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Copyright © 2014 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.
Effect of Geometrical Parameters on the Performance of Longitudinal Functionally Graded Femoral Prostheses *Azim Ataollahi Oshkour, †Hossein Talebi, *Seyed Farid Seyed Shirazi, *Yat Huang Yau, ‡Faris Tarlochan, and §Noor Azuan Abu Osman *Departments of Mechanical Engineering and §Biomedical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia; †Institute of Structural Mechanics, Bauhaus–Universitat Weimar, Weimar, Germany; and ‡Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University, Doha, Qatar
Abstract: This study aimed to assess the performance of different longitudinal functionally graded femoral prostheses. This study was also designed to develop an appropriate prosthetic geometric design for longitudinal functionally graded materials. Three-dimensional models of the femur and prostheses were developed and analyzed. The elastic modulus of these prostheses in the sagittal plane was adjusted along a gradient direction from the distal end to the proximal end. Furthermore, these prostheses were composed of titanium alloy and hydroxyapatite. Results revealed that strain energy, interface stress, and developed stress in the femoral prosthesis and the bone were influenced by prosthetic geometry and gradient index. In all of
the prostheses with different geometries, strain energy increased as gradient index increased. Interface stress and developed stress decreased. The minimum principal stress and the maximum principal stress of the bone slightly increased as gradient index increased. Hence, the combination of the femoral prosthetic geometry and functionally graded materials can be employed to decrease stress shielding. Such a combination can also be utilized to achieve equilibrium in terms of the stress applied on the implanted femur constituents; thus, the lifespan of total hip replacement can be prolonged. Key Words: Finite element analysis—Strain energy—Interface stress—Maximum principal stress—Minimum principal stress.
Total hip replacement (THR) is a surgical approach that can successfully relieve pain and restore hip joint function (1). Advances in technology help prosthesis designers and surgeons customize implants and prolong the lifespan of THR (2). However, revision surgery complications limit the life of THR, particularly for young and active patients (3). Furthermore, THR failure is usually caused by aseptic loosening (4). Prosthetic material and geometry affect prosthetic stiffness (rigidity) in aseptic loosening (5). Therefore, many experimental and theoretical approaches have been employed to investigate different prosthetic materials and
geometries. For instance, finite element analysis (FEA) is an effective tool used for the multiscale analysis and design of implants (6). Different implant designs can be analyzed more accurately by conducting FEA in a computer rather than performing timeconsuming, destructive, and costly mechanical and in vivo tests (7). FEA is commonly conducted to study artificial hip joint biomechanics and femoral prosthetic designs (8–11). Many FEA studies have also focused on the optimization of the geometry and material of femoral prostheses to develop THR with a long lifespan (12–17). Kuiper and Huiskes (18) and Hedia et al. (19,20) used functionally graded materials (FGMs) as appropriate substitutes for conventional materials used in hip implants. FGMs can also be used for orthopedic purposes (21). FGMs are engineering materials designed on the basis of biological structures (21,22). These materials exhibit adjustable mechanical and structural properties in continuous (gradient) or step-wise (graded) approaches (22). FGMs also
doi:10.1111/aor.12315 Received December 2013; revised February 2014. Address correspondence and reprint requests to Mr. Azim Ataollahi Oshkour, Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia. E-mail: [email protected]
Artificial Organs 2014, ••(••):••–••
2
A.A. OSHKOUR ET AL.
demonstrate better biocompatibility, fracture toughness, load bearing, and wearing resistance than their monolithic ceramic and metal counterparts (21,23,24). Various materials for implants, including glasses, metals (titanium alloys [Ti], chromecobalt alloys, and stainless steel), and ceramics (hydroxyapatite [HA], alumina, and zirconia), can be introduced as the main phases of FGMs. Among these materials, Ti is commonly used for implant designs because Ti alloys exhibit a lower modulus of elasticity (more flexibility), better biocompatibility, and stronger corrosion resistance than other alloys (25). HA is also commonly used because it displays numerous attractive properties, such as excellent bio-
compatibility, bioactivity, nontoxicity, and unique osteoinductivity for orthopedic applications; HA helps induce firm fixation between host bones and implants by forming a biological bond between an implant and a bone (26,27). To the best of our knowledge, studies focusing on FGMs and their potential applications in femoral prostheses have only employed two-dimensional FEA (18–20). Therefore, this study employed threedimensional (3D) FEA to evaluate different design configurations of longitudinal functionally graded femoral prostheses. Design configurations were proximal cross-section, distal cross-section, profile, and gradient index of FGMs.
