Performance improvement of total knee replacement joint ... - CiteSeerX

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:02

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Performance Improvement of Total Knee Replacement Joint through Bidirectional Functionally Graded Material Tawakol A. Enab Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O. 35516 Mansoura, Egypt. Tel.: +201097314632, Fax: +20502244690, Emails: [email protected] ; [email protected] Abstract— Total knee replacement (TKR) has become one of the most critical debates in orthopedic due to the simultaneous growing number of replacement and revision surgeries. The introduction of the knee prosthesis reduces stresses in nearly all regions of tibial bone due to the difference in Young’s modulus between implant material and bone. Therefore, Young’s modulus of the prosthesis materials is a critical design variable, because it largely determines how the load transferred via cement to bone. Moreover, functional gradation is one characteristic feature of living tissue. Consequently, the functionally graded materials (FGM) developed as a potential tibia tray material of TKR due to its improved capability of stress distribution. The current investigation evaluates and discusses the feasibility of using FGM tibial prosthesis by predicting knee implant biomechanical behavior using finite element analysis. We developed two-dimensional finite element models, which include the artificial knee and portions of the surrounding biological materials. These models compare the performance of four different tibial prostheses (titanium, CoCrMo, unidirectional and bidirectional FGM). We found that the use of FGM tibia trays will improve the performance and will increase the life of the total knee prosthesis.

Index Term--

Total Knee Replacement (TKR); Tibia tray; Stress shielding; Biomaterials; Functionally Graded Material (FGM); Finite Element Analysis (FEA).

I. INTRODUCTION Knee joint is one of the most complicated structures in the human body. It is the strongest joint, supports almost the whole body weight, and provides mobility. However, it commonly suffers from both acute injury and the development of osteoarthritis, which make the joint painful. Currently, total knee replacement (TKR) confidently established as a clinically efficacious modality for the relief of extreme pain associated with rheumatoid arthritis or trauma at the knee joint and restoring physical function in patients. On the other hand, TKR is one of the most critical debates in orthopedic due to the simultaneous growing number of replacement and revision surgeries. Therefore, there is an urgent need to reduce the rate of revision surgery by providing more durable knee prostheses which can be achieved by improving implant design, materials …etc [1-5]. Figure 1 shows the normal knee anatomy and a typical replacement joint which consists of a tibial base plate or tray, usually made of titanium alloys, stainless steel or cobalt

chromium molybdenum (CoCrMo), with an ultra-high molecular weight polyethylene (UHMWPE) tibial insert that acts as the bearing surface [6]. Nowadays, the development of new biomaterials for medical applications is one of the challenging tasks for materials science. Therefore, researchers have attempted to either develop new biomaterials or adapt existing materials in order to meet the demand for longer lasting and better functioning implants in the human body, which is especially desirable for younger, more active patients. The attempts of developing new biomaterials, alternative combinations of biomaterials, and biomaterials with multi-functional properties will overcome the shortcomings of current metals, ceramics and polymers [1, 2]. Such developed materials should improve artificial implants by simultaneously minimizing the wear debris, relative micro-motion and stress shielding effect taking into account the hierarchical structures of natural biomaterials. Functionally graded materials (FGMs) may provide the structure with synthetic biomaterials, which can resemble the natural biomaterials. Recently, FGMs introduced as promising biomaterials for dental implant [7-10], hip joint replacements [11-14] and knee joint replacements [15-19]. In knee prostheses, Pompe et al. [19] applied the concept of FGM to the tibial insert in order to improve the material’s tribological behavior. They developed an artificial biomaterial for knee joint replacement by building a graded coating structure consisting of ultra-high molecular weight polyethylene (UHMWPE) fiber reinforced high-density polyethylene combined with a surface of UHMWPE. Early investigations conducted by Enab [17] and Enab and Bondok [18] suggested the application of unidirectional functionally graded materials (1D-FGM) to the tibial tray of a TKR. They carried out a comparative study between FGMs and the existing material used in a tibial component based on the stress levels in the proximal region of the tibia, which showed the superiority of the proposed FGMs. Bahraminasab et al. [2, 15, 16] investigated the use of multi-functional materials as a possible solution to aseptic loosening by applying functionally graded biomaterials (FGBMs) for the femoral component of a TKR. They developed three-dimensional finite element models of the knee prosthesis to study the effect of using FGBM femoral component on distal femur stresses. They showed that by using the new FGBM compared to the existing material in a femoral

