# Biomechanical Analysis of Two Types of Oseointegrated Transfemoral Prosthesis
## 3 Results
### FEM Analyses  
The FEM analyses of all different fall scenarios converged at an average time of \(93\pm 10\) min.  
Table 3 reports the peak values of the equivalent von Mises stress on the external part of the femur and on the implant.  
It can be pointed out that the highest values were found for the FB BL scenario. This result agrees with the trends of the forces/moments over the time plotted in Figure 8. It is probable that very high values of the anteroposterior flexion moment (M\({}_{\rm zB}\)) measured during the FB BL scenario (Figure 8) overstress the implant/bone assembly. Figure 9 shows the plots of the maximum values of the von Mises stress on the bone during the falls. Only the values related to the OPL system have been reported because very similar trends have been observed using the two kinds of prostheses (OPRA and OPL). From these plots it is possible to detect at what time the peak values occur and also to correlate the variations of the maximum stress values on the bone and the imposed boundary conditions (Figure 8).  
In all analysed fall scenarios, both for the OPL and the OPRA system, the maximum values of the von Mises stress has been found on the abutment (Figure 10), which is always the most stressed part of the prosthesis. In the FB BL scenario, the maximum value of the von Mises stress on the prosthetic implant, both using the OPRA and the OPL implant, exceeded the ultimate tensile stress of the titanium alloy. In this condition, a failure of the abutment of the prosthesis is expected (Figure 10).  
Figure 8: Plots of forces and moments vs. time calculated for different fall scenarios: Fall Forward (FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall Backwards “By Push” (FB BP).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Femur**} & \multicolumn{2}{c}{**Implant**} \\ \hline  & **Screw-Type** & **Press Fit** & **Screw-Type** & **Press Fit** \\ \hline FF & 93 & 91 & 607 & 723 \\ FF BL & 59 & 49 & 913 & 855 \\ FB BL & 161 & 152 & 1286 & 1546 \\ FB BP & 63 & 59 & 602 & 557 \\ \hline \end{tabular}
\end{table}
Table 3: Peak values of the equivalent stress (MPa) calculated for different fall scenarios: Fall Forward (FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall Backwards “By Push” (FB BP).  
Figure 10: Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on the OPRA (**top**) and the OPL (**bottom**) prosthesis.  
Figure 9: OPL prosthesis: Plots of the maximum values of the equivalent stress on the bone during different fall scenarios: Fall Forward (FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall Backwards \"By Push\" (FB BP).  
Figure 11 shows the equivalent stress distributions on femur using the OPRA and the OPL implant. It can be noticed that in both cases the maximum value of the von Mises stress is very high but, probably, no failure of the bone occurs. This is because, due to very high stresses on the prosthesis, a failure of the abutment occurs before the bone could be damaged.  
Regarding the bone/implant interface, the H number, calculated through the Hoffman formula, was always lower than 1, thereby ensuring that no failure at the bone/implant interface occurs. The highest values, calculated for OPRA and OPL implants during FB BL fall scenario, are 0.58 and 0.27, respectively.