## 4 Discussion
Although good criterion-related validity and high reliability in the estimation of energy expenditure using the same heart rate monitoring device were established [41], the major contributing factors such as the physical activity and sedentary levels [42], and percentage of body fat [43] were not reflected. Additionally, a lower heart rate recorded during the IBP might have underestimated the whole-body metabolism and energy consumption. Therefore, we acknowledge the level of accuracy in estimating energy expenditure as a limitation. While accepted, our hypothesis was based on increased blood flow for a body position with 15\({}^{\circ}\) head-down tilt [21; 22; 23] and the lack of direct measures on blood flow parameters limit us to explain and interpret the observed benefits. As an elevated blood pressure during and after exercise is typical, performing IBP immediately after exercise may be harmful by applying additional pressure to blood vessels. When comparing the inversion duration (90\({}^{\circ}\) for 2 min) in previous reports [44; 45] to ours (90\({}^{\circ}\) for 13 s: Figure 2), we assume that the possibility of additional blood pressure was minimal. Additionally, our subjects' heart rate at the last minute of the treadmill run and the beginning of IBP were 183 and 121 bpm, respectively. A 2-min interval for the post-run measurements resulted in a 34% reduction in heart rate (183 to 121 bpm). Considering that both heart rate and blood pressure are linearly related to exercise intensity [46], a reduced heart rate value indirectly supports the idea that our subjects performing IBP were not in a deleterious situation. However, future studies should attempt to compare the change of blood flow volume and pressure during the recovery period to resolve our limitations. Lastly, the contraindications of IBP should be addressed since the IBP may be unsafe for pregnant individuals or those with abnormal blood pressure or other cardiovascular diseases, eye or ear injuries, or herniated discs. According to our data, a 10-min recovery strategy consisting of 5 min of IBP and a 5-min static stretch was the most effective of the tested protocols in removing blood lactate and minimizing energy expenditure during the acute recovery period (the first 30 min, postexercise). Therefore, the recovery condition including our IBP protocol is an appropriate strategy to enhance physical and psychological recovery. We particularly recommend this IBP protocol for athletes who complete several matches(events) within a few hours on a single day (e.g., tournaments for Taekwondo, Judo, weightlifting, fencing, wrestling, sprint cycling, and swimming). In the final stage of matches (e.g., after quarterfinals), the fatigue level would be high. In this situation, physical fitness and stamina can play bigger roles than technical and tactical strategies. Therefore, we recommend practicing our IBP method between matches. If an IBP device is unavailable, peer-assisted IBP or a supine position with legs elevated against a wall could be used instead. Conceptualization, M.S.K. and J.P. Methodology, J.P. Formal analysis, M.S.K. and J.P. Investigation, J.P. Data curation, M.S.K. Writing--original draft preparation, M.S.K. and J.P. Writing--review and editing, J.P. Supervision, J.P. Project administration, J.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This study received no specific grant from any funding agency. We thank [PERSON], [PERSON], and [PERSON] for their data collection and reduction. The authors declare no conflict of interest.