Finite element analysis of the effect of shape memory alloy on the stress distribution and contact pressure in total knee replacement.
Abstract: As a step towards developing a biomaterial for femoral component of total knee replacement, the goals of this study were to introduce NiTi shape memory alloy as a promising material for orthopedic implant and to evaluate the effect of different material properties on contact behavior of the joint and stress distribution of the femoral bone using finite element method. Two separate finite element analyses were performed; one with rigid bones and the other with deformable femur, at 0 degree of flexion angle under static loading condition. The results showed no difference between the various materials with regards to the peak contact pressure but considerable difference with regards to the Von Mises stresses. The results also demonstrated that stress values closer to the natural femur were obtained for NiTi implant compared with other metals. Hence, this finite element analysis showed that NiTi shape memory alloy can reduce the stress shielding effect on the femoral bone.
Article Type: Report
Subject: Shape-memory alloys (Mechanical properties)
Shape-memory alloys (Health aspects)
Shape-memory alloys (Usage)
Finite element method (Usage)
Stress concentration (Measurement)
Authors: Bahraminasab, Marjan
Sahari, B.B.
Hassan, Mohd Roshdi
Arumugam, Manohar
Shamsborhan, Mahmoud
Pub Date: 07/01/2011
Publication: Name: Trends in Biomaterials and Artificial Organs Publisher: Society for Biomaterials and Artificial Organs Audience: Academic Format: Magazine/Journal Subject: Health Copyright: COPYRIGHT 2011 Society for Biomaterials and Artificial Organs ISSN: 0971-1198
Issue: Date: July, 2011 Source Volume: 25 Source Issue: 3
Topic: Event Code: 440 Facilities & equipment
Product: Product Code: 3399492 Shape Memory Alloys NAICS Code: 331492 Secondary Smelting, Refining, and Alloying of Nonferrous Metal (except Copper and Aluminum)
Geographic: Geographic Scope: Iran Geographic Code: 7IRAN Iran
Accession Number: 304842715
Full Text: Introduction

Increasing trend to replace degraded and lost biological materials by artificial organs make total joint replacements as one of the most important current discussions in orthopedic, especially for hip and knee. One statistical study predicted that by the end of 2030, the number of total hip replacements will increase by 174% and total knee arthoplasties is estimated to grow by 673% from the present rate (1). It has been found that, current materials including stainless steel, titanium alloys and cobalt chromium with small amount of molybdenum (Co-Cr-Mo), which are used to fabricate femoral component of total knee replacement (TKR), cause to failure of implant after long-term use in the human body due to not fulfilling some vital requirements (2,3). Deficiencies of the presently used materials and yet-increasing trend to replace knee joint make it crucial to accelerate efforts on biomaterials. Shape memory alloys (SMA), made of NiTi, provide new insights in the design of biomaterials for artificial organs and advanced surgical instruments due to their superior properties (4-6). This material has been introduced as a good choice for orthopedic application due to combination of high recovery strain, high strength, unique high fatigue resistance, ductile properties, high dampening capacity (2,3,7) and enhanced biocompatibility (8-15). It has been reported that NiTi has high wear resistance compared to the Co-Cr-Mo alloy. In addition, it has a relatively low Young's modulus of d"48 GPa at body temperature that is much lower than that of current materials. These two last properties appear to be more important for femoral component of TKR to reduce wear of ultra high molecular weight polyethylene (UHMWPE), and to prevent femoral bone loss. NiTi (SMA), therefore can satisfy the biomaterial requirements which are generally favorable for orthopedic implants. However the biomaterial aspects of joint replacement is of importance, long-term performance of an implant only be attained by considering the biomechanical aspects of joint replacement simultaneously. Peak contact pressure and stress shielding effect are two biomechanical parameters that have critical importance in success of TKR. Peak contact pressure contributes in wear of UHMWPE in TKR which has been known as a main reason for failure of knee joint arthroplasty so far (16,17). Femoral bone loss as a common feature after total knee arthroplasties is partially attributed to stress shielding of the bone by the prosthesis (18). These biomechanical aspects have been predicted either by finite element analyses (FEA) or through in vitro experiments. However there have been many FEA and experimental studies on contact characteristics of TKR (19-24) and stress shielding of the bone (25-32), all of them investigated the existing biomaterials rather than promising ones. In this study FEA is used as a tool for material selection (33) since it enables the possibility of changing material properties of components and predicting the behavior before manufacturing any prototypes. So the objective of this paper is to examine NiTi shape memory alloy as a femoral component of TKR by measuring peak contact pressure of the tibiofemoral joint and stress distribution of the femoral bone through FEA. In this regard after modeling the human knee and validation, material properties of the natural knee are replaced with those of Co-Cr alloy, Ti alloy and NiTi SMA.

