Improve the performance of coated cemented hip stem through the advanced composite materials

Abstract

Design of hip joint implant using functionally graded material (FGM) (advanced composite material) has been used before through few researches. It gives great results regarding the stress distribution along the implant and bone interfaces. However, coating of orthopaedic implants has been widely investigated through many researches. The effect of using advanced composite stem material, which mean by functionally graded stem material, in the total hip replacement coated with the most common coated materials has not been studied yet. Therefore, this study investigates the effect of utilizing these two concepts together; FGM and coating, in designing new stem material. It is concluded that the optimal FGM cemented stem is consisting from titanium at the upper stem layers graded to collagen at a lower stem layers. This optimal graded stem coated with hydroxyapatite found to reduce stress shielding by 57% compared to homogenous titanium stem coated with hydroxyapatite. However, the optimal functionally graded stem coated with collagen reduced the stress shielding by 51% compared to homogenous titanium stem coated with collagen.

Keywords

Finite element FGM hip replacement coating stress shielding interface shear stress

1. Introduction

A comparison between clinical and radiologic results in 55 patients (110 hips) is carried out by Kim et al. [1] all hips is identical in geometry but different in the proximal surface treatment, some of them are with hydroxyapatite (HAp) coating and others are without coating. They concluded that after long-term follow-up, HA coating on the porous surfaces did not improve or diminish the survivorship of total hip arthroplasty. Darimont et al. [2] evaluated quantitatively the behavior of in vivo hydroxyapatite coated implants (HAp) in the rabbit over time. They concluded that the formation of bone was accelerated in presence of HAp. The results showed that HAp coating showed an extremely high bonding strength with bone.

The addition of a hydroxyapatite coating changes the immediate postoperative stability of a plasma-sprayed femoral stem as concluded by Race et al. [3]. The effects of different hydroxyapatite (HAp) coating thicknesses on osseointegration after dental implantation in dogs were evaluated [4]. The results suggested that HAp implant coating may positively affect early osseointegration, but coating thickness had no significant effect on ultimate osseointegration. Svehla et al. [5] examined the effect of HAp coating thickness on bone ingrowth and shear strength in a bilateral bicortical sheep model. They concluded that using 100 µm HAp thickness provided greater fixation and ingrowth and less resorption compared with the 50 µm thick layer. However, they did not observe any advantage in using a thicker HAp coating for the titanium substrates examined. Shear strength increased with time for all implants.

The mechanical properties of bioactive coatings on Ti6Al4V substrates were investigated by Ou et al. [6]. The aim was to observe the differences in the mechanical properties before and after immersion in collagen solution. The Young’s modulus of the pure hydroxyapatite, the disk and the coatings, was 3.6 GPa. After collagen incubation treatment, the composites had a Young’s modulus of 7.5 GPa.

The effect of fluoridated hydroxyapatite (FHAp) coatings on Ti6Al4V substrates on the interfacial shear strength and was investigated by many researches [7,8]. It is found that increasing fluorine in the coating increases the shear strength, and at the same time, the coating-substrate interfacial failure mode changes from brittle to ductile. Based on the cross-sectional analysis, a mechanism is proposed for the increased adhesion.

Three samples of coatings tested in a simulated body fluid under a corrosion test [9]. The first coating is TiO₂ layer. The second coating consists of two layers; the first layer is TiO₂ and the second layer containing 50% TiO₂ and 50% HAp. The third coating consists of three layers; TiO₂, 50% TiO₂ and 50% HAp, HAp. It was found that the first coating had the best corrosion resistance followed by the second and the third coatings. However, the second coating had a corrosion resistance with the best ability to bone bonding.

Xie et al. [10] investigated the feasibility of composite hip implant made from titanium (Ti) and Ti-high density polyethylene (Ti-HDPE). The new hip design is expected to promote bone ingrowth and enhance the interface strength.

Functionally graded material concept in designing a simplified cementless stem is investigated by Hedia et al. [11]. It is found that the optimal gradation is to change the elastic modulus gradually from HAp at the top of the stem to collagen at the bottom of the stem. They also optimized the material of the cementless actual stem model [12]. They found that the optimal stem graded from HAp at the top of the stem graded to bioglass at the bottom of the stem. They concluded that using FGM in the design of cementless hip stem solves the problem of stress shielding as well as decreases the interface shear stress between the implant and femur.

