# Damage-Based Assessment of the Risk of Cut-Out in
## 2 Materials and Methods
### Finite Element Models  
The three-dimensional finite models of male and female right femora generated from the CT data of the Visible Human Project ([PERSON] et al., 2017) by [PERSON] et al. [PERSON] et al. (2018) were used as the basis for this work. These models were qualitatively validated by showing that their computational predictions of bone strain were consistent with experimental measurements performed on cadaveric femora [PERSON] et al. (2018); [PERSON] et al. (2019). Considering an anteroposterior view, an unstable fracture classified as 31-A2.2 in the Muller AO classification system was modelled in Solidworks (Dassault Systemes, Waltham, MA, USA) with an angle of 43\({}^{\circ}\) between the fracture line and the femoral shaft axis (Dassault Systemes, Waltham, MA, USA), an opening angle of 6.5\({}^{\circ}\), and an intrusion distance of 95% of the fracture line length to simulate a severe scenario based on clinical experience. The fracture divided the bone model into two parts: a superior part (SP), including the femoral neck and head, and an inferior part (IP), including the femoral shaft. The fracture fragments were not included in the model. To virtually treat the simulated trochanteric fracture, a PFNA implant was modelled in Solidworks, in accordance with a real sample. The assembly of the components followed the guidelines of the surgical technique guide, with the blade being placed in eight positions (Figure 1): in the superior-inferior direction, central and inferior positions were considered; and for each of these positions, four discrete positions were considered along the medial-lateral direction. The four central positions were defined by placing the tip of the blade 5 mm, 10 mm, 15 mm, and 20 mm away from the femoral head surface, using screw lengths of 105 mm, 100 mm, 95 mm, and 90 mm, respectively. The four inferior positions were defined through the inferior translation of the central positions by half the distance between the blade axis and the inferior surface of the femoral neck [PERSON] et al. (2018). For all configurations, the blade was placed centrally in the anterior-posterior direction since it has been widely reported to reduce the risk of cut-out ([PERSON] et al., 2016; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019). Henceforth, and for the sake of simplicity, each geometry is referred to by a code starting with \"M\" or \"F\" if it belongs to the male or female femur, respectively; followed by \"Inf\" or \"Cent\" if it corresponds to the inferior or central positions; and by the distance, in mm, from the tip of the blade to the external surface of the femoral head that was used to generate the model. For instance, the central position with a distance of 10 mm to the femoral head surface for the male model is referred to as \"M-Cent-10\". \begin{table}
\begin{tabular}{c c c c} \hline  & **Tension** & **Compression** & **Source** \\ \hline \(D_{C}\) & 0.95 & 0.50 & [[PERSON] et al., 2019] \\ \(\varepsilon_{0}\) & 0.70\% & 1.04\% & [[PERSON] et al., 2019] \\ \(\varepsilon_{f}\) & 2.50\% & 4.00\% & [[PERSON] et al., 2019] \\ \hline \end{tabular}
\end{table} 
Table 1: Damage model parameters. \(D_{c}\), \(\varepsilon_{0}\), and \(\varepsilon_{f}\) represent the critical damage, yield strain, and strain at fracture, respectively. Isotropic, linear elastic material properties were assigned to all components [15]. The implant was made of a titanium alloy with a Young's modulus \(E=105\) GPa and a Poisson's ratio \(\
u=0.3\). Bone was modelled as an inhomogeneous material, with its Young's modulus as a function of density. The density distributions of the male and female femora were estimated assuming a linear relationship with the Hounsfield Units extracted from the CT images using Abaqus plug-in Bonemapy. The density was set to range between 0.01 g cm\({}^{-3}\) and 1.32 g cm\({}^{-3}\), which are typical density values for osteopororotic bones, as these fractures tend to occur mostly in the elderly population [15; 24].