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Finite element analysis of the effect of shape memory alloy on the stress distribution and contact pressure in total knee replacement

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
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  See discussions, stats, and author profiles for this publication at: Finite element analysis of the effect of shapememory alloy on the stress distribution andcontact pressure in total knee...  Article   in  Trends in Biomaterials and Artificial Organs · August 2011 CITATIONS 12 READS 140 5 authors , including: Some of the authors of this publication are also working on these related projects: Journal of Healthcare Engineering Special Issue on Advanced Concepts in Artifcial OrthopaedicImplants   View projectOffice exercise training to reduce MSD pain and improve range of motion   View projectMarjan BahraminasabSemnan University of Medical Sciences 30   PUBLICATIONS   362   CITATIONS   SEE PROFILE B. B. SahariUniversiti Putra Malaysia 123   PUBLICATIONS   1,202   CITATIONS   SEE PROFILE Mohd Roshdi HassanUniversiti Putra Malaysia 28   PUBLICATIONS   199   CITATIONS   SEE PROFILE Mahmoud ShamsborhanKhaje Nasir Toosi University of Technology 11   PUBLICATIONS   35   CITATIONS   SEE PROFILE All content following this page was uploaded by Mohd Roshdi Hassan on 02 December 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the srcinal documentand are linked to publications on ResearchGate, letting you access and read them immediately.  Trends Biomater. Artif. Organs, 25(3), 95-100 (2011)  Finite Element Analysis of the Effect of Shape Memory Alloy on theStress Distribution and Contact Pressure in Total Knee Replacement Marjan Bahraminasab a* , B.B. Sahari a,b , Mohd Roshdi Hassan a , Manohar Arumugam c , MahmoudShamsborhan 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 August2010; Available online 29 May 2011 As a step towards developing a biomaterial for femoral component of total knee replacement, the goals of this study were tointroduce NiTi shape memory alloy as a promising material for orthopedic implant and to evaluate the effect of different materialproperties on contact behavior of the joint and stress distribution of the femoral bone using finite element method. Two separatefinite element analyses were performed; one with rigid bones and the other with deformable femur, at 0 degree of flexion angleunder static loading condition. The results showed no difference between the various materials with regards to the peak contactpressure but considerable difference with regards to the Von Mises stresses. The results also demonstrated that stress valuescloser to the natural femur were obtained for NiTi implant compared with other metals. Hence, this finite element analysis showedthat NiTi shape memory alloy can reduce the stress shielding effect on the femoral bone. Introduction Increasing trend to replace degraded and lost biologicalmaterials by artificial organs make total joint replacementsas one of the most important current discussions inorthopedic, especially for hip and knee. One statisticalstudy predicted that by the end of 2030, the number oftotal hip replacements will increase by 174% and totalknee arthoplasties is estimated to grow by 673% fromthe present rate [1]. It has been found that, currentmaterials including stainless steel, titanium alloys andcobalt chromium with small amount of molybdenum (Co-Cr-Mo), which are used to fabricate femoral componentof total knee replacement (TKR), cause to failure ofimplant after long-term use in the human body due to notfulfilling some vital requirements [2,3]. Deficiencies of thepresently used materials and yet-increasing trend toreplace knee joint make it crucial to accelerate efforts onbiomaterials. Shape memory alloys (SMA), made of NiTi,provide new insights in the design of biomaterials forartificial organs and advanced surgical instruments dueto their superior properties [4-6]. This material has been introduced as a good choice for orthopedic applicationdue to combination of high recovery strain, high strength,unique high fatigue resistance, ductile properties, highdampening 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 ofd”48 GPa at body temperature that is much lower thanthat of current materials. These two last properties appearto be more important for femoral component of TKR toreduce wear of ultra high molecular weight polyethylene(UHMWPE), and to prevent femoral bone loss. NiTi(SMA), therefore can satisfy the biomaterial requirementswhich are generally favorable for orthopedic implants.However the biomaterial aspects of joint replacement isof importance, long-term performance of an implant onlybe attained by considering the biomechanical aspects of joint replacement simultaneously. Peak contact pressureand stress shielding effect are two biomechanicalparameters that have critical importance in success ofTKR. Peak contact pressure contributes in wear ofUHMWPE in TKR which has been known as a mainreason for failure of knee joint