INTRODUCTION
The insertion of an implant into the femur has created a new problem known as stress shielding. Most of the loads which come from patients’ weight and their activities are transferred to the implant (Kuiper, 1993; Paul, 1999). Thus, produce a reduction in stress especially at proximal medial part of the femur. Stress shielding emerges after several years of hip replacement operation. Failure to overcome this problem will create other problems such as bone resorption, loosening and micromotion. These problems provide bad effect to femur and finally the patients may require a revision surgery. The term revision surgery is used when replacing a previously replaced hip joint.
Previous researchers used optimization theory to get the best implant shape and material in reducing the problem of stress shielding (Hedia et al., 1996). Munting and Verhelpen (1995) had proved that bone would receive more load if stem can be eliminated from the prosthesis. Consequently, an artificial femoral head was designed and several screws were used for fixation. Joshi et al. (2000) have extended the work by using a few cables to support the head. Rietbergen and Huiskes (2001) concluded that the proximal load transfer was not improved with the shortened stem. Besides that, it was difficult to position correctly during operation and may possible to lose the initial stability. In other study, Gross and Abel (2001) introduced hollow geometry by increasing stem inner diameter to reduce stress shielding. However, the maximum stem stress has increased dramatically when bending was applied.
Stress shielding can also decreased if stem is more flexible (Bedzinski and Bemakiewiez, 1998; Sumner et al., 1998). However, Huiskes et al. (1992) mentioned that, flexible implant may produce higher stresses along interface. Kuiper (1993) has demonstrated the stress distribution between three different materials, i.e., cobalt chrome, titanium and isoelastic. From the result, it was verified that isoelastic of similar stiffness as the bone has created more stress at boneimplant interface at the distal end compared to other materials.
In this study, the optimum size of implant was obtained by using the rule of Multiple Criteria Optimization. ‘Multiple criteria’ is defined that the objective function could be more than one. It was explained through Eq. 14.
subjected to
Where F(x) = [f_{1}(x),….., f_{i}(x),….., f_{m}(x)]^{T} was a combination of several objectives.
Surface area at femur/implant interface and implant length were selected as constraints. Area at femur/implant interface should be maximized to permit more load could be transferred to the femur and hence prevented from stress shielding (Hedia et al., 1996). Meanwhile, implant length should be minimized to reduce stress shielding. Shorter stem would allow good load transfer and behave almost like normal situation which was without implant.
MATERIALS AND METHODS
Multicriteria optimization: Multicriteria optimization was used to optimise the implant size. FORTRAN was a programming software that has been used in this study. A reference design has been simplified so that it could be translated easily into mathematical equations. Figure 1 depicted the simplified implant.
Optimization parameter, objective functions and constraints must be determined
first before running the optimization process.

Fig. 1: 
The implant stem has been simplified for optimization purpose 

Fig. 2: 
Selected domain with dimensions and applied stresses 
Implant size has been selected as optimization parameter, whereas objective
functions were referred to the stresses acted to the implant. Constraints were
selected based on optimization parameter.
In order to reduce stress shielding, two objectives have been identified i.e., normal stress, σ (MPa) and shear stress, τ (MPa). Normal stress acting normal to an applied load, whereas shear stress was developed at an interface of femur/implant. Both objectives were directly related to implant outer surface, crosssectional area and length.
Both stresses were combined.
Constraints depend on femur anatomy and geometry of conventional implant. The
values would be manipulated between minimum and maximum limits. Equation
811 showed several constraints that were located on
implant.
A computer programming was developed to optimise the objective function or minimized stress shielding subjected to several of constraints (Fig. 2). The optimization parameter i.e., implant size would undergo for several of iterations until the final optimum parameter is obtained. Figure 3 showed a flowchart on how the programmed was made.
Finite element analysis: Method of Finite Element Analysis (FEA) was
applied to validate the optimum implant.

Fig. 3: 
Flowchart for optimization parameter 

Fig. 4: 
Model of (a) optimum implant and (b) implanted femur 
Model of optimum implant and femur was demonstrated in Figure
4 and analysed by using a commercial finite element software, i.e. IDEAS.
The analyses were made by comparing stress distributions between optimum and
reference implants. Optimum implant should have lower stress shielding as compared
to the reference implant. Mechanical properties used for finite element analysis
was shown in Table 1.