1411402-8383-IJMME-IJENS © April 2014 IJENS

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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:02 component, higher levels of stress can be realized in the adjacent bone area of the femur and as a consequence reduce harmful atrophy effects.

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FGMs is that no internal boundaries exist and the interfacial stress concentrations can be avoided. Moreover, they can be designed to achieve particular desired performances different from those of homogeneous or joined dissimilar materials. The advances in material synthesis technologies have encouraged the development of this new class of materials with promising applications in aerospace, transportation, energy, electronics and bio-medical engineering [20-26]. Therefore, FGMs are ideal candidates for the applications requiring multifunctional performance such as artificial implants. A. Volume fractions and rule of mixtures of 1D-FGM Volume fraction and rule of mixtures represent the most realistic way for representing the continuous gradation of the material properties in FGM. They overcome the drawbacks of exponential functions for representing the material properties. On the other hand, the use of the volume fraction and rule of mixtures make the analytical solution of the FGM problems very complicated. Therefore, the use of finite element method in such problems is the most effective tool and overcomes such difficulties. The simplified model of knee prostheses which was used before by Lewis et al. [27] will be applied in the current study. Therefore, the tibial tray will be considered as a plate of FGM with porosity p that is functionally graded from two basic constituents’ materials (i.e. material 1 and material 2). V1 and V2 are the volume fractions of material 1 and material 2 respectively. Volume fractions are distributed over y-direction (vertical distribution) which show better biomechanical performance as discussed early by Enab [17] and Enab and Bondok [18] (see Fig. 2a). Therefore, volume fractions are presented according to the following equations [28]: m

y  V 1   h V 2  1 V 1  Fig. 1. (a) Normal knee anatomy and (b) artificial knee implant components.

From the foregoing review of literature, it is worth noting that only the effect of using unidirectional functionally graded materials (1D-FGM) examined and showed some advantages over the existing materials used in TKR. Moreover, to our knowledge the application of bidirectional functionally graded materials (2D-FGM) in total knee replacement has not studied yet. Therefore, the current investigation sought to examine the effect of using 2D-FGM concept on the performance of cemented tibia tray component of total knee replacement. Furthermore, the present study compare tibia trays made from existing materials (i.e. CoCrMo or Ti alloy), 1D-FGM to a 2D-FGM from the perspective of the stresses at various parts in the tibia tray–cement–bone system. II. FUNCTIONALLY GRADED MATERIAL (FGM) Functionally graded materials (FGMs) represent a new generation of inhomogeneous composites. In FGMs, the volume fraction of the constituents varies gradually in some directions as a function of position. The main advantage of

(1) (2)

where h and y are the plate height and the vertical position of different points along it respectively. Moreover, m is a parameter that controls the composition variation through the tibial tray. For material 1 rich composition m < 1, while for material 2 rich composition m > 1. The variation of material 1 and material 2 composition in the current study assumed to be linear (i.e. m = 1). The porosity p of the FGM may be given by [28]: n z y   y   (3) p  A   1      h    h   n where 0  A  ((n  z ) / n ) (4) 1  (n / (n  z )) z A, n and z are arbitrary parameters that control the porosity and equal to 0.1, 1 and 1 respectively [17]. Finally, the following relations represent the FGM effective properties [28]. E O (1  p ) (5) E  p (5  8 )(37  8 ) 1 8(1  )(23  8 )


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   1 V 1  2 V 2

(7)

E0 is the elastic modulus when the porosity equals zero, E1 ,

1 and E2 , 2 are the elastic moduli and Poisson’s ratio of the material 1 and material 2, respectively.

