journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
Available online at www.sciencedirect.com
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Research Paper
Investigating stress shielding spanned by biomimetic polymer-composite vs. metallic hip stem: A computational study using mechano-biochemical model Pouria Tavakkoli Avvala, Saeid Samiezadeha, Va´clav Klikab, Habiba Bougheraraa,n a
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada Department of Mathematics, FNSPE, Czech Technical University in Prague, Prague, Czech Republic
b
ar t ic l e in f o
abs tra ct
Article history:
Periprosthetic bone loss in response to total hip arthroplasty is a serious complication
Received 5 June 2014
compromising patient’s life quality as it may cause the premature failure of the implant.
Received in revised form
Stress shielding as a result of an uneven load sharing between the hip implant and the
18 September 2014
bone is a key factor leading to bone density decrease. A number of composite hip implants
Accepted 22 September 2014
have been designed so far to improve load sharing characteristics. However, they have
Available online 8 October 2014
rarely been investigated from the bone remodeling point of view to predict a long-term
Keywords:
response. This is the first study that employed a mechano-biochemical model, which
Bone remodeling
considers the coupling effect between mechanical loading and bone biochemistry, to
Mechano-biochemical model
investigate bone remodeling after composite hip implantation. In this study, periprosthetic
Irreversible thermodynamics
bone remodeling in the presence of Carbon fiber polyamide 12 (CF/PA12), CoCrMo and Ti
Total hip arthroplasty
alloy implants was predicted and compared. Our findings revealed that the most
Composite hip implant
significant periprosthetic bone loss in response to metallic implants occurs in Gruen zone
Finite element method
7 (43% with CoCrMo; 35% with Ti) and 6 ( 40% with CoCrMo; 29% with Ti), while zone 4 has the lowest bone density decrease with all three implants ( 9%). Also, the results showed that in terms of bone remodeling, the composite hip implant is more advantageous over the metallic ones as it provides a more uniform density change across the bone and induces less stress shielding which consequently results in a lower post-operative bone loss ( 9% with CF/PA12 implant compared to 27% and 21% with CoCrMo and Ti alloy implants, respectively). & 2014 Elsevier Ltd. All rights reserved.
n
Corresponding author. Tel.: þ1 416 979 5000x7092; fax: þ1 416 979 5265. E-mail addresses: [email protected] (P. Tavakkoli Avval), [email protected] (S. Samiezadeh), [email protected] (V. Klika), [email protected] (H. Bougherara). http://dx.doi.org/10.1016/j.jmbbm.2014.09.019 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
δα
Nomenclature rα Aα lij k7j dð1Þ ½Ni ½Ni υαi ; υ0αi βi
1.
rate of αth reaction affinity of αth reaction phenomenological coefficients reaction rate coefficients first invariant of strain rate tensor concentration of Ni normalized concentration of Ni stoichiometric coefficients of substance Ni entering and leaving αth reaction, respectively sum of the initial molar concentration of relevant substances
Introduction
Total hip arthroplasty (THA) is one of the most successful surgeries which greatly improves the quality of life of patients with osteoarthritis (Callaghan et al., 2007; Pulido et al., 2007). Although the complications following THA has reduced in the last two decades (Dattani, 2007), bone loss following THA still remains a concern (Bugbee et al., 1997; Harris, 2001). Osteolysis due to wear particles release and stress shielding as a result of an uneven load distribution between the implant and the bone, are the main factors leading to periprosthetic bone loss (Shanbhag et al., 2006; Turner et al., 2005). This complication may contribute to increased pain, decreased function, loss of implant fixation, and consequently a revision surgery (Bugbee et al., 1997; Huiskes, 1993). Stress shielding is believed to result from the difference between the implant and the bone stiffness (Huiskes et al., 1992). Metallic implants traditionally made of stainless steel or cobalt–chrome, and recently made of titanium alloy, have a much higher elastic modulus compared to that in a human femur (Bougherara et al., 2007). A number of numerical, in vitro and in vivo studies reported that a more physiologic state following joint replacement could be achieved by lowering implant stiffness (Djerf and Gillquist, 1987; Evans and Gregson, 1994; Hedia, 2001; Lewis et al., 1984; Maistrelli et al., 1991). Several studies employed fiber-reinforced composites as an alternative material of choice capable of obtaining desired stiffness and strength in different directions (Ali et al., 1990; Bagheri et al., 2014; Woo et al., 1974). These implants showed improved load sharing characteristics and resulted in less deviation from the natural state of stress in the bone following implantation (Ali et al., 1990; Erkmen et al., 2011; Feerick et al., 2013; Fujihara et al., 2003; Hastings, 1978; Samiezadeh et al., 2014; Woo et al., 1974). Fiber reinforced composite hip implants have been designed to address stress shielding concerns while maintaining enough strength
and
corrosion
57
resistance
in
hip
replacements
(Akhavan et al., 2006; Bougherara et al., 2007; Katoozian et al., 2001; Mendes et al., 1988). However, one may not be able to thoroughly investigate the stress shielding spanned by flexible composite implants without investigating periprosthetic bone remodeling. On the other hand, there seem to be no data
ratio of the rate of αth reaction to that of second reaction flux of the ith substance Ji Dα effect of the mechanical loading (an approximation of dð1Þ ) on the αth reaction Δt time of loading trace of strain tensor εð1Þ Sðref Þ reference strain rate Dα ðref Þ influence of the reference strain rate on the αth reaction ρ bone density initial bone density ρ0 EBoneOld ; EBoneNew moduli of elasticity of old and new bone, respectively
regarding long term clinical follow-ups of patients who underwent composite hip replacement as they have not been widely used in humans. While few studies investigated the load distribution across the bone implanted with composite hip prosthesis (Bougherara et al., 2007; Katoozian et al., 2001; Li et al., 2003; Sridhar et al., 2010), only a handful of researchers predicted periprosthetic bone remodeling after such implantation (Bougherara et al., 2010a; Lim et al., 2003). Therefore, using realistic numerical models to predict bone remodeling in the presence of composite hip implants is of interest. There are several bone remodeling models, but most of these models are mechanical-based (Levenston and Carter, 1998; Prendergast and Taylor, 1994; Weinans et al., 1992), which predict bone adaptation based on mechanical stimuli (e.g. stress, strain, strain energy or mechanical damage) only. In other words, they take into account mechanical signals only to stimulate bone remodeling and thus fail to consider the underlying biological mechanisms that control the bone remodeling process. However, mechano-biochemical models (Klika and Marsik, 2010; Rouhi et al., 2007; Tavakkoli Avval et al., 2014) take into account biological mechanisms as well as mechanical loading as triggers for the bone remodeling mechanism, and therefore present a more realistic model. Previous studies (Bougherara et al., 2010a; Lim et al., 2003) used a strain energy density-based model (Weinans et al., 1992) to predict bone remodeling in the presence of a composite hip implant, thus ignored the role of biochemical reactions regulating bone remodeling. Bougherara et al. (2010a) also modeled the composite structure as an orthotropic body with three planes of symmetry (i.e. superior– inferior, medial–lateral, and anterior–posterior) rather than considering a set of orthotropic laminae through the thickness of the implant. In this investigation, a new mechano-biochemical model (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), which is more comprehensive in the sense that it involves the coupling effect between the mechanical loading and bone biochemistry, was used to predict longterm bone density distribution around a biomimetic hip stem made from fiber reinforced polymer composites (i.e. carbon fiber polyamide 12: CF/PA12). The results were then compared to those obtained in femurs implanted with titanium alloy (Ti) and cobalt–chrome–molybdenum (CoCrMo) implants.
58
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
2.