FIG. 1. Dimensions of (a) profile, (b) proximal cross-sections, and (c) distal cross-sections.
Artif Organs, Vol. ••, No. ••, 2014
EFFECT OF GEOMETRICAL PARAMETERS MATERIALS AND METHODS Components modeling Computer-aided design software (Solidworks 2012, Dassault Systèmes Solidworks Corp., Concord, MA, USA) was used to develop 3D models of femoral prostheses. These femoral prostheses were composed of five distal cross-sections, four proximal crosssections, and three profiles (Fig. 1). A 3D model of the bone was developed using Mimics (version 13; Materialise NV, Leuven, Belgium) according to a previous study (3). The femur and its prostheses were meshed with 3D tetrahedral elements. The approximate global sizes of 1.5 and 1 mm were used to mesh the femur and prostheses, respectively. FEA was performed in ABAQUS finite element software version 6.10 (ABAQUS, Inc., Providence, RI, USA). Boundary conditions The boundary conditions in this study were used according to previous studies (17,28,29). In Fig. 2, the
3
TABLE 1. Material properties of implanted femur components Material Cortical bone Spongy bone Cement Titanium alloys (Ti) Hydroxyapatite (HA)
Plane
E (GPa)
G (GPa)
v
xx yy zz — — — —
11.5 11.5 17.0 2.13 2.70 110 10
3.60 3.30 3.30 — — — —
0.51 0.31 0.31 0.30 0.35 0.30 0.30
E: Young’s modulus. G: Shear modulus. v: Poisson’s ratio.
femur was fixed at the distal end, and 3 and 1.25 kN were applied on the head of the prosthesis (P0) and lateral side of the femur in the proximal portion (P1) at an angle of 20°, representing an equivalent weight of 70 kg and abductor muscle load, respectively. Two scenarios can be considered at the bone–implant surface; these scenarios are nonbonded surfaces with a friction coefficient and bonded surfaces. The nonbonded condition represents an event before bone ingrowth, and the bonded condition is used for ideal bone ingrowth. The desired fixation in cementless prostheses is not obtained immediately after surgery; primary stability can be studied by modeling the prosthesis and bone immediately after surgery. In this study, nonbonded surfaces with a friction coefficient of 0.4 (30,31) and bonded surfaces were considered at the bone–implant surface. Material properties The femur is composed of a linear isotropic spongy bone and a linear transverse isotropic cortical bone (Table 1) (28,29). The FGMs composed of Ti–HA were used to design the hip prostheses. The variation in the elastic modulus (Ek) of the prostheses in a gradient direction can be expressed as power law equation (Eq. 1) (32). n
2K + h ⎞ ⎞ ⎛ ⎛ 2K + h ⎞ Ek = Ea ⎜ + Eb ⎜ 1 − ⎛ ⎝ 2 h ⎟⎠ ⎝ ⎝ 2 h ⎠ ⎟⎠ −
FIG. 2. Mesh and boundary condition.
n
h h ≤ K ≤ , 0 ≤ n ≤ ∞, 2 2
(1)
where Ea and Eb are the Young’s modulus in the distal part and the proximal part of the femur, respectively, n is the gradient index, K is the stem height of the longitudinal prosthesis from the distal end to the proximal end, and h is the length of the prosthesis in the longitudinal direction. In the functionally graded femoral prosthesis, the volume fraction of the ceramic phase of FGMs (HA) Artif Organs, Vol. ••, No. ••, 2014
4
A.A. OSHKOUR ET AL. (n) of 0, 0.1, 0.5, and 1 were considered in this study. An increase in the gradient index complicates FGM production and reduces the strength of prostheses because of an increase in HA ceramic phase. Therefore, the maximum gradient index was limited to 1 in this study. RESULTS AND DISCUSSION
FIG. 3. Variation of Young’s modulus along the Ti–HA prosthesis length for different gradient index.