B. Volume fractions and rule of mixtures of 2D-FGM Bidirectional functionally graded material (2D-FGM) is made of continuous gradation of three distinct material phases. It is fabricated in such a way that the volume fractions of the constituents are varied continuously in a predetermined composition profile. The volume fractions and porosity of the 2D-FGM at any arbitrary point may be treated as 1D-FGM that consists of two volume fractions VS (which is a mixture of V1 and V2), and V3. The subscripts 1, 2 and 3 denote material 1, material 2 and material 3 of the basic constituents, respectively. The two volume fractions, VS and V1, can be expressed as follows [28]:

V1 = 1, V2 = 0, V3 = 0 at y = h and x = 0 V1 = 0, V2 = 1, V3 = 0 at y = h and x = l V1 = 0, V2 = 0, V3 = 1 at y = 0 and x = 0 → l From the above volume fraction distribution, it is clear that the proposed volume fractions of the composition of 2D-FGM changes from 100% V1 at the plate left upper corner of the upper surface, to 100% V2 at the right upper corner of the upper surface and to100% V3 at the plate lower surface as shown in Fig. 2-b. Noting that, the composition variations of the 2D-FGM through the plate has different distributions depending upon the non-homogenous parameters mx and my. y (a)

V2

y

(6)

h

2/3  where E  E  E 2  (E 1  E 2 )V 1 O 2   2/3  E 2  (E 1  E 2 )(V 1 V 1 ) 

V1

my

y  V 3   h V S  1 V 3 

 where 0  A   n y  z y y  n y 

  

ny

  n y 1     n y  z y 

  

zy

   

(14)

nx   n x  z x   (15) V 1 V 2       n x   Here, mx and my are non-homogenous parameters that represent the composition distributions of the basic constituents materials in x- and y-directions and Ax , Ay , nx , ny, zx and zy are arbitrary parameters that control the porosity in x- and y-directions. From the proposed volume fractions at any point, as shown in Fig. 2-b, the volume fractions of the three basic constituent materials on each boundary surface are:

n zx  0  Ax   x   nx 

(b)

(9)

  y m y   x m x (11) V 2  1       h l       The porosity variation in y- and x-directions (py and px) can be given by [28]: ny zy y   y   (12) p y  A y   1      h    h   nx zy 2z y nx x   y   y   x   p x  A x   1  2       1     (13)  l   h  h     l  

nx

x

y

(8)

V2

V1

y

h

In the same way, the volume fractions V1 and V2 can be obtained by considering the upper surface of the 2D-FGM plate as 1D-FGM, and then V1 and V2 can be expressed as the following [28]:   y m y    x m x  (10) V 1  1     1     h l        

106

V3

x

x l Fig. 2. Coordinate system and volume fraction distribution for (a) 1D-FGM plate and (b) 2D-FGM plate

As the one dimensional FGM with some mathematical manipulation the rules of mixture for the 2D-FGM with porosity can be obtained. Therefore, for any point on the 2D-FGM plate with volume fractions V1, V2 and V3 as shown in Fig. 2-b, using the above mentioned equations, the rules of mixture for the different mechanical properties may be obtained by the subsequent relations [13, 28]: For Poisson’s ratio: (16)   1 V 1  2V  3V 3 where 1 , 2 and 3 are the Poisson’s ratios for material 1, material 2 and material 3, respectively. While the modulus of elasticity is given by [28]:

E 

E 0 y (1  p y )

1  p y (5  8 ) (37  8 ) / 8(1  ) (23  8 )

 E x  (E 3  E x )V 32/3 where E 0 y  E x   2/3  E x  (E 3  E x ) (V 3  1  V x )  Ex 

