterion, among BIS parameters, t_BISpeak achieved the highest AUC (0.57\pm 0.16), with BIS_min and T_BIS<40 performing near or below chance level. Among univariate CDA parameters, t_IES outperformed BIS parameters with the highest AUC (0.72\pm 0.12; Figure 4C) and led on specificity, precision, and F1, though slope achieved higher sensitivity. Among multivariate combinations, slope + t_IES again achieved the highest overall AUC (0.73\pm 0.13), while the full three-parameter model (“All”) achieved the highest sensitivity and F1 among multivariate combinations (Table 2).

To conclude, these results confirm that the three BIS parameters cannot reliably evaluate sensitivity to GA and underperform against the CDA parameters.

2.5 α −band appearance associated with BIS values between 40 and 60

To better correlate the ranges over which the BIS values evolve and the presence of IES and/or α −suppressions, we use the cosine similarity (Equation 11; see “Materials and Methods”). We compute this index between the BIS and the proportions of IES, αS, the power in the bands α and δ bands, and the maximum power frequency curve. The binarization procedure is described in Subsection 4.5. We found that the cosine similarity between BIS values B I S mid of 40–60 and the maximum power frequency f α is K ( A f α , B B I S mid ) = 0.81 [ 0.71 , 0.88 ] (median [IQR]). However, when the BIS is less than 30, as measured by the vector B B I S l o w 2, and the proportion of IES (respectively, αS) exceeds 5% (summarized in the vector A P IES, the similarity is K ( A P IES , B B I S l o w 2 ) = 0.26 [ 0.14 , 0.54 ] (respectively, K ( B B I S l o w 2 , A P α S ) = 0.37 [ 0.21 , 0.53 ]). For a BIS value of 30–40 B B I S l o w 1, the similarity with the IES (respectively, αS) proportion is K ( A P IES , B B I S l o w 1 ) = 0.02 [ 0,0.09 ] (respectively, K ( A P α S , B B I S l o w 1 ) = 0.12 [ 0.06 , 0.31 ]) (Figure 5A). At this stage, we conclude that the BIS is associated with the presence of a maximum frequency α −band and only weakly with the IES and α −S proportions.

Furthermore, we decided to explore how the α −rhythms mean that power is distributed with respect to three ranges of BIS values: 1) B I S ≤ 40, the mean power is 166 [ 71,336 ] μ V 2 / H z; 2) 40 ≤ B I S ≤ 60, we have 257 [ 99,508 ] μ V 2 / H z; and 3) 60 ≥ B I S, we have 59 [ 26,178 ] μ V 2 / H z. These distributions are significantly different: between 2) and 3), we found p < 0.001; between 1) and 3), p < 0.05; and between 1) and 2), p < 0.05 (Figure 5B). Similarly, we reported that the δ −rhythm indicate that power decreases as the value increases in the following three ranges: 1) 1602 [ 617,3512 ] μ V 2 / H z; 2) 741 [ 332,1937 ] μ V 2 / H z; and 3) 331 [ 142,531 ] μ V 2 / H z. Again, these distributions are significantly different: between 1) and 2), we obtained p < 0.05; between 2) and 3), p < 0.001; and between 1) and 3), p < 0.001 (Figure 5C). To conclude, the mean power of the α and δ −rhythms behaves differently depending on the three BIS value intervals. We statistically confirmed that a BIS of 40–60 is associated with the presence of the α −band. Finally, when the BIS decreases, the power of the EEG signal is concentrated on slower frequencies.

3 Discussion

In this study, we compare the ability of the Bispectral Index™ (BIS™) and the checkpoint decomposition algorithm (CDA) introduced by Sun and Holcman (2022) to anticipate the appearance of a large amount of IES. Using a logistic regression approach, this algorithm allows us to predict the sensitivity to GA directly from the induction phase by extracting and combining three parameters: the first occurrence time of an iso-electric suppression, the first occurrence time of a transient suppression of the α-rhythms (8–12 Hz), and the increasing rate for the proportion of α −band suppression. These parameters quantify key events in monitoring brain sensitivity and allow us to detect trends that generate a high amount of IES—a marker of brain sensitivity to GA. Although these parameters were previously validated, there was no comparison with other methods, such as the routinely used BIS commercialized by Medtronic.