decreased along the distal-to-proximal direction. Hence, the proximal and distal parts of the femoral prosthesis were the metal (Ti) and ceramic (HA) phases, respectively (Fig. 3). Four gradient indexes a
b 60 Mean strain energy (N.mm)
Mean strain energy (N.mm)
60 50 40 30 20 10 0
D1
D2
D3
D4
50 40 30 20 10 0
D5
P1
P2 P3 P4 Proximal cross-sections
Distal cross-sections
c
d 60
60 Mean strain energy (N.mm)
Mean strain energy (N.mm)
The appropriate design of femoral prostheses is complicated. Implants should be mechanically compatible with the host bone, and its material should tolerate harsh biological environments of the body (33). The mechanical compatibility of the prosthesis with the bone is a function of prosthetic stiffness. The stiffness of femoral prostheses is determined by prosthetic cross-section and the modulus of elasticity (5). The mismatch between prosthesis and bone stiffness changes bone normal loading, resulting in bone
50 40 30 20 10 0 Profile 1
Profile 2 Profile
50
30 20 10 0
Profile 3
FIG. 4. Mean strain energy variation for (a) different distal cross-sections, (b) different proximal cross-sections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
40
m = 0.4
Bonded Interface property
e Mean strain energy (N.mm)
60 50 40 30 20 10 0
0.0
0.1
0.5
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
1.0
EFFECT OF GEOMETRICAL PARAMETERS resorption and loosening. To achieve good compatibility in stiffness between bones and implants, we used FGMs in different femoral prostheses with a gradient direction along the prosthesis length from the distal end to the proximal end (Fig. 3). We also examined different aspects of the femoral prosthetic geometry (Fig. 1). These aspects include different profiles (Profile 1, Profile 2, and Profile 3), different proximal cross-sections (P1, P2, P3, and P4), and different distal cross-sections (D1, D2, D3, D4, and D5). The results of the mean strain energy (SE), mean von Mises stress (VMS), mean maximum principal stress (MAPS), mean minimum principal stress (MIPS), and mean interface stress (IS) are discussed in this section. The SE at the proximal metaphysis of the femur was presented to address the stress shielding level of the femoral prosthesis. The VMS portrays the developed stress in the femoral prostheses.
a
60 Mean von Mises stress (MPa)
Mean von Mises stress (MPa)
MAPS and MIPS show bone stress distribution at lateral and medial sides, respectively. The IS shows shear stress variation in the bone–implant interface for a nonbonded implant–bone surface. Figure 4a,e illustrates the SE variation at the proximal metaphysis of the bone for five distal crosssections, four proximal cross-sections, three profiles, two implant–bone interface conditions, and four gradient indexes. The distal cross-sections slightly affected the SE variation (Fig. 4a). The prostheses with the proximal cross-sections of P1 and P4 produced maximum and minimum amounts of SE on the proximal metaphysis of the femur (Fig. 4b). The prostheses with the proximal cross-sections of P2 and P3 induced the same SE in the bone and in the midrange value of the SE generated by prostheses with P1 and P4 proximal cross-sections (Fig. 4b). The prostheses developed from Profile 1 and Profile 3 provoked almost the same and higher SE than the
b
60 50 40 30 20 10 0
c
D2 D3 D4 Distal cross-sections
40 30 20 10
D5
P1
P2 P3 P4 Proximal cross-sections
d 60 Mean von Mises stress (MPa)
50 40 30 20 10 Profile 1
Profile 2 Profile
50
FIG. 5. Mean von Mises variation for (a) different distal cross-sections, (b) different proximal cross-sections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
40 30 20 10 0
Profile 3
m = 0.4 Bonded Interface property
e 60 Mean von Mises stress (MPa)
0
50
0 D1
60 Mean von Mises stress (MPa)
5
50 40 30 20 10 0 0.0
0.1
0.5
1.0
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