Materials and Methods

Geometries of bony structures and soft tissues were taken from a healthy human knee of a 24-year old man. Solid models of the femur and tibia and geometries of soft tissues including articular cartilages and menisci, were obtained from the magnetic resonance images (MRI).

[FIGURE 1 OMITTED]

Each image was taken at 3.2 mm interval in a sagittal plane. These data were used to create a three dimensional computer aided design (3D CAD) model in order to import into ABAQUS 6.8 software for FEA. The model consisted of two bony structures (femur and tibia), articular cartilages and menisci. The model does not include ligaments. Figure 1 shows different parts of the knee joint model. The finite element mesh generation was performed resulting in 41709 linear 4-noded tetrahedron elements for articular cartilages and menisci (25293 for femoral cartilage, 9130 for tibial cartilage, 3866 for lateral meniscus and 3420 for medial meniscus). Two separate simulations were performed where in one simulation bony structures were modeled as rigid with 16414 linear 3-noded rigid triangular elements and in the second one, deformable femur was meshed by linear 4-noded tetrahedron elements.

Contact pairs were defined as femoral cartilage/medial meniscus, femoral cartilage/lateral meniscus, tibial cartilage/medial meniscus, tibial cartilage/lateral meniscus and tibial cartilage /femoral cartilage resulting in six contact-surface pairs. General contact condition involving small sliding of pairs was applied on the model and all contact surfaces were assumed to be frictionless.

In order to validate the model, static loads equivalent to 0, 500, 734, 800, 1000, 1500, 2000 and 2500 N were applied on the model at 0[??] flexion angle and the results were compared with previous experimental and FEA studies(34-37). The cartilage was defined as a homogeneous linearly isotropic elastic material with E=15MPa and [??]=0.475 (38) and the menisci were modeled as linearly elastic, transversely isotropic material with moduli of 20MPa in the radial and axial directions and 140MPa in circumferential direction. The in-plane and out-of-plane Poisson's ratio were 0.2 and 0.3 respectively and the shear modulus was considered 50MPa (39-42). Horn attachments were represented by 10 linear springs with 200 N/mm stiffness resulted in 2000N/mm total stiffness.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The femur and tibia were modeled as rigid in first simulation because they have much larger stiffness compared to that of soft tissues. This is time efficient in a non-linear analysis and as confirmed from previous study [37] that this simplification has no considerable effect on contact variables. In the second simulation, the femur was modeled as deformable material under static load of 800 N at [0.sup.^] flexion angle to determine stress distribution on the cancellous bone. Femoral cortical bone was modeled as orthotropic elastic with [E.sub.1]=12 (GPa), [E.sub.2]=13.4 (GPa), [E.sub.3]=20 (GPa), [G.sub.12]=4.53 (GPa), [G.sub.13]=5.61 (GPa), [G.sub.23]=6.23 (GPa), [[??].sub.12]=0.38, [[??].sub.13]=0.22 and [[??].sub.23]=0.24 (43) where direction 1,2 and 3 were radial, circumferential and the long axis of the bone respectively. The cancellous bone was assumed to behave homogeneous linearly isotropic with modulus of 0.4 GPa and a Poisson's ratio of 0.3 [37]. For boundary conditions, in both simulations, the tibia was constrained from rotation and translation in all directions and femur was fixed from rotating in all three directions and was free to translate in anterior-posterior, medial-lateral and inferior-superior axes. Figure 2 shows the mesh generation of the knee joint.

[FIGURE 4 OMITTED]

For evaluation of the metallic biomaterial performance, it was assumed that the geometry of the implant is the same as that of natural knee. The material properties of femoral cartilage were replaced by cobalt chromium alloy, Ti alloy and NiTi shape memory alloy. Cobalt chromium alloy, Ti-6Al-4V and NiTi (SMA) were defined as homogeneous linearly isotropic elastic materials with E=200GPa, [??]=0.3, E=114 GPa, [??]=0.32 (44) and E=39, [??]=0.46 (45,46) respectively. The material properties of UHMWPE were used to replace the menisci. Stress strain behaviors of UHMWPE and the SMA material are shown in Figure 3 (a) and (b). Since the strain value is small, for the material study, linear elastic homogeneous behavior was assumed.

Results and Discussion

Verifying the results of FEA for natural knee

The results of peak contact pressure for different magnitudes of force for natural (human) knee are demonstrated in Figure 4. The stresses were calculated at the contact regions and it was found that the total stress multiples by area equilibrate the total applied load in the knee joint which is transferred through the femur-meniscus, femur-tibia, and meniscus-tibia. The computed reaction forces also are in the equilibrium with the applied load at each loading condition. However the FE solution may have satisfied the equilibrium, representing that the finite element solution was accurate to some extent, confidence in the verification of the model itself were achieved by comparing the predicted values of the peak contact pressure with the previously reported simulated and experimental data. Among the various researches that have measured the peak contact pressure on the tibiofemoral joint (34-37,48-51), the following researches were used for comparison to the data of the present study (34-37).

