Reduced stress shielding with limited micromotions using a carbon-fiber composite biomimetic hip stem: a finite element model

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Reduced stress shielding with limited micromotions using a

carbon-fiber composite biomimetic hip stem: a finite element model

Caouette, C.; Yahia, L’H.; Bureau, M. N.

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DOI: 10.1177/0954411911412465

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Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine

C Caouette, L'H Yahia and M N Bureau

stem: a finite element model

Reduced stress shielding with limited micromotions using a carbon fibre composite biomimetic hip

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Reduced stress shielding with limited micromotions

using a carbon fibre composite biomimetic hip stem:

a finite element model

C Caouette1, L’H Yahia1, and M N Bureau2*

1

Laboratory of Innovation and Analysis of Bioperformance (LIAB), E´ cole Polytechnique de Montre´al, Montre´al, Quebec, Canada

2_{Industrial Materials Institute, National Research Council of Canada, Boucherville, Quebec, Canada}

The manuscript was received on 22 November 2010 and was accepted after revision for publication on 13 April 2011.

DOI: 10.1177/0954411911412465

Abstract: Total hip arthroplasty (THA) enjoys excellent rates of success in older patients, but younger patients are still at risk of aseptic loosening and bone resorption from stress shielding. One solution to the stress shielding problem is to use a hip stem with mechanical properties matching those of cortical bone. The objective of the present study was to investigate numeri-cally the biomechanical performance of such a biomimetic hip stem based on a hydroxyapa-tite (HA)-coated carbon fibre composite. A finite element model (FEM) of the biomimetic stem was constructed. Contact elements were studied to model the bone–implant interface in a non-osseointegrated and osseointegrated state in the best way. Three static load cases repre-senting slow walking, stair climbing, and gait in a healthy individual were considered. Stress shielding and bone–implant interface micromotions were evaluated and compared with the results of a similar FEM based on titanium alloy (Ti–6Al–4V). The composite stems allowed for reduced stress shielding when compared with a traditional Ti–6Al–4V stem. Micromotions were slightly higher with the composite stem, but remained below 40 mm on most of the HA-coated surface. It is concluded that a biomimetic composite stem might offer a better compro-mise between stress shielding and micromotions than the Ti–6Al–4V stem with the same external geometry.

Keywords: hip prosthesis, biomimetic material, composite material, finite element analysis

1 INTRODUCTION

1.1 Total hip arthroplast modelling

Despite a high clinical success rate, total hip arthro-plasties (THAs) present a number of problems, espe-cially for younger patients with active lifestyles who are likely to suffer aseptic loosening due to bone resorption mainly caused by osteolysis and stress shielding [1]. The use of composite materials in orthopaedics is an attempt to solve some of these problems. The so-called ‘isoelastic stems’ developed in the 1980s were aimed at providing a more natural

stress distribution in the proximal femur, in the hope of reducing stress shielding and bone resorption [2– 4]. Other, more contemporary studies have attempted to create stems made of composite materials (e.g. carbon fibre and polyetheretherketone (PEEK) [5], carbon or glass fibre and polyethylenimine (PEI) [6], and metallic core with a flexible composite outer layer [7]). One of these studies aimed to mimic the flexural rigidity of the natural femur [6], another study sought to reproduce the strain energy density observed in the natural femur by optimizing ply orientation within the material [5], and another attempted to axially modulate the elastic modulus of the stem [7].

However, high micromotions at the bone–implant interface prevented long-term bone fixation of isoelastic stems, leading to clinical failures [8, 9]. *Corresponding author: Industrial Materials Institute, National

Research Council of Canada, Boucherville QC, J4B 6Y4, Canada. email: martin.bureau@cnrc-nrc.gc.ca

For successful osseointegration and good primary stability, threshold values of micromotions varying between 30 mm [10–12], 40 mm [13], and 100– 200 mm [14–16] have been proposed. Higher micro-motions will lead to the formation of a fibrous layer rather than proper osseointegration.

