One of the most fundamental and historically established methods for evaluating neural activity in the brain is power spectrum analysis. This method can capture changes in neural networks associated with aging [24], development [25–27], and pathological conditions [17] through variations in the spectral components [reviewed in [28]]. Interactions across regions in the brain lead to the maturity of neural networks, which results in the emergence of faster components such as theta, alpha, beta, and gamma bands [25–27]. However, neonates and infants predominantly exhibit delta band activity, which reflects the immaturity of the brain and is commonly observed during both wakefulness and sleep stages [26]. In cases of neonatal encephalopathy, the decreased delta band power and the shape of the power spectrum profile in the delta frequency band correlate with increased disease severity [10, 12, 13]. Therefore, power spectrum analysis can be considered one of the relatively well-established methods for detecting abnormalities in neonatal neural activity.

The complexity analysis of neural activity signals—captured using EEG or magnetoencephalography—can be used to identify the developmental stage of neural networks in neonates and infants [25, 29]. The complexity of EEG signals at a single electrode reflects the neural interactions. In contrast, functional connectivity measures that assess synchronization between neural activities across regions require data from numerous electrodes to capture these interactions [17, 19, 30]. Therefore, complexity analysis can be particularly advantageous, especially when simple EEG devices with a restricted number of electrodes are used. Over the past several decades, researchers aiming to calculate the complexity of neural activity have proposed several metric types, which include Lyapunov exponnet to evaluate chaotic dynamics [31], fractal dimensions [16], and various types of entropy [17–19]. Sample entropy (SampEn), a widely used metric for assessing the complexity and unpredictability of time-series data [32], works by determining the frequency of recurring similar patterns within the dataset given a specific tolerance level. Lower SampEn values indicate greater regularity, whereas greater SampEn values reflect increased randomness or greater complexity. SampEn is considered to be more reliable than approximate entropy (ApEn) for shorter and noisier data because it excludes self-matching patterns. Fuzzy entropy (FuzzyEn) has been proposed as an alternative to SampEn [33]. While SampEn calculates complexity by binarizing the entropy values, FuzzyEn applies fuzzy logic to represent these values more precisely, thereby avoiding binary simplification. This approach helps minimize information loss [33]. Consequently, FuzzyEn can calculate complexity from an even shorter time-series dataset than that required by SampEn [34].

The complexity analysis of EEG signals in the context of HIE has been extensively explored [8, 9]. Nemomssa et al. demonstrated that in cases of HIE that progress to cerebral palsy, the accuracy of complexity metrics (such as SampEn, permutation entropy, and spectral entropy) that were applied to alpha-band slow components derived through empirical mode decomposition were high [8]. Mbanuzue et al. demonstrated that the decrease in both permutation entropy and spectral entropy within the slow components (corresponding to the delta band) of the EEG signals correlated with the cognitive decline observed when the patients were two years old [9]. Both studies found that the topological characteristics of functional connectivity (e.g., radius, transitivity, global efficiency, and characteristic path length) strongly correlated with their corresponding EEG signal components [8, 9]. Therefore, complexity analysis has been extensively utilized to capture the alternation of neural activity patterns associated with HIE, and thereby has significantly advanced current research.

Although complexity analysis of EEG signals has been extensively explored in the context of HIE [8, 9], it has not yet been applied to the detection of asphyxia, which represents an earlier stage before the onset of HIE. Given that early intervention is critical in improving neonatal outcomes, addressing complexity analysis at the asphyxia stage is essential for developing early detection methods. Furthermore, no prior studies have combined complexity analysis with the well-established EEG power spectrum analysis. Leveraging multiple metrics from the same physiological signal to enhance detection performance has been proposed in other fields [17, 28, 35], and applying such an approach to the complexity and power analysis of EEG signals in asphyxia represents a promising avenue for improving detection accuracy.

We collected data from 30 neonates—21 healthy newborns and nine with asphyxia—from the Department of Neonatology at the pediatric intensive care unit (PICU) and NICU of K.R.M.T. Wongsonegoro Regional Public Hospital. The nine neonates with asphyxia constituted the clinical group. We diagnosed the neonates with asphyxia on the basis of the criteria outlined by the American College of Obstetrics and Gynaecology (ACOG), American Academy of Pediatrics (AAP), and World Health Organization. The asphyxia group comprised two mild, five moderate, and two severe cases. No neonate with asphyxia exhibited HIE. In contrast, the sex-, weight-, and age-matched control group comprised 21 neonates with no reported history of neuropsychiatric disorders. Table 1 presents the demographic characteristics of both groups. This study was conducted in accordance with ethical standards to ensure the safety, privacy, and wellbeing of all participants involved. Ethical approval was obtained from the KRMT Wongsonegoro Regional Public Hospital (approval number 093/Kom.EtikRSWN/VII/2024), granted on July 26, 2024. This study adhered to all relevant ethical guidelines, including informed consent from the participants, confidentiality of data, and ensuring that the participants were not exposed to unnecessary risks. All procedures were reviewed to ensure alignment with both national and international ethical standards for research involving human participants.

