# Upper Limb Orthoses: Integrating Topology Optimization and 3D Printing for Custom Fit and Function
## 3 Generating the Design Domain and the Associated FE Model
### Developing the FE Model
#### 3.4.3 Determination of Load Cases  
This investigation focuses on wrist braces intended to support the healing process of fractures located at the distal end of the radius. To replicate the forces acting on the brace precisely, two key load cases were established: radial deviation and wrist flexion. These scenarios are based on the forces applied to the brace during common wrist activities, encompassing radial and ulnar deviations, along with wrist flexion and extension, as outlined in previous studies [28] (refer to Table 1 and Figure 7a,b). The maximum forces for these load cases were estimated based on torque values reported in the literature [28]. These torque values were divided by 0.1 m, the distance from the metacarpophalangeal joints to the wrist, to calculate the maximum forces applicable to a sample of 50 healthy individuals without hand or wrist pathologies. However, it is crucial to recognize that patients with distal radius fractures typically cannot exert maximum forces due to factors such as pain and swelling. Therefore, for this study, the FE analysis was conducted using loads that are 10% of the maximum isometric forces achievable by healthy individuals. This adjustment ensures that the simulation more accurately reflects the reduced forces experienced by patients in real-world scenarios, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Cases** & **Radial Deviation** & **Wrist Flexion** \\ \hline Turning Force (Nm) & 11.33 & 14.81 \\ Study Forces 10\% (N) & 11.33 & 14.81 \\ Applied Force Direction & \(-\)Y axis & \(-\)Z axis \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Loads cases and constraints by Vanswearingen [28]. Figure 7: Load cases and constraints applied on each researched case: (**a**) radial deviation, (**b**) wrist flexion, (**c**) 22 point forces (the green color represents the constraints). as outlined in Table 1. In the FE model of the wrist brace, forces were applied to the areas of the brace most likely to encounter these loads during wrist movements (see Figure 7a,b). This approach aims to closely mimic actual loading conditions and ensure that the simulation results effectively represent the realistic stress and strain on the wrist brace structure. The forces applied by the hand-wrist to the splint were quantified using specialized pressure sensors, each with a thickness of 0.20 mm, as detailed by [15]. These sensors measured forces at 22 distinct points on the splint. The force magnitudes at each of these 22 points are summarized in Table 2. It is essential to note that these forces were applied perpendicular to the relevant surfaces of the FE model, as illustrated in Figure 7c. This method ensures that the simulated loading conditions closely reflect the actual forces experienced by the splint, enhancing the accuracy of the model. In the first two load cases, the forearm is assumed to be at rest, while the upper arm and wrist are free to move but limited due to the application of the splint. This means that, on the back surface of the splint, all six degrees of freedom are bound. A second restriction is also applied for these cases to the middle of each surface of each splint model, creating a three-point applied force system so that the interactions that are simulated between the brace and the hand-wrist represent as much as possible the real ones. Accordingly, in the third load case that is studied, it is assumed that the surface of the splint at both the rear and front ends is at rest, so in the corresponding areas, all six degrees of freedom are bound, while a load is applied to the middle of each surface of the model at various points along and around the structure, simulating the forces that develop when applying a splint. It is important to note that in all three load cases studied in the present work, the two individual pieces of the brace, which arise in the stage of the manufacturing process, are considered to be fully connected. Therefore, the FE model does not include any bounds on the surfaces where these pieces are connected.