and biochemical affinity of the reactions (or concentration of substances participating in the reactions):
Materials and methods
2.1. Mechano-biochemical model (thermodynamic-based model) In the mechano-biochemical model (thermodynamic-based model) which was developed and validated in previous studies (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), only bone resorption and formation phases were considered in the bone remodeling mechanism. Bone was hypothesized as a thermodynamic system capable of exchanging energy, matter and entropy with its surroundings (Fig. 1). The mechanism of bone remodeling was divided into five biochemical interactions (i.e. formation of multinucleated osteoclasts, old bone decomposition, production of osteoblast activator, osteoid production, and calcification) which are in the form of Menten–Michaelis enzyme reaction (Michaelis and Menten, 1913), i.e., kþα
E þ S ⇆ SE-E þ P kα
ð1Þ
Enzyme (E) retroactively binds to substratum (S) to form the complex of SE which then decomposes to enzyme (E) and product (P). The details of biochemical reactions regulating bone remodeling mechanism were provided in the Appendix A as well as our previous study (Tavakkoli Avval et al., 2014). As shown in the Appendix, these biochemical reactions (Eqs. (A.1)–(A.5)) contain 15 substances (N1 ,MCELL,MNOC,N4 ,BoneOld , …and N15 ) whose concentration will be denoted by ½N1 ,½MCELL,½MNOC, ½N4 ,½BoneOld , … and ½N15 , respectively. In the thermodynamic-based model, it was assumed that a coupling effect between mechanical and biological mechanisms drives the bone remodeling process. Mechanobiochemical coupling is in its early stages of recognition. However, there are experimental findings confirming this phenomenon, e.g. in a well controlled chemical environment of Belousov–Zhabotinski reactions in gels (Chen et al., 2012). In order to include the mechanical effects on biochemical reactions, the standard law of mass action was replaced by a modified version, represented by Eq. (2), which takes into account the coupling between the applied mechanical load
n
n
i¼1
i¼1
0
rα ¼ lαα Aα þ lαυ dð1Þ ¼ kþα ∏ ½Ni υαi k α ∏ ½Ni υαi þ lαυ dð1Þ
ð2Þ
where the rate and affinity of the αth biochemical reaction (α is the reaction number) are denoted by rα and Aα , respectively. Phenomenological and reaction rate coefficients are shown by lαυ and k7α , respectively. dð1Þ denotes the first invariant of the strain rate tensor, representing the rate of volume change. υαi and υ0αi are the stoichiometric coefficients of the mixture of substance Ni entering and leaving the αth reaction, respectively. Also, the concentration of substance Ni is denoted by ½Ni . Using the modified version of the law of mass action, the time evolution of the concentration of all biochemical substances involved in the bone remodeling mechanism was described by a set of differential equations whose stationary solution are provided through Eqs. (3)–(7) (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 1 D1 þ J3 þ J14 ½MCELL ¼ ð3Þ β1 þ β1 2 þ 4 2 δ1 ½BoneOld ¼
1 β7 þ 2β3 2½MCELL 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi# 2 J D3 þ β7 þ 2β3 2½MCELL þ 4 14 þ 2J14 2D2 δ3 ð4Þ
1 1 J D3 ½ActOB ¼ ½BoneOld β7 þ 14 β10 þ 2 2 δ3 ½BoneOld 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 J14 D3 J14 D4 5 ½BoneOld β7 þ þ4 þ β10 þ 2 δ4 δ3 ½BoneOld ð5Þ 1 J D4 ½Osteoid ¼ β13 β10 þ 14 2 δ4 ½ActOB sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi3 J14 D4 2 J14 D5 5 þ4 þ β13 β10 þ δ5 δ4 ½ActOB ½BoneNew ¼ ½Osteoid þ β10
J14 D4 δ4 ½ActOB
ð6Þ
ð7Þ
where δα denotes the ratio of the rate of αth reaction to the second reaction. ½Ni and Ji are the normalized concentration and flux of substance Ni , respectively. βi is the sum of the initial molar concentration of relevant substances. Also, Dα represents the effect of mechanical loading (an approximation of dð1Þ ) on the αth biochemical reaction which is expressed as follows (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), Dα ¼
Fig. 1 – Schematic demonstration of bone as a thermodynamic system.
1 jεð1Þ j Dα ref Δt S ref
ð8Þ
where εð1Þ is the trace of strain tensor. Sðref Þ and Dα ðref Þ are constants describing the reference strain rate and the influence of the reference strain rate on the αth reaction, respectively. Also, the time of loading is denoted by Δt. The values of all model parameters which characterize the biochemical
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
reactions have been provided in our previous study (Tavakkoli Avval et al., 2014).
2.2.
Density and elastic modulus of bone
Bone density (ρ) is related to the initial bone density (ρ0), the normalized concentration of old bone ½BoneOld and new bone ½BoneNew according to the following law of mass and mixture (Bougherara et al., 2010b; Tavakkoli Avval et al., 2014): ð9Þ ρ ¼ ρ0 ½BoneOld þ ½BoneNew In literature, different empirical and experimental relationships between the elastic modulus and density of the bone have been provided (Helgason et al., 2008). Using power law Table 1 – Material properties of CF/PA12, polymeric core, CoCrMo and Ti alloy (Bougherara et al., 2007, 2010a; Turner et al., 2005). Material
Property
Value
CF/PA12 (lamina)
EL ET GLL GLT νLL νLT Ply type
66.5 GPa 2.72 GPa 19.5 GPa 2.7 GPa 0.04 0.26 Woven
Polymeric core
E ν
1 GPa 0.2
CoCrMo
E ν
210 GPa 0.3
Ti alloy
E ν
114 GPa 0.3
59
relation between density and Young’s modulus, the elastic modulus of the bone was calculated (Eq. (10)). Helgason et al. (2008) experimentally determined that the exponent of density in power law relation is site-specific with a magnitude between 1.4 and 3. In the current study, the magnitude of 2 was used. ½BoneOld þ EBoneNew E ¼ EBoneOld ½BoneOld þ ½BoneNew 2 ½BoneNew ρ ð10Þ ρ0 ½BoneOld þ ½BoneNew where EBoneOld and EBoneNew represent Young’s modulus of the old and new bones, respectively.
2.3.
Development of computer-aided design (CAD) models
A large left 4th generation composite femur (model 3406, sawbones, Vashon, WA, USA) was fully scanned by GE LightSpeed VCT 64 Slice CT scanner (0.5 0.5 mm/pixel resolution, and 0.5 mm slice thickness). The CT scan images were saved in DICOM format and imported into Mimics software (The Materialise, Leuven, Belgium) to generate a three-dimensional (3D) model, and subsequently to create two distinct bodies (i.e. cortical and cancellous bodies). The 3D CAD model was then imported into SolidWorks software (SolidWorks Corp., Dassualt Systèmes, Concord, MA, USA) for virtual implantation. The femoral head (and neck) was split from the rest of the femur by using split features at an angle of 55 degrees with respect to the transverse anatomical plane along the greater trochanter. A portion of the proximal cancellous bone was removed to simulate surgically-generated bone loss during total hip replacement. The model of hip stem proposed by Bougherara et al. (2007) was then inserted into the proximal end of the femur. Therefore, we were able to create a CAD model whose femoral shaft was used for both pre- and postoperative bone remodeling simulations. This enabled us to
Fig. 2 – (a) CAD model with loads and constraints, (b) meshed intact femur, (c) meshed post-operative femur.
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journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
make a precise comparison between the density distribution of the intact (pre-operative) and post-operative femurs. The hip stem is straight, follows the antecurvation of the femoral shaft and has an oval cross-section. The composite hip stem is composed of a 3 mm thick substructure made of CF/PA12 lamina with stacking sequence of (7451)6 and an internal polymeric core (Bougherara et al., 2007) (Subscript ‘6’ signifies that the composite hip implant is made from six woven plies with 7451 fiber orientation). The geometry of the metallic hip stems were the same as the composite one; however, the related material properties (CoCrMo or Ti alloy: Table 1) were assigned to the substructure as well as to the internal core in finite element analysis (FEA). The CAD model of the hip stem was developed by commercially available software (CATIA V5R13, Dassault systemes, Montreal, CA) (Bougherara et al., 2007).
2.4.
Finite element modeling (FEM)
The prepared CAD model was imported into ANSYS Workbench 14.5 (ANSYS Inc., Canonsburg, Pennsylvania, USA). The bone and internal core of the implant were meshed by Quadratic Tetrahedrons elements (SOLID187), whereas the composite layers (laminate) were meshed using Linear Triangle elements (SHELL181). Surface-to-surface contact elements (CONTA174 and TARGE170) were used to mesh all interfaces. In order to simulate the physiological loading, muscle and hip joint reaction forces (Bitsakos et al., 2005) representing 45% of gait cycle were applied to the model (Fig. 2) as this instance of the gait produces the maximum loading on the femur (Frankel and Nordin, 1980). To avoid stress concentration, muscle and hip joint reaction forces were distributed over several nodes of
Fig. 3 – Iterative process of the thermodynamic-based model for simulating bone remodeling.
