Finite Element analysis of stress state in the cement of total hip prosthesis with elastomeric stress barrier

A BSTRACT . In the total hip prosthesis, according to different positions of the patient, there are a variety of loads acting on femoral head which generate stress concentration in the cement called polymethylmethacrylat (PMMA) and consequently in interfaces stem/cement/bone. This load transfer can provoke loosening of the implant from the femoral bone. This paper focused on optimal stress distribution in the total hip prosthesis and devoted to the development of a redesigned prosthesis type in order to minimize stress concentration in the cement. This study investigated the effect of elastomeric stress barrier incorporated between the stem and femoral head using 3D-finite element analysis. The proposed model provided an acceptable solution for load transfer reduction to the cement. This investigation enabled an increase of the service life of total hip prosthesis avoiding the loosening.


INTRODUCTION
any hip prostheses and fixation techniques have been introduced in orthopedics in recent years. Recently, the cemented total hip replacement based on Charnley low friction arthroplasty has proven outstandingly successful. The causes for long-term failure are characterized by the stem fracture, inadequate cementing or bad placement, but the introduction of high strength metal alloys and improved cemented techniques can increase their service lifetime. The stress patterns in the bone-prosthesis structure depend of the magnitudes and the orientations of the loads, the geometries of the structure, the mechanical properties of the materials and the physical conditions at material connections. During the polymethylmethacrylat (PMMA) polymerization process, exothermic chemical reaction leads to a crack formation when its propagation depends to practiced exercise activity by the patients as described by Charef and Serier [1] in one hand and in another hand stress analysis on stem is analyzed as performed by Colić et al. [2]. M Mahmoud et al. [3] analyzed revision of the well-fixed broken stem of cemented hemiarthroplasty using anterolateral proximal femoral window. Also, the polished stems were predicted to induce a lower failure probability of cement mantle and higher integrity of the cement-stem interface when compared to the roughened stem and notable developments have included ceramic hip resurfacing and mini hip stems treated by [4]- [6] while topology and lattice in the optimized hip prosthesis design were performed to reduce stress shielding as shown by He et al. [7]. The Finite Element Method (FEM) is very suitable technique to interrelate these aspects quantitatively as shown by Huiskes and Chao [8] while Huiskes and Boeklagen [9] introduce a method of numerical shape optimization for prosthetic designs to minimize interface stresses. However, stress shielding of the femur is known to be a principal factor in aseptic loosening of hip replacements for that Joshi et al. [10] present a study which explore the hypothesis that through redesign, a total hip prosthesis can be developed to substantially reduce stress shielding and fracture behavior has been investigated of different alloy materials used in total hip prosthesis replacement implants by Sedmak et al. [11] and Gross and Abel [12] consider the use of a hollow stemmed hip implant for reducing the effects of stress shielding, while maintaining acceptably low levels of stress in the cement using finite element modeling. Also, no relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed by Lennon and Prendergast [13] which allows direct observation of damage accumulation around cemented femoral components of total hip replacements. About the experimental part, a project is based on the clinical observation that higher subsidence (distal migration) correlates with early revision of hip prostheses to develop a pre-clinical testing platform for cemented femoral hip implants as measured by Maher and Prendergast [14]. The relationship between cement fatigue damage and implant surface finish in proximal femoral prostheses has been treated by Lennon et al. [15] and has shown that, despite generally higher stresses in cement mantles of polished stems, the micro-damage does not apparently accumulate at a faster rate for those stems. A numerical study with four different stem shapes of varying curvatures for hip prosthesis was conducted by Senalp et al. [16] to determine the fatigue endurance of cemented implant and to reduce sliding of the implant in the bonecement. The effect of the position and orientation of a crack in the cement mantle under various loads using the finite element method has been studied [17][18][19]. In this work, a three dimensional finite element method was employed to analyze both conventional and proposed prosthesis. In the second one, an elastomeric stress barrier is incorporated between the stem and the femoral head in order to reduce the force transfer to the cement developed by Mehdi et al. [20]. The two models were modeled using Solidworks CAD Sofware.

MATERIALS AND METHODS
he total hip prosthesis with the principal components is presented in Fig. 1 while Fig. 2 shows two geometrical prosthesis models which are studied here: conventional model and redesigned model with an incorporated elastomer between the stem and the femoral head.

BOUNDARY CONDITIONS
s shown in Fig. 3b, the bottom of the femoral bone (cancelleous and cortical) is considered embedded: Ux=Uy=Uz=URx=URy=URz=0, while that of the cement is blocked only along the axis (zz): Uz=0. All interfaces are assumed fully bonded to ensure prosthesis stability.