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A.A. OSHKOUR ET AL. index (n) and Young’s modulus of the main phases of FGMs. Therefore, the variation in n affected the prosthesis stiffness and consequently SE. In this study, an increase in gradient index also increased the volume fraction of the ceramic phase with less modulus of elasticity. As a result, prosthesis stiffness declined and SE increased proportionally with an increase in the gradient index. An increase in SE as stiffness decreased is consistent with the findings of Simões and Marques (15). The maximum SE was observed in the prostheses with a circular proximal cross-section, Profile 1 or Profile 3, and gradient index of 1. The developed stress in the femoral prostheses is presented in Fig. 5. The VMS behavior was similar to the SE variation with respect to distal cross-sections and proximal cross-sections (Fig. 5a,b). The profiles elicited no significant effect on the stress distribution of the prostheses. The prostheses with a nonbonded
prostheses with Profile 2, respectively (Fig. 4c). The implant–bone surface condition elicited no significant effect on SE variation (Fig. 4d). The SE increased with a gradient index (Fig. 4e). The effect of the distal cross-sections on SE variation was lower than that of the proximal cross-sections. This result was observed because the SE is applied to quantify the proximal metaphysis of the femur and the area of the distal cross-sections was less than that of the proximal cross-sections. The distal cross-sections of the prostheses shifted to the proximal cross-sections along the profiles of the prostheses. Therefore, the profiles not only control the load transfer mechanism from the hip joint to the bone (34) but also affect prosthetic stiffness (rigidity) and accordingly SE. The interface properties elicited no significant effect on SE because the prosthetic stiffness is independent of the interface properties. The elasticity of prosthesis in the gradient direction is a function of the gradient a
b 2.0 Mean maximum principal stress (MPa)
Mean maximum principal stress (MPa)
2.0
1.5
1.0
0.5
0.0
1.0
0.5
0.0 D1
D2 D3 D4 Distal cross-sections
D5
P1
c
P2 P3 P4 Proximal cross-sections
d 2.0 Mean maximum principal stress (MPa)
2.0 Mean maximum principal stress (MPa)
1.5
1.5
1.0
0.5
0.0
1.5
1.0
0.5
0.0 Profile 1
Profile 2 Profile
FIG. 6. Mean maximum principal stress variation for (a) different distal crosssections, (b) different proximal crosssections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
Profile 3
m = 0.4
Bonded Interface property
e Mean maximum principal stress (MPa)
2.0
1.5
1.0
0.5
0.0 0.0
0.1
0.5
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
1.0
EFFECT OF GEOMETRICAL PARAMETERS
(36) obtained a similar result. The prostheses with distal cross-sections of D1 and D2 produced similarly greater MAPS in the bone compared with those with distal cross-sections of D3, D4, and D5. The prostheses with proximal cross-sections of P1 and P2 caused more MAPS in the bone than those with proximal cross-sections of P3 and P4. The distal cross-sections showed less effect on MIPS than the proximal crosssection. This result can be attributed to the peak value of the MIPS found beneath the neck at the proximal section of the femur. The prostheses with proximal cross-sections of P1 and P4 stimulated the highest and the lowest MIPS in the femur, respectively. The effect of profiles and interface conditions on MAPS was different from that on MIPS. Profile 2 and nonbonded interface induced higher MAPS on the lateral side of the femur and introduced less MIPS on the medial side of the bone. The MAPS and MIPS slightly increased with gradient index. The
implant–bone surface condition exhibited more stress than the prostheses with a bonded implant–bone surface condition. An increase in the gradient index resulted in a decrease in the mismatch between the stiffness of the bone and the prosthesis by reducing prosthetic stiffness. Thus, bone and prosthesis shared a higher load and VMS developed in the prostheses compared with SE that decreased as gradient index increased. El-Sheikh et al. (17) and Ramos et al. (14) also demonstrated that the stress in the femoral prosthesis is reduced as stiffness is decreased. The maximum stress criterion can predict bone failure showing
Copyright © 2014 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.