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
greater (and lesser) trochanter and femoral head, respectively. To avoid rigid body motion, the degrees of freedom of all nodes at the distal femur were fixed. Mesh sensitivity was then investigated resulting in a total number of body elements and nodes to be 243,486 and 346,389 for the intact femur, 128,420 and 184,422 for the implanted femur, respectively (Fig. 2). The contacts between all surfaces were considered to be bonded, similar to other studies (Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012; Turner et al., 2005). It should be mentioned that for the composite hip implant, the stacking sequence of the laminate as well as the material properties of CF/PA12 (Table 1) were assigned to the composite hip implant by ACP (Pre) module of ANSYS Workbench 14.5. The algorithm of bone remodeling simulation is illustrated in Fig. 3. To simulate bone remodeling using the mechanobiochemical model, the meshed femur was imported into ANSYS Parametric Design Language (APDL). Forces and constraints were then applied to the model in the same manner as done in ANSYS Workbench simulations. In order to obtain bone density distribution throughout the intact femur, in the first iteration of numerical simulation, cortical and cancellous were modeled as homogenous structures with the initial density of 0.98 g/cm3 (ρ0) which is the average value of cortical bone with 1.64 g/cm3 and cancellous bone with 0.32 g/cm3. The mechano-biochemical model (thermodynamic-based model) is not sensitive to the initial density. In other words, in the thermodynamic-based model, the initial density does not have a significant effect on the final bone density distribution, similar to some other models (Kuhl and Balle, 2005; Balle, 2004). To model the intact femur, cortical and cancellous material properties (Ebrahimi et al., 2012) were assigned to their corresponding bodies. The hip implant (embedded into the femur) was also considered as cancellous bone. In the next iterations, the new properties of each element were calculated based on the concentration of old and new bones remained/produced inside the element. Similar to several other studies (Behrens et al., 2009; Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012; Turner et al., 2005), each bone element was considered as an isotropic material whose Young’s modulus was calculated by Eq. (10). The thermodynamic-based model, defined by Eqs. (3)–(7), was applied to finite element analysis through a user-defined macro. FEA yielded the trace of strain tensor, ε(1), to calculate the values of Dα by using Eq. (8). Dα were then entered into Eqs. (3)–(7) to calculate the values of ½BoneOld and ½BoneNew of each element. The density and elastic modulus of each element were obtained by Eqs. (9) and (10), respectively. These new material properties were considered for the next iteration of FEA, and the process was repeated until no significant change in the density of the elements was observed. It was assumed that the convergence and consequently the final density distribution are obtained when ConvCrio0.0001 (Eq. (11)). ConvCri ¼
1 n ðtÞ ∑ ρi ρiðt 1Þ ni¼1
To simulate periprosthetic bone remodeling in the presence of the implant, the elements of the head (and neck) of the intact femur were removed (unselected). The corresponding material properties (CoCrMo or Ti alloy or CF/PA12 (for composite lamina)) were assigned to the implant (Table 1). The initial material properties of each element of the immediate post-operative femur were chosen from the same element in the post convergence-intact femur (inhomogeneous femur). The joint reaction force was then transferred to the hip implant. Finally, the thermodynamic-based model was again applied to simulate bone response to THA and Eq. (11) was used to control the convergence.
3.
Results
3.1.
Bone density convergence
The convergence of simulations was controlled by Eq. (11) so that when no significant change in the density of the elements was observed, it was considered as a converged solution. The convergence of bone remodeling simulations for four constructions is shown in Fig. 4. As depicted, the average density change over all elements approached zero after approximately 40 iterations.
3.2.
Pre- and post-operative bone density distributions
Distribution of density throughout the intact femur is illustrated in Fig. 5(a) and (b). The range of density predicted by the model was between 0.35 and 1.75 g/cm3. The maximum value of density was observed in the cortical bone located at the mid-shaft. Our results showed that in addition to a dense cortical bone around the medullary canal, a dense cancellous bone between the calcar and the location of hip joint reaction force is developed. Periprosthetic bone density distribution in response to CoCrMo, Ti alloy and CF/PA12 hip implants is illustrated in Fig. 6. The location of the maximum density was still at the cortical bone in the mid-femoral shaft. Comparing the density distributions after THA (Fig. 6) implies that the stiffest hip
ð11Þ
where n and t are the number of elements and iteration number, respectively.
61
Fig. 4 – Convergence of bone remodeling simulations.
62
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
Fig. 5 – Bone density distribution in intact femur (a) obtained by the thermodynamic-based model in posterior view, (b) obtained by the thermodynamic-based model in posterior view-coronal plane, (c) obtained by X-ray (reproduced with permission from Truong et al., 2006).
Fig. 6 – Bone density distribution after THA with (a) CoCrMo, (b) Ti alloy, (c) CF/PA12 composite hip implant.
implant (CoCrMo) induced more stress shielding into the proximal femur such that low density regions (0.34–0.8 g/ cm3) were dominant in the femur embedded with CoCrMo compared to that with the composite hip stem. Therefore, the results of simulations revealed that biomimetic composite hip stem promotes proximal load transfer to the femur
compared to the metallic conventional ones, and hence, reduces the amount of bone resorption in response to implantation. To examine the density distribution in detail, the femur was divided into seven zones commonly known as Gruen zones (Gruen et al., 1979). These seven zones describe mainly the regions surrounding the proximal part of femur
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
63
Fig. 7 – Percent change in bone density in response to the hip implants made from (a) CoCrMo, (b) Ti alloy, (c) CF/PA12. Cutting plane line in all three constructions passes through the proximal metaphysis. MX and MN indicate the location of maximum bone formation and maximum bone resorption, respectively.
Fig. 8 – Graph showing the percentage of bone loss in Gruen zones in response to implantations.
and are clinically used to assess the outcome of the hip replacement surgery.
3.3.
Percent change in the bone density
Percent change in the femoral density in response to the implantation of hip stems is presented in Fig. 7. According to this figure, in all three simulations, the severe periprosthetic bone loss ( 72%) occurred in the calcar region while the maximum bone formation ( þ60%) happened at a region located near the distal end of the implants where the load sustained by the implant is transmitted to the bone. As illustrated in Fig. 7, the stiffness of implants plays a key role in the periprosthetic bone density distribution. It can be observed that only a small portion of the medial femur embedded with composite hip stem was subjected to a severe
bone loss ( 72% to 30%) unlike the femurs with Ti alloy and CoCrMo implants. In addition, section views whose cutting plane passes through the proximal metaphysis depict that a moderately dense trabeculae was developed in the case of composite hip implant only. The results shown in Fig. 8 confirms the advantage of the composite hip stem over metallic ones in terms of induced stress shielding as the femur embedded with composite hip stem showed less total bone loss ( 9%) compared to 21% and 27% in the presence of Ti alloy and CoCrMo, respectively. This figure also reveals that the maximum bone loss among Gruen zones were approximately 43% (zone 7), 35% (zone 7), and 10% (zone 2) in response to CoCrMo, Ti and composite hip stems, respectively. The proposed mechano-biochemical model also predicted an equal minimum bone loss (9% in zone 4) for all three hip stems. In addition, the difference in the amount of bone loss in response to the metallic implants was obvious in different Gruen zones. On the contrary, the level of bone loss in response to the composite hip implant was approximately the same in all Gruen zones so that its standard deviation (0.60%) was much lower than those with Ti alloy (9.13%) and CoCrMo (12.29%) implants. This small deviation shows that the pattern of stress in the femur embedded with the composite implant was more uniform than those with the metallic ones.
4.
Discussion
4.1.
General findings and comparison to prior studies
To improve load sharing characteristics between the bone and the implant, a number of composite hip implants have been designed so far (Akhavan et al., 2006; Bougherara et al., 2007; Katoozian et al., 2001; Mendes et al., 1988). However,
64
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
there is a lack of data regarding the long term behavior of the bone in response to such implants as they have not been widely used in humans. Hence, it is critical to predict the bone’s long-term response in the presence of composite prosthesis by realistic numerical models. In the current study, the bone remodeling response of the femurs implanted by CoCrMo, Ti alloy and CF/PA12 composite hip stems were simulated by a mechano-biochemical model. According to our findings, the composite hip implant is more advantageous over the metallic ones in terms of bone remodeling as it induces less stress shielding and provides more uniform density change across the bone. The range of femoral density predicted by the mechanobiochemical model was between 0.35 and 1.75 g/cm3 which is consistent with clinical observations (Hodgskinson and Currey, 1990; Hoiberg et al., 2007). According to our results, a dense cortical bone was formed around the medullary canal while the internal regions of the mid-shaft were composed of a lowstiffness material which agrees with computed tomography (CT) results obtained by Truong et al. (2006). This study also revealed that a dense cancellous bone carrying stress from the superior contact surface to the calcar region is developed in the femoral neck which is consistent with bone morphology (Truong et al., 2006) and a numerical study (Kuhl and Balle, 2005). Similar to the study by Bougherara et al. (2010a), periprosthetic bone loss in response to metallic implants was more severe than that in the presence of composite hip stem as low density regions (0.34–0.8 g/cm3) were dominant in the femur embedded with CoCrMo compared to that with the composite hip stem. It can be explained by the fact that stiff implants carry a greater portion of the applied load compared to flexible ones. Subsequently, according to the load sharing rule, less load portion is bore by a femur with a stiff implant compared to the one embedded with a flexible implant. On the other hand, based on Wolff’s law (Wolff, 1892) and Frost’s mechanostat theory (Frost, 1990) bone remodeling is stimulated by the local mechanical elastic deformation of bone; thus, bone adapts its properties according to the mechanical load acting upon it. According to these theories, reduction in mechanical load causes bone to adapt itself by reducing its density. That is why a femur implanted with a stiff implant is subjected to more severe bone loss compared to a femur with a flexible one as the former carries less mechanical load. Our findings also showed an extreme cortical resorption at the medial edge of the implants in the proximal metaphysis analogous to Huiskes et al. (1992). Furthermore, in the presence of CF/PA12 implant only, some moderate trabecular densification was found at the vicinity of the prosthesis which can boost implant stability; this can be considered as another benefit for the composite hip stem. In this study, the maximum local bone loss ( 72%) was found in the calcar region which is in agreement with the observation of Kilgus et al. (1993). Also, the maximum local bone formation ( þ60%) was formed in a region located at the vicinity of the distal tip of the stem. Kroger et al. (1998) similarly found bone mineral density increase in the regions close to the distal implant. This can be justified by the fact that loads sustained by the implant are transferred to the bone through the distal tip of the stem resulting in a stress concentration which consequently induces a deposition of bone mass.