Following the proposal of a real-time method that could be used to evaluate sensitivity and adapt dose administration, we compared the CDA with BIS parameters (minimum, time to reach the minimum, and time spent below 40) during the first 10 min. Previously, the general consensus was to use a low BIS minimum (nadir) (Rigouzzo et al., 2019) as a marker of sensitivity. However, we showed that this marker is not effective.

Furthermore, we reported that the CDA could detect sensitivity to propofol anesthesia in a population of children and young adults. Among the three parameters we extracted from the BIS, we found that the minimum value had a higher AUC than the other two. This was in agreement with Bruhn et al. (2000a), suggesting that BIS values below 40 decrease proportionally as the IES ratio increases. A low minimum BIS correlates with the presence of IES and thus relates to sensitivity. We conclude that the CDA can identify the trends generating IES using first-passage events, whereas BIS only provides an alert when IES have already appeared (Sun and Holcman, 2022).

We note here that the present predictive framework uses an IES-based sensitivity criterion—the time t IES of the very first iso-electric suppression event during induction—to predict whether the total accumulated IES duration will exceed 12 s over the first 30 min of anesthesia. It is important to clarify, however, that these two quantities are fundamentally distinct: t IES captures the timing of a single, often sub-second transient event occurring during the induction window, whereas the sensitivity label is defined by the cumulative IES burden measured over more than 30 min or the entire anesthesia period, including the maintenance phase, well after the induction window closes. The appearance of a single early IES event does not imply that IES will persist or recur; the underlying hypothesis is that the earlier this first event occurs, the more fragile the thalamocortical circuit is likely to be, and therefore the more prone it is to generate subsequent suppressions. This constitutes a predictive relationship. Furthermore, the two other CDA parameters—the first occurrence time of alpha-suppression t α S and the slope of the α S proportion—are entirely independent of IES and contribute independently to the prediction. Most importantly, the second sensitivity criterion—the propofol concentration required to maintain BIS at 50—is completely independent of IES by construction. Finally, linking induction-phase EEG sensitivity to postoperative clinical outcomes such as delirium or hemodynamic instability remains an important future direction, though the relationship between early EEG features and such outcomes is still an open research question (Fritz et al., 2016).

The large inter-individual variability in brain responses to hypnotic agents, such as sevoflurane or propofol, calls for a general approach to identify sensitivity trends. Pharmacological kinetics or dynamics model approximations provide a time scale but do not reveal the exact sensitivity, confirming the general interest for the present type of real-time algorithms that can connect conceptualized real-time engineering methods with clinical needs.

Recent advances in EEG-based anesthesia monitoring have explored complementary directions to the present work. On one hand, deep learning approaches have demonstrated the feasibility of predicting anesthesia depth from drug infusion history using architectures that combine LSTM, Transformer, and Kolmogorov–Arnold networks (Wang et al., 2025). However, these methods target sedation depth during the maintenance phase and require large multichannel datasets, whereas the CDA addresses a distinct and earlier clinical question: predicting individual brain sensitivity during the first 10 minutes of induction using only three interpretable parameters extracted from a single frontal EEG channel. On the other hand, the neurophysiological basis of our approach is supported by the finding that low pre-induction frontal alpha power constitutes an EEG phenotype for a vulnerable brain, associated with increased propensity for burst suppression at lower drug concentrations than expected (Shao et al., 2020). This is consistent with our observation that the early disappearance of alpha-band oscillations α −S during induction is a significant predictor of subsequent IES accumulation. Finally, the age heterogeneity of our cohort (6–38 years) is directly relevant in light of studies showing that EEG patterns during general anesthesia are strongly age-dependent: frontal alpha oscillations are absent or immature in infants under 6 months (Cornelissen et al., 2015), and cross-frequency coupling features evolve continuously from childhood to adulthood (Liang et al., 2021), with the distinct delta–alpha phase-amplitude coupling pattern absent before 1 year of age. Taken together, these findings underscore both the complementarity of the CDA with respect to contemporary approaches and the importance of age-stratified validation in future prospective studies.

