# Sleep Apnea Classification Using the Mean Euler-Poincare Characteristic and AI Techniques
Atrial fibrillation (AF) is widely related to OSA problems, as mentioned in [13; 14], where the authors conducted questionnaires and home sleep studies to check this relation. Researchers have explored two approaches to detect sleep apnea events in the literature: feature engineering-based techniques and deep learning-based methods. In the first category, the ECG signal is analyzed, and different features are extracted from the P-wave (atrial depolarization), QRS complex (ventricular depolarization), and T-wave (ventricular repolarization), which reflect different cardiac cycle phases. For example, [PERSON] et al. presented a cost-effective, noninvasive algorithm for detecting sleep apnea using single-lead ECG. By analyzing heart rate variability and QRS complexes, the algorithm accurately classifies apnea episodes, achieving 84.7% accuracy and demonstrating high potential for sleep medicine applications [15]. [PERSON] explored the utility of using a single-lead ECG to determine sleep stages and detect OSA across 30-s epochs throughout the night, potentially replacing more complex polysomnography systems. Data from 18 subjects, including 10 diagnosed with OSA, revealed promising results: support vector machines (SVMs) and quadratic discriminant analysis (QDA) achieved over 82% accuracy in classifying sleep stages and around 88% in detecting OSA. Using the RR-interval (time interval between two successive R-peaks in an ECG), three features were extracted, resulting in high classification performance. This suggests that single-lead ECG, combined with SVM or QDA, could effectively monitor sleep and OSA. However, integrating additional physiological features could further enhance accuracy [16]. [PERSON] et al. described an algorithm that detects sleep apnea using ECG features and a combined convolutional neural network (CNN) and long short-term memory (LSTM) recurrent network [17]. Using the same combination of networks, we looked at the work by [PERSON] and [PERSON] [18], which reported accuracy, sensitivity, and specificity of 88.13%, 84.26%, and 92.27%, respectively. Feature extraction using machine learning (ML) methods was employed to detect OSA events. In the study by [PERSON] et al. [19], wavelet transform was used to extract features from the sub-bands and classify them using various ML methods. In the work of [PERSON] et al., the HRV analysis and ECG-derived respiration (EDR) were used to extract complementary information using a residual group network [20]; their results had an accuracy of 90.3%, a sensitivity of 87.6%, and a specificity of 91.9%. [PERSON] et al. demonstrated a CNN that learned features from the ECG, reaching a sensitivity of 88.2% in classification [21]. Instead of relying on an overall diagnostic analysis of the entire biomedical signal, certain studies focus on determining if a patient is experiencing apnea by analyzing specific indicators. One approach measures the variation in oxygen saturation over a short interval (12 s) [22; 23]; other indicators include non-linear methods mentioned in [24]. [PERSON] et al. used Holter-ECG to screen for sleep-disordered breathing (SDB) by comparing it with nocturnal polygraphy (PG) in 50 cardiology patients. The ECG estimates demonstrated strong agreement with PG, exhibiting high specificity (0.96) and good sensitivity (0.77) for detecting significant SDB, promising an effective, cost-efficient method for SDB screening [25]. Some studies have adopted an approach of using fragments of the signal, such as analyzing it minute by minute [26] or using windows of varying sizes [27], to identify occurrences of apnea instead of making an overall diagnosis of OSA, which is generally regarded as the responsibility of physicians. Various biomedical signals are utilized for the classification and diagnosis of OSA. For instance, the photoplethysmography signal ([28], the \(S_{p}O_{2}\) signal [24; 29; 30], the oronasal air flow signal [31], the ECG signal [23; 26], and so on.