Our results endorse the advantage of the composite hip stem over the metallic ones in terms of induced stress shielding as the femur embedded with the composite hip stem showed less total bone loss (9%) compared to 21% and 27% in the presence of Ti and CoCrMo, respectively. Bougherara et al. (2010a) reported that the bone loss with CF/PA12 stem is approximately between 10% and 20% while it lies between 25% and 50% when Ti stem is used. In comparison with the results of Bougherara et al. (2010a), our findings (total bone loss of 9% for composite and 21% for Ti) are close to the lower bands. This can be justified by the inherent difference between the numerical models used for bone remodeling simulations. In contrast to Bougherara et al. (2010a) who used the strain energy density model (Huiskes et al., 1992; Weinans et al., 1992) for predicating bone loss, the current study employed the mechano-biochemical model to simulate the response of bone to the presence of composite and metallic implants. The mechano-biochemical model considers the role of biochemical reactions for regulating bone remodeling mechanism so that in the absence of mechanical loading, the bone resorbs partially by approximately 50% (Tavakkoli Avval et al., 2014) due the presence of biochemical stimulus that triggers bone remodeling. However, in the strain energy density model, bone resorbs completely in the absence of mechanical loading (Bougherara et al., 2010b). In comparison with the clinical study conducted by Skoldenberg et al. (2006) using a cementless titanium hip implant, the current amount of predicted periprosthetic bone loss in response to Ti hip stem, in Gruen zone 7 ( 35%), 6 ( 29%), 4 ( 9%), and 1 ( 20%) are in good agreement with the range of their observations (zone 7: 40% to 10%, zone 6: 30% to þ1%, zone 4: 9% to þ4%, zone 1: 36% to 12%). Moreover, our predicted bone loss for all Gruen zones including zone 5 ( 15%), 3 ( 16%), and 2 ( 26%) are in the range of the results predicted by Kuhl and Balle (2005). In response to the CoCrMo implant (with Young’s modulus of 210 GPa), the maximum predicted bone loss in Gruen zones was 43% which occurred in zone 7 and is close to the maximum bone loss of 40% (zone 7) in the presence of stainless steel (with Young’s modulus of 193 GPa) observed by Niinimaki and Jalovaara (1995). The amount of bone loss in response to the composite hip implant was approximately the same ( 9%) in all Gruen zones which resulted in a lower standard deviation (0.60%) compared to the metallic implants (9.13% for Ti alloy; 12.29% for CoCrMo). This small deviation implies that the femur embedded with the composite hip implant is not subjected to excessive stress concentration, therefore is under a lower risk of fracture, which can be counted as another privilege of CF/PA12 implant. In response to the metallic hip implants, the current study showed that the maximum bone loss ( 43% for CoCrMo and 35% for Ti) among Gruen zones occur in zone 7 similar to other clinical and numerical studies (Huiskes et al., 1992; Kilgus et al., 1993; Kroger et al., 1996, 1998; Li et al., 2007; Niinimaki and Jalovaara, 1995; Stukenborg-Colsman et al., 2012; Turner et al., 2005; Yamaguchi et al., 2000). Furthermore, the next most severe periprosthetic bone loss ( 40% for CoCrMo and 29% for Ti) happened in zone 6 which agrees with the results of Kilgus et al. (1993). The minimum bone loss ( 9%) among Gruen zones was reported to be in zone 4 (the most distal region) which is consistent with other
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
studies (Behrens et al., 2009; Huiskes et al., 1992; Li et al., 2007) which reported the minimum bone density decrease occurs in the most distal region of interest. Interestingly, the amount of bone loss in this zone was the same in all three constructions. This can be explained by the fact that since all the loads shared with the implant, regardless of its material, are transmitted to zone 4, this zone is subjected to the same amount of bone density decrease. According to our findings, bone loss in response to the metallic implants progressively declined (except for an increase from Gruen zone 1 to 2) as the region of interest moves distally from the proximal metaphysis to mid-diaphysis, which agrees with Li’s results (Li et al., 2007). In addition, our study revealed that the sequence of severity of bone loss (from maximum to minimum) in Gruen zones is as follows: zone 7, 6, 2, 1, 3, 5, and 4 for both femurs embedded with CoCrMo and Ti which is consistent with the long term observations of Li et al. (2007).
4.2.
Limitations of the study
Although the results agree well with the bone morphology and literature and provide validated quantitative data that can be used to optimize hip implants’ design, the model has some limitations and simplifications. Similar to several studies (Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012) bonded contacts were considered in the current study. This bonded contact is meant to mimic complete interdigitation of bone around the hip stem. In the current work, anisotropic behavior of the bone was ignored as each element was assumed to have an isotropic material. In our model, the concept of coupling is based on linear non-equilibrium thermodynamics and thus is phenomenological. Thus, we cannot relate it directly to actual mechanosensing or mechanotransduction processes in cells. Furthermore, the mechanical stimuli in the simulations do not include any viscous effects. We have also assumed that the trace of strain tensor regulates bone cells response, however, other mechanical stimuli such as transport of nutrients and fluid flow could be considered. In addition, we disregarded kinetics of some of the known control mechanisms in bone remodeling such as RANKL-RANK-OPG chain which may play a role in regulating the bone remodeling process. In the proposed model the computational steps are unrelated to the real time. However, the iterative process was assumed converged when no significant change in the density of the elements was observed which, from the clinical point of view, is considered as the long-term response when the femoral density gets to a stable condition. We also tried to bring insight into bone loss due to stress shielding phenomenon, and the density decrease caused by chemical diseases was not considered. Moreover, our treatment of the bone remodeling process is that it is a coordinated sequence of bone resorption and formation. This coordination is somewhat simplistic but the model can be straightforwardly extended to contain a lot more details about the control mechanisms involved (Klika et al., 2013). Furthermore, it does not include shape-changing processes such as modeling or desorption alone. Also, the remodeling of the Haversian system and hemi-osteons are treated similarly although the actual
65
mechanisms do not coincide. Likewise, we did not distinguish primary from secondary osteons. Our approach is more phenomenological as we tried to capture the changes in the tissue density in a given voxel by relating the average remodelling activity to mechanical and chemical factors. These are some of the limitations of the model where one consequence is the limited spatial resolution in the outcome.
5.
Conclusion
In conclusion, the mechano-biochemical model which considers the coupling effect between the mechanical loading and biochemical affinities as stimuli for bone remodeling, was implemented in this study to simulate the long-term behavior of the femur in response to CF/PA12, Ti alloy and CoCrMo hip implants. The predicted bone density distribution before and after THA agree well with bone morphology and literature. It was revealed that the most significant periprosthetic bone loss in response to metallic implants occur in Gruen zone 7 and 6. On the contrary, zone 4 has the lowest bone density decrease with all three implants. Also, the results showed that in terms of bone remodeling, the composite hip implant is more advantageous over the metallic ones as it induces less stress shielding, develops a moderately dense trabeculae at the vicinity of the implant, and provides more uniform bone density change following THA.
Acknowledgments This research is supported by the Natural Sciences and Engineering Research Council of Canada-Discovery Grant (NSERC/355434-2009). The authors would like to thank Ms. Angela Peragine for proofreading the manuscript.
Appendix A. Biochemical reactions involved in bone remodeling mechanism Osteoclasts are the only cells that are able to resorb bone tissues. These cells initially exist as mononuclear cells, MCELL. In order to be activated, mononuclear cells have to be coupled to multinucleated complex, MNOC, whose formation can be characterized by the following reaction. ðα ¼ 1 Þ
kþ1
N1 þ MCELL ⇆ MNOC þ N4 k1
ðA:1Þ
N1 is the mixture of substances initiating the reaction with the mononuclear cells. N4 is the remaining product from the first reaction (α¼ 1). In the next step (α¼2), which is so-called bone decomposition, multinucleated osteoclasts act on the bone to break it down: ðα ¼ 2 Þ
kþ2
MNOC þ BoneOld ⇆ N6 þ N7 k2
ðA:2Þ
where Bone Old is the abbreviation for old bone. N6 and N7 are the products resulting from the degradation of the old bone.
66
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
N7 is then used in the production of osteoblasts activator (ActOB) as described in the following reaction. ðα ¼ 3Þ
kþ3
N7 þ BoneOld ⇆ ActOB þ N9 k3
ðA:3Þ
The activators act on the osteoblasts, OB, which causes them to secrete collagen and produce Osteoid which is the unmineralized bone: ðα ¼ 4Þ
kþ4
ActOB þ OB ⇆ Osteoid þ N12 k4
ðA:4Þ
N9 and N12 are the remaining products of the 3rd (α¼3) and 4th (α¼4) reactions, respectively. The last and longest reaction (α¼ 5) in the bone remodeling process is the mineralization of Osteoid. N13, the substratum initiating bone calcification, is embedded into the bone’s matrix to form the new bone (Bone New) according to: ðα ¼ 5Þ
kþ5
N13 þ Osteoid ⇆ BoneNew þ N15 k5
ðA:5Þ
N15 is the remaining material in the bone formation reaction.