Besides the use of new materials, other avenues have been explored to improve stress distribution within the implanted femur. Improvement of cross-sectional stem shape is one such avenue: a recent study by Sabatini and Goswami [17] concluded that anatomical circular and elliptical cross-sections pro-duce a smoother stress field than trapezoidal cross-sections and therefore produce less stress shielding. Another study by Gross and Abel [18] also showed that a hollow stem led to less stress shielding than its solid counterpart; it was also found that reducing the elastic modulus would also reduce stress shield-ing. However, it is noted in the literature that opti-mizing the shape of a stem made of a homogeneous metallic material is not sufficient to create a stem that reproduces the stiffness of the natural femur [6]. Clinical failures of more flexible implants under-lined the importance of proper pre-clinical testing of new designs, for which finite element analysis (FEA) is a most widely used tool [19–23] and the method of choice to evaluate new stem concepts [18, 24, 25] both from an economical and an ethical point of view. Femoral bone modelling is a subject well covered in the literature [26–30]. Composite femur models are considered an acceptable substi-tute for pre-clinical testing of implants [31]. FEA boundary conditions for hip implants have been validated experimentally for metallic implants [16, 32, 33] and are indiscriminately used for healthy femurs or other types of implants. Most authors use bonded implants and only specify a friction coeffi-cient [34] and contact surface behaviour [20, 35] and avoid or neglect a key aspect to finite element method (FEM) modelling of a cementless implant: bone–implant interface modelling [24]. Also, very few authors specify their complete contact condi-tions or justify their choices [16, 36, 37].

1.2 Biomimetic concept

Preliminary finite element studies were conducted to assess the validity and theoretical performance [38, 39] of a biomimetic stem concept previously developed. Unlike isoelastic stems that simply tried to match the bending stiffness of the femoral bone and were generally made of metallic materials, the current biomimetic stem is made of a polymer com-posite material that mimics the modulus of elasticity of bone. It therefore does not introduce a soft surface

layer apposed to the host bone, as was the case with some isoelastic stem designs. The biomimetic stem was constructed and mechanically tested for partial validation of the preliminary finite element model [40]; this step insured that the finite element model represented the real material and not a mathematical optimization of a theoretical material, as is some-times the case with FEM studies on composite mate-rials [41]. The purpose of this study is to investigate numerically the performance of the biomimetic hip stem using this partially validated finite element model, and to assess its performance when com-pared with a conventional metallic stem with the same external geometry. Prior to these simulations, a realistic bone–implant interface is described.

2 MATERIALS AND METHODS

2.1 Stem concept

The biomimetic stem concept is aimed at reprodu-cing the natural physical structure of the femur, with its cortical outer shell and its weaker interior of trabecular bone. The stem is made of a biocompati-ble material, as indicated by in vitro cytotoxicity and in vivo tissue response, showing good osseoin-tegration and proliferation of osteoblasts and their progenitors within the hydroxyapatite (HA) coating in histological sections of a rabbit model [42], and by good bone apposition with minimal inflamma-tion (haematoxylin and eosin (H&E) staining) and no osteolysis when exposed to purposely produced debris from grit blasting in a rat model [43]. This material consisted of a continuous carbon-fibre-reinforced polyamide 12 (CF/PA12) moulded into a hollow stem structure by an inflatable bladder moulding process. The carbon fibre volume fraction is 0.55; the moulding process has been optimized to obtain compressive properties (refer to Table 1) close to those of cortical bone [44, 45]. In the initial biomimetic concept, a polymeric core was included in the hollow stem to mimic trabecular bone, but this core was deemed unnecessary after a finite ele-ment study showed it had negligible influence on principal stresses in the femur [38].

The femoral stem geometry is inspired from an anatomical cementless design (see Fig. 1) and is modified from commercial designs. It has an oval cross-section, follows the ante curvature of the femoral shaft, and has a neck-shaft angle of 135°. It consists of a CF/PA12 hollow stem (wall thickness of 3 mm) coated in the proximal region with a semi-crystalline HA layer [46] to facilitate bone growth and integration. The titanium (Ti) stem used for

comparison shares its external geometry with the biomimetic stem, but is not hollow to reflect the fact that commercial cementless designs are not hollow. 2.2 Bone–implant interface

2.2.1 Contact element study

Large sliding surface-to-surface contact elements available in the Ansys v10 software (Ansys,