3.1 Sensitivity versus dosage

Avoiding anesthetic overdose is especially relevant to avoid damaging the brains of young children (Liu et al., 2020). This task requires quantifying brain sensitivity that could be possible using EEG. Similarly, in the brains of elderly people, suppression of neuronal cortical activity appears with IES segments (Tang et al., 2022) in patients with damaged cortical circuits or cognitive deficits. With the high number of correlations between IES and depressed EEG and postoperative complications, alteration of behavior confirms the general interest in individualizing anesthesia and thus restricting the therapeutic range, as we can now recognize that anesthesia overdose is actually more predominant than expected.

As shown in the present study, the present CDA could be used in parallel with the BIS to define a patient’s sensitivity during the induction phase of GA. This alerts the practitioner early to the patient’s sensitivity, whereas the BIS is used solely to assess the level of sedation. It remains premature at this stage to define how sensitivity could be translated into an optimal dose regulation. Each patient has an intrinsic excitation–inhibition balance of neuronal circuits that evolves with age and controls the thalamo-cortical loop (Hughes and Crunelli, 2005). Transient EEG suppressions are a response to pharmacological perturbation of the brain. Whether sensitivity is encoded in suppression time patterns remains difficult to determine.

3.2 Population specificity

Children generally exhibit greater resilience to anesthetic drugs than adults; thus, monitoring their sensitivity requires distinct considerations. This resistance may be attributed to specific pharmacokinetics—a high metabolic rate—which requires higher doses for effective anesthesia in pediatric patients (Rigouzzo et al., 2019). To mitigate the potential risk of overdoses, the CDA could be used and extended to target-controlled infusion (TCI) propofol or remifentanil.

Our findings suggest that the CDA holds promise for clinical evaluation across diverse age groups, from children to adults. Moreover, it would be interesting to evaluate the algorithm’s efficacy on very young children, with a particular focus on determining its potential to prevent burst suppression, given their higher cortical sensitivity. Considering the scarcity of α-band activity before 1 year of age (Cornelissen et al., 2015; Liang et al., 2021), it becomes imperative to explore alternative forms of oscillatory activity that may be indicative of sensitivity to general anesthesia. This would provide a more nuanced understanding of anesthetic responses in pediatric populations, offering potential avenues for refining anesthesia administration in these vulnerable patients.

3.3 Clinical application

From a clinical perspective, the CDA parameters can be combined into a single sensitivity probability index (Sun and Holcman, 2022): during the first 10 min of propofol induction, the algorithm detects the first occurrences of IES and αS events and tracks the rate of increase of αS proportion in real time. These three values are fed into the logistic regression model to produce a sensitivity probability P ( S = 1 ), which can be displayed as a complementary alert alongside the BIS trace. Observing P ( S = 1 ) exceeding a threshold (e.g., 0.7) during induction would be an alert to the patient’s propensity for IES accumulation and could indicate a possible reduction in the target hypnotic concentration. Importantly, the therapeutic range for a sensitive patient should be substantially narrower than for a non-sensitive patient, and the CDA provides an early, individualized estimate of this range from the very beginning of anesthesia.

3.4 Limitations

One limitation of this study is the relatively small cohort (n = 50). Although our results show consistent and robust differences between the CDA and BIS parameters across multiple analyses (“Methods” and “Supp. Info.”), confirmation in a larger, ideally prospective, multi-center dataset would be important to establish the generalizability of these findings. Note that the third (but not first or second) predictor logistic regression model falls below the recommended events-per-variable threshold of 10, and results from this model should be interpreted cautiously.

Although the dataset was acquired in 2005–2006, the induction protocol, the neurophysiological phenomena analyzed, and the BIS algorithm used for comparison remain largely consistent with current practice, supporting the relevance of the present analysis.

Finally, future research should evaluate whether parameters derived from more recent monitors (e.g., PSI from Masimo and entropy modules) provide complementary or superior predictive value for induction-phase sensitivity and whether deep learning approaches (Wang et al., 2025) trained on larger multichannel EEG cohorts can improve upon the parsimonious CDA framework presented here.

4 Materials and methods

4.1 Artifact segmentation

We segmented the mechanical noise using the EEG signal power within a sliding window of length 10 s with 50% overlap. A time segment P i is considered an artifact when the power within such a window exceeds thrice the median absolute deviation (MAD), defined as the median of the absolute deviations from the data’s medianfor i = 1,2 , … , N, where N is the number of time windows. The MAD provides a consistent estimate of the standard deviation and thus is used to detect outliers in our data. Artifact segments are then corrected using the wavelet quantile normalization algorithm (Dora and Holcman, 2022; Dora et al., 2022).

