# Patellofemoral Joint Stress During Front and Back Squats at Two Depths
## 2 Materials and Methods
### Procedures  
After a two-minute walking warm-up on a treadmill at a self-selected pace, 47 surface-based retroreflective markers were placed on the participant's skin or tight-fitting clothing (Figure 1). Four markers were placed on their head, six markers on the trunk, five markers on the pelvis, 16 markers bilaterally on the upper extremities, and 16 markers bilaterally on the lower extremities. All subjects were provided the same model athletic shoe (Saucony, Zealot, Lexington, MA, USA) to minimize any confounding effects of footwear. Fifteen cameras (Motion Analysis Corporation, Santa Rosa, CA, USA) and two force platforms (Model 4080, Bertec Corporation, Columbus, OH, USA) were used to collect motion and analog data at 180 Hz and 1800 Hz, respectively. Figure 1 shows the 47-marker set in the static position, the cameras, and the force platforms. Marker data (three-dimensional marker locations) and force platform data (ground reaction force and moments) were used in a 44 degree-of-freedom (DOF) musculoskeletal model (Human Body Model; Motekforce Link, Amsterdam, Netherlands) with 18 rigid segments to calculate joint kinetics, kinematics, and muscle forces. The trunk was modeled as two segments coupled to provide 3-DOF, the hip was modeled as a ball-and-socket joint with 3-DOF, the knee joint was modeled as a 1-DOF hinge joint, the subtalar joint as a 1-DOF joint, and the ankle joint as a 2-DOF. Three hundred individual muscle tendon units were represented. Figure 1: Custom 47 retro-reflective marker set with camera and force plate placements. Each participant's leg length was measured from the greater trochanter of the femur to the ipsilateral lateral malleolus of the fibula. Squats were then performed to a depth of 60% or 80% of each participant's leg length, individualizing depth relative to the length of the participant's leg. Using this method of measurement, 60% of the leg length measured from the lateral malleolus represented a greater squat depth. An elastic band was tethered behind each participant to act as a tactile cue for squat depth termination when their posterior thigh segment contacted the band. Five minutes were provided for each participant to practice each squat and warm up. Participants randomly performed one set of five repetitions for each squat condition: front squat at 60% leg length, front squat at 80% leg length, back squat at 60% leg length, and back squat at 80% leg length (Figures 2 and 3). One minute of rest was provided between each squat condition. A metronome set to 60 beats per minute standardized the rate of squatting. Trials were repeated if the participant's squat did not match the cadence of the metronome, or they did not reach the correct depth as indicated by contact with the band. Adequate time was provided for rest to prevent fatigue and injury. Each participant performed the squat with a 20.41 kg bar, regardless of squat condition, individual body weight, or individual strength. This fixed load was selected to maintain consistency across all conditions and within-subject comparisons; however, we acknowledge that this approach may limit inter-individual comparisons, as the absolute load does not account for differences in participants' body mass or strength capacities. Skeletal model kinematics were determined with a kinematic solver using global optimization. Joint moments were obtained from equations of motion and inverse dynamics. Muscle forces were then determined from the joint moments by minimizing a static cost function where the sum of squared muscle activations was related to maximum muscle strength. A recurrent neural network was used to solve for static optimization. Total quadriceps force was calculated by summing the individual muscle forces from the rectus femoris, vastus medialis, vastus lateralis, and vastus intermedius. The following set of equations were used to determine the two-dimensional patellofemoral joint reaction force (PFJRF) load based on \(k\)[21].