###### Abstract
Monitoring of these changes enables observation of respiratory patterns and respiratory control responses. Studies have demonstrated that RIP calibrated a priori is accurate during exercise conditions [16]. The maximum physical load, ACP, is typically determined using the maximum values of SV and VO\({}_{2}\)[7]; however, several other methods of evaluating ACP have been developed. The American College of Sports Medicine recommends using 40%, 60%, 80%, and 85% of VO\({}_{2}\) max for developing prescriptions for various exercise intensity levels, and 55%, 70%, 85%, or 90% of HRmax may be used as indices of these VO\({}_{2}\)max levels [17]. Hence, the percentage of HRmax can be used as a proxy for VO\({}_{2}\)max. Studies have also examined breathing patterns before and after the induction of inspiratory fatigue during incremental exercise. BR increased from 22.5 \(\pm\) 4.4 (SD) during rest to 27.0 \(\pm\) 6.7 breaths/min (\(p\) < 0.02) at 75% of maximum work load following the induction of fatigue [18]. Training at sub-maximal physical loads is key for athletes because it does not cause exhaustion, has high training efficiency, and avoids the risk of injuries caused by ACP [8]. Various studies have explored metrics that could indicate sub-max training, such as HR variability (HRV) and SV variability (SVV). No gold standard exists for measuring the optimal training load (TL). One study used HRV indices to evaluate TL during exercise. Another study demonstrated that ratings of perceived exertion (RPE), blood lactate (BLa), and HF could be used to determine TL, and RPE and BLa were negatively correlated with HF [19]. In a previous study, we attempted to identify indicators for determining sub-max to avoid ACP. We determined that SVV has a high-correlation bandwidth with HRV. Moreover, the maximum cross-correlation R value between SVV and HRV at sub-max was significantly greater than that at rest and significantly lower than that during ACP. The spectral analysis correlation coefficient between SVV and HRV during ACP was less than those at all other stages [20]. Although the ACP assessment metrics are clear, the sub-max physical load assessment metrics are still insufficiently accurate. The complexity of a physiologic signal may be a helpful metric in both dynamical models of biological control systems and bedside diagnostics [21]. Disease and aging appear to reduce the adaptive capacity of individuals, and loss of complexity has been proposed to be a generic feature of pathologic dynamics [22]. Entropy is an appropriate measure of the complexity of a time series. Signals from diseased individuals have lower entropy values than those from healthy individuals [23]. Time series signals, such as HR variability, respiratory rate, and gait, generated by healthy physiological systems are complex [22]. Low signal complexity has been associated with system dysfunction. For example, fatigue resulted in a substantial loss of knee extensor torque complexity, as measured by signal entropy [22]. Complexity is associated with system adaptability, and fatigue-induced loss of complexity may contribute to an inability to engage in sustained physical exercise [24]. Because entropy is an effective measure of complexity, it has been increasingly used in recent studies. [PERSON] first introduced the concept of entropy in thermodynamics [25]. [PERSON] first applied entropy to information science [26]. Kolmogorov entropy was the first introduction of the concept of fractals to entropy theory [27]. [PERSON] introduced approximate entropy (ApEn), which was derived from Kolmogorov entropy [28]. ApEn can be used to quantify temporal unpredictability for various applications, such as medical-physiological research (e.g., HR), meteorology, and finance. ApEn has been used in numerous clinical applications [29]. However, the self-matching of sequences in the ApEn technique may produce inconsistent results if the sequence length of a data set is changed.