# Horizontal functionally graded material coating of cementless hip prosthesis.

IntroductionMetallic biomaterials are remarkably important for the reconstruction of failed tissue, especially failed hard tissue, to improve the quality of life of the patient. The demand for metallic biomaterials is increasing rapidly because the world population is getting increasingly older, and elderly people have a higher risk of hard tissue failure. The biological and mechanical biocompatibility of metallic biomaterials requires much improvement. Furthermore, the biofunctionality of metallic biomaterials is at present inadequate, and needs to be improved [2]. The development of new metallic alloys for biomedical applications is described and developed by Niinomi et. al. [2]. New low modulus b-type titanium alloys for biomedical applications are still currently being developed. Strong and enduring b-type titanium alloy with a low Young's modulus are being investigated. Simon et. al. [3] focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. They generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. Hu et. al. [4] used Collagen I as an additive to the dilute electrolyte used for deposition of HAP coating. The modified HAP coating has a crystal structure similar to that of the natural bone. However the mechanical properties of HAP coatings have been improved after immersion in collagen as investigated by Liang Ou et. al. [5].

Functionally graded materials (FGM) were fabricated by Watari et. al. [6] for bio-medical application, especially for implant application, and the effect of gradient structure was evaluated. Stress distributions on dental implants made of functionally graded biomaterials (FGBM) are investigated numerically by Kaman and Celik [7]. As a result, with increasing material gradient parameter (n), the equivalent stress decreases, but the minimum stress distribution increases. A new functionally graded dental implant coating is designed by Hedia [8], they also studied the effect of coating thickness. They found that using a functionally graded coating of 150pm thickness, graded from titanium at the apex to collagen at the root, will reduce the maximum von Mises stress in the bone by 19% and 17% compared to collagen and hydroxyapatite coating respectinely.

A three-dimensional finite element model of a functionally graded femoral prosthesis created by Oshkour et. al. [9]. The model consisted of a functionally graded materials (FGMs) femoral prosthesis, cement, and femur. The hip prosthesis was composed of FGMs made of titanium alloy, chrome-cobalt, and hydroxyapatite. A multi-objective design optimization of a FGM femoral component is carried out by Bahraminasab et. al. [10] using finite element analysis (FEA) and response surface methodology (RSM). , the optimal FGM showed better results; on average 3.8%, 13.6%, and 0.6% improvements were found in the mean stress of the femur, mean micromotion of the interface and wear index of insert, respectively. Hedia et. al. [11] optimized the material of the cementless actual stem model. 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.

A new design of the cementless hip stem coating using vertical functionally graded material was found by Hedia and Noha [1]. It is found that using vertical FGM coating leads to diminishing stress shielding at the medial proximal region of the femur. In addition, it reduces the interface shear stress between the coating and bone that affects the long term stability of the hip implant. The effect of HAP coating thickness on osseointegration for dental implants in dogs was evaluated by Zhang et. al. [12]. The results showed that HAP coating has a great effect on early osseointegration. However, the thickness of the coating has no obvious effect on osseointegration. while Svehla et. al. [13] examined the effect of coating thickness on the shear strength and bone ingrowth in a sheep model. The results showed that 100pm thick HAP layer has a better fixation and ingrowth and less resorption compared with other coating thickness. They didn't recommend the using of thicker HAP coating for Ti substrates.

Studies from the previous literature have focused on improving the mechanical property of prostheses for bone and implant stiffness matching. It is found from literature that most researchers studied the effect of using FGM on the prosthesis material while few researches have been found on developing a functionally graded coating on Ti substrates. The concept of FGM was applied on coating only for dental implants. The application of the functionally graded coating on the artificial human joints has not been studied well. However, the effect of coating thickness is not obvious and clear through many dental and bone implants researches. Therefore, the aim of this work is to find an optimal horizontal FGM coating for cementless hip joint implant with a suitable coating thickness. The objective of this optimization study is to reduce the stress shielding occurred in the femur bone after Ti stem implantation and diminishes the shear stress at the coating / bone interfaces.

