## 4 Discussion  
The most recent published study introduced an automated method for identifying the aerobic threshold using Heart Rate (HR) data gathered during the Cardiopulmonary Exercise Test (CPET), specifically in adult athletes, including rowers and amateurs [6]. This current research aimed to expand the application of this innovative method by validating its reliability across a broader sample. Specifically, we tested the method's effectiveness across different demographic groups, including variations in age, gender, and fitness levels, as well as among individuals with diverse health conditions, such as obesity and cardiovascular diseases, and those undergoing treatment with beta-blockers. By examining these variations, we aimed to establish the method's robustness and adaptability in detecting the AerT under a wide range of physiological conditions, ensuring its relevance for both general health and specialized athletic training. Our study extended the automated detection method to 111 time series from individuals between 11 and 70 years old and including various health conditions (healthy children, obese individuals, and cardiac patients). The tests were administered on both treadmills and cycle-ergometers, necessitating different incremental protocols to achieve a consistent total exercise time and thereby yielding comparable HR time series [6; 7; 8]. The post-hoc power of the F-test increased from 0.88 for a 27-subject sample [6] to 0.999 for our expanded sample of 111 subjects. In the present research, the HR values derived from the automated RQA-based method were not significantly different from those obtained using the gold standard ventilatory equivalents-based method (Gex), as evidenced by a \(p\)-value greater than 0.05. Furthermore, a strong correlation (r > 82%) and an acceptable Technical Error (TE) of 8% were observed. Importantly, despite the potential effects of beta-blockers in cardiac patients altering the HR variability during exercise, the RQA-based method proved to be reliable for this group. However, it's worth noting that in individuals with heart conditions, the use of heart rate as an exercise threshold marker is compromised by medication effects. For a more accurate exercise prescription in these cases, reliance on the Rating of Perceived Exertion (RPE) is advised [4]. General physiological considerations could be confirmed through intergroup comparisons. For instance, regular exercise enhances cardiovascular efficiency, reflected in higher HR and maximum oxygen consumption (VO\({}_{\text{2 max}}\)) values among athletes and young athletes when compared to obese or cardiac patients [1; 3; 8]. Age-related factors like lung volume also exhibited expected trends. The RQA-based method shows promising future applications in the detection of AerT, a fundamental and complex challenge of exercise physiology [26]. By analyzing the recurrence patterns in physiological signals, RQA could provide deeper insights into  
Figure 6: [PERSON] plot for (**a**) HR (bpm) and (**b**) VO\({}_{\text{2}}\) (mL/min) at AerT. The participants are divided into athletes (group A, blue cross), obese (group O, red circle), cardiac patients (group C, light-blue diamond), and young athletes (group Y, yellow circle), respectively. The horizontal black line corresponds to bias (mean difference), and the dashed horizontal black line to the lower and upper limits of agreement (LOA); LOAs are calculated as the mean difference \(\pm\)1.96 standard deviations (SD). the complex interplay of physiological processes and the critical thresholds demarcating different metabolic states. This enables personalized threshold identification, capturing unique patterns specific to each individual test. For the young athletes' group, it's crucial to consider the physiological uniqueness of adolescence, including growth spurts and changes in aerobic capacity. Tailored reference values and assessment methods are needed for this population [27].