Effect of Geometrical Parameters on the Performance of Longitudinal Functionally Graded Femoral Prostheses *Azim Ataollahi Oshkour, †Hossein Talebi, *Seyed Farid Seyed Shirazi, *Yat Huang Yau, ‡Faris Tarlochan, and §Noor Azuan Abu Osman *Departments of Mechanical Engineering and §Biomedical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia; †Institute of Structural Mechanics, Bauhaus–Universitat Weimar, Weimar, Germany; and ‡Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University, Doha, Qatar
Abstract: This study aimed to assess the performance of different longitudinal functionally graded femoral prostheses. This study was also designed to develop an appropriate prosthetic geometric design for longitudinal functionally graded materials. Three-dimensional models of the femur and prostheses were developed and analyzed. The elastic modulus of these prostheses in the sagittal plane was adjusted along a gradient direction from the distal end to the proximal end. Furthermore, these prostheses were composed of titanium alloy and hydroxyapatite. Results revealed that strain energy, interface stress, and developed stress in the femoral prosthesis and the bone were influenced by prosthetic geometry and gradient index. In all of
the prostheses with different geometries, strain energy increased as gradient index increased. Interface stress and developed stress decreased. The minimum principal stress and the maximum principal stress of the bone slightly increased as gradient index increased. Hence, the combination of the femoral prosthetic geometry and functionally graded materials can be employed to decrease stress shielding. Such a combination can also be utilized to achieve equilibrium in terms of the stress applied on the implanted femur constituents; thus, the lifespan of total hip replacement can be prolonged. Key Words: Finite element analysis—Strain energy—Interface stress—Maximum principal stress—Minimum principal stress.
Total hip replacement (THR) is a surgical approach that can successfully relieve pain and restore hip joint function (1). Advances in technology help prosthesis designers and surgeons customize implants and prolong the lifespan of THR (2). However, revision surgery complications limit the life of THR, particularly for young and active patients (3). Furthermore, THR failure is usually caused by aseptic loosening (4). Prosthetic material and geometry affect prosthetic stiffness (rigidity) in aseptic loosening (5). Therefore, many experimental and theoretical approaches have been employed to investigate different prosthetic materials and
geometries. For instance, finite element analysis (FEA) is an effective tool used for the multiscale analysis and design of implants (6). Different implant designs can be analyzed more accurately by conducting FEA in a computer rather than performing timeconsuming, destructive, and costly mechanical and in vivo tests (7). FEA is commonly conducted to study artificial hip joint biomechanics and femoral prosthetic designs (8–11). Many FEA studies have also focused on the optimization of the geometry and material of femoral prostheses to develop THR with a long lifespan (12–17). Kuiper and Huiskes (18) and Hedia et al. (19,20) used functionally graded materials (FGMs) as appropriate substitutes for conventional materials used in hip implants. FGMs can also be used for orthopedic purposes (21). FGMs are engineering materials designed on the basis of biological structures (21,22). These materials exhibit adjustable mechanical and structural properties in continuous (gradient) or step-wise (graded) approaches (22). FGMs also
doi:10.1111/aor.12315 Received December 2013; revised February 2014. Address correspondence and reprint requests to Mr. Azim Ataollahi Oshkour, Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia. E-mail: [email protected]
Artificial Organs 2014, ••(••):••–••
2
A.A. OSHKOUR ET AL.
demonstrate better biocompatibility, fracture toughness, load bearing, and wearing resistance than their monolithic ceramic and metal counterparts (21,23,24). Various materials for implants, including glasses, metals (titanium alloys [Ti], chromecobalt alloys, and stainless steel), and ceramics (hydroxyapatite [HA], alumina, and zirconia), can be introduced as the main phases of FGMs. Among these materials, Ti is commonly used for implant designs because Ti alloys exhibit a lower modulus of elasticity (more flexibility), better biocompatibility, and stronger corrosion resistance than other alloys (25). HA is also commonly used because it displays numerous attractive properties, such as excellent bio-
compatibility, bioactivity, nontoxicity, and unique osteoinductivity for orthopedic applications; HA helps induce firm fixation between host bones and implants by forming a biological bond between an implant and a bone (26,27). To the best of our knowledge, studies focusing on FGMs and their potential applications in femoral prostheses have only employed two-dimensional FEA (18–20). Therefore, this study employed threedimensional (3D) FEA to evaluate different design configurations of longitudinal functionally graded femoral prostheses. Design configurations were proximal cross-section, distal cross-section, profile, and gradient index of FGMs.