Materials and Methods

Properties of FGM Femoral Stem Implant Coating

This study considers the coating of the cementless hip stem as a horizontal FGM. The material properties of the coating graded in the horizontal direction from E1 at the inner layer of the coating adjacent to the femoral stem, to E2 at the outer layer of the coating adjacent to the femoral bone as shown in figure 1. The volume fractions of the FGM coating composites calculated according to the following relations: [14, 15]

[V.sub.2] = [(x/t).sup.m] (1)

[V.sub.1] = 1 - [V.sub.2] (2)

where, x is the horizontal position within the stem coating, t is the total thickness of the coating, and m is a composition variation of the FGM coating. When m < 1, the FGM coating is rich in the material at the outer layer of the coating. However, when m > 1 this means that the FGM coating will be rich in the material at the inner layer of the coating. Note that 0 < m [less than or equal to] 10.

The equivalent elastic modulus at different regions of the coating calculated from the following equations [11, 14]:

E = [E.sub.0] (1 - p)/1 + p(5 + 8v)(37 - 8v)/{8(1 + u)(23 + 8u)} (3)

where: [E.sub.0] = [E.sub.2] [[E.sub.2] + ([E.sub.1] - [E.sub.2])/[E.sub.2] + ([E.sub.1] - [E.sub.2])([V.sup.2/3.sub.1] - [V.sub.1])] (4)

n = [n.sub.1] [V.sub.1] + [n.sub.2] [V.sub.2] (5)

where, [n.sub.1] and [n.sub.2] are the Poisson's ratio of the two-phase FGM, respectively.

p is the porosity of the FGM coating calculated from the following equations:

P = A (x/t) [1- [(x/t).sup.z]] (6)

where A represents the porosity in the mixture calculated using the following equation:

[((n + z)/n).sup.n]/1 - [(n/(n + z)).sup.z] [greater than or equal to] A [greater than or equal to] 0 (7)

where m, n, z are arbitrary constants.

Finite Element Model and Optimization Technique

A coated cementless femoral Ti stem, as well as, stainless steel stem has been studied in this work. The thickness of the implant coating was taken from literature. It was changed from 100 to 500[micro]m. The geometry of the left femur for an old man was taken before by Hedia et. al. [16]. A 2-D plane stress was used with varying thickness for more accurate results. The thickness of the stem, coating, and femur is calculated by transferring the actual 3-D to an equivalent 2-D model [16]. It is assumed that the stem, coating, and the femoral bone are perfectly bonded. The femur is loaded with 750N giving a resultant force R = 2670N and an abductor muscle force F = 1973N [17]. The tension banding force Q is neglected as it makes a little difference in the overall stress distribution [16]. The cortical bone was fixed distally. The applied loads and fixations are shown in figure 2, and the finite element mesh is shown in figure 3.

The main goal of this study is to find the optimal material gradation of the coating. The purpose of using FGM coating is to overcome the mismatch between the stem stiffness and the femur. The high stiffness of the stem can cause stress shielding phenomenon at the medial proximal region of the femur, which leads to bone resorption. However, the lower stiffness of the stem increased stress concentration at the interfaces between the implant and the femur leads to decrease stability of the implant. In order to have the optimal material gradation the optimization technique applied through the ANSYS package. The computer programs are written with the parameters specified in the ANSYS software to calculate the material properties at each layer of the graded coating. The optimization technique analysis for this study is:

a. Objective Function: to minimize the stress shielding problem by maximizing von Mises stress at the medial proximal region of the femur.

b. Design Variables:

(1) Change the elastic modulus of the two-phase composites of FGM coating E1 and E2 within a large different values of biomaterials 1GPa [less than or equal to] E1, E2 [less than or equal to] 210 GPa

(2) Change the parameter of the composition variation, m within a range 0 < m [less than or equal to] 10

(3) Change the coating thickness within the range used in literature 100[micro]m [less than or equal to] t [less than or equal to] 500 [micro],m

c. State Variables:

(1) The maximum interface shear stress in bone at the lateral coating / bone interface to be less than the maximum interface shear stress using uncoated Ti stem. However, its minimum value is an arbitrary small value (e.g. 5 MPa).

[tau] arbitrary value [less than or equal to] [tau] lateral FGM coating [less than or equal to] [tau] lateral uncoated Ti

(2) The maximum interface shear stress in bone at the medial coating / bone interface to be less than the maximum interface shear stress using uncoated Ti stem. However, its minimum value is an arbitrary small value (e.g. 5 MPa).