EEGs were recorded using a Neuro-DCcap EEG system (East Medic Corporation, Kanazawa City, Japan) that was developed for basic medical research. The EEG system consists of eight electrodes (F3, F4, C3, C4, P1, P2, O1, and O2) and a reference electrode positioned at Fz. Standard bipolar derivations (F3-C3, C3-P3, P3-O1, F4-C4, C4-P4, and P4-O2) were employed. The impedance of each electrode was maintained at below 40 KΩ. The EEG data were sampled at 250 Hz and bandpass-filtered between 1.5 and 50 Hz.

The EEG data were recorded for 30–60 min. Following data acquisition, segments of the EEG recordings were processed using the artifact subspace reconstruction (ASR) algorithm in the EEGLAB toolbox; the algorithm identified and removed artifacts; moreover, we selected a continuous 20-second epoch with artifact levels below the threshold for further analysis. In total, we obtained one, two, and three epochs from one, 15, and 14 neonates, respectively.

For the FuzzyEn analysis, we conducted a repeated-measures analysis of variance (ANOVA). The group (healthy neonates vs. neonates with asphyxia) served as a between-participant factor; six electrode pairs and 30 temporal scales as within-participant factors. The Greenhouse–Geisser correction was applied to account for sphericity violations, and statistical significance was set at an α level of 0.05. The F-values obtained from the ANOVA reflect the comparison of variance within and between the groups. Post-hoc t-tests were used to further explore the effects of each group and interactions across the electrode pairs and temporal scales. The Benjamini–Hochberg false discovery rate (FDR) correction was applied to control for multiple comparisons across the 180 p-values generated from the six electrode pairs and 30 temporal scales (q < 0.05).

To analyze absolute power, we performed repeated-measures ANOVA again, with group (healthy neonates vs. neonates with asphyxia) as the between-participant factor and six electrode pairs as within-participant factors. Greenhouse-Geisser correction and an α level of 0.05 were applied again. The F-values obtained from the ANOVA reflect the comparison of variances between and within groups. Post hoc t-tests were used to assess the differences between groups and interactions across the electrodes. Log-transformed absolute powers were used to assume normal distribution. To account for multiple comparisons, FDR correction was also applied to the six p-values generated from the six electrode pairs (q < 0.05).

Receiver operating characteristic (ROC) curve analysis was performed to assess the ability of the model to distinguish asphyxia. A logistic regression model incorporating FuzzyEn and absolute power was developed to predict the probability of asphyxia for each participant. True- and false-positive rates were calculated for a threshold range (0–1.0) across both groups. The identification accuracy was quantified using the area under the ROC curve (AUC), with AUC values serving as indicators of classification performance. A logistic regression model based on FuzzyEn, absolute power, and their combination was used to evaluate the classification accuracy, where an AUC of 1.0 indicates perfect identification, and an AUC of 0.5 corresponds to chance-level identification. Here, a leave-one-out cross-validation (LOOCV) was used [37]. Pearson's correlation r between FuzzyEn and absolute power was used for multicollinearity in the logistic regression. As the multicollinearity criterion, |r| > 0.9 was set.

We compared the FuzzyEn between the asphyxia and control groups at each temporal scale τ and for each electrode pair. Figure 2A shows the dependence of FuzzyEn on the temporal scale τ across electrode pairs in both control and asphyxia groups. Table 2 presents the results of the repeated-measures ANOVA for FuzzyEn. The analysis revealed a significant main-group effect, and no interaction effects were observed for group × electrode-pair, group × scale, and group × electrode-pair × scale. Figure 2B shows the dependence of t-value on temporal scale τ as the post-hoc t-test. These results confirmed the significantly smaller FuzzyEn in the asphyxia group, in particular, in 1 ≤ τ ≤ 30 at P3-O1 (q < 0.05).

To compare our method with the relatively well-established power spectrum analysis used for detecting abnormalities in neonatal neural activity [10, 12, 13], we compared the absolute power of the delta band between the asphyxia and control groups for each electrode pair. Figure 3A shows the dependence of the absolute power of the delta band across electrode pairs in the control and asphyxiated groups. Table 3 presents the results of the repeated-measures ANOVA for these powers. We observed a significant main-group effect but no interaction effect for group × electrode-pair. In Figure 3B, as their post-hoc t-test, t-values of absolute power between the both groups among electrode-pairs were shown. These results indicated the significantly smaller absolute power at F4-C4, C3-P3, and P3-O1 in the asphyxia group (q < 0.05).

The logistic regression model identified asphyxia using a significant reduction in FuzzyEn at P3-O1 shown in Figure 2B and absolute power at F4-C4, C3-P3, and P3-O1 shown in Figure 3B. Figure 4 showed the ROC for classifiers of controls and asphyxia groups by logistic regression based on the averaged FuzzyEn in temporal-scale range 1 ≤ τ ≤ 10 at P3-O1 and absolute power at F4-C4, C3-P3, and P3-O1. AUC was enhanced by the combination of FuzzyEn and absolute power when compared with cases that used them separately. Considering that the current asphyxia group includes relatively few participants in comparison with healthy group, evaluation for precision-recall curve, which places more emphasis on detecting asphyxia cases, is important. The result shown in Supplementary material demonstrated that the same tendency with the case using ROC was obtained.