## 2 Materials and Methods
### Geometry Data Acquisition  
For each patient, preoperative MRI scans of the native hip joint (hi-res, voxel-size 1.8 mm) and an overview MRI of the distal femur and the pelvis were conducted. Additionally, standard pre- and postoperative radiographs (anterior-posterior projection) of the hip joint treated with THR were acquired. The study was approved by the local ethics committee (EK 175052011). Written informed consent was obtained from all patients before participation.  
The MRI files of the patients were imported in the software package Amira (v.5.4.1, Zuse Institute Berlin, Berlin, Germany; Thermo Fisher Scientific, Waltham, MA, USA), to reconstruct the 3D bone surface models using triangulated surfaces. The 3D surface models of the bony structure of the femur and acetabulum were obtained (Figure 1) by manually segmenting the bony structures slice per slice. Subsequently, the resulting 3D surface models were smoothed and converted into surfaces of mathematically defined non-uniform rational B-splines (NURBS) using Geomagic Studio (v.2013, 3D Systems, Rock Hill, SC, USA) [59]. In this manner, we enabled the subsequent virtual implantation of THR implants.  
Accordingly, an established joint coordinate system of the pelvis was generated according to [PERSON] et al. [18]. The pelvic coordinate system was created, originating out of the center of rotation of the hip joint, by fitting a sphere into the articulating joint surface of the acetabulum and defining its orientation using anatomical landmarks. The \(x\)-axis connected the right and left spinae iliac anterior superior; the \(z\)-axis touched the public symphysis and was directed cranially. Consequently, the \(y\)-axis was defined perpendicular to the \(x\)- and \(z\)-axis. The axes were translated into the center of rotation, and the Cartesian coordinate system, which refers to the anterior pelvic plane, was set up. In anatomical terms, this means that the \(x\)-axis represents the medio-lateral direction; the \(y\)-axis, the anterior-posterior direction; and the \(z\)-axis, the inferior-superior direction.  
The femoral coordinate system was generated using the anatomical frontal, sagittal, and transversal planes, which were defined by anatomical landmarks [18]. The frontal plane was defined as being tangential to three points: the most posterior points of the  
Figure 2: Virtually implanted total hip replacement (Bicontact® hip stem and Plasmacup® SC acetabular cup with a ceramic-on-ceramic bearing). The virtual implantation was carried out by an experienced orthopedic surgeon. Implant design parameters are subject to variation for the implant shaft (neck-to-shaft angle CCD, neck length L, head offset O, neck length L, and head diameter H) as well as for the acetabular cup (diameter C) of the analyzed total hip replacement.  
medial and lateral femoral cordyles, and the most posterior point of the trochanter minor. The sagittal plane was perpendicular to the frontal plane and contained the most lateral points of the condylus lateralis and trochanter major. Additionally, the transversal plane was perpendicular to the frontal and sagittal plane and contained the most distal point of the femoral cordyles. Additionally, the condylar notch was marked to allow reconstruction of the mechanical axis after virtual implantation. The defined planes were transformed into the center of rotation of the hip joint, which was defined using a spherical best-fit algorithm at the femoral head and acetabulum.  
The virtual implantation of the THR and the ROM analyses were conducted with the CAD software Creo Parametric (v.2.0, Parametric Technology Corporation, Boston, MA, USA) according to the preoperatively planned and postoperatively reconstructed situation, where the components were aligned under the supervision of one experienced orthopedic surgeon using clinical imaging data.