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Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Research Paper
Investigating stress shielding spanned by biomimetic polymer-composite vs. metallic hip stem: A computational study using mechano-biochemical model Pouria Tavakkoli Avvala, Saeid Samiezadeha, Va´clav Klikab, Habiba Bougheraraa,n a
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada Department of Mathematics, FNSPE, Czech Technical University in Prague, Prague, Czech Republic
b
ar t ic l e in f o
abs tra ct
Article history:
Periprosthetic bone loss in response to total hip arthroplasty is a serious complication
Received 5 June 2014
compromising patient’s life quality as it may cause the premature failure of the implant.
Received in revised form
Stress shielding as a result of an uneven load sharing between the hip implant and the
18 September 2014
bone is a key factor leading to bone density decrease. A number of composite hip implants
Accepted 22 September 2014
have been designed so far to improve load sharing characteristics. However, they have
Available online 8 October 2014
rarely been investigated from the bone remodeling point of view to predict a long-term
Keywords:
response. This is the first study that employed a mechano-biochemical model, which
Bone remodeling
considers the coupling effect between mechanical loading and bone biochemistry, to
Mechano-biochemical model
investigate bone remodeling after composite hip implantation. In this study, periprosthetic
Irreversible thermodynamics
bone remodeling in the presence of Carbon fiber polyamide 12 (CF/PA12), CoCrMo and Ti
Total hip arthroplasty
alloy implants was predicted and compared. Our findings revealed that the most
Composite hip implant
significant periprosthetic bone loss in response to metallic implants occurs in Gruen zone
Finite element method
7 (43% with CoCrMo; 35% with Ti) and 6 ( 40% with CoCrMo; 29% with Ti), while zone 4 has the lowest bone density decrease with all three implants ( 9%). Also, the results showed that in terms of bone remodeling, the composite hip implant is more advantageous over the metallic ones as it provides a more uniform density change across the bone and induces less stress shielding which consequently results in a lower post-operative bone loss ( 9% with CF/PA12 implant compared to 27% and 21% with CoCrMo and Ti alloy implants, respectively). & 2014 Elsevier Ltd. All rights reserved.
n
Corresponding author. Tel.: þ1 416 979 5000x7092; fax: þ1 416 979 5265. E-mail addresses: [email protected] (P. Tavakkoli Avval), [email protected] (S. Samiezadeh), [email protected] (V. Klika), [email protected] (H. Bougherara). http://dx.doi.org/10.1016/j.jmbbm.2014.09.019 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
δα
Nomenclature rα Aα lij k7j dð1Þ ½Ni ½Ni υαi ; υ0αi βi
1.
rate of αth reaction affinity of αth reaction phenomenological coefficients reaction rate coefficients first invariant of strain rate tensor concentration of Ni normalized concentration of Ni stoichiometric coefficients of substance Ni entering and leaving αth reaction, respectively sum of the initial molar concentration of relevant substances
Introduction
Total hip arthroplasty (THA) is one of the most successful surgeries which greatly improves the quality of life of patients with osteoarthritis (Callaghan et al., 2007; Pulido et al., 2007). Although the complications following THA has reduced in the last two decades (Dattani, 2007), bone loss following THA still remains a concern (Bugbee et al., 1997; Harris, 2001). Osteolysis due to wear particles release and stress shielding as a result of an uneven load distribution between the implant and the bone, are the main factors leading to periprosthetic bone loss (Shanbhag et al., 2006; Turner et al., 2005). This complication may contribute to increased pain, decreased function, loss of implant fixation, and consequently a revision surgery (Bugbee et al., 1997; Huiskes, 1993). Stress shielding is believed to result from the difference between the implant and the bone stiffness (Huiskes et al., 1992). Metallic implants traditionally made of stainless steel or cobalt–chrome, and recently made of titanium alloy, have a much higher elastic modulus compared to that in a human femur (Bougherara et al., 2007). A number of numerical, in vitro and in vivo studies reported that a more physiologic state following joint replacement could be achieved by lowering implant stiffness (Djerf and Gillquist, 1987; Evans and Gregson, 1994; Hedia, 2001; Lewis et al., 1984; Maistrelli et al., 1991). Several studies employed fiber-reinforced composites as an alternative material of choice capable of obtaining desired stiffness and strength in different directions (Ali et al., 1990; Bagheri et al., 2014; Woo et al., 1974). These implants showed improved load sharing characteristics and resulted in less deviation from the natural state of stress in the bone following implantation (Ali et al., 1990; Erkmen et al., 2011; Feerick et al., 2013; Fujihara et al., 2003; Hastings, 1978; Samiezadeh et al., 2014; Woo et al., 1974). Fiber reinforced composite hip implants have been designed to address stress shielding concerns while maintaining enough strength
and
corrosion
57
resistance
in
hip
replacements
(Akhavan et al., 2006; Bougherara et al., 2007; Katoozian et al., 2001; Mendes et al., 1988). However, one may not be able to thoroughly investigate the stress shielding spanned by flexible composite implants without investigating periprosthetic bone remodeling. On the other hand, there seem to be no data
ratio of the rate of αth reaction to that of second reaction flux of the ith substance Ji Dα effect of the mechanical loading (an approximation of dð1Þ ) on the αth reaction Δt time of loading trace of strain tensor εð1Þ Sðref Þ reference strain rate Dα ðref Þ influence of the reference strain rate on the αth reaction ρ bone density initial bone density ρ0 EBoneOld ; EBoneNew moduli of elasticity of old and new bone, respectively
regarding long term clinical follow-ups of patients who underwent composite hip replacement as they have not been widely used in humans. While few studies investigated the load distribution across the bone implanted with composite hip prosthesis (Bougherara et al., 2007; Katoozian et al., 2001; Li et al., 2003; Sridhar et al., 2010), only a handful of researchers predicted periprosthetic bone remodeling after such implantation (Bougherara et al., 2010a; Lim et al., 2003). Therefore, using realistic numerical models to predict bone remodeling in the presence of composite hip implants is of interest. There are several bone remodeling models, but most of these models are mechanical-based (Levenston and Carter, 1998; Prendergast and Taylor, 1994; Weinans et al., 1992), which predict bone adaptation based on mechanical stimuli (e.g. stress, strain, strain energy or mechanical damage) only. In other words, they take into account mechanical signals only to stimulate bone remodeling and thus fail to consider the underlying biological mechanisms that control the bone remodeling process. However, mechano-biochemical models (Klika and Marsik, 2010; Rouhi et al., 2007; Tavakkoli Avval et al., 2014) take into account biological mechanisms as well as mechanical loading as triggers for the bone remodeling mechanism, and therefore present a more realistic model. Previous studies (Bougherara et al., 2010a; Lim et al., 2003) used a strain energy density-based model (Weinans et al., 1992) to predict bone remodeling in the presence of a composite hip implant, thus ignored the role of biochemical reactions regulating bone remodeling. Bougherara et al. (2010a) also modeled the composite structure as an orthotropic body with three planes of symmetry (i.e. superior– inferior, medial–lateral, and anterior–posterior) rather than considering a set of orthotropic laminae through the thickness of the implant. In this investigation, a new mechano-biochemical model (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), which is more comprehensive in the sense that it involves the coupling effect between the mechanical loading and bone biochemistry, was used to predict longterm bone density distribution around a biomimetic hip stem made from fiber reinforced polymer composites (i.e. carbon fiber polyamide 12: CF/PA12). The results were then compared to those obtained in femurs implanted with titanium alloy (Ti) and cobalt–chrome–molybdenum (CoCrMo) implants.
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2.