Many researchers studied the importance of using different coating materials on hip implant. Others were studied the effect of using composite or FGM cementless hip stem. However, the effect of using the functionally graded cemented stem material in the total hip replacement coated with the most common coated materials has not been studied yet. Thus, the aim of this investigation is to design a new coated stem through the concept of FGM.

2. Materials and numerical methods

2.1. Computational method for determination of FGM mechanical properties

In this study a Charnley cemented titanium femoral stem coated with hydroxyapatite and then coated with collagen, as the most common coating materials, has been used in this analysis. The concept is to design a coated cemented titanium femoral stem using the functionally graded material. The cemented stem is designed to be graded in the vertical direction. The material of the stem is graded from a material with an elastic modulus $E_{1}$ at the lower stem surface, to a material with an elastic modulus $E_{2}$ at the upper stem surface. The Charnley model of the stem and its gradation is illustrated in Fig. 1. The graded stem and its lateral and medial coating are magnified to be clear as shown in Fig. 2. The volume fractions of the coated functionally graded stem material composites are calculated from the following equations [13,14]: $\begin{array}{l} V_{2} = {(y / h)}^{m}, & (1) \\ V_{1} = 1 - V_{2}, & (2) \end{array}$ where $V_{1}$ and $V_{2}$ are the volume fractions of the coated functionally graded stem material, y is the vertical distance of the cemented stem, h is the total stem length and m is a composition variation parameter of the functionally graded stem constituents. When m is less than 1, the functionally grade stem is rich in the material at the upper stem surface. However, when m is greater than 1, the functionally graded stem will be rich in the material at the lower stem surface. The values of m ranged as $0 < m ⩽ 10$ .

Fig. 1.

The functionally graded coated stem model. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

Fig. 2.

The magnified graded stem with coating. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

The equivalent elastic modulus at different surface layers of the cemented stem is calculated from the following equation [12,13]: $\begin{array}{l} E = \frac{E_{0} (1 - p)}{1 + p (5 + 8 ν) (37 - 8 ν) / {8 (1 + ν) (23 + 8 ν)}}, & (3) \\ E_{0} = E_{2} [\frac{E_{2} + (E_{1} - E_{2}) V_{1}^{2 / 3}}{E_{2} + (E_{1} - E_{2}) (V_{1}^{2 / 3} - V_{1})}], & (4) \end{array}$ where $ν = ν_{1} V_{1} + ν_{2} V_{2},$ (5) where $ν_{1}$ and $ν_{2}$ are the Poisson’s ratio of the two-phase FGM, respectively. E is the modulus of elasticity of the material with porosity. $E_{0}$ is the modulus of elasticity of the material without porosity. p is the porosity of the FGM cemented stem determined from the following equations: $p = A {(y / h)}^{n} [1 - {(y / h)}^{z}],$ (6) where A represents the porosity in the mixture determined using the following equation: $\frac{{((n + z) / n)}^{n}}{1 - {(n / (n + z))}^{z}} ⩾ A ⩾ 0,$ (7) where m, n, z are arbitrary constants.

The mechanical properties of the functionally graded stem are calculated from the previous equations by programming these equations using the ANSYS Parametric Design Language (APDL). Therefore, these equations are applied on the finite element model of the hip prosthesis which will be described in the following section.

