###### Abstract  
Sub-maximal physical load (sub-max) training is optimal for athletes. However, few methods can directly assess whether training is sub-max. Therefore, this study aimed to identify metrics that could assess sub-max training by predicting maximal physical load, helping athletes to avoid the risks associated with maximal training. Physiological data were collected from 30 participants in a bicycle incremental exercise experiment, including the R-R interval (RR), stroke volume (SV), breath-to-breath interval (BB), and breathing rate (BR). Sample Entropy (SampEn) analysis was used to assess the complexity of the physiological data. BR increased with exercise time but could not be used to identify the sub-max stage; however, SampEn BB could effectively identify the sub-max stage (\(p<0.05\)), as could the novel indicators SampEn SV and cardiac output (\(p<0.01\)). This study also identified the threshold value of each SampEn value in sub-max, which can be used as a sports science indicator to assess the load of athletes. The results suggest that SampEn-based indicators can be used to assess sub-max and maximal physical load. These findings can be used as a guide for quantitative exercise healthcare. sub-maximal physical load; breathing; cardiovascular response; sample entropy 202313813381338133813381381381338  
indefinitely; it has a maximum size, and thus, a maximum SV exists. The aerobic capability plateau (ACP) is a state in which the left ventricle is unable to expand due to cardiac fatigue after exercise for an excessive intensity or duration; at the ACP, SV can no longer increase, and EICF may occur. ACP typically occurs in maximum physical load training, and the maximum value of SV and oxygen consumption (VO\({}_{2}\)) is the standard metric for the clinical judgment of a person's ACP [7]. Researchers have demonstrated that training in the stage before ACP is optimal for increasing athletic performance [8]. Training at sub-maximal load (sub-max) can avoid exhaustion and enhance the training efficiency of athletes [8]. ACP may lead to myocardial injuries due to ventricular tachycardia or fibrillation [9]. ACP may also directly cause right ventricular overload and left ventricular dysfunction. It may also cause patchy myocardial fibrosis, particularly in the atria, interventricular septum, and right ventricle, which creates a substrate for atrial and ventricular arrhythmias [10]. Studies have indicated that ventricular dysfunction occurs after prolonged and intense exercise. One study reported that the right ventricular volume increased after a race, but the right ventricular postrace ejection fraction decreased by 9% relative to the baseline [11]. Although the left ventricular volume increases after exercise, the ejection fraction remains unchanged. These findings indicate that investigating exercise-related health care is critical for increasing safety during sports [12]. [PERSON] demonstrated that the impedance cardiogram (ICG) method operates under the principle that blood has electrical impedance. ICG could be used to obtain accurate SV values [13]. Another study demonstrated that ICG can be performed during dynamic exercise. Furthermore, SV measurements produced using ICG have been compared with gold standard measurements and found to be accurate [14]. Cardiac echocardiography can also be used to measure SV; however, echocardiogram measurements must be performed at a precise angle, which is challenging during dynamic exercise. Therefore, ICG is the optimal method of measuring SV during exercise. Breathing rate (BR) can be measured using spirometry and body plethysmography [15]. However, the wearing of a mask during exercise can be restrictive. Respiratory inductance plethysmography (RIP) is a noninvasive method for measuring BR. In RIP, a participant was two straps with insulated coils around the thorax and abdomen; obtaining the waveform through these coils through a transducer and demodulating it can reveal changes in the diameter of the thorax and abdomen during respiration.