and biochemical affinity of the reactions (or concentration of substances participating in the reactions):
Materials and methods
2.1. Mechano-biochemical model (thermodynamic-based model) In the mechano-biochemical model (thermodynamic-based model) which was developed and validated in previous studies (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), only bone resorption and formation phases were considered in the bone remodeling mechanism. Bone was hypothesized as a thermodynamic system capable of exchanging energy, matter and entropy with its surroundings (Fig. 1). The mechanism of bone remodeling was divided into five biochemical interactions (i.e. formation of multinucleated osteoclasts, old bone decomposition, production of osteoblast activator, osteoid production, and calcification) which are in the form of Menten–Michaelis enzyme reaction (Michaelis and Menten, 1913), i.e., kþα
E þ S ⇆ SE-E þ P kα
ð1Þ
Enzyme (E) retroactively binds to substratum (S) to form the complex of SE which then decomposes to enzyme (E) and product (P). The details of biochemical reactions regulating bone remodeling mechanism were provided in the Appendix A as well as our previous study (Tavakkoli Avval et al., 2014). As shown in the Appendix, these biochemical reactions (Eqs. (A.1)–(A.5)) contain 15 substances (N1 ,MCELL,MNOC,N4 ,BoneOld , …and N15 ) whose concentration will be denoted by ½N1 ,½MCELL,½MNOC, ½N4 ,½BoneOld , … and ½N15 , respectively. In the thermodynamic-based model, it was assumed that a coupling effect between mechanical and biological mechanisms drives the bone remodeling process. Mechanobiochemical coupling is in its early stages of recognition. However, there are experimental findings confirming this phenomenon, e.g. in a well controlled chemical environment of Belousov–Zhabotinski reactions in gels (Chen et al., 2012). In order to include the mechanical effects on biochemical reactions, the standard law of mass action was replaced by a modified version, represented by Eq. (2), which takes into account the coupling between the applied mechanical load
n
n
i¼1
i¼1
0
rα ¼ lαα Aα þ lαυ dð1Þ ¼ kþα ∏ ½Ni υαi k α ∏ ½Ni υαi þ lαυ dð1Þ
ð2Þ
where the rate and affinity of the αth biochemical reaction (α is the reaction number) are denoted by rα and Aα , respectively. Phenomenological and reaction rate coefficients are shown by lαυ and k7α , respectively. dð1Þ denotes the first invariant of the strain rate tensor, representing the rate of volume change. υαi and υ0αi are the stoichiometric coefficients of the mixture of substance Ni entering and leaving the αth reaction, respectively. Also, the concentration of substance Ni is denoted by ½Ni . Using the modified version of the law of mass action, the time evolution of the concentration of all biochemical substances involved in the bone remodeling mechanism was described by a set of differential equations whose stationary solution are provided through Eqs. (3)–(7) (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 1 D1 þ J3 þ J14 ½MCELL ¼ ð3Þ β1 þ β1 2 þ 4 2 δ1 ½BoneOld ¼
1 β7 þ 2β3 2½MCELL 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi# 2 J D3 þ β7 þ 2β3 2½MCELL þ 4 14 þ 2J14 2D2 δ3 ð4Þ
1 1 J D3 ½ActOB ¼ ½BoneOld β7 þ 14 β10 þ 2 2 δ3 ½BoneOld 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 J14 D3 J14 D4 5 ½BoneOld β7 þ þ4 þ β10 þ 2 δ4 δ3 ½BoneOld ð5Þ 1 J D4 ½Osteoid ¼ β13 β10 þ 14 2 δ4 ½ActOB sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi3 J14 D4 2 J14 D5 5 þ4 þ β13 β10 þ δ5 δ4 ½ActOB ½BoneNew ¼ ½Osteoid þ β10
J14 D4 δ4 ½ActOB
ð6Þ
ð7Þ
where δα denotes the ratio of the rate of αth reaction to the second reaction. ½Ni and Ji are the normalized concentration and flux of substance Ni , respectively. βi is the sum of the initial molar concentration of relevant substances. Also, Dα represents the effect of mechanical loading (an approximation of dð1Þ ) on the αth biochemical reaction which is expressed as follows (Bougherara et al., 2010b; Klika and Marsik, 2010; Tavakkoli Avval et al., 2014), Dα ¼
Fig. 1 – Schematic demonstration of bone as a thermodynamic system.
1 jεð1Þ j Dα ref Δt S ref
ð8Þ
where εð1Þ is the trace of strain tensor. Sðref Þ and Dα ðref Þ are constants describing the reference strain rate and the influence of the reference strain rate on the αth reaction, respectively. Also, the time of loading is denoted by Δt. The values of all model parameters which characterize the biochemical
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
reactions have been provided in our previous study (Tavakkoli Avval et al., 2014).
2.2.
Density and elastic modulus of bone
Bone density (ρ) is related to the initial bone density (ρ0), the normalized concentration of old bone ½BoneOld and new bone ½BoneNew according to the following law of mass and mixture (Bougherara et al., 2010b; Tavakkoli Avval et al., 2014): ð9Þ ρ ¼ ρ0 ½BoneOld þ ½BoneNew In literature, different empirical and experimental relationships between the elastic modulus and density of the bone have been provided (Helgason et al., 2008). Using power law Table 1 – Material properties of CF/PA12, polymeric core, CoCrMo and Ti alloy (Bougherara et al., 2007, 2010a; Turner et al., 2005). Material
Property
Value
CF/PA12 (lamina)
EL ET GLL GLT νLL νLT Ply type
66.5 GPa 2.72 GPa 19.5 GPa 2.7 GPa 0.04 0.26 Woven
Polymeric core
E ν
1 GPa 0.2
CoCrMo
E ν
210 GPa 0.3
Ti alloy
E ν
114 GPa 0.3
59
relation between density and Young’s modulus, the elastic modulus of the bone was calculated (Eq. (10)). Helgason et al. (2008) experimentally determined that the exponent of density in power law relation is site-specific with a magnitude between 1.4 and 3. In the current study, the magnitude of 2 was used. ½BoneOld þ EBoneNew E ¼ EBoneOld ½BoneOld þ ½BoneNew 2 ½BoneNew ρ ð10Þ ρ0 ½BoneOld þ ½BoneNew where EBoneOld and EBoneNew represent Young’s modulus of the old and new bones, respectively.
2.3.
Development of computer-aided design (CAD) models
A large left 4th generation composite femur (model 3406, sawbones, Vashon, WA, USA) was fully scanned by GE LightSpeed VCT 64 Slice CT scanner (0.5 0.5 mm/pixel resolution, and 0.5 mm slice thickness). The CT scan images were saved in DICOM format and imported into Mimics software (The Materialise, Leuven, Belgium) to generate a three-dimensional (3D) model, and subsequently to create two distinct bodies (i.e. cortical and cancellous bodies). The 3D CAD model was then imported into SolidWorks software (SolidWorks Corp., Dassualt Systèmes, Concord, MA, USA) for virtual implantation. The femoral head (and neck) was split from the rest of the femur by using split features at an angle of 55 degrees with respect to the transverse anatomical plane along the greater trochanter. A portion of the proximal cancellous bone was removed to simulate surgically-generated bone loss during total hip replacement. The model of hip stem proposed by Bougherara et al. (2007) was then inserted into the proximal end of the femur. Therefore, we were able to create a CAD model whose femoral shaft was used for both pre- and postoperative bone remodeling simulations. This enabled us to
Fig. 2 – (a) CAD model with loads and constraints, (b) meshed intact femur, (c) meshed post-operative femur.
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journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
make a precise comparison between the density distribution of the intact (pre-operative) and post-operative femurs. The hip stem is straight, follows the antecurvation of the femoral shaft and has an oval cross-section. The composite hip stem is composed of a 3 mm thick substructure made of CF/PA12 lamina with stacking sequence of (7451)6 and an internal polymeric core (Bougherara et al., 2007) (Subscript ‘6’ signifies that the composite hip implant is made from six woven plies with 7451 fiber orientation). The geometry of the metallic hip stems were the same as the composite one; however, the related material properties (CoCrMo or Ti alloy: Table 1) were assigned to the substructure as well as to the internal core in finite element analysis (FEA). The CAD model of the hip stem was developed by commercially available software (CATIA V5R13, Dassault systemes, Montreal, CA) (Bougherara et al., 2007).
2.4.
Finite element modeling (FEM)
The prepared CAD model was imported into ANSYS Workbench 14.5 (ANSYS Inc., Canonsburg, Pennsylvania, USA). The bone and internal core of the implant were meshed by Quadratic Tetrahedrons elements (SOLID187), whereas the composite layers (laminate) were meshed using Linear Triangle elements (SHELL181). Surface-to-surface contact elements (CONTA174 and TARGE170) were used to mesh all interfaces. In order to simulate the physiological loading, muscle and hip joint reaction forces (Bitsakos et al., 2005) representing 45% of gait cycle were applied to the model (Fig. 2) as this instance of the gait produces the maximum loading on the femur (Frankel and Nordin, 1980). To avoid stress concentration, muscle and hip joint reaction forces were distributed over several nodes of
Fig. 3 – Iterative process of the thermodynamic-based model for simulating bone remodeling.
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greater (and lesser) trochanter and femoral head, respectively. To avoid rigid body motion, the degrees of freedom of all nodes at the distal femur were fixed. Mesh sensitivity was then investigated resulting in a total number of body elements and nodes to be 243,486 and 346,389 for the intact femur, 128,420 and 184,422 for the implanted femur, respectively (Fig. 2). The contacts between all surfaces were considered to be bonded, similar to other studies (Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012; Turner et al., 2005). It should be mentioned that for the composite hip implant, the stacking sequence of the laminate as well as the material properties of CF/PA12 (Table 1) were assigned to the composite hip implant by ACP (Pre) module of ANSYS Workbench 14.5. The algorithm of bone remodeling simulation is illustrated in Fig. 3. To simulate bone remodeling using the mechanobiochemical model, the meshed femur was imported into ANSYS Parametric Design Language (APDL). Forces and constraints were then applied to the model in the same manner as done in ANSYS Workbench simulations. In order to obtain bone density distribution throughout the intact femur, in the first iteration of numerical simulation, cortical and cancellous were modeled as homogenous structures with the initial density of 0.98 g/cm3 (ρ0) which is the average value of cortical bone with 1.64 g/cm3 and cancellous bone with 0.32 g/cm3. The mechano-biochemical model (thermodynamic-based model) is not sensitive to the initial density. In other words, in the thermodynamic-based model, the initial density does not have a significant effect on the final bone density distribution, similar to some other models (Kuhl and Balle, 2005; Balle, 2004). To model the intact femur, cortical and cancellous material properties (Ebrahimi et al., 2012) were assigned to their corresponding bodies. The hip implant (embedded into the femur) was also considered as cancellous bone. In the next iterations, the new properties of each element were calculated based on the concentration of old and new bones remained/produced inside the element. Similar to several other studies (Behrens et al., 2009; Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012; Turner et al., 2005), each bone element was considered as an isotropic material whose Young’s modulus was calculated by Eq. (10). The thermodynamic-based model, defined by Eqs. (3)–(7), was applied to finite element analysis through a user-defined macro. FEA yielded the trace of strain tensor, ε(1), to calculate the values of Dα by using Eq. (8). Dα were then entered into Eqs. (3)–(7) to calculate the values of ½BoneOld and ½BoneNew of each element. The density and elastic modulus of each element were obtained by Eqs. (9) and (10), respectively. These new material properties were considered for the next iteration of FEA, and the process was repeated until no significant change in the density of the elements was observed. It was assumed that the convergence and consequently the final density distribution are obtained when ConvCrio0.0001 (Eq. (11)). ConvCri ¼
1 n ðtÞ ∑ ρi ρiðt 1Þ ni¼1
To simulate periprosthetic bone remodeling in the presence of the implant, the elements of the head (and neck) of the intact femur were removed (unselected). The corresponding material properties (CoCrMo or Ti alloy or CF/PA12 (for composite lamina)) were assigned to the implant (Table 1). The initial material properties of each element of the immediate post-operative femur were chosen from the same element in the post convergence-intact femur (inhomogeneous femur). The joint reaction force was then transferred to the hip implant. Finally, the thermodynamic-based model was again applied to simulate bone response to THA and Eq. (11) was used to control the convergence.