FIG. 1. Dimensions of (a) profile, (b) proximal cross-sections, and (c) distal cross-sections.
Artif Organs, Vol. ••, No. ••, 2014
EFFECT OF GEOMETRICAL PARAMETERS MATERIALS AND METHODS Components modeling Computer-aided design software (Solidworks 2012, Dassault Systèmes Solidworks Corp., Concord, MA, USA) was used to develop 3D models of femoral prostheses. These femoral prostheses were composed of five distal cross-sections, four proximal crosssections, and three profiles (Fig. 1). A 3D model of the bone was developed using Mimics (version 13; Materialise NV, Leuven, Belgium) according to a previous study (3). The femur and its prostheses were meshed with 3D tetrahedral elements. The approximate global sizes of 1.5 and 1 mm were used to mesh the femur and prostheses, respectively. FEA was performed in ABAQUS finite element software version 6.10 (ABAQUS, Inc., Providence, RI, USA). Boundary conditions The boundary conditions in this study were used according to previous studies (17,28,29). In Fig. 2, the
3
TABLE 1. Material properties of implanted femur components Material Cortical bone Spongy bone Cement Titanium alloys (Ti) Hydroxyapatite (HA)
Plane
E (GPa)
G (GPa)
v
xx yy zz — — — —
11.5 11.5 17.0 2.13 2.70 110 10
3.60 3.30 3.30 — — — —
0.51 0.31 0.31 0.30 0.35 0.30 0.30
E: Young’s modulus. G: Shear modulus. v: Poisson’s ratio.
femur was fixed at the distal end, and 3 and 1.25 kN were applied on the head of the prosthesis (P0) and lateral side of the femur in the proximal portion (P1) at an angle of 20°, representing an equivalent weight of 70 kg and abductor muscle load, respectively. Two scenarios can be considered at the bone–implant surface; these scenarios are nonbonded surfaces with a friction coefficient and bonded surfaces. The nonbonded condition represents an event before bone ingrowth, and the bonded condition is used for ideal bone ingrowth. The desired fixation in cementless prostheses is not obtained immediately after surgery; primary stability can be studied by modeling the prosthesis and bone immediately after surgery. In this study, nonbonded surfaces with a friction coefficient of 0.4 (30,31) and bonded surfaces were considered at the bone–implant surface. Material properties The femur is composed of a linear isotropic spongy bone and a linear transverse isotropic cortical bone (Table 1) (28,29). The FGMs composed of Ti–HA were used to design the hip prostheses. The variation in the elastic modulus (Ek) of the prostheses in a gradient direction can be expressed as power law equation (Eq. 1) (32). n
2K + h ⎞ ⎞ ⎛ ⎛ 2K + h ⎞ Ek = Ea ⎜ + Eb ⎜ 1 − ⎛ ⎝ 2 h ⎟⎠ ⎝ ⎝ 2 h ⎠ ⎟⎠ −
FIG. 2. Mesh and boundary condition.
n
h h ≤ K ≤ , 0 ≤ n ≤ ∞, 2 2
(1)
where Ea and Eb are the Young’s modulus in the distal part and the proximal part of the femur, respectively, n is the gradient index, K is the stem height of the longitudinal prosthesis from the distal end to the proximal end, and h is the length of the prosthesis in the longitudinal direction. In the functionally graded femoral prosthesis, the volume fraction of the ceramic phase of FGMs (HA) Artif Organs, Vol. ••, No. ••, 2014
4
A.A. OSHKOUR ET AL. (n) of 0, 0.1, 0.5, and 1 were considered in this study. An increase in the gradient index complicates FGM production and reduces the strength of prostheses because of an increase in HA ceramic phase. Therefore, the maximum gradient index was limited to 1 in this study. RESULTS AND DISCUSSION
FIG. 3. Variation of Young’s modulus along the Ti–HA prosthesis length for different gradient index.