M A D = m e d i a n ∣ P i − m e d i a n P ∣ , (1)

4.2 IES and αS segmentation

In brief, an IES is a transient period during which the EEG signal becomes nearly flat, reflecting a transient electrical silence of cortical activity. An alpha-suppression (αS) is a period during which the characteristic alpha-band oscillations (8–12 Hz) disappear from the signal while the overall EEG amplitude may remain elevated (Cartailler et al., 2019). Both events are detected automatically using adaptive, signal-derived amplitude thresholds established and validated by Sun and Holcman (2022), to which we refer for the full algorithmic specification and pseudocode. The mathematical definitions used in the present analysis are given below.

We recall that the EEF is first segmented following the procedure described by Sun and Holcman (2022). We filtered the EEG signal S ( t ) in the range 8−16 Hz to obtain the signal S α ( t ). We normalized S α ( t ) by its root mean square (RMS) to obtainwhereWe computed the difference D ( t ) (respectively, D α ( t )) between the upper and lower envelopes obtained by interpolating S ( t ) (respectively, S α ( t )) local maxima and minima. We then defined two thresholds, based on the absolute (respectively, relative) amplitude for IES (respectively, α −S).

S ̂ α t = S α t R M S S α , (2)

R M S S α = 1 T f − T 0 ∫ T 0 T f S α 2 s d s . (3)

T IES = min 8 , median D t , (4)

T α S = min 0.25 , median D α t , (5)

Finally, we define IES (respectively, α −S) segments Ω IES (respectively, Ω α S) as the time intervals such that the amplitude of S ̂ α is smaller than the threshold T α S, the amplitude of S ( t ) is smaller (respectively, greater) than the threshold T IES, and the intervals’ total duration is at least 1 s (respectively, 0.5 s). These conditions can be summarized mathematically thus:

Ω IES = t ⊂ T 0 , T f such that ∣ S t ∣ < T IES & ∣ S ̂ α I ∣ < T α S & ∣ I ∣ ≥ 1 s , (6)

Ω α S = t ⊂ T 0 , T f such that ∣ S t ∣ > T IES & ∣ S ̂ α I ∣ < T α S & ∣ t ∣ ≥ 0.5 s . (7)

4.3 BIS recordings and relevant parameters

BIS values were recorded using a BioSensor (Aspect Medical Systems) connected to a Cardiocap II monitor (Datex, General Electric). The recording was done continuously using Rugloop II software at a 4 Hz sample rate. We then estimated the relevant parameters from the EEG signal and the BIS as follows. where μ measures the total length of interval subsets.

• Time point T 0 is the reference corresponding to the beginning of the induction phase (hypnotic injection). To standardize the comparison of statistical parameters across patients and evaluate sensitivity, we set the duration to 10 min.
• First occurrence time of an IES ( t IES ) and an α −S ( t α S ), as well as the slope a of the α −S proportions, are defined (Sun and Holcman, 2022) with respect to the initial time point T 0.
• The minimum of the BIS is the lowest value reached within the induction phase [ T 0 , T 0 + 10 ] min. We have

B I S min = min t ∈ T 0 , T 0 + 10 min B I S t . (8)

• The first peak time of the BIS is the instant where it reached its minimum:

t BISpeak = arg min t ∈ T 0 , T 0 + 10 min B I S t . (9)

• The total time spent by the BIS under 40 during the induction is defined by

T B I S < 40 = μ t such that B I S t < 40 & t ∈ T 0 , T 0 + 10 min , (10)

4.4 Patient sensitivity labeling

To label a patient as sensitive to GA, we used two different criteria: 1) when the EEG presented at least a minimum of 12 s in IES during the first 30 min of anesthesia (Sun and Holcman, 2022); 2) when the propofol concentration was found to be less than 3 μ g . m l − 1 to maintain a BIS value at 50. We separated our patient cohort into two groups, sensitive versus non-sensitive, using both criteria.