2.2. Finite element model of the cemented hip prosthesis

Charnley cemented hip joint is modeled in this analysis. The geometry of the model was taken from a real femoral bone with a higher degree of accuracy. The left femur of an old man was selected for modeling. Nine contiguous longitudinal CT scan slices were obtained using a GE9800 Research Scanner. The actual dimensions of the model were generated using the Analyzer software [15,16]. The femur is loaded with the resultant joint force R and the abductor muscle force F, as in the stance phase of slow walking, whereas the tension banding force Q, of the iliotibial tract is ignored. The partial body weight is assumed to be 750 N, giving $R = 2670 N$ and $F = 1973 N$ [15–18]. The distal cortical bone of the femur is fixed in all directions; all loading conditions are illustrated in Fig. 1. A two-dimensional plane stress with varying thickness is used in this analysis for more accurate results [15–17]. The thickness of the stem, coating, cement and femoral bone is determined by transferring the actual three dimensional to an equivalent two-dimensional model [15–17]. It is assumed that the stem, coating and the femoral bone are perfectly bonded [16,17]. The components of the implanted femur are meshed by 8-node quadrilateral elements, and mesh refinements are designed to achieve accurate results that are independent of mesh size. The final model consisted of 38,213 8-node quadrilateral elements with a maximum node numbers of 115,244, and 230,488 degrees of freedom in total for the purpose of finite element stress analysis. The finite element mesh of the model is shown in Fig. 3. The materials of bone, cement and coating of the model are assumed to be isotropic, linearly elastic and homogenous. Values of the mechanical properties are extracted from the literature. However, the mechanical properties of the stem material will be calculated from equations which discussed in details in the previous section. These mechanical properties will be optimized in this study as discussed in the following section.

Fig. 3.

The finite element mesh. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

2.3. Numerical optimization formulation

In this study the coated stem is designed as a functionally graded material stem to overcome the problem of stiffness mismatch between the stem and the femur bone, which is the main reason for stress shielding problem occurred at the proximal medial region of the femur. The objective function, design variables and state variables are illustrated as follows.

Objective function.
Maximizing von Mises stress at the medial proximal region of the femur to minimize the stress shielding. The stress shielding value is calculated from the following equation $stress shielding = \frac{stress reduction for FGM stem - stress reduction for coated titanium stem}{stress reduction for coated titanium stem} .$ (8)

Thus, the objective function as follows: $Z = min S$ , where S is the stress shielding calculated from the von Mises stress in the medial proximal region of the femur.

The design variables for the problem are:
(1)
The elastic modulus of the two composites ( $E_{1}$ , $E_{2}$ ) of functionally graded material $E_{1}$ and $E_{2}$ is changed within a large different biomaterials elastic modulus values, $1 GPa ⩽ E_{1}, E_{2} ⩽ 210 GPa .$ (9)
(2)
The composition variation parameter of the functionally graded material of stem is changed within the range obtained from literature, $0 < m ⩽ 10 .$ (10)

The constraints for the problem are:
(1)
The value of the maximum interface shear stress in cement at the lateral cement/coating and cement/bone interfaces is to be less than the allowable shear stress of cement (polymethylmetacrylate). The allowable shear ( $τ_{all}$ ) stress is taken as 10 MPa, where the ultimate shear strength of polymethylmetacrylate (PMMA) equal 50 MPa [19] and a safety factor is taken as 5. However, its minimum value is an arbitrary ( $τ_{arbitrary value}$ ) small value (e.g. 0.1 MPa), $τ_{arbitrary value} ⩽ τ_{lateral cement of FGM coated stem} ⩽ τ_{all} .$ (11)
(2)
The value of the maximum interface shear stress in cement at the medial cement/coating and cement/bone interfaces is to be less than the allowable shear stress ( $τ_{all}$ ) of PMMA which is equal 10 MPa. However, its minimum value is an arbitrary ( $τ_{arbitrary value}$ ) small value (0.1 MPa), $τ_{arbitrary value} ⩽ τ_{medial cement of FGM coated stem} ⩽ τ_{all} .$ (12)

The optimization procedure is carried out using the ANSYS commercial software package. However, the values of the von Mises stress which is used to calculate the objective function are function for the design variables $E_{1}$ , $E_{2}$ and m. The interface shear stress τ in the constraints is also function for the design variables $E_{1}$ , $E_{2}$ and m. A program is written to calculate the properties of each layer of the graded coating, using the ANSYS parametric design language APDL, to find the optimal graded material of the stem. The optimal design of the cemented hip stem will be coated with the most common coating materials. The first coating material is hydroxyapatite (HAP), while the second coating material is collagen.

