This study retrospectively focused on the analysis of EEG recordings using the RQA method; therefore, different EEG recordings were combined and standardized to create an EEG database. Detailed information on the experimental models related to the included recordings is provided in the relevant references (Kantar-Gok et al. 2017, Karlsson et al. 2022). Ethical approval was additionally obtained for this study (Approval no: 2025.06.B.004). Rats (female, weighing 250–300 g, Wistar rats, aged three months) were randomly divided into four groups: Group 1: rats were sham operated and treated with saline (i.p. and gavage) (S, n = 18); Group 2: rats were sham operated and treated with saline (i.p.) and RA (gavage) (R, n = 18); Group 3: rats were treated with D-galactose (i.p.) and saline (gavage) (DG, n = 18); Group 4: rats were treated concomitantly with D-galactose (i.p.) and RA (gavage) (DGR, n = 18). D-Galactose (80 mg/kg/day) was administered by i. p. injection and RA (50 mg/kg/day) was given via gavage for 60 days. All experiments were approved by the Akdeniz University Animal Care and Use Committee and were performed in accordance with the European Community directive.

EEG was recorded between 09:00 am and 02:00 p.m. Rats were anesthetized (24 g/100 ml) with intraperitoneal injections of urethane (1.2 g/kg, Sigma-Aldrich, St Louis, MO, USA). The head of the anesthetized animal was attached to the standard stereotaxic frame, and four small holes (1.5 mm diameter) were drilled for the placement of the stainless-steel electrodes. Recording electrodes were placed bilaterally on temporal (AP:−4.5 mm, ML:−3.5 and + 3.5 mm) and frontal cortices (AP:+5 mm, ML:−2 and +2 mm) and reference and ground electrodes were placed on the cerebellar skull. The anesthetized animal was moved into a sound-attenuated recording room. The EEG signal was amplified (Brainamp EEG/EP Amplifier, Brain Products, Munich, Germany), band- pass filtered (0.1–300 Hz), and digitized at a 1000 Hz sampling rate (Brainvision Recorder, Brain Products, Munich, Germany). EEG signal was recorded for 10 min.

The EEG data were filtered (0.1–150 Hz) and each period was segmented into 2 s epochs. Frequency analysis was performed using a fast Fourier transform (FFT) algorithm with a 10% Hanning window and spectral EEG powers computed. The EEG variables chosen were absolute power in two frequency bands, delta (0.5–3.5 Hz), theta (4–8 Hz). Filtering and segmentation were performed with the BrainVision Analyzer program (Brain Products GmBH). Each EEG epoch exported to MATLAB and all RQA analyses were performed in MATLAB.

Since its introduction by Eckmann et al., RQA has been widely utilized as a nonlinear analytical method for understanding the dynamics of non-periodic time series (Eckmann et al. 1987). Owing to the inherently non-linear and non-stationary characteristics of EEG signals, RQA has become a valuable tool for identifying hidden patterns associated with physiological events and neurodynamic processes (Pitsik 2025).

In the present study, following the completion of standard preprocessing procedures, the EEG data were segmented into 2-second epochs, and RQA was applied specifically to the delta and theta frequency bands.

All the RQA analysis were performed using custom MATLAB scripts implemented based on established algorithms described in the referenced (Marwan and Kurths 2002). In accordance with established practices reported in previous literature, the embedding dimension (m = 5), time delay (τ = 26 samples), and fixed recurrence rate (RR = 12.5%; lmin=vmin = 2) for RQA were optimized through average mutual information, false nearest neighbors screening and sensitivity analyses across all segments and then fixed for the study (Supplementary Fig. 1) (Bonnette et al. 2020, Riehm et al. 2024). Although τ = 26 samples correspond to a short temporal delay, the effective embedding window ((m − 1)τ ≈ 104 ms) spans a substantial portion of the theta cycle and a meaningful segment of the delta cycle. Thus, the analysis captures the continuous structural evolution (microdynamics) of band-limited oscillations within a phase-space trajectory, rather than treating signal values (data points) such as certain time like peak amplitude. This fixed thresholding approach was employed to mitigate common issues in RQA application, such as the need for individualized threshold estimation and the variability of recurrence density across epochs. By maintaining a constant RR, the comparability and interpretability of recurrence plots across different EEG segments were improved. The recurrence plot examples for each group are presented in Fig. 1.

The representative recurrence plot examples for each group. Qualitative inspection of the recurrence plots reveals that aged animals (c) exhibit denser and more elongated diagonal and vertical structures compared to the sham group. These visual patterns represent the physical manifestation of increased DET and LAM, signaling a transition toward more predictable and rigid neural states in aging, which are visibly softened in the RA-treated group d. Both axes represent time indices of the EEG signal and that recurrence points indicate temporal similarity between system states. a rats were sham operated and treated with saline (i.p. and gavage) (sham) (S); b rats were sham operated and treated with saline (i.p.) and RA (gavage) (R); c rats were treated with D-galactose (i.p.) and saline (gavage) (DG); d rats were treated concomitantly with D-galactose (i.p.) and RA (gavage) (DGR)

Subsequently, key RQA-based features—Determinism (DET), Entropy (ENTR), and Laminarity (LAM)—were extracted from the recurrence plots. These features offer critical insights into the signal dynamics: DET reflects the degree of predictability or regularity within the signal; ENTR quantifies the complexity of the deterministic structures, capturing the richness of the pattern distributions; and LAM measures the proportion of recurrent points forming laminarity (vertical structures), which indicates the tendency of the system to remain in the same state over time.

The mathematical formulations of these parameters are defined as follows in the subsequent Eq. 

$$DET=\frac}}}^ lP\left( l \right)}}}^ lP\left( l \right)}}$$

(1)

$$ENTR= - \mathop \sum \nolimits_}}}^ p\left( l \right)lnp\left( l \right)$$

(2)

$$LAM=\frac}}}^ lP\left( l \right)}}}^ lP\left( l \right)}}$$

(3)

where l is the length of diagonal lines, N is the maximal line length, P(l) is the number of diagonal line which length is l.

Statistical analysis of data was performed by using one-way ANOVA and Tukey test (The Tukey test inherently corrects for multiple comparisons to control the family-wise error rate) were used for comparing subgroups by SPSS (SPSS 18.0, SPSS Inc., Chicago, IL) software for Windows. During comparison, values smaller than 0.05 (p < 0.05) were accepted significantly for all results. Data are represented as mean ± SEM.