Fig. 5: 
Boundary conditions applied to implanted femur 
Model of implant and femur were divided into small elements type linear tetrahedron. The element length for implant was 1.0 mm. The element lengths given to femur were varied. It was 1.0 mm at femur/implant interface and 2.0 to 3.0 mm as it grew far away from the interface. The load of 3 kN was applied at proximal end of the implant and it was 11° from the vertical axis (Yoon et al., 1989). Symmetrical surface of femur and implant was only permitted displacement in x and y directions. The distal end of femur was rigidly fixed in x, y and z directions, that were Ux = 0, Uy = 0 and Uz = 0. Implant/femur was considered as perfectly bonded. All materials were assumed homogeneous and linearly isotropic. Finite element model for optimum implant inside the femur was shown in Fig. 5.
RESULTS
Figure 68 pointed out the comparison of
stress shielding occurred when using reference and optimum implant. From the
result, it showed that stress had been reduced almost half with the use of optimum
implant. The reduction was 42.32% in implant made by CobaltChrome and 43.51%
in implant made by Titanium Alloy.
Figure 9 and 10 showed stress distributions
developed in femur along symmetrical axis of femur/implant interface. Commonly,
femur received less loads when using reference implant. The implant shielded
the load from going to the femur. When femur received less loads, it definitely
would caused the problem of stress shielding. From Fig. 9
and 10, it was found that the optimum implants have been
successfully transferred more load to the femur.
Femur received more stress with the use of optimum implant than reference implant. For optimum CobaltChrome implant, stress developed in femur was increased 42.39% compared to reference implant. For optimum Titanium Alloy implant, stress developed in femur was increased 48.58% compared to its reference.
DISCUSSION
Minimized the stresses: The stresses in both optimum implants were successfully
reduced, hence increased their life span. Implant with optimum size increased
contact area at femur/implant interfaces as well as encouraged the transfer
of the load. Stress was reduced 43.51% with the use of optimum CobaltChrome.
The optimum implant made of Titanium Alloy, stress reduction was 42.32%. Figure
6 and 7 showed the comparison between optimum and conventional
implants.
Comparison in different implant materials: Titanium alloy and cobaltchrome:
Different implant material would give different value of stresses. It was due
to different in mechanical properties.

Fig. 6: 
Stresses comparison in Titanium Alloy implant 

Fig. 7: 
Stresses comparison in Cobaltchrome implant 
Based on the analysis, it was found that the difference in stress distributions
occurred in optimum implants made by Titanium Alloy and CobaltChrome was only
0.84%. Figure 8 showed the stresses distributions in both
optimum models.
Bones absorbed the stress: Femur needed enough stress to maintain its
structure and health. Figure 9 and 10 showed
Von Mises stresses that were absorbed by femur. Stress distributions occurred
in femur could give a clear picture about the effect of implant to femur. Conventional
implant reduced the stress that normally transferred to the femur. This situation
might create the problem of stress shielding. However, the use of optimum implant
allowed the stress to be absorbed in an optimum manner by femur as well as distributed
uniformly to all its surfaces. Femur could absorb more stress from implant if
contact area between femur/implant interfaces was maximized. The optimum contact
gave more space for the load to be transferred along the interface, hence could
minimise the stress shielding problem.
Stable stress distribution: Stress was well and steadily distributed
from implant to femur could be seen in Fig. 9 and 10.
The failure to distribute the stress either in cemented femur or cement less
femur would give a negative effect to femur.

Fig. 8: 
Stresses comparison in both optimum implants 

Fig. 9: 
Von Mises stresses occurred in femur for Titanium Alloy implant 
Minor failure of femur would begin until it finally become more serious if
not being treated immediately. The understanding on how stress being distributed
throughout the implanted femur would allow to a good design of an implant.
Contact area between femur/implant interfaces needed to be maximized to increase
a perfection of load distribution. Implant was considered as perfectly bonded
to the femur, hence permitted stress to move directly to femur. For the case
of cemented femur, cement would act as a medium of transferring stress to the
femur (Kuiper, 1993). If stress was transferred well, it would reduce the risk
of femur failure such as crack, loosening and micromotion. Bone needed adequate
stress to maintain its characteristics.

Fig. 10: 
Von Mises stresses occurred in femur for CobaltChrome implant 
CONCLUSION
Method of multi criteria optimization has been applied effectively in this study. It produced an optimum hip implant that met all required criteria. The optimum implant was analysed and compared with reference implant. From stress analysis, it was found that the optimum implant could reduce the stress shielding at almost 50%. This reduction was due to larger contact area at interface and shorter of implant length.