# Knee Loading Asymmetries During Descent and Ascent Phases of Squatting After ACL Reconstruction
## 2 Materials and Methods
### Sqats  
Three-dimensional motion analysis was used to examine participants' bilateral squats. Kinematic and kinetic data were simultaneously collected with two embedded force platforms (1080 Hz; Bertec Corporation, Columbus, OH, USA) and an eight-camera motion capture system (120 Hz; Qualisys Inc, Goteborg, Sweden). Passive retroreflective markers (14 mm) were placed on anatomical landmarks of the trunk, pelvis and lower extremities as previously described, including the sternum, C7, T10 and bilateral acromia, upper back, posterior superior iliac spine (PSIS), iliac crest, anterior superior iliac spine (ASIS), medial and lateral femoral epicondyles, medial and lateral malleoli, superior and inferior heel and the first and fifth metatarsal heads [15]. In addition, rigid shells, each containing four retroreflective markers, were secured bilaterally at the lateral thigh and shank.  
Participants first completed a 1-s static trial in anatomical position [15]. After this calibration trial, the markers on the ASIS, femoral epicondyles, malleoli and first metatarsal heads were removed prior to dynamic trials. As part of a larger testing protocol (gait, single-leg squats, drop vertical jumps), participants then completed three sets of five bilateral squats with arms crossed over the chest [16]. They were instructed to squat to a comfortable depth at a self-selected speed without further instruction or practice.  
Marker trajectories were labeled in Qualisys Track Manager and exported to Visual3D (HAS-Motion, Kingston, ON, Canada). Target and ground reaction force (GRF) data were low-pass filtered using a fourth-order bidirectional Butterworth filter with a 12 Hz cutoff frequency [1].  
A subject-specific model including the trunk and lower extremities was created using measured height and mass to estimate segment lengths and joint centers as previously described [1]. To account for the marker diameter and its base, virtual landmarks were offset by 9 mm toward the underlying bone [17]. Virtual ASIS and PSIS landmarks were used to create a Visual 3D composed pelvis. Hip joint centers were estimated using the method of Bell et al., knee joint centers were defined as the midpoints between the virtual femoral epicondyle landmarks, and ankle joint centers were defined as the midpoints between the virtual malleolar landmarks [18; 19].  
Each squat was segmented into descent and ascent phases. The start of the squat was defined when vertical center-of-mass velocity exceeded 0.02 m/s downward, and the end of the squat was defined when upward center-of-mass velocity decreased below 0.02 m/s (Figure 1). The lowest vertical center-of-mass position determined the transition point between the descent and ascent phases. External knee and hip moments were calculated using an inverse dynamics approach, and joint impulses for the descent and ascent phases were computed using the trapezoidal rule [20].  
Variables of interest included vertical ground reaction force impulse (vGRFi), external knee flexion moment impulse (KFMi), ratio of external hip flexion to knee flexion moment impulse (hip-to-knee ratio (HKRi)) and time spent in the descent and ascent phase. Data from the 3 middle squats (second, third and fourth) of each set of squats (9 total squats averaged) was averaged to account for more variable movement patterns during the first and fifth squats of each set [1]. For each variable, an interlimb ratio (ILR) was calculated using this equation: involved limb/uninvolved limb. An ILR of 1 indicates an equal distribution of load between limbs (vGRFi), between knees (KFMi) or between the hip and knee joints across limbs (HKRi). An ILR of less than 1 for vGRFi and KFMi indicates lower loading in the injured limb or knee compared to the uninjured limb or knee. An ILR greater than 1 for the HKRi indicates a greater contribution of loading in the hip than the knee in the injured limb compared to the uninjured limb. Time spent during the descent and ascent phases was expressed in seconds.