(17)

(18)

E 0 x (1  p x ) (19) 1  p x (5  8 x ) (37  8 x ) / 8 (1  x ) (23  8 x )


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 E 1   E 2  E 1 V 22/3  E 0x    2/3  E 1  (E 2  E 1 )(V 2 V 2 ) 

(20)

 x  1V 1  2V 2

(21)

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noting that Vx = VS (which is a mixture of V1 and V2). III. FINITE ELEMENT MODELING The finite element method (FEM) as a powerful computational tool has been widely used to improve the design of artificial joint prostheses and to minimize the expensive experimental trials. Many investigations conducted, using the FEM, to understand the biomechanical performance of various joint implant designs as well as the effect of various factors on implant success. Thus, FEM used to analyze the natural knee and knee implants models, where natural knee models used as a guideline to determine whether the responses of implant models are reasonable. To reduce the aseptic loosening which is a significant problem affecting the life of current TKRs, a new functionally graded material has been designed to replace the existing materials usually used. This will help in understanding the biological response of the bone around the implant, which results in designing more effective bone defect implants. Therefore, two-dimensional finite element models of the knee prosthesis developed to investigate the effect of using 2D-FGMs used in the design of the tibial component in TKR. A. Model geometry Nowadays, different designs of the knee implant components are available. Almost all designs have tibial insert fabricated from ultra-high-molecular-weight polyethylene (UHMWPE). However, on the other hand knee implant designs have some noteworthy differences; for example, tibial component designs may have one straight central stem, one posteriorly-angled central stem, two or more short pegs, or both stem and pegs [27]. Therefore, the developed models comprise the tibial component that has only the central stem and its tibial insert, anchored in the resected proximal tibia with acrylic bone cement. Commercially Finite Element Method (FEM) package ANSYS used to develop the TKR models. The dimensions of simplified knee joint are taken as used before by Lewis et al. [27] (Fig. 3a). Since, the modeled component and insert may be viewed as notional or representative, no attempt was made to insure that the dimensions of the modeled tibial component and insert were the same as those of any design in clinical use. Early investigations [17, 18] show that, the results of simplified representative models for half knee and full knee have the same trends. Therefore, to reduce the intensive computations and requirement of high computer memory capacity simplified representative models for half knee were used. These models assume that loads applied normally to the surface of the tibial component on the posteromedial and posterolateral sides are equal as indicated early by Miyoshi et al. [29].

Fig. 3. Model of the assembled construct for TKR shows (a) the different materials, (b) gross mesh of the FE model shows loading and boundary conditions.

B. Material properties Four models developed depending on the tibial component material. CoCrMo used as tibial component material for the first model, while titanium alloy used in the second model. In the third model FGM tibial component with unidirectional functionally graded structures along the vertical direction composed of titanium (Ti) and hydroxyapatite (HAP) used to satisfy both mechanical and biocompatible properties requirements. Finally, the fourth model had FGM tibial component with bidirectional functionally graded structures composed of titanium (Ti), hydroxyapatite (HAP) and collagen. Table (I) shows the mechanical characteristics of the materials used in the developed finite element models. Noting that, mechanical properties of bone, PMMA cement, tibial component, and UHMWPE tibial insert were taken from literatures [13, 27, 30]. In addition, all materials are typical of those used in commercial total joint prostheses and consider being isotropic, linearly elastic and homogeneous. Moreover, the elastic moduli for the basic constituents of the 1D-FGM (i.e. HAP and titanium) were taken as E1 = 40 GPa and E2 = 110 GPa respectively [13]. On the other hand, it is suggested that the elastic moduli for the three basic constituents of the 2D-FGM (i.e. HAP, titanium and collagen) were taken as E1 = 40 at the left upper corner of the tibial component, E2 = 110 GPa at the right upper corner and E3 = 1 GPa lower surface (see Fig. 2-b), while Poisson’s ratio is assumed equal 0.3 for all FGM constituents [13]. Volume fraction and rule of mixtures of 1D- and 2D-FGM concepts, which were discussed before, are adopted using the above mentioned finite element models through the ANSYS finite element program. Actually, there is no specified material module for the direct analysis of FGM in ANSYS [31]. Consequently, the present study use a simplest method involves the assignment of properties to each element individually. Therefore, the elastic parameters for each element calculated from the values at the element centroid to achieve step-like