4.5 Correlation measures between EEG events and BIS values

We describe now a method to generate binary vectors for correlating BIS with IES and α −S. For that goal, we generated two binary vectors A = ( a 1 , … ) and B = ( b 1 , … ), where a 1 , b 1 ∈ { 0,1 }. We first partitioned the EEG time series into discrete time points ( t 1 , t 2 , … ). When the α −band is present (respectively, absent) during the consecutive time point t k , … t k + q, we set a k = 1 , … , a k + q = 1 (respectively, a k = 0 , … , a k + q = 0). We then construct the following vectors:

• A P α S has coordinates a P α S = 1 when the proportions of α −S exceed 5% in a sliding window and 0 otherwise;
• A P IES has coordinates a P IES = 1 when the proportions of IES exceed 5% in a sliding window and 0 otherwise;
• A f α has component 1 when the maximum power frequency inside the band (6–30 Hz) is located inside the α −band (8–12 Hz).

We applied the same procedure for constructing the vector B associated with the presence or absence of the BIS in the following cases.

• B B I S mid: b B I S mid = 1 when the BIS is between 40 and 60 and 0 otherwise.
• B B I S low: b B I S low = 1 when the BIS is less than 40 and 0 otherwise.
• B B I S l o w 1: b B I S l o w 1 = 1 when the BIS is between 30 and 40 and 0 otherwise.
• B B I S l o w 2: b B I S l o w 2 = 1 when the BIS is less than 30 and 0 otherwise.

To assess the relationship between these binary vectors, we applied the cosine similarity formula defined by the relationwhere A and B are the two vectors and ∣ A ∣ is the number of 1 in A and A . B is the scalar product. Similarity K measures the presence of elements of A and B in the same position: when the two vectors contain 1 in all coordinates, then K = 1. When the positive coordinates of A and B never overlap, then K = 0. Note that the computation of the cosine similarity is independent of the time partition.

K A , B = ∣ A . B ∣ ∣ A ‖ B ∣ , (11)

4.6 Predicting patient sensitivity probability P ( S = 1 )

To evaluate patient sensitivity, we first applied a logarithm transformation to the normalized first α −S and IES occurrence times. We then quantified the predictive value of the six parameters from the two sets previously described using random sub-sampling cross-validation (Kohavi et al., 1995), which consists of generating multiple random data splits with a fixed ratio of 70% for training and 30% for testing. In each sampling, considering each combination of the three parameters, we trained and tested a logistic regression model (Kleinbaum et al., 2002) for the two sensitivity criteria (see SI for a different k-fold analysis).

We estimated patient sensitivity from two sets of variables, one derived from the BIS and the other from the CDA. Overall patient sensitivity was computed as the output of the logistic regression classifier using the parameters collected during the induction phase of GA. The conditional probability for the sensitivity S to take either 0 (non-sensitive) or 1 (sensitive) is defined bywhere the variables { v 1 , … , v n } are the parameters { a , t IES * , t α S * , B I S min , t peak , T B I S < 40 } and the coefficients ( ω 0 , … , ω n ) are estimated from the logistic regression optimization procedure.

P S = 1 ∣ v 1 , … , v n = 1 1 + exp − ω 0 + ∑ k = 1 n ω k v k , (12)

4.7 AUC-statistical evaluation

To evaluate patient sensitivity, we used stratified repeated k-fold cross-validation with k = 5 folds and 10 randomized repetitions, yielding 50 iterations in total. Stratification ensures that the proportion of sensitive and non-sensitive patients is preserved in each fold, which is particularly important given the modest cohort size ( n = 50 ).

Each patient is assigned to the test set exactly once per repetition, guaranteeing unbiased coverage of the full cohort. The 10 repetitions with re-randomized fold assignments provide stable estimates of the mean AUC and its variability. In each iteration, sensitivity, specificity, precision, and F1-score were computed at the Youden-optimal threshold ( J = sensitivity + specificity − 1 ) determined exclusively from the training folds to avoid data leakage, and all metrics were subsequently averaged across the 50 iterations. The two blocks are consistent with each other and replace all previous references to “70/30 random sub-sampling” in both “Methods” and the figure caption.

