## 1 Introduction  
Total Hip Arthroplasty (THA) is considered an effective treatment to improve the function of hip joint failure caused by: arthritis [1] (including osteoarthritis, rheumatoid arthritis, traumatic arthritis, and arthritis caused by other reasons, e.g., the microbleeds in joint capsule of congenital afibrinogenemiapatients [2]), fractures [3], malignant bone tumors [4], and so on. However, the main complication of THA, aseptic loosening [5], has plagued both patients and clinicians for many years. Next to aseptic loosening, periprosthetic infection and the subsequent biofilm formation presented a common reason for revision of THA [6,7]. The antibacterial potential of different implant materials and the strategy to avoid infection is discussed within literature [8,9]. At present, the implant to bone micromotion is considered the most important mechanical factors of aseptic loosening which represents one of the top five reasons for revision surgery [10]. The current gold standard to assess the implant to bone migration in vivo is Roentgen Stereophotogrammetric Analysis (RSA) [11,12]. The RSA method calculates implant to bone migration using rigid body kinematics. To define a rigid body of the implants surrounding bone, at least three tantalum markers must be intraoperatively injected into cancellous bone. To define the implant component as a rigid body, available RSA methods use specific approaches. (i) Marker-based RSA uses additional attached tantalum markers to the implant; model-based RSA uses on the one hand (ii) surface models of the implant, resulting out of Reverse Engineering (RE), or Computer Aided Design (CAD), or (iii) Elementary Geometrical Shape (EGS) models on the other hand [11,13]. The continuous development of the methodology should allow a more extensive application of it. The introduction of model-based RSA (mbRSA) replaced the additionally attached implant markers of marker-based RSA method by matching a three dimensional (3D) surface implant model to implants projection contour on X-ray films [13]. By using mbRSA, the possibility of an implant marker occlusion could be avoided, and more complex designs, for which additional implant marking presents a challenge, could be overcome. Interchangeable applicability between the gold standard marker-based RSA and mbRSA approach was proved in experimental and clinical settings for surface models [14,15] as well as for EGS approach [13,16,17]. The models required for mbRSA can be derived from RE, CAD, or EGS. Both RE and CAD model have the characteristic that they are highly close to the actual shape of an implant, so that they can be easily matched up with the implant contour on X-ray images. An EGS model uses 3D geometric shapes, likewise spheres, cones, etc., to represent the implant, which will then be partially matched to the implant contours (Figure 1). For example, the femoral ball head component can be matched with a sphere and the distal part of hip stem component can be matched with a cone. mbRSA-EGS uses three virtual markers calculated from the hip stem geometry to represent the rigid body of stem component [13]. The first virtual marker is allocated to the center of femoral ball head, which is represented by the sphere. The second virtual marker represents the femoral stem tip, located at the projection of the lowest tip point on the longitudinal axis of applied EGS cone model. The projection of the first maker (origin center first virtual marker; center of the ball head) on the longitudinal axis of cone model defined the third virtual marker. Remember, this determination of the femoral stem as a rigid body (by three virtual markers) using EGS models requires a stable head-taper connection [17]. Migrations of the stem component relative to femur bone (represented by maker model) were calculated using rigid body kinematics. This EGS approach enables us to create an individual model with each applied implant size for migration detection within a clinical study.