## 7 Conclusions  
In this paper, we proposed a system that measures the knee conditions of athletes during practice using stretch sensors installed on a knee supporter and notifies the ACL injury risk based on the estimated knee flexion and valgus angles derived from the sensor data. In the evaluation experiment, participants wearing the supporter-type device performed activities such as running and jumping, and the stretch sensor values and knee joint angles during these activities were collected to verify whether the proposed system could estimate knee flexion and valgus angles.  
The evaluation results show that the knee flexion angle estimation accuracy was good even with models trained on data from other users. The method using the RFR as the machine learning algorithm and instantaneous stretch sensor values as features achieved an MAE of 8.73\({}^{\circ}\). For the knee valgus angle, models trained on the user's own data had a better estimation accuracy. The method using the RFR and instantaneous stretch sensor values along with the past 20 samples of instantaneous values achieved an MAE of 0.81\({}^{\circ}\). The estimation of knee valgus angles required the user's own data, and since the user could measure the ground truth of knee flexion angles under the same conditions, it is suggested that the user's own data should also be used for knee flexion angle estimation.  
Even using the gold standard 3D motion captures, the knee valgus angles for intense motion may show large variations. Since this was an evaluation of how much the data deviate from the motion capture data, the ground truth value might not be accurate for movements where the motion captures were unreliable. The difficulty in obtaining truthful values for the frontal plane motion of the knee is a limitation of this research.  
Therefore, when purchasing the proposed system, users need to exercise in an environment similar to that of this experiment, where stretch sensor values and knee joint angles can be measured for about an hour. They should collect their own data, build a machine-learning model using this data, and integrate the model into the system for use. Although the estimation accuracy of knee valgus angles with data from other users was low, the results suggest that it might be possible to estimate knee flexion and valgus angles by creating machine learning models based on trends in stretch sensor values and knee valgus angles during flexion. Hence, if the knee bending characteristics can be confirmed in advance, the proposed system could potentially be used without the user needing to collect stretch sensor values and knee joint angles during exercise.  
In future work, we plan to create a lower limb model to verify whether the system can estimate knee joint angles for movements that are difficult to obtain in vivo and could potentially result in ACL injuries.  
Conceptualization, K.H. and T.T.; methodology, R.T., A.O., K.H. and T.T.; software, R.T.; validation, R.T., A.O., K.H. and T.T.; formal analysis, R.T., A.O., K.H., M.T. ([PERSON]) and T.T.; investigation, R.T., A.O., K.H., M.T. ([PERSON]) and T.T.; resources, R.T., A.O., K.H. and M.T. ([PERSON]); data curation, R.T. and M.T. ([PERSON]); writing--original draft preparation, R.T.; writing--review and editing, A.O. and T.T.; visualization, R.T.; supervision, K.H., T.T. and M.T. ([PERSON]); project administration, K.H. and T.T.; funding acquisition, K.H. and T.T. All authors have read and agreed to the published version of the manuscript. This work was supported by JSPS KAKENHI, Grant Number JP17K17913.  
This study was conducted in accordance with the Declaration of Helsinki, and approved by the Ethics Committee of Kobe University (No. 05-47, 2023).  
Informed Consent Statement: Informed consent was obtained from all participants involved in this study.  
Data available on request due to the privacy restriction.  
The authors declare no conflicts of interest.