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Table 1 shows the comparisons between the obtained values of peak contact pressure from the present work with those of previous studies. For calculation of the differences with the experimental values, the average was considered. It can be seen that, the present results compares quite well with other researches with maximum difference of about 3.38% and average difference of 1.728%. Hence the obtained data from present study is therefore verified. Furthermore the results of deformable model were presented in Table 2 in order to validate those results.

Contact pressure for various materials

Maximum contact stresses were measured on the polyethylene parts and also on the tibial cartilage when femoral part was chromium cobalt alloy, Ti-6Al-4V and NiTi shape memory alloy. The results were shown in table 3. It can be seen that there were no major difference in the results for different materials.

For more confidence on the results, the menisci were replaced by a flat plate of UHMWPE and the maximum contact pressure was obtained on the plate, but it was found that the magnitude of this parameter was same for all the materials.

Stress distribution for different materials

In this section all stresses were normalized to those determined from the model of an intact femur. The stress distributions were analyzed for all models under transverse and sagittal planes along 4 paths placed parallel to medial-lateral direction and the long axis of the bone respectively as shown in Figure 5 and Figure 6. However all the implant materials give lower magnitude of stresses on the femur (with the same trend), from the comparison of different materials, it can be seen that the stress distribution on the femur with NiTi (SMA) are much closer to that of intact femur, for example table 4 shows the differences in normalized Von Mises stresses with natural femur in path1 (Figure 5a) at proximal distance of 0, 2, 7, 12, 17 mm for various materials. The general order of stress values similarity to the natural femur in all paths is as follow:

Intact Femur> NiTi>Ti-6Al-4V>Cr-Co alloy

Figure 7 also shows the similarity of stress patterns of the implant materials with natural knee. It can be observed that NiTi has the most similar pattern with the human knee.

Conclusion

NiTi shape memory alloys (SMA) have been introduced to have great potential for medical application such as orthopedic implantation. The results of the present study under static load of 800 N at 0^ flexion angle showed no difference on peak contact pressure for different materials. Also it has been found that NiTi (SMA) reduced Von Mises stresses less than Cr-Co alloy and Ti-6Al-4V. So it can be concluded that NiTi SMA can reduce the stress shielding effect and consequently loss of the femoral bone which provides loosening of the implant.

However the limitation of this study is the assumption of same geometry of the implant and human knee. Also the results were limited to the static loading condition. So future research works will examine the effect of NiTi shape memory alloy on the actual implant geometries and under dynamic loading situation.

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Marjan Bahraminasab (a) *, B.B. Sahari (a,b), Mohd Roshdi Hassan (a), Manohar Arumugam (c), Mahmoud Shamsborhan (d)

(a) Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, Malaysia

(b) Institute of Advanced Technology, ITMA, Universiti Putra Malaysia, Malaysia

(c) Department of Orthopedic Surgery, Faculty of Medicine and Health Science, Universiti Putra Malaysia, Malaysia

(d) Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

Received 31 July 2010; Accepted 18 August 2010; Available online 29 May 2011
Table 1: Differences between maximum contact pressure (MPa) of
current study and previous researches

Literature      Haut Donahue   Ahmed et   Fukubayashi and
/ results       et al., [37]   al., [34]   Kurosawa [36]

                    2.25         2.03          2.73
Present study       2.22         2.05           2.7
difference          0.03        -0.02          0.03
Error%             1.33%         -1%           1.1%

Literature      Fukubayashi and   Brown and
/ results        Kurosawa [36]    Shaw [35]

                     3.83            6.5
Present study         3.9           6.72
difference           -0.07          -0.22
Error%              -1.83%         -3.38%

Table 2: Results of deformable and rigid model

                           Maximum contact
                              pressure
                           (MPa) at 800 N    Differences   Errors%

Haut Donahue et al., [37]       2.25             --          --
Present study with
  rigid bones                   2.22            0.03        1.33%
Present study with
  deformable femur              2.20            0.05        2.22%

Table 3: The results of peak contact pressure for different
materials
            Peak contact pressure on
            polyethylene parts (MPa)
                                       Peak contact pressure on
            medial       lateral       the tibial cartilage (MPa)

Cr-Co        2.707       0.9783                 3.523
Ti-6Al-4V    2.707       0.9785                 3.522
NiTi         2.707       0.9786                 3.519

Table 4: Differences in normalized Von Mises stresses with
natural femur

Proximal distance
from femoral        0      2      7      12     17
component (mm)

Cr-Co              0.70   0.67   0.58   0.47   0.40
Ti-6Al-4V          0.63   0.59   0.50   0.39   0.32
NiTi               0.50   0.46   0.37   0.27   0.22
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