4.8 Statement about data acquisition

This study was based on EEG signals recorded during a previous randomized study conducted in children and adults who were anesthetized with propofol (Rigouzzo et al., 2019). The purpose of this previous study was to investigate the relationship between BIS and propofol concentration. Among the patient cohort, we excluded those who did not possess either BIS measures or concentration annotations or whose EEG signal quality was low (no visible α and δ bands during the maintenance phase, signal contaminated with artifacts, and/or cuts). In total, 50 patients were included in the study. Data were collected between 2005 and 2006. In patients aged 6–38 years undergoing for middle ear surgery, anesthesia was administered by target-controlled infusion of propofol using the Kataria model in children and the Schnider model in adults. Steady-state periods were performed at a fixed randomized concentration between 2, 3, 4, 5, and 6 μ g . m l − 1 propofol. In addition, a steady-state period was obtained during which the BIS was maintained at 50 ± 5.

This study was approved by the Ethics Committee CPP, Saint-Antoine, Paris, France (approval number: 04605). Written informed consent was obtained from children and their parents. Data were collected between 2005 and 2006, and the study was published in 2008. The protocol has, therefore, been carried out in accordance with the ethical standards laid down in the Declaration of Helsinki 1964 and its subsequent amendments.

For the present study, we retrospectively analyzed EEG from patients who had a complete set of EEG recordings, including the steady-state period performed at BIS 50. The anesthetic protocol and the procedures for EEG signal acquisition and recording are described in detail by Rigouzzo et al. (2019) and summarized in Table 3.

TABLE 3. Patient demographics and EEG and BIS statistical features.

4.9 General anesthesia protocol, EEG recordings, and patient monitoring

General anesthesia was performed with target-controlled infusion (TCI) of propofol, followed by continuous administration of remifentanil (0.25 μg.k g − 1 . m i n − 1). Before surgery, all subjects received premedication with oral antihistamine hydroxyzine (1 mg. k g − 1). At induction, propofol was administered with an initial target concentration of 6 μ g . m l − 1. The subjects were then intubated by cuffed tracheal tube after a single dose curarization by atracurium besilate (0.5 mg. k g − 1) and mechanically ventilated with an air-oxygen mixture and a breathing frequency of 14–20 m i n − 1 to obtain an E T CO2 of 30–35 mmHg. Propofol concentration was then maintained at 2–6 μ g . m l − 1 according to the Schnider model for post-pubertal subjects and the Kataria model for pre-pubertal subjects (Ab et al., 2017).

The decision to administer extra medication was left to the discretion of the anesthesiologist in the operating room in accordance with the institution’s standard-of-care protocol. EEG monitoring was accompanied by standard monitoring, which included the bispectral index (BIS), pulse oxygen saturation (SpO₂), heart rate (CF), systolic and diastolic blood pressures (SBP and DBP), mean arterial pressure (MAP), and temperature.

EEG recordings were obtained using the Brain-Quick Program Stem II (Micromed, France) with a single-channel recording from electrodes placed on the forehead and the left and right (reference) mastoids (Rigouzzo et al., 2008). The signals were sampled at 100 Hz. We used MATLAB R2021a software to perform the statistical analysis. The significance level used in this study was α = 0.05. The values were expressed in the mean ± standard deviation. Variables were compared using Student’s t-test or Wilcoxon–Mann–Whitney test as appropriate.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmede.2026.1810804/full#supplementary-material

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Footnotes

Edited by: Lia Morra, Polytechnic University of Turin, Italy

Reviewed by: Cong Yu, Chongqing Medical University, China

Çiğdem Altıntop, Erciyes University, Türkiye

Footnotes

EEG, electroencephalogram; GA, general anesthesia; TCI, target-controlled infusion; α −S, alpha-suppression; IES, iso-electric suppression; BIS, bispectral index; CDA, checkpoint decomposition algorithm; DoA, depth of anesthesia; MAD, median absolute deviation; RMS, root mean square; STFT, short-time Fourier transform; ROC, receiver operating characteristic; AUC, area under the curve; PK/PD, pharmacokinetics/pharmacodynamics; SpO 2, peripheral oxygen saturation; SBP, systolic blood pressure; DBP, diastolic blood pressure; MAP, mean arterial pressure; ETCO 2, end-tidal carbon dioxide partial pressure; CF, cardiac frequency.