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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:02 material properties. Theoretically, when the number of material elements increases, the real profile of FGM properties accurately represented. Table I Properties of materials represented in the FE models

Material

Modulus of elasticity (MPa)

Poisson's ratio

14000 7000

0.3 0.3

Cancellous bone a. Top b. Top-middle c. Middle d. Bottom

300 150 100 50

0.2 0.2 0.2 0.2

PMMA cement

2150

0.46

UHMWPE

2300

0.25

79000 208000

0.36 0.3

40000 110000

0.3 0.3

40000 110000 1000

0.3 0.3 0.3

Cortical bone a. Top b. Bottom

Tibial base a. Ti-13Nb-13Zr b. CoCrMo c. 1D-FGM  Hydroxyapatite (HAP)  Titanium d. 2D-FGM  Hydroxyapatite (HAP)  Titanium  Collagen

C. Boundary conditions and assumptions The present half knee simplified representative models did not include some effective elements such as ligaments (refer to Fig. 1). The distal end of the model was completely fixed in position and direction as described early by Lewis et al [27] (Fig. 3b). The applied load assumed constant and normally distributed on the bearing surface of the UHMWPE tibial insert. Therefore, a total load of 1000 N applied normally to the surface of the UHMWPE tibial insert as discussed early by Enab [17]. Additionally, in the present analysis, all materials used in the tibial prostheses assumed isotropic and linearly elastic. Heterogeneous bone properties modeled by considering different properties for cortical bone (top and bottom) and cancellous bone (top, top-middle, middle and bottom) regions. Furthermore, rigidly bonded interface assumed between implant components and bone. In addition, the developed stresses and strains on each material are in the elastic zone. Similar simplified model used before through many studies [17, 18, 27]. These assumptions considered to assess the performance improvement of total knee replacement joint through unidirectional and bidirectional functionally graded material. Subsequently, by finding the optimal FGM tibia tray

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design, extended study can be carried out on any real tibia prosthesis using 3D models. D. Finite element model verification The aim of the present investigation is to improve the design of total knee tibial component, using bidirectional functionally graded materials concept to overcome stress shielding and stress concentration problems, which affect the life of total knee replacements. Since the analysis of the current study based entirely on finite element modeling and its results, the verification of the developed finite element models considered very essential. Consequently, to demonstrate the validity of the current simplified representative 2D finite element models, the obtained results of the developed models were compared to results obtained from other 2D and 3D models that have been carried out through other studies [27, 32, 33] which have approximately the same properties, dimensions, and nearly the same loading conditions. The comparison shows a good agreement in von-Mises stresses between the developed model results and those of the other models. Noting that, the stress values are not exactly identical, but the trends of the stresses in each model are significantly similar. IV. RESULTS AND DISCUSSION Improving bone-cement and/or bone-prosthesis interfaces; which are among the factors that can lead to serious loosening of the artificial knee implant; via novel materials represent an important method to get better TKR design. Functionally graded materials (FGMs) may provide the structure with synthetic biomaterials that can resemble the natural biomaterials in this respect. In the current investigation finite element analysis used to study the effect of tibia tray material on the stresses developed in artificial knee. A comparative study carried out between four tibia tray materials (CoCrMo, titanium alloy, unidirectional FGM (1D-FGM) and bidirectional FGM (2D-FGM)) based on the maximum von-Mises and shear stresses developed at each constituent of the artificial knee as well as the different interfaces. Tibia tray made of 2D-FGM reduced von-Mises stresses developed within the tibia tray by about 58% and 31% compared to CoCrMo and Ti alloy tibia trays respectively (Fig. 4a). While, 1D-FGM tibia tray reduced the developed von-Mises stresses by about 46% and 13% compared to CoCrMo and Ti alloy tibia trays respectively. On the other hand, Fig. 4b shows that 2D-FGM tibia tray increased von-Mises stresses developed in cement by about 3% compared to CoCrMo tibia tray and decreased it by about 4% compared to Ti alloy tibia tray. However, 1D-FGM tibia tray will increase the von-Mises stresses developed in the cement by about 14% and 6% compared to CoCrMo and Ti alloy tibia trays respectively. Furthermore, Fig. 4c shows that 2D-FGM tibia tray has a negligible increasing (less than 1%) in von-Mises stresses developed in top cancellous bone part compared to CoCrMo tibia tray. Alternatively, it decreased the developed von-Mises stresses by about 4% compared to Ti alloy tibia tray. While for top middle cancellous bone part, the developed von-Mises


