## 4 Discussion  
For the first time, 3D analyses based on state-of-the-art GA and VA were combined successfully to assess a representative THA population. The overall scope was to measure the patterns and extremes of motion in standard and demanding motor tasks in terms of the ROM and peak rotations in the three anatomical planes at the replaced hip, as well as measure the corresponding StL distance. The THAs were successful and the patients had very good clinical results at the follow-up; therefore, the present observations do represent a realistic picture of the StL interaction in the worst case scenario. GA confirmed that standard motor tasks, i.e., those typical of daily living, do not require a large ROM at the replaced hip, and that very large joint rotations were instead reached in those tasks that were particularly demanding. Nevertheless, no StL contact was measured in any patient in any of these tasks; therefore, it can be deduced that the limits of the ROM after a THA was associated with the soft tissues rather than to the StL impingement. 3D GA- and VA-based evaluations provided accurate and original findings regarding the overall segment and joint motion and the possible StL contacts, i.e., prosthetic cup-to-neck contact. In general, successful THAs were observed for all implanted femoral heads, with these including those usually considered to have large diameters. In this context, GA revealed a good overall functional recovery and very large hip joint rotations in all three anatomical planes for both the standard and demanding motor tasks. Despite these large rotations, the StL distances calculated using VA were all found to be large enough to exclude this contact after considering the instrumental errors. Additionally, there was a clear trend for larger ROMs and smaller cut-to-neck distances for the larger head diameters. The present novel technique of the StL distance calculation deserves a few considerations. This technique is based on established techniques of prosthesis component pose estimation, even during motion, which relies on good quality 2D fluoroscopy images and relevant detailed 3D CAD models. This technique was originally established for knee joint replacements [35; 44] and has recently been extended to THAs [33; 40; 41; 42], though for a limited number of motor tasks. The large amount of literature in this area shows that the overall accuracy is smaller than 1 mm and 1\({}^{\circ}\), which is good enough for the conclusions of this study. Of interest to physicians and designers involved in THAs is the information about the anatomical plane and the extent to which additional joint motion is necessary to get the real StL final impingement from the measured extreme positions. In other words, it would be very interesting to work out how far these replaced joints were from contact with the prosthesis components. To investigate this, careful computer simulations would be necessary: starting from the CAD models and the absolute and relative positions of the two prosthesis components in the three anatomical planes, further known rotations at the components should be applied to the models until contact is achieved, where this should be done in several different combinations of motion in the three planes. This is a complex exercise, \begin{table}
\begin{tabular}{c c} \hline \hline
**Motor Tasks** & **StL Distance** \\ \hline \multirow{2}{*}{Squat} & \(11.4\pm 6.1\) \\  & (\(5.2\div 21.9\)) \\ \hline \multirow{2}{*}{High step flexion} & \(8.7\pm 5.2\) \\  & (\(2.3\div 17.3\)) \\ \hline \multirow{2}{*}{Tailor sitting} & \(13.0\pm 5.9\) \\  & (\(2.2\div 19.8\)) \\ \hline \multirow{2}{*}{Lunge forward} & \(11.8\pm 5.1\) \\  & (\(3.0\div 19.6\)) \\ \hline \multirow{2}{*}{Lunge backward} & \(11.9\pm 5.4\) \\  & (\(2.3\div 21.6\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stem-to-liner (StL) distance (in mm) from the 3D VA; the mean \(\pm\) standard deviation value from all patients, along with (min \(\div\) max) values, are shown.