## 4 Discussion  
Several studies have assessed the behavior of different hip prostheses under loads and boundary conditions (Table 1). Comparing them represents a challenging task. Even though most studies agree that the neck area is where the stress and strain values concentrate [2; 9; 14; 45; 52], those results are functions of the activity assessed, which vary from study to study, as well as their boundary conditions. This research evaluated the most common hip stem geometries reported in the literature (Table 1) using a multi-objective analysis under the same criteria, enabling the comparison between them. The selected Exeter stem showed most of the geometry dimensions required for its parametrization [29; 48], including complete experimental validation reports using strain gauges. It has a smooth geometry without sharp edges, which minimizes the stress concentration due to abrupt geometry changes. The 10-node quadratic tetrahedron elements are commonly used for the FEM assessment on irregular and curved geometries [2; 15; 29; 31]. This work agrees with those and considered the 10-node quadratic as the best option for this type of study. The authors suggest the use of a uniform size element for similar geometries will aid in comparing the results; the 2.4 mm size used in this study worked very well for all the implant assessments. However, a smaller element size would be required for smaller stem geometries (pediatric stems) or complex stem geometry. Even though some authors report smaller element sizes ranging from 0.004 to 1.5 mm [2; 28; 31; 47], in this work, the selected element size (2.4 mm) gives the lowest percentage of error after comparing it with the outcome of [PERSON] et al. [29], by comparing the stems only. Using smaller values could represent a disadvantage in data processing, mainly if the bone-stem interface is considered in the simulation or if cartilage analysis is desired [53; 54; 55; 56]. This work focused only on the stem behavior and not on the interaction of bone-stem, simplifying the assessment by using regular geometries as the block used in the assembly. For similar studies, simple geometries have been used [29; 45; 52]. A concrete block with an elasticity modulus of 30 GPa like the one used here has a very similar elasticity modulus to the human bone previously reported [8; 11; 12; 16], which gives us a reasonable idea of the bone's reaction. The femoral head is commonly used for the load application [14; 21; 28; 29; 42; 45; 47], and it is considered the best zone by the authors to place the load because it resembles the mechanisms of action of the prosthesis at the hip joint. The trapezoidal cross-section area showed the most significant decrease in stress within the range of 1.96-9.6% in four of the six activities, which agrees with the results given by [PERSON] et al. [2], [PERSON] et al. [9], and [PERSON] et al. [28]. They reported that the trapezoidal area showed the best performance using the multi-objective analysis. In addition, it showed the most consistent cross-sectional area behavior along the stem (Table 5). Using a trapezoidal cross-sectional area improves the stability of the bone-implant junction because a geometry with pronounced edges restricts the motion and acts as an anchor, which increases the possibility of avoiding micro-movement. Analysis of the different cross-sections exhibited that the trapezoidal cross-section had a higher effect on reducing micro-movements than smother geometries, such as circular, elliptical, and oval ones [9; 57]. This finding agreed with the study by [PERSON] and [PERSON] [45], where it was found that the femur stability increases with the use of rectangular and trapezoidal sections. Profile 2 with the trapezoidal cross-section (P2-T) showed the lowest stress results in four out of six activities (Appendix A), which are the most likely activities to be repeated every day [28], including \"Down stairs\", which was the most critical activity identified for the stems (activity 4).