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Max. von Mises stress (MPa) at tibia tray

25

20

15

10

5

0

CoCrMo

Ti Alloy

1D-FGM

2D-FGM

Tibia tray material

(b) Max. von Mises stress (MPa) at cement

A. Tibia tray – UHMWPE tibial insert interface Fig. 5 displays the developed von-Mises stresses and shear stresses distributions at tibia tray-UHMWPE tibial insert interface. For this interface, 2D-FGM tibia tray presents the minimum and more uniformly distributed von-Mises stresses while CoCrMo tibia tray presents the maximum von-Mises stresses. Compared to CoCrMo and Ti alloy tibia trays, 2D-FGM tibia tray decreases the maximum von-Mises stress developed at the tibia tray-UHMWPE tibial insert interface by about 76% and 61% respectively. Whilst 1D-FGM tibia tray decreases the maximum von-Mises stress developed at the tibia tray-UHMWPE interface by about 65% and 42% compared to CoCrMo and Ti alloy tibia trays respectively (Fig. 5a). Contrary, 2D-FGM tibia tray has unfavorable effect on shear stresses developed at this interface since maximum shear stress increases obviously compared to other tibia tray materials (Fig. 5b). While 1D-FGM tibia tray increases the maximum shear stress developed by about 29% and 13% compared to CoCrMo and Ti alloy tibia trays respectively. Consequently, it can be concluded that by using 1D-FGM or 2D-FGM tibia trays, von-Mises stresses reduced and tend to be more uniformly distributed. However, at the same time, there is an increasing in the shear stresses, but in general, shear stresses still minimum than the allowable shear stress for the weaker material (i.e. the UHMWPE tibial insert).

(a)

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 CoCrMo

Ti Alloy

1D-FGM

2D-FGM

Tibia tray material

Canc. Bone (Top)

Canc. Bone (Top Mid.)

2.5

Maximum von Mises stress (MPa) at cancellous bone

stresses decreased by about 24% and 28% compared to CoCrMo and Ti alloy tibia trays respectively. Moreover, Fig. 4c shows that 1D-FGM tibia tray will increase the von-Mises stresses developed in the top and top middle cancellous bone parts by about 11% and 6% respectively compared with CoCrMo tibia tray and by about 4% and 1% compared to Ti alloy tibia tray respectively. Additionally, tibia tray material has a negligible effect on the developed stresses at the middle and bottom cancellous bone parts due to their distant from the load. Moreover, for cortical bone parts, tibia tray material has a very small effect on developed stresses because cortical shell has a small contact with cement. It is worth to note that, 1D-FGM reduces the stresses developed in tibia tray while it shows an increasing in the developed stresses at cement and bone parts. On the other hand, 2D-FGM results in the minimum stresses developed in tibia tray while it shows an intermediate stress values developed at cement and top cancellous bone part compared to CoCrMo and Ti alloy tibia trays. In addition, it results in the minimum stress values developed at top middle cancellous bone part. The distinction in behavior of 1D-FGM and 2D-FGM may be explained by the variation in material gradation directions. However, in general, the reduction in tibia tray stresses and the increasing in bone stresses will decrease the stress shielding of the bone and prevent implant loosening. This may be explained by the fact that the higher the stiffness of the tibia tray material, the lower the displacement it undergoes and the lower the stresses it transfers to the bone via cement material.

