# In-Vivo Quantification of Knee Deep-Flexion in Physiological Loading Condition trough Dynamic MRI
## 3 Results  
The rotational and translational MAE for the different pairs of tested planes are reported in Table 1, considering this measure as an indicator of the system accuracy. The optimal planes show the lowest errors. The registration accuracy estimated on the simulated DMRI for the three subjects was 1.8\({}^{\circ}\)\(\pm\) 1.4 and 1.2 mm \(\pm\) 0.8, for rotations and translations, respectively. In Figure 6, the bone registration on the two DMRI planes is depicted. Figure 7 shows the comparison among knee motion as reconstructed from a real DMRI exam and as estimated through static scans for the three volunteers, while Figure 8a shows the three repetitions for one volunteer. The overall repeatability for the three volunteers was 3.2\({}^{\circ}\) and 1.3 mm.Over the 1456 perturbations of the initial registration, 97.6% (1421) resulted in differences below 0.5\({}^{\circ}\) and 0.5 mm with respect to the unperturbed motion (Figure 8b). In the remaining 2.4% of cases (35), the reconstruction error was significantly detectable, resulting in average rotational and translational differences of 17.3\({}^{\circ}\)\(\pm\) 7.7 and 9.7 mm \(\pm\) 4.5, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Plane Combination** & **Rotational MAE** [\({}^{\circ}\)] & **Translational MAE [mm]** \\ \hline Sag-Cor & \(1.8\pm 1.5\) & \(1.8\pm 1.7\) \\ Sag-Ax1 & \(2.8\pm 2.4\) & \(1.8\pm 1.4\) \\ Sag-Ax2 & \(\mathbf{1.0\pm 0.7}\) & \(1.4\pm 0.9\) \\ Sag-Med & \(2.4\pm 1.4\) & \(1.6\pm 1.4\) \\ Sag-Lat & \(1.8\pm 1.1\) & \(1.3\pm 1.5\) \\ Cor-Ax1 & \(3.2\pm 4.6\) & \(4.2\pm 4.8\) \\ Cor-Ax2 & \(3.0\pm 3.0\) & \(2.4\pm 1.9\) \\ Cor-Med & \(2.8\pm 2.5\) & \(1.7\pm 1.6\) \\ Cor-Lat & \(2.5\pm 2.1\) & \(1.9\pm 1.7\) \\ Ax1-Ax2 & \(3.1\pm 2.3\) & \(1.4\pm 0.8\) \\ Ax1-Med & \(2.2\pm 1.9\) & \(1.4\pm 1.4\) \\ Ax1-Lat & \(3.5\pm 1.9\) & \(5.5\pm 5.8\) \\ Ax2-Med & \(5.0\pm 3.2\) & \(2.7\pm 2.7\) \\ Ax2-Lat & \(2.3\pm 1.5\) & \(2.8\pm 2.5\) \\ Med-Lat & \(1.8\pm 1.1\) & \(\mathbf{1.2\pm 0.6}\) \\
**Opt1-Opt2** & \(\mathbf{1.0\pm 0.5}\) & \(\mathbf{0.7\pm 0.4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rotational and translational MAE for each of the tested combinations of DMRI planes. Figure 6: Representation of the bone registration, on the two optimal DMRI planes, at different flexion angles. The registered femur intersection with the planes is depicted in blue, while the tibia–fibula complex intersection is depicted in red. Figure 7: Comparison between knee kinematics reconstructed from dynamic (blue) and static (black) MRI. The Abduction/adduction (AA), internal/external rotation (IE), anterior/posterior (AP), proximal/distal (PD), and medial/lateral (ML) translations are plotted vs. the knee flexion angle. The specific scanner employed in this study offers several advantages. Being open, it allows a considerable range of motion. Moreover, the possibility to scan the person in vertical position allows for the analysis of the articulation under the action of the weight and the muscles, thus resulting in a more physiological loading condition. The 2D/3D registration algorithm shows a rotational and positional accuracy below 2\({}^{\circ}\) and 1.5 mm, where the latter is in the order of magnitude of twice the in-plane dimension of the DMRI voxel for this study. The registration accuracy is reasonably limited by the low intensity of the magnetic field of the employed scanner. It has, indeed, been shown that motion tracking through DMRI is proportional both to the strength of the magnetic field and to the velocity of the tracked object [18]. Other studies investigating the knee through DMRI achieved higher accuracy using higher intensities [15]. Nevertheless, the achieved accuracy is still enough to allow for the characterization of the physiological and pathological knee kinematics, while the low intensity of the magnetic field makes the analysis practically non-invasive and compatible, to some extent, with measures on patients with articular prostheses or other small medical devices.