3.
Results
3.1.
Bone density convergence
The convergence of simulations was controlled by Eq. (11) so that when no significant change in the density of the elements was observed, it was considered as a converged solution. The convergence of bone remodeling simulations for four constructions is shown in Fig. 4. As depicted, the average density change over all elements approached zero after approximately 40 iterations.
3.2.
Pre- and post-operative bone density distributions
Distribution of density throughout the intact femur is illustrated in Fig. 5(a) and (b). The range of density predicted by the model was between 0.35 and 1.75 g/cm3. The maximum value of density was observed in the cortical bone located at the mid-shaft. Our results showed that in addition to a dense cortical bone around the medullary canal, a dense cancellous bone between the calcar and the location of hip joint reaction force is developed. Periprosthetic bone density distribution in response to CoCrMo, Ti alloy and CF/PA12 hip implants is illustrated in Fig. 6. The location of the maximum density was still at the cortical bone in the mid-femoral shaft. Comparing the density distributions after THA (Fig. 6) implies that the stiffest hip
ð11Þ
where n and t are the number of elements and iteration number, respectively.
61
Fig. 4 – Convergence of bone remodeling simulations.
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journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
Fig. 5 – Bone density distribution in intact femur (a) obtained by the thermodynamic-based model in posterior view, (b) obtained by the thermodynamic-based model in posterior view-coronal plane, (c) obtained by X-ray (reproduced with permission from Truong et al., 2006).
Fig. 6 – Bone density distribution after THA with (a) CoCrMo, (b) Ti alloy, (c) CF/PA12 composite hip implant.
implant (CoCrMo) induced more stress shielding into the proximal femur such that low density regions (0.34–0.8 g/ cm3) were dominant in the femur embedded with CoCrMo compared to that with the composite hip stem. Therefore, the results of simulations revealed that biomimetic composite hip stem promotes proximal load transfer to the femur
compared to the metallic conventional ones, and hence, reduces the amount of bone resorption in response to implantation. To examine the density distribution in detail, the femur was divided into seven zones commonly known as Gruen zones (Gruen et al., 1979). These seven zones describe mainly the regions surrounding the proximal part of femur
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
63
Fig. 7 – Percent change in bone density in response to the hip implants made from (a) CoCrMo, (b) Ti alloy, (c) CF/PA12. Cutting plane line in all three constructions passes through the proximal metaphysis. MX and MN indicate the location of maximum bone formation and maximum bone resorption, respectively.
Fig. 8 – Graph showing the percentage of bone loss in Gruen zones in response to implantations.
and are clinically used to assess the outcome of the hip replacement surgery.
3.3.
Percent change in the bone density
Percent change in the femoral density in response to the implantation of hip stems is presented in Fig. 7. According to this figure, in all three simulations, the severe periprosthetic bone loss ( 72%) occurred in the calcar region while the maximum bone formation ( þ60%) happened at a region located near the distal end of the implants where the load sustained by the implant is transmitted to the bone. As illustrated in Fig. 7, the stiffness of implants plays a key role in the periprosthetic bone density distribution. It can be observed that only a small portion of the medial femur embedded with composite hip stem was subjected to a severe
bone loss ( 72% to 30%) unlike the femurs with Ti alloy and CoCrMo implants. In addition, section views whose cutting plane passes through the proximal metaphysis depict that a moderately dense trabeculae was developed in the case of composite hip implant only. The results shown in Fig. 8 confirms the advantage of the composite hip stem over metallic ones in terms of induced stress shielding as the femur embedded with composite hip stem showed less total bone loss ( 9%) compared to 21% and 27% in the presence of Ti alloy and CoCrMo, respectively. This figure also reveals that the maximum bone loss among Gruen zones were approximately 43% (zone 7), 35% (zone 7), and 10% (zone 2) in response to CoCrMo, Ti and composite hip stems, respectively. The proposed mechano-biochemical model also predicted an equal minimum bone loss (9% in zone 4) for all three hip stems. In addition, the difference in the amount of bone loss in response to the metallic implants was obvious in different Gruen zones. On the contrary, the level of bone loss in response to the composite hip implant was approximately the same in all Gruen zones so that its standard deviation (0.60%) was much lower than those with Ti alloy (9.13%) and CoCrMo (12.29%) implants. This small deviation shows that the pattern of stress in the femur embedded with the composite implant was more uniform than those with the metallic ones.
4.
Discussion
4.1.
General findings and comparison to prior studies
To improve load sharing characteristics between the bone and the implant, a number of composite hip implants have been designed so far (Akhavan et al., 2006; Bougherara et al., 2007; Katoozian et al., 2001; Mendes et al., 1988). However,
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journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
there is a lack of data regarding the long term behavior of the bone in response to such implants as they have not been widely used in humans. Hence, it is critical to predict the bone’s long-term response in the presence of composite prosthesis by realistic numerical models. In the current study, the bone remodeling response of the femurs implanted by CoCrMo, Ti alloy and CF/PA12 composite hip stems were simulated by a mechano-biochemical model. According to our findings, the composite hip implant is more advantageous over the metallic ones in terms of bone remodeling as it induces less stress shielding and provides more uniform density change across the bone. The range of femoral density predicted by the mechanobiochemical model was between 0.35 and 1.75 g/cm3 which is consistent with clinical observations (Hodgskinson and Currey, 1990; Hoiberg et al., 2007). According to our results, a dense cortical bone was formed around the medullary canal while the internal regions of the mid-shaft were composed of a lowstiffness material which agrees with computed tomography (CT) results obtained by Truong et al. (2006). This study also revealed that a dense cancellous bone carrying stress from the superior contact surface to the calcar region is developed in the femoral neck which is consistent with bone morphology (Truong et al., 2006) and a numerical study (Kuhl and Balle, 2005). Similar to the study by Bougherara et al. (2010a), periprosthetic bone loss in response to metallic implants was more severe than that in the presence of composite hip stem as low density regions (0.34–0.8 g/cm3) were dominant in the femur embedded with CoCrMo compared to that with the composite hip stem. It can be explained by the fact that stiff implants carry a greater portion of the applied load compared to flexible ones. Subsequently, according to the load sharing rule, less load portion is bore by a femur with a stiff implant compared to the one embedded with a flexible implant. On the other hand, based on Wolff’s law (Wolff, 1892) and Frost’s mechanostat theory (Frost, 1990) bone remodeling is stimulated by the local mechanical elastic deformation of bone; thus, bone adapts its properties according to the mechanical load acting upon it. According to these theories, reduction in mechanical load causes bone to adapt itself by reducing its density. That is why a femur implanted with a stiff implant is subjected to more severe bone loss compared to a femur with a flexible one as the former carries less mechanical load. Our findings also showed an extreme cortical resorption at the medial edge of the implants in the proximal metaphysis analogous to Huiskes et al. (1992). Furthermore, in the presence of CF/PA12 implant only, some moderate trabecular densification was found at the vicinity of the prosthesis which can boost implant stability; this can be considered as another benefit for the composite hip stem. In this study, the maximum local bone loss ( 72%) was found in the calcar region which is in agreement with the observation of Kilgus et al. (1993). Also, the maximum local bone formation ( þ60%) was formed in a region located at the vicinity of the distal tip of the stem. Kroger et al. (1998) similarly found bone mineral density increase in the regions close to the distal implant. This can be justified by the fact that loads sustained by the implant are transferred to the bone through the distal tip of the stem resulting in a stress concentration which consequently induces a deposition of bone mass.