decreased along the distal-to-proximal direction. Hence, the proximal and distal parts of the femoral prosthesis were the metal (Ti) and ceramic (HA) phases, respectively (Fig. 3). Four gradient indexes a
b 60 Mean strain energy (N.mm)
Mean strain energy (N.mm)
60 50 40 30 20 10 0
D1
D2
D3
D4
50 40 30 20 10 0
D5
P1
P2 P3 P4 Proximal cross-sections
Distal cross-sections
c
d 60
60 Mean strain energy (N.mm)
Mean strain energy (N.mm)
The appropriate design of femoral prostheses is complicated. Implants should be mechanically compatible with the host bone, and its material should tolerate harsh biological environments of the body (33). The mechanical compatibility of the prosthesis with the bone is a function of prosthetic stiffness. The stiffness of femoral prostheses is determined by prosthetic cross-section and the modulus of elasticity (5). The mismatch between prosthesis and bone stiffness changes bone normal loading, resulting in bone
50 40 30 20 10 0 Profile 1
Profile 2 Profile
50
30 20 10 0
Profile 3
FIG. 4. Mean strain energy variation for (a) different distal cross-sections, (b) different proximal cross-sections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
40
m = 0.4
Bonded Interface property
e Mean strain energy (N.mm)
60 50 40 30 20 10 0
0.0
0.1
0.5
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
1.0
EFFECT OF GEOMETRICAL PARAMETERS resorption and loosening. To achieve good compatibility in stiffness between bones and implants, we used FGMs in different femoral prostheses with a gradient direction along the prosthesis length from the distal end to the proximal end (Fig. 3). We also examined different aspects of the femoral prosthetic geometry (Fig. 1). These aspects include different profiles (Profile 1, Profile 2, and Profile 3), different proximal cross-sections (P1, P2, P3, and P4), and different distal cross-sections (D1, D2, D3, D4, and D5). The results of the mean strain energy (SE), mean von Mises stress (VMS), mean maximum principal stress (MAPS), mean minimum principal stress (MIPS), and mean interface stress (IS) are discussed in this section. The SE at the proximal metaphysis of the femur was presented to address the stress shielding level of the femoral prosthesis. The VMS portrays the developed stress in the femoral prostheses.
a
60 Mean von Mises stress (MPa)
Mean von Mises stress (MPa)
MAPS and MIPS show bone stress distribution at lateral and medial sides, respectively. The IS shows shear stress variation in the bone–implant interface for a nonbonded implant–bone surface. Figure 4a,e illustrates the SE variation at the proximal metaphysis of the bone for five distal crosssections, four proximal cross-sections, three profiles, two implant–bone interface conditions, and four gradient indexes. The distal cross-sections slightly affected the SE variation (Fig. 4a). The prostheses with the proximal cross-sections of P1 and P4 produced maximum and minimum amounts of SE on the proximal metaphysis of the femur (Fig. 4b). The prostheses with the proximal cross-sections of P2 and P3 induced the same SE in the bone and in the midrange value of the SE generated by prostheses with P1 and P4 proximal cross-sections (Fig. 4b). The prostheses developed from Profile 1 and Profile 3 provoked almost the same and higher SE than the
b
60 50 40 30 20 10 0
c
D2 D3 D4 Distal cross-sections
40 30 20 10
D5
P1
P2 P3 P4 Proximal cross-sections
d 60 Mean von Mises stress (MPa)
50 40 30 20 10 Profile 1
Profile 2 Profile
50
FIG. 5. Mean von Mises variation for (a) different distal cross-sections, (b) different proximal cross-sections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
40 30 20 10 0
Profile 3
m = 0.4 Bonded Interface property
e 60 Mean von Mises stress (MPa)
0
50
0 D1
60 Mean von Mises stress (MPa)
5
50 40 30 20 10 0 0.0
0.1
0.5
1.0
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
6