109

(c)

2.0

1.5

1.0

0.5

0.0 CoCrMo

Ti Alloy

1D-FGM

2D-FGM

Tibia tray material Fig. 4. Maximum developed von Mises stresses achieved with different prosthesis materials in (a) tibia tray, (b) cement and (c) cancellous bone.


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tray deformations, which decrease the stresses it transfers to the bone via cement material. Also, it can be noted from Fig. 6b that, 1D-FGM tibia tray results in an increase in the shear stresses at cement-tibia tray interface under the tibia tray plate. While 2D-FGM tibia tray presents shear stresses between those of CoCrMo and Ti alloy. However, shear stresses still minimum than the allowable shear stress for the cement material since the cement shear strength ranges from 4.72 to 7.98 MPa, with a mean value of 5.94 MPa [34].

12 CoCrMo

(a)

TiAlloy 1D-FGM

10

2D-FGM

Von Mises stress (MPa)

110

8

6

4 12

(a)

CoCrMo

2

TiAlloy 10

1D-FGM

0

5

10

15

20

25

30

Distance x from the center in mm

1.5

(b)

CoCrMo TiAlloy


2D-FGM

0

6

4

1D-FGM

1.0

2D-FGM

Shear stress (MPa)

8

2

0.5 0 3

6

9

0.0

12

15

18

21

24

27

30

Distance x from the center in mm 0.6

-0.5

(b)

CoCrMo TiAlloy 0.4

-1.0

1D-FGM

-1.5 0

5

10

15

20

25

30


Fig. 5. Distributions of (a) von Mises stresses and (b) shear stresses along tibia tray-UHMWPE interface.

B. Cement – tibia tray interface Fig. 6 shows von-Mises stresses and shear stresses distributions along cement-tibia tray interface under the tibia tray plate. It can be noted that both 1D-FGM and 2D-FGM reduce the developed von-Mises stresses at this interface. Compared to CoCrMo and Ti alloy tibia trays, 2D-FGM tibia tray decreases the maximum von-Mises stress developed at cement-tibia tray interface under the tibia tray plate by about 59% and 33% respectively. On the other hand, using 1D-FGM tibia tray bring about a reduction of 58% and 32% in the maximum von-Mises stresses at this interface compared to CoCrMo and Ti alloy tibia trays respectively. Therefore, using functionally graded materials to fabricate tibia trays (1D-FGM or 2D-FGM) will reduce the developed von-Mises stresses, which will resulted in a more uniformly stress distribution with stress values in a more physiological range. Furthermore, this reduction in the developed von-Mises stresses may be explained by the fact that stiffer tibia tray material reduces tibia

Shear stress (MPa)

2D-FGM 0.2

0.0

-0.2

-0.4

-0.6 3

6

9

12

15

18

21

24

27

30


Fig. 6. Distributions of (a) von Mises stresses and (b) shear stresses at cement-tibia tray interface under the tibia tray plate.

Fig. 7 shows von-Mises stresses and shear stresses distributions along cement-tibia tray interface around tibia tray post. It can be noted that, for 1D-FGM, CoCrMo and Ti alloy tibia trays there are negligible differences in the von-Mises and shear stresses around the tibia tray post at cement-tibia tray interface except around the upper part of the post. On the contrary, 2D-FGM shows an evidently reduction in von-Mises and shear stresses developed around the tibia tray post at this interface compared to the other different tibia tray materials.