The new design of cemented FGM stem coated with HAP and collagen is analyzed. The effect of this new design on the stress shielding of the proximal femur bone will be analyzed. On the other hand, it is important to study the effect of this new design on the interface shear stress distribution in cement along cement/coating and cement/bone interfaces.
3. Results

In this study the analysis is initially started with two stem designs; the first is a homogenous titanium stem with an elastic modulus equals 110 GPa coated with HAp, while the second is homogenous titanium stem coated with collagen. Then the optimization process is started with the previously discussed objective function, design variables and state variables. The optimization results showed that the optimal functionally graded material of the cemented coated stem is titanium at the upper stem layers graded to collagen at the lower stem layers, with a composition variation parameter m equals 5, which means that the composition is rich in collagen. This optimal graded stem is coated first with 500 µm HAp and then with 500 µm collagen. von Mises stresses at the proximal medial femur is compared between the homogenous coated titanium stem and the FGM coated stem. However, the values of the interface shear stress at the lateral and medial cement/coating and cement/bone interfaces are also studied. These results are illustrated below:

The lateral interface shear stress in cement at cement/coating interface is illustrated in Fig. 4. It is found that the values of the interface shear stress are higher at the middle parts and decreased gradually to the distal and proximal parts. It is found that in the case of FGM stem coated with HAp the maximum shear stress in cement at this interface is higher compared to homogenous titanium stem coated with HAp. However, this maximum value is less than the allowable shear stress of PMMA by 80%. On the other hand, the maximum shear stress in cement in the case of FGM stem coated with collagen is higher compared to homogenous titanium stem coated with collagen. However, this maximum value is less than the allowable shear stress of PMMA by 82%.

Fig. 4.

Interface shear stress in cement at lateral cement/coating interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

Fig. 5.

Interface shear stress in cement at lateral cement/bone interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

The lateral interface shear stress in cement at cement/bone interface is illustrated in Fig. 5. The maximum values of the interface shear stress are concentrated around the middle region of the femur and decreased gradually to the distal and proximal parts. It is found that in the case of FGM stem coated with HAp the maximum shear stress in cement at this interface is higher compared to homogenous titanium stem coated with HAp. However this maximum value is less than the allowable shear stress of PMMA by 77%. On the other hand, in the case of FGM stem coated with collagen the maximum shear stress in cement at this interface is higher compared to homogenous titanium stem coated with collagen. However this maximum value is less than the allowable shear stress of PMMA by 77%.

Fig. 6.

Interface shear stress in bone at lateral cement/bone interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

The lateral interface shear stress in bone at cement/bone interface is illustrated in Fig. 6. It is found that the values of the interface shear stresses at the middle are greater than those of the distal and proximal regions of the femur. The maximum interface shear stress in bone in case of the FGM stem coated with HAp is increased by 13% compared to homogenous titanium stem coated with HAp. However, the maximum interface shear stress in bone in the case of FGM stem coated with collagen is increased by 12% compared to homogenous titanium stem coated with collagen.

Fig. 7.

Interface shear stress in cement at medial cement/coating interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

Fig. 8.

Interface shear stress in cement at medial cement/bone interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

The medial interface shear stress in cement at cement/coating and cement/bone interfaces are shown in Figs 7 and 8, respectively. The maximum interface shear stress along these interfaces are concentrated proximally and gradually decreased towards the distal part of the femur. It is found that the maximum interface shear stress in cement in the case of FGM stem coated with HAp and collagen is increased compared to homogenous titanium stem coated with HAp and collagen. However, these maximum values are less than the allowable shear stress of PMMA by 42% and 62%, respectively as in Fig. 7. However, in Fig. 8 the maximum values in cement are less than the allowable shear stress of PMMA by 38% and 41%, respectively.

Fig. 9.

Interface shear stress in bone at medial cement/bone interface. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

The medial interface shear stress in bone at cement/bone interface is shown in Fig. 9. High stress values located along the distal and proximal regions of the femur, while these stresses values are reduced at the middle femur part. The maximum interface shear stress in bone in the case of FGM stem coated with HAp is increased by 24% compared to homogenous titanium stem coated with HAp. However, the maximum interface shear stress in bone in the case of FGM stem coated with collagen is increased by 27% compared to homogenous titanium stem coated with collagen.

