## 2 Materials and Methods
### Data Analysis  
The resulting radiographs of the implant-bone model setting from the three wear simulation protocols and seven pelvic orientations were analysed by 2D\({}_{\text{wear}}\) and 3D\({}_{\text{wear}}\) approaches.  
For the 2D\({}_{\text{wear}}\) method, wear analysis was performed using plain radiographs and the wear analysis tool of a standard digital surgical planning software (mediCAD Classic, version 5.1, mediCAD Hectec GmbH, Landshut, Germany). Wear detection could be performed with two or more follow-up radiographic images. According to the instructions for use provided by the manufacturer, the wear procedure was only applicable for acetabular cups with a spherical outer contour and a bearing couple PE inlay with a ceramic or metal ball head. Radiographs required the presence of a calibration sphere within the radiographs  
Figure 3: Pelvic model element and its alignment options. (**a**) Local coordinate system based on an anatomical axis of the pelvic model element. (**b**) Anterior/posterior inclination up to \(\pm\)5 deg of so-called pelvic tilt, presenting a motion within the sagittal plane, representing rotation around the medio-lateral axis. (**c**) Lateral inclination up to \(\pm\)5 deg of so-called pelvic obliquity, presenting a motion within the frontal plane and rotation around the anterior-posterior axis. (**d**) Pelvic rotation up to \(\pm\)5 deg, presenting a motion within the transverse plane and rotation around the cranio-caudal axis.  
(original mediCAD calibration sphere, diameter: 25 mm; tolerance: \(\pm\)0.1 mm). To enable THA wear detection within two scaled X-ray images, a correctly drawn reference line, detected ball head centres, and acetabular cup centres were required. The reference line was located and defined by the Kohler's \"tear drop\" or by the tangent of the os ischii. The centre of the femoral ball head was defined by the centre point of a circle over three detected points on the circumference of the femoral ball head. This procedure was done manually by the clinician or technician performing the analysis. The same procedure was carried out for the acetabular cup component: with three points on the cup rim, the resulting centre point of the circle was created by the software.  
For the 3D\({}_{\text{wear}}\) method, wear analysis was performed using RSA image pairs and a model-based RSA approach using elementary geometrical shape (EGS) models to calculate wear (MBRSA v.4.1, RSAcore, LMUC, Leiden, The Netherlands). EGS model spheres and hemispheres were used to represent the femoral ball head and the acetabular cup component. Scaling of these EGS models was performed according to the known diameter of both components. Counter-detection for the ball head and cup was performed at the region of interest within the left and right RSA image pair. Pose estimation algorithms matched the detected contour within the RSA image pair (actual contour) to the virtual contour of the EGS models, until the three-dimensional pose and orientation of the models within the RSA image pair were matched. Relative wear, presenting the displacement of the centre of the ball head model with respect to the cup model, was calculated in consecutive examinations relative to the reference (baseline) examination.  
The wear results obtained from 2D\({}_{\text{wear}}\) and 3D\({}_{\text{wear}}\) approaches were compared to set-point wear values.