## 2 Materials and Methods  
Four pairs of fresh-frozen cadaver knees (8 knees, 4 male knees) with a mean age of 72 \(\pm\) 7 years were used in this study. All specimens were macroscopically intact and did not exhibit any gross pathology. After they had been thawed, the cadaveric knees were dissected carefully, while retaining the femur, tibia, patella, ligament, patellar tendon, quadriceps, skin, and subcutaneous fat surrounding the knee joint. The femur and tibia were cut at 29 cm from the knee joint line. The quadriceps were separated into individual components: rectus femoris (RF), vastus intermedius (VI), vastus lateralis (VL), and VM. This separation was performed with a guide using fascial planes between muscles. For each cadaver, one knee was randomly assigned to undergo TKA and the other was assigned to a control condition group that did not undergo TKA. All TKA surgical procedures were performed by a single surgeon using a standard cruciate-retaining prosthesis instrumentation system (LOSPA; Corentec Co. Ltd., Seoul, Korea) with a high-conformity tibial insert design. Both the femur and tibia were secured within cylinder tubing (3.5 cm diameter and 9 cm height) filled with resin (Illinois Tool Works Inc., Cincinnati, OH, USA). The femur and tibia were fixed to the knee simulator system in a state of full knee-joint extension. The knee-simulator system can provide 4 degrees of freedom at the femur and the tibia jigs (Figure 1). However, in the current study, the simulator system provided 2 degrees of freedom at the femur and one degree of freedom at the tibia (Figure 2). Flexion motion was controlled by lowering the crossbar on the knee-simulator system to induce rotation of the femur jig and tibia jig at 3\({}^{\circ}\)/s. This was driven by a linear actuator at a speed of 40 mm/s. The reaction forces and moments in the knee joint were quantified through a 6-axis load cell with a sampling frequency of 1000 Hz (Advanced Mechanical Technology Inc., Watertown, MA, USA) mounted on the bottom of the tibia jig of the simulator system (Figure 2). The coordinate system of the knee joint was defined as the \(x\)-axis in the anterior/posterior direction, \(y\)-axis in the medial/lateral direction, and \(z\)-axis in the proximal/distal direction (Figure 2). The knee flexion angle was then measured continuously from 0\({}^{\circ}\) to 90\({}^{\circ}\), using 2 inertial measurement unit sensors (SEED Tech Co., Ltd., Bucheon, Korea) attached to the posterior-proximal position of the femur and the posterior-distal position of the tibia (Figure 2). The coordinate system of the inertial measurement unit sensors at the femur and tibia were defined as the \(x\)-axis in the medial-lateral direction, \(y\)-axis in the anterior-posterior direction, and \(z\)-axis in the proximal-distal direction (Figure 2). Each quadriceps muscle (RF/VI, VM, and VL) was clamped and connected to loading weights through a wire loop. The muscle force distribution of the quadriceps for the normal loading condition was applied on the basis of muscle cross-sectional area data, as previously reported (VM: 31 N; RF/VI: 49 N; VL: 45 N) [25; 26; 27; 28; 29; 30]. To simulate VM impairment, we set the muscle force for VM in the muscle force distribution of the quadriceps to zero (VM: 0 N; RF/VI: 49 N; VL: 45 N). The force directions were adjusted in accordance with the primary fiber direction of respective musculature [25; 27]. The force direction of RF/VI was set equal to the femoral axis in the frontal plane. In the sagittal plane, the RF/VI was then placed at an angle of 16.8\({}^{\circ}\)\(\pm\) 1.3\({}^{\circ}\) anterior to the femoral axis. The force directions of the VM and VL were placed at angles of 28.9\({}^{\circ}\)\(\pm\) 0.7\({}^{\circ}\) and 24.5\({}^{\circ}\)\(\pm\) 2.0\({}^{\circ}\) relative to the femoral axis in the frontal plane, and 13.6\({}^{\circ}\)\(\pm\) 1.2\({}^{\circ}\) posterior to the femoral axis in the sagittal plane. The test for each condition was then repeated 3 times to confirm reproducibility.