Fig. 10.

Comparison between von Mises stresses at the proximal medial femur for different stem types and natural femur. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

Figure 10 is a comparison between von Mises stress values along the proximal medial region of the femur for the homogenous titanium stem coated with HAp, homogenous titanium stem coated with collagen and the FGM stem coated with HAp and collagen. All these four designs are also compared with a stem made from flexible material ( $E = 20 GPa$ ), which represents the natural bone, as previously used by many other authors [20,21]. The values of von Mises stress in the proximal bone using a stem with $E = 20 GPa$ is compared with those obtained by Kang et al. [22] to validate the model. The flexible stem is used to study the effect of the new FGM coated stem on solving the stress shielding problem at this region of the femur. It is found that the distribution of the von Mises stresses along the proximal medial part of the femur in the case of FGM coated stem is nearly the same as that of the natural bone. However, the stress distribution of the homogenous coated titanium stem along the same region of the femur is lower compared to FGM coated stem which produce high stress shielding.

The maximum von Mises stress value for FGM coated stem designs and for homogenous coated titanium stem are compared by the maximum value for the natural bone as illustrated in Fig. 11. It is found that the stress shielding is reduced by 57% in the case of FGM stem coated with HAp compared to homogenous titanium stem coated with HAp. However, the stress shielding is reduced by 51% in the case of FGM stem coated with collagen compared to homogenous titanium stem coated with collagen.

Fig. 11.

Comparisons between maximum von Mises stress at the proximal medial femoral bone for different stem types and natural femur. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151277.)

4. Discussion

Previous studies showed a problem is occurred when using pure metallic implant in the hip prosthesis. These problems can be summarized to; stress shielding due to the mismatch of the Young’s modulus between the stiff implant and the femur, and the lack of fixation between the implant and the cement bone. This study tried to find the solution of these problems by using the FGM concept with coating for design of the hip implant.

In this investigation it is concluded to design the coated stem from titanium at the upper stem layers graded to collagen at the lower stem layers. Design a stem graded from stiff material at the top surface and flexible at the lower surface was concluded previously by Kuiper and Huiskes [21,23] and by Hedia et al. [11,24]. Titanium and collagen which recommended to be used as a stem graded material in this design are proved to be the best biomaterials used in orthopedic applications [25,26]. The use of HAp coated is more effectively for biomedical application due to their excellent biocompatibility [27].

This analysis increased the interface shear stress in cement along the medial and lateral cement interfaces. The maximum interface shear stress at the medial interfaces does not exceed 6 MPa, while the maximum value at the lateral interfaces does not exceed 2.25 MPa. These values of the maximum interface shear stress in cement are safe and acceptable compared to the value of the ultimate shear strength of polymethylmetacrylate which is ranged between 40 and 50 MPa [28] (which produced allowable shear stress 10 MPa) and the yield strength which is between 80 and 90 MPa [29].

In order to validate these numerical results, a flexible Charnley stem with an elastic modulus equals to the elastic modulus of the natural bone ( $E = 20 GPa$ ) is investigated as previously used by many authors [20,21]. A good agreement is found between the stress predictions at the proximal medial region in the case of using flexible stem and those reported by others [30,31].

5. Conclusions

A new design of cemented functionally graded material stem coated with hydroxyapatite and collagen is succeed to reduce stress shielding at the proximal medial femoral bone. The optimal stem design will improve the total hip replacement performance and increase the life of the joint. However, the optimal functionally graded stem designed to change in the vertical direction from titanium at the upper layers graded to collagen at the lower stem layers.

The optimal FGM stem coated with hydroxyapatite reduced stress shielding by 57% compared to titanium stem coated with hydroxyapatite. However, the optimal FGM stem coated with collagen reduced stress shielding by 51% compared to titanium stem coated with collagen.

The interface shear stress in cement along the lateral cement interfaces does not exceed 2.25 MPa. However, it does not exceed 6 MPa along the medial cement interfaces. Both these values are acceptable compared with the allowable shear stress of polymethylmetacrylate.

Footnotes

Acknowledgement

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (135-004-D1433). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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