## 1 Introduction  
Anterior cruciate ligament (ACL) injury is a serious sports injury that requires ACL reconstruction (ACLR) surgery and a rehabilitation period of 6-12 months to return to sports [1, 2]. Owing to advances in ACLR techniques and rehabilitation, many athletes are now able to return to sports [1, 3, 4, 5, 6]. However, even after spending a lot of time in rehabilitation and finally returning to sports, 15-23% of athletes still suffer a second ACL injury (i.e., graft tear or contralateral ACL injury) [7]. When returning to sports, it is necessary to carefully assess any movement that may cause a second ACL injury.  
One factor that predicts ACL injury is the large vertical ground reaction force (VGRF) during landing [8]. A simulation study using cadavers showed that an increase in the compressive force of the tibofemoral joint causes posterior displacement of the femur, leading to ACL injury [9]. Therefore, a large VGRF during landing is considered a risk factor for primary and secondary ACL injuries. In fact, the peak VGRF during single-leg landing after ACLR tends to be higher in the involved limb than in the uninvolved limb, especially in those who have lower quadriceps strength in the involved limb than in the uninvolved limb [10]. Furthermore, interlimb asymmetry in the knee extension moment during landing is one of the risk factors for secondary ACL injury [11], which is also related to interlimb asymmetry in VGRF [12]. Therefore, assessment of the VGRF during landing is important for patients who have undergone ACLR and are aiming to return to sports.  
A force plate is required to measure the VGRF, which is usually used in a laboratory setting. However, since the evaluation of movement after ACLR is mainly performed in clinical and athletic settings, it is not realistic to evaluate VGRF in a laboratory setting. Therefore, researchers have been seeking alternative methods for estimating the VGRF in clinical settings [13, 14]. A wearable inertial measurement unit (IMU) is one of the tools that can be used for clinical motion evaluation [15, 16, 17, 18, 19, 20]. A wearable IMU attached to the body can measure triaxial acceleration. In recent years, wearable IMUs have also been frequently used for motion evaluation after ACLR [21]. In a previous study of healthy participants, a significant positive correlation was found between the peak acceleration from the wearable IMU and the peak VGRF during single-leg landing [14]. However, the relationship between acceleration and VGRF during landing in patients after ACLR remains unclear. Patients who have undergone ACLR have been shown to have a different landing strategy than healthy individuals [22]; therefore, the association between acceleration from IMUs and VGRF may differ between healthy individuals and patients after ACLR. Furthermore, it is unknown whether acceleration from IMUs can detect interlimb asymmetry in the VGRF during landing after ACLR. Clarifying the relationship between acceleration and VGRF during landing in patients after ACLR could lead to the development of alternative methods for evaluating the VGRF in clinical settings.  
The purpose of this study was to determine the relationship between VGRF and acceleration from IMUs during single-leg drop landing after ACLR. In addition, the present study examined whether acceleration from IMUs could identify interlimb asymmetry in the VGRF during landing after ACLR. The hypothesis was that, as in previous studies on healthy participants [14], a significant correlation would be found between VGRF and acceleration after ACLR during landing, and interlimb asymmetry would be detectable.