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ultimate shear stress (1.0–2.0MPa) of cancellous bone [35, 36]. This increasing in shear stresses may be explained by the increasing in stress transformability from the cement to bone, which will reduce the bone stress shielding. Furthermore, in Fig. 8 it is worth to note that due to the effect of suddenly change in the properties of cancellous bone parts (i.e. the top and top middle cancellous bone parts) there is a suddenly change in von-Mises stress distribution results.

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Fig. 7. Distributions of (a) von Mises stresses and (b) shear stresses at cement-tibia tray interface around tibia tray post.

C. Bone–cement interface Fig. 8 presents the distribution of a von-Mises stresses and shear stresses along the bone-cement interface under the tibia tray plate. It shows a comparison between the proposed tibia tray materials. It is worth to note that, 1D-FGM tibia tray presents the maximum von-Mises and shear stresses at the bone-cement interface. It increases the maximum von-Mises stress developed at this interface by about 59% and 17% compared to CoCrMo and Ti alloy tibia trays respectively. While, 2D-FGM tibia tray increases the maximum von-Mises stress developed at the bone-cement interface by about 7% compared to CoCrMo tibia tray and decreases it by about 22% compared to Ti alloy tibia tray. This means that, using 1D-FGM tibia tray may be favored since it will transfer more stresses from tibia tray to bone via cement material compared to that appears in case of using other tibia tray materials. However, 1D-FGM tibia tray increases the developed shear stresses at bone-cement interface while 2D-FGM tibia tray results in minimum shear stresses. Fortunately, maximum shear stresses for all of the proposed tibia trays materials are lower than the

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Fig. 8. Distributions of (a) von Mises stresses and (b) shear stresses at bone-cement interface under the tibia tray plate.

Fig. 9 shows von-Mises stresses and shear stresses distributions around tibia tray post at bone-cement interface. Also, as in cement-tibia tray interface it can be observed that, for 1D-FGM, CoCrMo and Ti alloy tibia trays there are negligible differences in the von-Mises and shear stresses around the tibia tray post at bone-cement interface except around the upper part of the post. While 2D-FGM tibia tray shows an increase in the developed von-Mises stresses at this interface. However, the maximum von-Mises stress for 2D-FGM tibia tray still the lower compared to other tibia tray materials. In addition, there is another advantage of 2D-FGM tibia tray represented in the reduction of shear stresses


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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:02 developed around the post at bone-cement interface. Moreover, in 2D-FGM tibia tray the maximum interface shear stress reduced and the stresses distributed more uniformly to some extent. This means that an improvement in distributed load transfer from post to bone which is a point of concern to avoid the risk of interface failure.

differences in interface stresses around the post compared to the CoCrMo, Ti alloy and 1D-FGM tibia trays.  Therefore, the use of FGM tibia tray in TKR is attractive because it will reduce the bone stress shielding and the possibility of implant loosening which will increase the implant life. Furthermore, FGM properties can be designed to vary in a certain pattern to meet the desired requirements at different regions in the knee joint system, which required further research.

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REFERENCES

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Fig. 9. Distributions of (a) von Mises stresses and (b) shear stresses at bone-cement interface around tibia tray post.

V. CONCLUSIONS  Finite element analysis employed to demonstrate the effectiveness of using unidirectional and bidirectional functionally graded material (1D-FGM and 2D-FGM) tibia trays to reduce stress-shielding effect which is the primary cause of aseptic loosening in TKR.  The developed models aid the achievement of an optimal design and performance of FGM knee implant at low computational costs.  While 1D-FGM allows to transfer more stress to bone via cement material, 2D-FGM shows the minimum and more uniformly distributed shear stresses for all interfaces except the tibia tray-UHMWPE tibial insert interface. Furthermore, only 2D-FGM tibia tray show a significant

[13]

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[15]

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