arthroplasty so far [16,17].Femoral bone loss as a common feature after total kneearthroplasties is partially attributed to stress shielding ofthe bone by the prosthesis [18]. These biomechanicalaspects have been predicted either by finite elementanalyses (FEA) or through in vitro experiments. Howeverthere have been many FEA and experimental studies oncontact characteristics of TKR [19-24] and stress shielding of the bone [25-32], all of them investigated theexisting biomaterials rather than promising ones. In thisstudy FEA is used as a tool for material selection [33]since it enables the possibility of changing material  96 M. Bahraminasab, B.B. Sahari, M.R. Hassan , M. Arumugam, M. Shamsborhan  properties of components and predicting the behaviorbefore manufacturing any prototypes. So the objective ofthis paper is to examine NiTi shape memory alloy as afemoral component of TKR by measuring peak contactpressure of the tibiofemoral joint and stress distributionof the femoral bone through FEA. In this regard aftermodeling the human knee and validation, materialproperties of the natural knee are replaced with those ofCo-Cr alloy, Ti alloy and NiTi SMA. Materials and methods Geometries of bony structures and soft tissues were takenfrom a healthy human knee of a 24-year old man. Solidmodels of the femur and tibia and geometries of softtissues including articular cartilages and menisci, wereobtained from the magnetic resonance images (MRI).Each image was taken at 3.2 mm interval in a sagittalplane. These data were used to create a three dimensionalcomputer aided design (3D CAD) model in order to importinto ABAQUS 6.8 software for FEA. The model consistedof two bony structures (femur and tibia), articular cartilagesand menisci. The model does not include ligaments. Figure1 shows different parts of the knee joint model. The finiteelement mesh generation was performed resulting in41709 linear 4-noded tetrahedron elements for articularcartilages and menisci (25293 for femoral cartilage, 9130for tibial cartilage, 3866 for lateral meniscus and 3420 formedial meniscus). Two separate simulations wereperformed where in one simulation bony structures weremodeled as rigid with 16414 linear 3-noded rigid triangularelements and in the second one, deformable femur wasmeshed by linear 4-noded tetrahedron elements.Contact pairs were defined as femoral cartilage/medialmeniscus, femoral cartilage/lateral meniscus, tibialcartilage/medial meniscus, tibial cartilage/lateral meniscusand tibial cartilage /femoral cartilage resulting in sixcontact-surface pairs. General contact condition involvingsmall sliding of pairs was applied on the model and allcontact surfaces were assumed to be frictionless.In order to validate the model, static loads equivalent to0, 500, 734, 800, 1000, 1500, 2000 and 2500 N wereapplied on the model at 0ˆ flexion angle and the resultswere compared with previous experimental and FEAstudies[34-37]. The cartilage was defined as a homogeneous linearly isotropic elastic material withE=15MPa and õ=0.475 [38] and the menisci were modeledas linearly elastic, transversely isotropic material withmoduli of 20MPa in the radial and axial directions and140MPa in circumferential direction. The in-plane and out-of-plane Poisson’s ratio were 0.2 and 0.3 respectivelyand the shear modulus was considered 50MPa [39-42].Horn attachments were represented by 10 linear springswith 200 N/mm stiffness resulted in 2000N/mm totalstiffness.The femur and tibia were modeled as rigid in firstsimulation because they have much larger stiffnesscompared to that of soft tissues. This is time efficient in anon-linear analysis and as confirmed from previous study[37] that this simplification has no considerable effect oncontact variables. In the second simulation, the femur wasmodeled as deformable material under static load of 800N at 0ˆ flexion angle to determine stress distribution onthe cancellous bone. Femoral cortical bone was modeled Literature  / results Haut Donahueet al., [37] Ahmed et al., [34] Fukubayashi and Kurosawa [36] Fukubayashi and Kurosawa [36] Brown and Shaw [35] 2.25 2.03 2.73 3.83 6.5 Present study 2.22 2.05 2.7 3.9 6.72 difference 0.03 −0.02 0.03 −0.07 −0.22 Error% 1.33% −1% 1.1% −1.83% −3.38% Table 1: Differences between maximum contact pressure (MPa) of current study and previous researchesFigure 1: Different parts in 3D model of human kneeFigure 2: Mesh generation of the knee joint  Finite Element Analysis in Total Knee Replacement   97 as orthotropic elastic with E 1 =12 (GPa), E 2 =13.4 (GPa),E 3 =20 (GPa), G 12 =4.53 (GPa), G 13 =5.61 (GPa), G 23 =6.23(GPa), õ 12 =0.38, õ 13 =0.22 and õ 23 =0.24 [43] wheredirection 1,2 and 3 were radial, circumferential and thelong axis of the bone respectively. The cancellous bonewas assumed to behave homogeneous linearly isotropicwith modulus of 0.4 GPa and a Poisson’s ratio of 0.3[37]. For boundary conditions, in both simulations, the tibiawas constrained from rotation and translation in alldirections and femur was fixed from rotating in all threedirections and was