[tau] arbitrary value [less than or equal to] [tau] medial FGM coating [less than or equal to] [tau] medial uncoated Ti

Results

The finite element model is optimized using the previous objective function, design, and state variables. It is concluded that the optimal gradation of the coating material for the model changing the Young's modulus from E1 = 1GPa (collagen) at the inner coating layer adjacent to the stem, graded to E2 = 5 GPa (hydroxyapatite) at the outer coating layer adjacent to the femoral bone. The optimal value of the composition variation m equals 0.1 which mean that the FGM coating is rich in HAP. The optimal value of the coating thickness equals 500pm. The results of the coating model are illustrated through the following Figures:

1. The lateral and medial interface shear stress in bone at bone / coating interfaces are illustrated in figure 4 and figure 5, respectively. It's found that the maximum shear stress for both lateral interface and medial interface is concentrated at the distal part of the interface, decreased gradually towards the proximal region. The maximum shear stress for both lateral interface and medial interface is occurred using non coated Ti stem. However, the minimum value of the maximum shear stress is occurred using the optimal FGM coating on Ti stem.

2. von Mises stress in bone at the medial proximal region of the femoral bone is illustrated in figure 6. It is found that the minimum von Mises stress values is occurred using uncoated Ti stem. However, the values of von Mises stress along all medial proximal regions are increased using the optimal FGM coating on Ti stem.

3. Figure 7 illustrates the maximum values of the shear stress along the lateral and medial interfaces. The maximum interface shear stress using the optimal FGM coating on Ti stem gives the best results for both the lateral and medial interfaces. The maximum lateral shear stress using the optimal FGM coating is reduced by 18% and 6% compared to uncoated Ti stem and Ti stem coated with HAP, respectively. However, the maximum medial interface shear stress using the optimal FGM coating is reduced by 35% and 8% compared to uncoated Ti stem and Ti stem coated with HAP, respectively.

4. Figure 8 illustrates the maximum von Mises stress values at the medial proximal region. It is found that using the FGM coating on Ti stem increases the maximum von Mises stress by 60% and 15% compared to uncoated Ti stem and Ti stem coated with HAP, respectively.

Discussion

In the implanted joint, the stiffer implant carries the majority of the load, which was actually carried by the bone itself before implantation. The resulting implant induced stress-shielding and subsequent bone remodeling causes bone resorption around the implant [18]. In the human body, biological materials often have the structure of FGMs and are multi functional. FGMs therefore, provide the structure that engineered biomaterials should essentially possess. In this study the effect of design the coating of cementless hip prosthesis as horizontal FGM was studied, while in a previous study which was carried out by Hedia and Noha [1] the effect of design the coating of cementless hip prosthesis as vertical FGM was studied. It was shown that both studied are succeeded to solve the stress shielding problem at the media proximal region of the hip joint. However the shear stresses at the medial and lateral interfaces are also reduced through both FGM designs. The composition variation parameter for the optimal design makes the FGM coating rich in HAP. The position of HAP adjacent to bone will increase the rate of bone ingrowth and positively affect the mechanical stability of the implant. Many researches study the advantages of HAP coating to achieve earlier and fixation strength and to reduce the healing time and pain after surgery [19-21]. Recent researches focus on the advantages of adding some materials, like collagen which used in this investigation, in improving the effect of the coating on the stability and shear strength of the coating [4, 5, 22]. It's found in this study that changing the coating thickness does not significantly affect the stress distribution. This result is similar to that obtained by many researches [12, 13].

Conclusions

The optimal coating material is found to be 500 pm thickness of collagen at the inner layer of the coating adjacent to stem graded to hydroxyapatite at outer layer of the coating adjacent to the femoral bone, with composition variation parameter makes the coating rich in hydroxyapatite.

The maximum von Mises stress at the medial proximal region of the femur is increased by 60% compared to uncoated Ti stem and increased by 15% compared to hydroxyapatite coated Ti stem.

The maximum lateral shear stress is reduced by 18% compared to uncoated Ti stem and reduced by 6% compared to hydroxyapatite coated Ti stem.

The maximum medial shear stress is reduced by 35% compared to uncoated Ti stem and reduced by 8% compared to hydroxyapatite coated Ti stem.

References

[1.] H.S. Hedia, N. Fouda, "Design Optimization of Cementless Hip Prosthesis Coating through Functionally Graded Material", Computational Materials Science, 87, 83-87 (2014).

[2.] M. Niinomi, M. Nakai, J. Hieda, "Development of new metallic alloys for biomedical applications", Acta Biomaterialia, 8, 3888-3903 (2012).

[3.] U. Simon, P. Augat, A. Ignatius, L. Claes, "Influence of the stiffness of bone defect implants on the mechanical conditions at the interface--a finite element analysis with contact", Journal of Biomechanics, 36, 1079-1086 (2003).

