## 2 Materials and Methods
### FE Modeling Approach
#### 2.4.1 EF-Bone Design Boundary Conditions  
Figure 5 presents the three different bone areas considered in this study: cancellous proximal and distal ends and cortical middle shaft. The application area of the boundary conditions is similar with that presented in [33] for a male tibia bone.  
Figure 4: Ansys Mechanical Element quality metrics.  
Figure 5: Tibia bone description.  
In the distal end of the tibia (Figure 6a), the talocrural joint area of 417 mm\({}^{2}\), corresponding to the mean ankle cartilage contact area as in [34], was fixed. According to [PERSON] et al. [42], this area is located slightly more laterally and centrally on the talocrural joint surfaces as seen in the left side of Figure 6.  
The tibia was loaded at the proximal end (Figure 6b) by an applied axial force corresponding to the weight of a 70 kg male at the areas shown on right side of Figure 6, corresponding to the mean lateral and medial tibio-femoral contact area for 30 to 90 degrees of knee flexion.  
Three different loading scenarios are analyzed with applied gravity load in \(Z\)- direction of 0.1 g (70 N) corresponding to lying down and swing stance position [12; 22], 0.5 g (350 N) corresponding to two-legs stance position, and 1 g (700 N) corresponding to one-leg stance cases, necessary to be able to walk without assistance.  
As per [PERSON] et al. [43], the contact was located in the central side of both lateral and medial tibia articular cartilage. The size of the medial contact areas is 122 mm\({}^{2}\). In all knees, the medial contact area is slightly larger than the lateral. The lateral, anterior, and posterior borders of the tibial articular cartilage have no contact.  
The displacement in the XY transverse plane was constrained to take into account the knee joint and the fixing point in a future test bench.  
The contacts between the fragment, callus, and bone, the three K-wires, and the distal end/fragment and between the two pins and middle tibia bone were modeled with friction coefficient of 0.4 [12; 30], and adjusted to touch interface treatment. These settings were used to improve contact accuracy, given the fact that the bodies are just about to come into contact or include a very small gap. Bonded contact was considered for the other elements of the EF such as between fasteners and K-wires or ring connections.  
Reactions at pin interface were analyzed to assess the level of load transfer assured by EF in with callus at fracture site configurations only, and thus its effectiveness while healing. The sum of reaction forces from upper and lower side of the contact were considered as the pins are squeezed by the compressed bone resulting in reaction forces in Z+ direction in one side and Z- on the other side as shown in Figure 7.  
Figure 6: Boundary conditions application areas: (**a**) distal end of the tibia showing the clamped talocrural region; (**b**) proximal end of the tibia with applied axial force at the tibio-femoral contact areas (lateral and medial), and constraints in the X and Y directions (dX = 0, dY = 0).  
As presented in the research methodology (Figure 1), for some configurations, wire pre-tension of up to 1000 N was considered in order to evaluate the impact on the global stiffness of the EF and to increase its effectiveness.