ANALYSIS AND RESULTS
umerical analysis of the two models under identical loading and boundary conditions was carried out using Abaqus code based on finite element method (FEM) [22]. In order to compare stress levels, choice was on the cement body (PMMA), principal connexion between stem and bone ensures the stability of the prosthesis. Fig. 4 presents the equivalent von Mises stress distribution in the cement (PMMA) in conventional and proposed models. It was observed that the high levels of stress values located in the stem/cement interface zone in the conventional model for the 3 situations are reduced in the proposed up to 35%. This is due to the presence of the elastomeric material which plays a stress barrier role while forces are transferring into the interface. Stress distribution in the cement body (PMMA) led to trajectories choice: external interface bone/cement AB-CD and internal interface stem/cement EFG as indicated in Fig. 5. Fig. 6 shows the stress plot on the AB path for the three load cases. It is clear that point A is subjected to the highest levels of stress values for both models. Nevertheless, it is observed that in point A stress level increases in the proposed prosthesis case compared to the conventional one. The difference of this increase for the largest values varies for the three load cases 13.2% (9.8 MPa to 11.1 MPa) 14

Load 3 Conventional model Proposed model
In Fig. 7 stresses are shown on the CD trajectory, indicating the concentrated stress in point C with a lower level than point A for the two models. In the proposed model, the stresses also increase with a percentage varying from 42.8% (6.3 MPa to 9.0 MPa), and 40.9% (6.6 MPa to 9.3 MPa) to 45.9% (6.1 MPa to 8.9 MPa). The stress path in the EFG interface is shown in Fig. 8 for the three different loads. In the conventional model it is noted that in point E, stresses are greater compared to those observed throughout the cement body. Contrary, in the proposed prosthesis the most concentrated zone observed a decrease in stress of 42.5% (15.5 MPa to 8.9 MPa), 42.0% (15.7 MPa to 9.1 MPa) and 42.4% (15,8 MPa at 9.1 MPa) under Load 1, Load 2 and Load 3 respectively. In particular, the case of the monopodal position seems to be the most dangerous.
In the proposed prosthesis, it is noted that the stress levels decreased in this interface and in particular in the point E which was the most stressed area in the whole body of the cement in the conventional prosthesis. The reduction in these highest stresses in the stem/cement interface, which is the most sensitive, is estimated approximately 42% depending of the load.

DISCUSSIONS
inite element analysis has shown, that the most stressed area of the cement in the conventional hip prosthesis are in the vicinity of point E, in the internal cement/stem interface, being 15.5 MPa, 15.7 MPa and 15.8 MPa with the three load types respectively. This is due to the eccentric compression loads inducing a bending moment that tends to debond the stem from the cement. This interface stress level proves to be dangerous since it can initiate an interfacial F crack propagating down the prosthesis causing the loosening. Also, highest risk situations are those of walking down stairs and the monopodal position. However, the latter is not in common use while the descent of stairs can be frequent and cyclic if the patient lives in a building without elevator. A solution of stress deconcentration is proposed to solve this problem. This involves introducing an elastomeric material between the femoral head and the stem which made it possible to reduce the stress level in point E by redistributing stress field in the cement. This elastomer, through its deformation, reduced a force transfer rate to the prosthesis components allowing more even distribution of stress in the entire cement body. In the proposed prosthesis, for all the applied loads, the presence of the elastomer reduced the stress concentration at the point E in the conventional prosthesis by more even distribution of the stress field at the stem/cement interface. These redistributed stresses in the cement have increased at point A, 11.1 MPa, 11.3 MPa and 12.8 MPa, and are the highest compared to those of the other points. Consequently, the high stress levels in this concentrated interfacial zone stem/cement are reduced substantially while some other zones will increase their stress levels without reaching the peaks previously noted. However, the stress levels noted at points E and G which presented in important difference in the conventional prosthesis as 15.

CONCLUSIONS
n this finite element analysis of both conventional and elastomeric prosthesis, it was concluded that: -The obtained stresses in cement/stem interface using the new proposed prosthesis with elastomeric material are generally lower than those found with the conventional model. -Relative high stresses were observed at the cement/stem interface of the conventional model with the three load types. -The use of soft and flexible elastomer positioned between the stem and the femoral head with low rigidity is able to reduce the load transfer to cement. -The maximum stress concentration has moved from the cement/stem interface (in the conventional model) and reduced to the bone/cement interface (proposed model) because of the static equilibrium of forces in the new system. -The stress levels reduction in the cement of the proposed prosthesis is estimated at 42%. In conclusion, the use of a shock absorbing elastomeric material appears to play a key role in the charge of transfer mechanism and the cement response. This stress absorber reduces the stress on the cement and thus increases its service life avoiding the loosening.