[4.] R. Hu, C. Lin, H. Wang, T. Tao, "Modulation effects of collagen I on the structure of electrochemically deposited hydroxyapatite coating", Materials Letters, 64, 915-917 (2010).

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[7.] M.O. Kaman, N. Celik, "Effects of Thread Dimensions of Functionally Graded Dental Implants on Stress Distribution", World Academy of Science, Engineering and Technology, 78, 2020-2026 (2013).

[8.] H.S. Hedia, "Effect of coating thickness and its material on stress distribution for dental implant", Journal of Medical Engineering & Technology, 31(4), 280-287 (2007).

[9.] A.A. Oshkour, N.A. Abu Osman, Y.H. Yau, F. Tarlochan, W.W. Abas, "Design of new generation femoral prostheses using functionally graded materials: A finite element analysis", journal of Engineering in Medicine, 227 (1), 3-17 (2012).

[10.] M. Bahraminasab, B.B. Sahari, K.L. Edwards, F. Farahmand, T.S. Hong, M. Arumugam, A. Jahan, "Multi-objective design optimization of functionally graded material for the femoral component of a total knee replacement", Materials and Design, 53, 159-173 (2014).

[11.] H.S. Hedia, M.A.N. Shabara, T.T. El-midany, N. Fouda, "Improved design of cementless hip stems using two-dimensional functionally graded materials", Journal of Biomedical Materials Research -Part B Applied Biomaterials, 79, 42-49 (2006).

[12.] S. Zhang, Z. Xianting, W. Yongsheng, C. Kui, W. Wenjian, "Adhesion strength of sol-gel derived fluoridated hydroxyapatite coatings", Surface & Coatings Technology, 200, 6350-6354 (2006).

[13.] M. Svehla, P. Morberg, W. Bruce, B. Zicat, W. R. Walsh, "The Effect of Substrate Roughness and Hydroxyapatite Coating Thickness on Implant Shear Strength", The Journal of Arthroplasty, 17(3), 304-311 (2002).

[14.] H.S. Hedia, "Design of functionally graded dental implant in the Presence of Cancellous Bone", Journal of Biomedical Materials Research Part B Applied Biomaterials, 75, 74-80 (2005).

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[16.] H.S. Hedia, D.C. Barton, J. Fisher, "Shape optimization of a Charnley prosthesis based on the fatigue notch factor", Bio-Medical Materials and Engineering, 6, 199-217 (1996).

[17.] H.S. Hedia, D.C. Barton, J. Fisher, T.T. El Midany, "Effect of FE idealization, load conditions and interface assumptions on the stress distribution and fatigue notch factor in the human femur with endoprosthesis", Bio-Medical Materials and Engineering, 6, 135-152 (1996).

[18.] T. Majima, K. Yasuda, T. Tsuchida, "Stress shielding of patellar tendon: effect on small-diameter collagen fibrils in a rabbit model", J Orthop Sci, 8, 836-841 (2003).

[19.] P. Choudhury, D.C. Agrawal, "Sol-gel derived hydroxyapatite coatings on titanium substrates", Surface & Coatings Technology, 206, 360365 (2011).

[20.] A. Race, D. Christopher, B. Heffernan, P.F. Sharkey, "The Addition of a Hydroxyapatite Coating Changes the Immediate Postoperative Stability of a Plasma-Sprayed Femoral Stem", The Journal of Arthroplasty, 26(2), 289-295 (2011).

[21.] W. N. Capello, J. A. D'Antonio, M. T. Manley, J. R. Feinberg, "Bioceramics in Total Hip Arthoplasty: Hydroxyapatite Coating, Seminars in Arthroplasty, 17, 153-160 (2006).

[22.] R. R. Kumar, S. Maruno, "Functionally graded coatings of HA-G-Ti composites and their in vivo studies", Materials Science and Engineering A, 334 (1,2), 156-162 (2002).

N. Fouda

Mansoura University, Faculty of Engineering, Mansoura, Egypt

Correspondence: e-mail: foudanoha@yahoo.com

Received 6 January 2014; Accepted 31 May 2014; Available online 1 June 2014

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Title Annotation: | Original Article |
---|---|

Author: | Fouda, N. |

Publication: | Trends in Biomaterials and Artificial Organs |

Article Type: | Report |

Date: | Apr 1, 2014 |

Words: | 3243 |

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