# Development of a Generic Numerical Transtibial Model for Limb-Prosthesis System Evaluation
## 2 Materials & Methods
### Boundary Conditions  
Three load cases were analysed in the simulation to cover the donning phase, single-leg stance and gait. The results of previous studies have shown that a numerical analysis of the prosthesis donning is necessary, as the initial stress affects the results in the following steps [30]. Due to the rectification of the socket, the contact pressure was distributed to the preferred areas after the donning. The first step in the simulation was carried out by solving the initial interference fit between the socket and the residual limb. The second load step was the commonly used vertical loading of the limb-prosthesis system, representing a single-leg stance. A vertical force of 850 N was applied to the rigid femoral cavity, approximating the 50 th percentile weight for adult males of all races and ethnicities in the United States, which is 85.6 kg according to the 2008 National Health Statistic Reports [24]. Although the average European male weight, as stated in AnyBody Repository, is 77 kg, a higher weight was used to fit into the P5 loading level, which ranges from 80 kg to 100 kg according to ISO 10328 [31]. The reason for the higher weight was to test the applicability of the model at higher loads compared to the P3 (up to 60 kg) and P4 (from 60 kg to 80 kg) load levels. The same loading level was also used for the static analysis of the gait. The simulated P5 load case was developed based on the experimental tests, including all participants, some of whose body mass also exceeded 100 kg. The load case was divided into the P5 I and P5 II conditions, referring to the heel strike and push-off phases of gait, respectively. Each condition was simulated in two steps: (1) Settling test force--forces and moments occurring during the normal gait cycle, (2) Proof test force--a rare severe event where the loads and moments are much higher than in the previous step. To comply with the Standard, the prosthetic structures should remain undamaged and fully functional in both cases. All numerical load steps and their magnitude are listed in Table 3.  
As described in the previous subsection, the bones and other prosthetic components were rigid and connected via remote points. This results in the direct action of forces and moments on the distal part of the socket and the femoral cavity. The force line passes through the remote points Ft at the upper end and the Fb at the lower end. At Ft, translations \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Component** & **Material Model** & **References** & **Parameters** \\ \hline \multirow{2}{*}{Soft tissue} & \multirow{2}{*}{[PERSON] first order} & \multirow{2}{*}{[PERSON] et al. [27]} & MU1 = 0.012 MPa \\  & & & A1 = 14 \\  & & & D1 = 1.67 MPa\({}^{-1}\) \\ \hline \multirow{3}{*}{Silicone liner} & \multirow{3}{*}{[PERSON] third order} & \multirow{3}{*}{[PERSON] et al. [28]} & C10 = 0.2014 MPa \\  & & & C20 = 0.00115 MPa \\ \cline{1-1}  & & & C30 = 0.00041 MPa \\ \cline{1-1}  & & & D1 = 3 MPa\({}^{-1}\) \\ \hline \multirow{2}{*}{Socket} & \multirow{2}{*}{Linear–elastic} & \multirow{2}{*}{[PERSON] et al. [29]} & E = 4991 MPa \\ \cline{1-1}  & & & \(\gamma\) = 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material models and their parameters used in the simulation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Loading Step/Loading Condition** & **Magnitude [N]** \\ \hline \multicolumn{2}{c}{Donning} & Solving interference \\ \hline \multicolumn{2}{c}{Vertical force (single leg stance)} & 850 \\ \hline \multirow{2}{*}{ISO P5 I (heel strike)} & Settling test force & 1024 \\ \cline{2-2}  & \multicolumn{2}{c}{Proof test force} & 2240 \\ \hline \multirow{2}{*}{ISO P5 II (push off)} & Settling test force & 920 \\ \cline{1-1}  & \multicolumn{2}{c}{Proof test force} & 2013 \\ \hline \end{tabular}
\end{table} 
Table 3: Description of the loading steps with related magnitude. were restricted in all directions, but all rotations were free.