## 2 Materials and Methods  
In the following section, the previously validated musculoskeletal model of the lower right extremity [38], which is used in this study, is briefly presented. The developed multibody model to consider TKRs with three different MB design variants is then outlined. Two modeling strategies are finally proposed and assessed in terms of the kinematics of the knee joint and computation time during an active squat movement. Musculoskeletal Multibody Simulation Model of the Knee Joint for Different Mobile-Bearing Design Variants  
In the present study, the musculoskeletal model of the lower right extremity includes a posterior cruciate-retaining TKR and undergoes a squat motion. This model was based on the fourth \"Grand Challenge Competition to Predict In Vivo Knee Loads\" open-source dataset [39] and Twente Lower Extremity Model 2.0 [40]. More precisely, the model integrates a variant of the computed muscle controller with static optimization to compute the muscle forces necessary to mimic the squat movement based on the motion capturing within a forward dynamics multibody simulation [38; 41]. The predicted knee joint contact forces were successfully validated against in vivo measured knee forces from the telemetric knee replacement [39]. To virtually implant MB TKRs, native bone geometries are necessary. Therefore, we reconstructed the native geometries of the femur, tibia, fibula, and patella from the preoperative CT data of the open-source dataset [39]. For this purpose, the DICOM files were imported into the software AMIRA(r) (v5.4.1, Zuse Institute Berlin, Berlin, Germany; Thermo Fisher Scientific, Waltham, MA, USA) to segment the bone geometries, after which the 3D reconstruction was performed in Geomagic Studio (v2013, 3D Systems, Rock Hill, SC, USA). The positioning and orientation of the implant components were conducted in Geomagic Studio based on the segmented and reconstructed osseous geometries from CT scans of the male patient (age = 88 years, height = 168 cm, and weight = 66.7 kg) [39]. The virtual implantation and bone resections were conducted based on anatomical landmarks (e.g., transepicondylar axis). The implant components were virtually positioned on bones according to the surgical guideline and verified by an experienced orthopedic surgeon. In the current study, we used the Columbus(r) uniaxially rotating platform TKR design (Aesculap AG, Tuttlingen, Germany) as a baseline TKR design from which the two other design variants were derived. The implant size of the Columbus(r) rotating platform was chosen to ensure a similar dimension to the previously implanted posterior cruciate-retaining TKR. In this context, the size of the femoral component was F6N with a tibial baseplate of T4 and a patellar component of P5. The femoral component represents a multi-radius design, and the tibial tray has a symmetrical deep-dish design (Figure 1). The tibial insert rotates about the centrally located pin P\({}_{\text{C}}\) on the planar surface of the tibial tray. To limit the maximum extent of internal-external rotation of the tibial insert relative to the tibial tray, another pin positioned on the anterior region P\({}_{\text{A}}\) of the planar surface of the tibial tray glides in a guide groove positioned on the bottom surface of the tibial insert [42]. This design variant corresponds to type I according to [PERSON] and [PERSON] [18; 43]. The multibody model of the lower extremity (Figure 2) consists of the pes, tibia, fibula, patella, pelvis, and torso, as well as the implant components. Specifically, the body weight (\(m\) = 66.7 kg) of the male subject (age = 88 years, height = 168 cm) with a neutral limb alignment was considered [41], and the mass of each body part was defined as a function of the patient's body weight using regression equations [44]. The ligament structures were modeled as nonlinear springs using a mathematical model [45; 46].