Our results endorse the advantage of the composite hip stem over the metallic ones in terms of induced stress shielding as the femur embedded with the composite hip stem showed less total bone loss (9%) compared to 21% and 27% in the presence of Ti and CoCrMo, respectively. Bougherara et al. (2010a) reported that the bone loss with CF/PA12 stem is approximately between 10% and 20% while it lies between 25% and 50% when Ti stem is used. In comparison with the results of Bougherara et al. (2010a), our findings (total bone loss of 9% for composite and 21% for Ti) are close to the lower bands. This can be justified by the inherent difference between the numerical models used for bone remodeling simulations. In contrast to Bougherara et al. (2010a) who used the strain energy density model (Huiskes et al., 1992; Weinans et al., 1992) for predicating bone loss, the current study employed the mechano-biochemical model to simulate the response of bone to the presence of composite and metallic implants. The mechano-biochemical model considers the role of biochemical reactions for regulating bone remodeling mechanism so that in the absence of mechanical loading, the bone resorbs partially by approximately 50% (Tavakkoli Avval et al., 2014) due the presence of biochemical stimulus that triggers bone remodeling. However, in the strain energy density model, bone resorbs completely in the absence of mechanical loading (Bougherara et al., 2010b). In comparison with the clinical study conducted by Skoldenberg et al. (2006) using a cementless titanium hip implant, the current amount of predicted periprosthetic bone loss in response to Ti hip stem, in Gruen zone 7 ( 35%), 6 ( 29%), 4 ( 9%), and 1 ( 20%) are in good agreement with the range of their observations (zone 7: 40% to 10%, zone 6: 30% to þ1%, zone 4: 9% to þ4%, zone 1: 36% to 12%). Moreover, our predicted bone loss for all Gruen zones including zone 5 ( 15%), 3 ( 16%), and 2 ( 26%) are in the range of the results predicted by Kuhl and Balle (2005). In response to the CoCrMo implant (with Young’s modulus of 210 GPa), the maximum predicted bone loss in Gruen zones was 43% which occurred in zone 7 and is close to the maximum bone loss of 40% (zone 7) in the presence of stainless steel (with Young’s modulus of 193 GPa) observed by Niinimaki and Jalovaara (1995). The amount of bone loss in response to the composite hip implant was approximately the same ( 9%) in all Gruen zones which resulted in a lower standard deviation (0.60%) compared to the metallic implants (9.13% for Ti alloy; 12.29% for CoCrMo). This small deviation implies that the femur embedded with the composite hip implant is not subjected to excessive stress concentration, therefore is under a lower risk of fracture, which can be counted as another privilege of CF/PA12 implant. In response to the metallic hip implants, the current study showed that the maximum bone loss ( 43% for CoCrMo and 35% for Ti) among Gruen zones occur in zone 7 similar to other clinical and numerical studies (Huiskes et al., 1992; Kilgus et al., 1993; Kroger et al., 1996, 1998; Li et al., 2007; Niinimaki and Jalovaara, 1995; Stukenborg-Colsman et al., 2012; Turner et al., 2005; Yamaguchi et al., 2000). Furthermore, the next most severe periprosthetic bone loss ( 40% for CoCrMo and 29% for Ti) happened in zone 6 which agrees with the results of Kilgus et al. (1993). The minimum bone loss ( 9%) among Gruen zones was reported to be in zone 4 (the most distal region) which is consistent with other
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
studies (Behrens et al., 2009; Huiskes et al., 1992; Li et al., 2007) which reported the minimum bone density decrease occurs in the most distal region of interest. Interestingly, the amount of bone loss in this zone was the same in all three constructions. This can be explained by the fact that since all the loads shared with the implant, regardless of its material, are transmitted to zone 4, this zone is subjected to the same amount of bone density decrease. According to our findings, bone loss in response to the metallic implants progressively declined (except for an increase from Gruen zone 1 to 2) as the region of interest moves distally from the proximal metaphysis to mid-diaphysis, which agrees with Li’s results (Li et al., 2007). In addition, our study revealed that the sequence of severity of bone loss (from maximum to minimum) in Gruen zones is as follows: zone 7, 6, 2, 1, 3, 5, and 4 for both femurs embedded with CoCrMo and Ti which is consistent with the long term observations of Li et al. (2007).
4.2.
Limitations of the study
Although the results agree well with the bone morphology and literature and provide validated quantitative data that can be used to optimize hip implants’ design, the model has some limitations and simplifications. Similar to several studies (Huiskes et al., 1992; Kuhl and Balle, 2005; Lerch et al., 2012) bonded contacts were considered in the current study. This bonded contact is meant to mimic complete interdigitation of bone around the hip stem. In the current work, anisotropic behavior of the bone was ignored as each element was assumed to have an isotropic material. In our model, the concept of coupling is based on linear non-equilibrium thermodynamics and thus is phenomenological. Thus, we cannot relate it directly to actual mechanosensing or mechanotransduction processes in cells. Furthermore, the mechanical stimuli in the simulations do not include any viscous effects. We have also assumed that the trace of strain tensor regulates bone cells response, however, other mechanical stimuli such as transport of nutrients and fluid flow could be considered. In addition, we disregarded kinetics of some of the known control mechanisms in bone remodeling such as RANKL-RANK-OPG chain which may play a role in regulating the bone remodeling process. In the proposed model the computational steps are unrelated to the real time. However, the iterative process was assumed converged when no significant change in the density of the elements was observed which, from the clinical point of view, is considered as the long-term response when the femoral density gets to a stable condition. We also tried to bring insight into bone loss due to stress shielding phenomenon, and the density decrease caused by chemical diseases was not considered. Moreover, our treatment of the bone remodeling process is that it is a coordinated sequence of bone resorption and formation. This coordination is somewhat simplistic but the model can be straightforwardly extended to contain a lot more details about the control mechanisms involved (Klika et al., 2013). Furthermore, it does not include shape-changing processes such as modeling or desorption alone. Also, the remodeling of the Haversian system and hemi-osteons are treated similarly although the actual
65
mechanisms do not coincide. Likewise, we did not distinguish primary from secondary osteons. Our approach is more phenomenological as we tried to capture the changes in the tissue density in a given voxel by relating the average remodelling activity to mechanical and chemical factors. These are some of the limitations of the model where one consequence is the limited spatial resolution in the outcome.
5.
Conclusion
In conclusion, the mechano-biochemical model which considers the coupling effect between the mechanical loading and biochemical affinities as stimuli for bone remodeling, was implemented in this study to simulate the long-term behavior of the femur in response to CF/PA12, Ti alloy and CoCrMo hip implants. The predicted bone density distribution before and after THA agree well with bone morphology and literature. It was revealed that the most significant periprosthetic bone loss in response to metallic implants occur in Gruen zone 7 and 6. On the contrary, zone 4 has the lowest bone density decrease with all three implants. Also, the results showed that in terms of bone remodeling, the composite hip implant is more advantageous over the metallic ones as it induces less stress shielding, develops a moderately dense trabeculae at the vicinity of the implant, and provides more uniform bone density change following THA.
Acknowledgments This research is supported by the Natural Sciences and Engineering Research Council of Canada-Discovery Grant (NSERC/355434-2009). The authors would like to thank Ms. Angela Peragine for proofreading the manuscript.
Appendix A. Biochemical reactions involved in bone remodeling mechanism Osteoclasts are the only cells that are able to resorb bone tissues. These cells initially exist as mononuclear cells, MCELL. In order to be activated, mononuclear cells have to be coupled to multinucleated complex, MNOC, whose formation can be characterized by the following reaction. ðα ¼ 1 Þ
kþ1
N1 þ MCELL ⇆ MNOC þ N4 k1
ðA:1Þ
N1 is the mixture of substances initiating the reaction with the mononuclear cells. N4 is the remaining product from the first reaction (α¼ 1). In the next step (α¼2), which is so-called bone decomposition, multinucleated osteoclasts act on the bone to break it down: ðα ¼ 2 Þ
kþ2
MNOC þ BoneOld ⇆ N6 þ N7 k2
ðA:2Þ
where Bone Old is the abbreviation for old bone. N6 and N7 are the products resulting from the degradation of the old bone.
66
journal of the mechanical behavior of biomedical materials 41 (2015) 56 –67
N7 is then used in the production of osteoblasts activator (ActOB) as described in the following reaction. ðα ¼ 3Þ
kþ3
N7 þ BoneOld ⇆ ActOB þ N9 k3
ðA:3Þ
The activators act on the osteoblasts, OB, which causes them to secrete collagen and produce Osteoid which is the unmineralized bone: ðα ¼ 4Þ
kþ4
ActOB þ OB ⇆ Osteoid þ N12 k4
ðA:4Þ
N9 and N12 are the remaining products of the 3rd (α¼3) and 4th (α¼4) reactions, respectively. The last and longest reaction (α¼ 5) in the bone remodeling process is the mineralization of Osteoid. N13, the substratum initiating bone calcification, is embedded into the bone’s matrix to form the new bone (Bone New) according to: ðα ¼ 5Þ
kþ5
N13 þ Osteoid ⇆ BoneNew þ N15 k5
ðA:5Þ
N15 is the remaining material in the bone formation reaction.
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