free to translate in anterior-posterior,medial-lateral and inferior-superior axes. Figure 2 showsthe mesh generation of the knee joint.For evaluation of the metallic biomaterial performance, itwas assumed that the geometry of the implant is the sameas that of natural knee. The material properties of femoralcartilage were replaced by cobalt chromium alloy, Ti alloyand NiTi shape memory alloy. Cobalt chromium alloy, Ti-6Al-4V and NiTi (SMA) were defined as homogeneouslinearly isotropic elastic materials with E=200GPa, õ=0.3,E=114 GPa, õ=0.32 [44] and E=39, õ=0.46[45,46] respectively. The material properties of UHMWPE wereused to replace the menisci. Stress strain behaviors ofUHMWPE and the SMA material are shown in Figure 3(a) and (b). Since the strain value is small, for the materialstudy, linear elastic homogeneous behavior was assumed. Results and discussion Verifying the results of FEA for natural kneeThe results of peak contact pressure for differentmagnitudes of force for natural (human) knee aredemonstrated in Figure 4. The stresses were calculatedat the contact regions and it was found that the total stressmultiples by area equilibrate the total applied load in theknee joint which is transferred through the femur-meniscus, femur-tibia, and meniscus-tibia. The computedreaction forces also are in the equilibrium with the appliedload at each loading condition. However the FE solutionmay have satisfied the equilibrium, representing that thefinite element solution was accurate to some extent,confidence in the verification of the model itself wereachieved by comparing the predicted values of the peakcontact pressure with the previously reported simulatedand experimental data. Among the various researchesthat have measured the peak contact pressure on thetibiofemoral joint [34-37,48-51], the following researches were used for comparison to the data of the present study[34-37] . Table 1 shows the comparisons between the obtainedvalues of peak contact pressure from the present workwith those of previous studies. For calculation of thedifferences with the experimental values, the average wasconsidered. It can be seen that, the present resultscompares quite well with other researches with maximumdifference of about 3.38% and average difference of1.728%. Hence the obtained data from present study istherefore verified. Furthermore the results of deformablemodel were presented in Table 2 in order to validate thoseresults.Contact pressure for various materialsMaximum contact stresses were measured on thepolyethylene parts and also on the tibial cartilage when Figure 3: Stress– strain behavior of (a) nonlinear UHMWPEmaterial model [20,47] (b) NiTi (SMA)[45]Figure 4: Peak contact pressure on the tibial plateau  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 2: Results of deformable and rigid model  98 M. Bahraminasab, B.B. Sahari, M.R. Hassan , M. Arumugam, M. Shamsborhan  Figure 5: A comparison of the normalized von Mises bonestresses resulting from changes in the material propertiesof the implant. Stresses are shown for natural femur, Cr-Coalloy, Ti-6Al-4V and NiTi in sagittal plane with distance of46mm from medial side of the medial condyle (a) 20 mmposterior to anterior (b) 30 mm posterior to anteriorFigure 6: A comparison of the normalized von Mises bonestresses resulting from changes in the material propertiesof the implant. Stresses are shown for natural femur, Cr-Coalloy, Ti-6Al-4V and NiTi in transverse plane with distanceof 5 mm from distal femur (a) 20 mm posterior to anterior (b)30 mm posterior to anteriorFigure 7: stress pattern for (a) natural knee (b) Cr-Co alloy(c) Ti-6Al-4V (d) NiTi (SMA) femoral part was chromium cobalt alloy, Ti-6Al-4V andNiTi shape memory alloy. The results were shown in table3. It can be seen that there were no major difference inthe results for different materials.For more confidence on the results, the menisci werereplaced by a flat plate of UHMWPE and the maximumcontact pressure was obtained on the plate, but it wasfound that the magnitude of this parameter was same forall the materials.Stress distribution for different materialsIn this section all stresses were normalized to thosedetermined from the model of an intact femur. The stressdistributions were analyzed for all models under transverseand sagittal planes along 4 paths placed parallel to medial-lateral direction and the long axis of the bone respectivelyas shown in Figure 5 and Figure 6. However all the implantmaterials give lower magnitude of stresses on the femur(with the same trend), from the comparison of differentmaterials, it can be seen that the stress distribution onthe femur with NiTi (SMA) are much closer to that of intactfemur, for example table 4 shows the differences innormalized Von Mises stresses with natural femur in path1(Figure 5 a) at proximal distance of 0, 2, 7, 12, 17 mm forvarious materials. The general order of stress valuessimilarity to the natural femur in all paths is as follow:Intact Femur> NiTi>Ti-6Al-4V>Cr-Co alloy
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