A.A. OSHKOUR ET AL. index (n) and Young’s modulus of the main phases of FGMs. Therefore, the variation in n affected the prosthesis stiffness and consequently SE. In this study, an increase in gradient index also increased the volume fraction of the ceramic phase with less modulus of elasticity. As a result, prosthesis stiffness declined and SE increased proportionally with an increase in the gradient index. An increase in SE as stiffness decreased is consistent with the findings of Simões and Marques (15). The maximum SE was observed in the prostheses with a circular proximal cross-section, Profile 1 or Profile 3, and gradient index of 1. The developed stress in the femoral prostheses is presented in Fig. 5. The VMS behavior was similar to the SE variation with respect to distal cross-sections and proximal cross-sections (Fig. 5a,b). The profiles elicited no significant effect on the stress distribution of the prostheses. The prostheses with a nonbonded
prostheses with Profile 2, respectively (Fig. 4c). The implant–bone surface condition elicited no significant effect on SE variation (Fig. 4d). The SE increased with a gradient index (Fig. 4e). The effect of the distal cross-sections on SE variation was lower than that of the proximal cross-sections. This result was observed because the SE is applied to quantify the proximal metaphysis of the femur and the area of the distal cross-sections was less than that of the proximal cross-sections. The distal cross-sections of the prostheses shifted to the proximal cross-sections along the profiles of the prostheses. Therefore, the profiles not only control the load transfer mechanism from the hip joint to the bone (34) but also affect prosthetic stiffness (rigidity) and accordingly SE. The interface properties elicited no significant effect on SE because the prosthetic stiffness is independent of the interface properties. The elasticity of prosthesis in the gradient direction is a function of the gradient a
b 2.0 Mean maximum principal stress (MPa)
Mean maximum principal stress (MPa)
2.0
1.5
1.0
0.5
0.0
1.0
0.5
0.0 D1
D2 D3 D4 Distal cross-sections
D5
P1
c
P2 P3 P4 Proximal cross-sections
d 2.0 Mean maximum principal stress (MPa)
2.0 Mean maximum principal stress (MPa)
1.5
1.5
1.0
0.5
0.0
1.5
1.0
0.5
0.0 Profile 1
Profile 2 Profile
FIG. 6. Mean maximum principal stress variation for (a) different distal crosssections, (b) different proximal crosssections, (c) different profiles, (d) different interface properties, and (e) different gradient indexes.
Profile 3
m = 0.4
Bonded Interface property
e Mean maximum principal stress (MPa)
2.0
1.5
1.0
0.5
0.0 0.0
0.1
0.5
Gradient index
Artif Organs, Vol. ••, No. ••, 2014
1.0
EFFECT OF GEOMETRICAL PARAMETERS
(36) obtained a similar result. The prostheses with distal cross-sections of D1 and D2 produced similarly greater MAPS in the bone compared with those with distal cross-sections of D3, D4, and D5. The prostheses with proximal cross-sections of P1 and P2 caused more MAPS in the bone than those with proximal cross-sections of P3 and P4. The distal cross-sections showed less effect on MIPS than the proximal crosssection. This result can be attributed to the peak value of the MIPS found beneath the neck at the proximal section of the femur. The prostheses with proximal cross-sections of P1 and P4 stimulated the highest and the lowest MIPS in the femur, respectively. The effect of profiles and interface conditions on MAPS was different from that on MIPS. Profile 2 and nonbonded interface induced higher MAPS on the lateral side of the femur and introduced less MIPS on the medial side of the bone. The MAPS and MIPS slightly increased with gradient index. The
implant–bone surface condition exhibited more stress than the prostheses with a bonded implant–bone surface condition. An increase in the gradient index resulted in a decrease in the mismatch between the stiffness of the bone and the prosthesis by reducing prosthetic stiffness. Thus, bone and prosthesis shared a higher load and VMS developed in the prostheses compared with SE that decreased as gradient index increased. El-Sheikh et al. (17) and Ramos et al. (14) also demonstrated that the stress in the femoral prosthesis is reduced as stiffness is decreased. The maximum stress criterion can predict bone failure showing
