Porous Lattice Structure of Femoral Stem for Total Hip Arthroplasty

Total Hip Arthroplasty (THA) is one of the surgical procedures carried out satisfactorily in procedures for osteoarthritis and trauma lesions. ATC surgery reduces pain and improves the quality of life of young patients. Therefore, it is of great importance to improve the properties of hip implants, since current implants do not match their lifespan with the life expectancy of a young patient. This is because the solid prostheses that currently exist have a higher Young's modulus, and therefore are too rigid compared to the bone tissue. On the other hand, the cyclic and conti-nuous loads to which the hip joint is subjected in daily activities, can cause loosening and consequent implant loss The present work proposes an implant manufactured with a porous lattice structure, which aims to reduce stiffness, allow bone growth and a more effective mechanical load transfer. Three computational models subjected to static charges were evaluated and compared: 1) healthy femur, 2) implanted femur with a commercial prosthesis, and 3) implanted femur with a prosthesis with lattice structure. For the computational analysis it was decided to perform a static analysis of a person standing on the left foot; a load equivalent to the body weight was applied on the head of the femur, balancing the reaction forces in the system of forces (contact force, body weight, and abductor mus-cle).. The results were shown in terms of displacement, compression and deformation. The model implanted with a prosthesis with a lattice design presented a slight decrease in displacement, and a decrease in compression and deformation values, which indicated that the proposed design has a better distribution and transport of the loads through its structure.


INTRODUCTION
Total Hip Arthroplasty (THA), is one of the most successful surgical treatments for osteoarthritis [1] [2].
More than half a million THA procedures take place in the United States and United Kingdom per year. The surgery involves the resection of the neck and head of the femur and part of the acetabulum cup in order to introduce an implant to replace the structure and function of the joint [3] [4] . Bones are exposed to frequent mechanical stimulation and they have the ability to reorganize their own topology and adapt to the loads applied over osseous structure. This principle, known as the Wolff Law, states that the osseous remodelling (deposition or reabsorption of bone tissue) depends on the amount of mechanical stimulation [5] . However, when an implant is introduced in the femur, bone resorption (loss of adjacent bone) may appear due to stress shielding.
Stress shielding is an undesirable result of the difference in stiffness between the prothesis and the natural material they replace [6] .
Mechanically speaking, it is necessary that the hip implant withstands the mechanical loads inside the hip during daily activities. To avoid progressive and allocated damage, various design techniques have surfaced to create a new type of hip implant made with microstructure of a cell-like array. This means that instead of being a totally solid implant, it is a material manufactured by layers with pores. Modifying the structural properties of the implant causing a reduction of the stiffness. This will reduce stress shielding and prevents osteolysis. In addition, the optimization of pore size in the implant could improve the deformation interface between bone and implant [7] .
The life expectancy of young patients who undergo TCA is a problem when it does not match the lifetime of commercial implants, this is due to the difference in the value of modulus of rigidity between implant (femoral stem) and bone tissue, which results in an increase of stress shielding and bone resorption, which in time leads to implant loss and therefore a revision surgery is needed. The rigidity of metallic stem implants could be reduced by using porous structures.
These porous structures could also promote osseointegration, and achieve a long term fixation which would avoid the problems of a revision surgery [8] [9] .
Finite Element Analysis (FEA) is a very powerful tool that enables exploring possible solutions to biological problems. FEA makes it possible to predict the mechanical behaviour of hip implants. The computational simulation by finite element depends on several parameters such as: geometry, material properties, boundary conditions and constraints [10] .
Additive manufacturing (AM) is the process of creating a three-dimensional object layer by layer by deposition of material. Usually, additive manufacturing techniques melt powder material to create parts with an internal network as structure. Two techniques are currently used: SLM (Selective Laser Melting) and EBM (Electron Beam Melting) [11] . The solid femoral stem (DePuy® Corail size 11) shown in Figure 1, was used for the second analysis.

METODOLOGY
For the third analysis, the stem geometry was modified with a creation of a lattice structure (Figure 2), through out a series of pores of diameter of 0.31 mm.   These porous series consisted in two lattice arrays.
The first array was done in the frontal plane (XZ) at the proximal a zone of the femoral stem, just below the area that protrudes from the dissected region of the femur model. The second array arrangement was placed in the plane YZ so that they coincide with the pores made in the plane XZ resulting in the geometry shown in Figure 3.   Table 2 and Figure 4.

Displacement
Femur deformation was evaluated for the three different models (healthy femur, femur implanted with commercial prosthesis, and femur implanted with modified prosthesis with lattice structure, shown in The close similarity of the results obtained for maximum displacement in the implanted models may be caused by the fact that the lattice structure did not have the most optimal pore size for this application, since most of the femoral stem still has a solid structure and In the simulation the forces of body weight are applied on an acetabular cup and the force of the greater abductor muscle was located in the greater trochanter region in order to simplify the study [12] . The   identical to the commercial stem, in addition to the lattice geometry used, i.e. circular pores, which might have not been the most suitable geometrical shape for this application and mechanical transfer of loads.

Elastic Strain
To compare the elastic strain in the different regions of interest, the surfaces of the femur were divided using the Gruen zones, established as shown in Figure   8 through to Figure 11 show the elastic strain obtained in the characteristic tension and compression areas in each model studied. The average values of the elastic strain found in the Gruen zones can be seen in Table 3, Table 4, and Table 5.
The values obtained in the present work for each of the regions of tension and compression are similar to those shown by Moya [12] . These values obtained for elastic strain, expressed by the tension and compression regions, are a characteristic behaviour in the structure of the femoral bone. The load distribution performed by the internal trabecular networks achieve this effect by directing the loads to the femur's longitudinal structure (shaft), and to the external periphery [13] .

Stress
Finally, the last point to evaluate was the equivalent stress to analyse the effect of the loads through their structures for the three models. For this, a point at the compression area and at the middle of the proximal region of the femur was selected, the maximum value of stress was compared with the results obtained in the work of Moya [12] . The results obtained by Moya, for the healthy femur and femur implanted with a commercial prosthesis were of 16 MPa and 13 MPa respectively.
The intact model seen in Figure 12 showed a superficial stress of 8.9 MPa at the zone of interest. The resulting stress for the model implanted with a commercial   As future work, the objective is to design through lattice structures, an arrangement of artificial trabeculae to efficiently transport and direct the loads through the walls of the femoral shaft.