Canonsburg, USA) were used to model the bone– implant interface. The force vector for these contact elements is P ty tz 8 < : 9 = ; (1)

where P is the normal contact pressure, and ty and

tz are tangential contact stresses in the y and z

directions of the local element coordinate system, with x as the normal to the element surface. When an augmented Lagrangian or penalty method is cho-sen as contact algorithm, this force vector is calcu-lated using the following formulae

P = 0 Knun  if un.0 if un<0 (2) ty, z= Ktuy, z msKnun  if ffiffiffiffiffiffiffiffiffiffiffiffiffi t2_y+ t2_z q tlim\0(sticking) if ffiffiffiffiffiffiffiffiffiffiffiffiffit2_y+ t2_z q tlim= 0(sliding) (3)

where Knand Ktare the normal and tangential

con-tact stiffness (similar to spring stiffness), ms is the

static friction coefficient, unis the contact

penetra-tion distance, and uyand uzare the slip distances in

the y and z directions. The slip distances in the y and z directions are used to obtain sliding distance, which in this case translates to bone–implant micro-motions. As can be seen in equation (3), a sticking frictional contact behaves like a linear spring and offers sliding resistance independently of the pres-ence of friction, whereas a sliding frictional contact exhibits frictional behaviour only.

The shear behaviour of the contact (sticking or sliding) is determined by tlim (sliding will occur

regardless of pressure magnitude if shear stress reaches this value) and the friction model

tlim= msP + b (4)

t

j j < tlim(sticking)

t

j j . tlim(sliding) (5)

Fig. 1 Stem geometry used in the current study (dimensions in mm)

Table 1 Material properties of the composite material structure compared with bone and other traditional stem materials

Material/tissue Density (g/cm3_{) Modulus (GPa) Strength (MPa) Poisson’s ratio}

Trabecular bone 0.03–0.12 0.04–1.0 1.0–7.0 0.01–0.35

Cortical bone 1.6–2.0 12–20 150 0.28–0.45

Ti–6Al–4V 4.4–4.7 106 780–1050 0.33

Composite (compression) 1.2–1.6 5–14 53–220 0.3

Composite (tension) 12–30 70–250 0.36

where b is contact cohesion (shear stress supported by the contact interface when P = 0). A non-null contact cohesion will increase the value of tlimand

prevent the contact from going into sliding mode if contact pressure is too low, meaning the interface will offer resistance to sliding even in the absence of friction, up to the value of b. For a shear stress above the value of b, the bond will break and the contact element will go into sliding mode, i.e. the interface will behave as a purely frictional interface.

To determine the combined effect of these para-meters on contact sliding distance, a small model was constructed to study the contact elements. This model consists of two hollow tubes with a taper angle of 6° (Fig. 2). The dimensions of the tubes are similar to a cross-section of the proximal region of the femur with a composite stem implanted. The contact region was modelled with standard type con-tacts (i.e. frictional behaviour as described above) using an augmented Lagrangian contact algorithm. Parameters of normal and tangent stiffness (Kn and

Kt) and of static friction (ms) were varied to study

their effect on micromotions. Two cases were investi-gated: contact cohesion (b) of zero (i.e. completely debonded implant with purely frictional interface)

and contact cohesion set at a value high enough to ensure a sticking behaviour of the contact elements (i.e. perfectly osseointegrated implant, set at 60 MPa (value representative of HA ultimate tensile strength) for the purposes of the contact element study and measured experimentally for the implant models).

2.2.2 Mechanical testing of bone–implant interface

Assuming that living bone replaces the HA layer at the stem surface during osseointegration [47], the assumption is made that bone–implant interface parameters can be measured on a HA–implant interface as the adhesion between the composite structure and the ‘bone-type’ HA layer. This assumption is supported by the fact that osteoblast proliferation within the HA layer of the composite was seen in a rabbit model [42], suggesting the HA layer is progressively replaced by living bone and is penetrating the implant tie layer. It is hypothesized that this adhesion measure is not influenced by the properties of the HA layer itself, since it is very thin (\100 mm). This hypothesis is supported by adhe-sion results reported previously [48] showing an adhesive mode of failure for these coatings.

Fig. 2 Tubular model used in the contact elements study: (a) schematic drawing with dimen-sions; (b) finite element mesh

Interface cohesion (parameter b) and tangent rigidity (parameter Kt) were measured

experimen-tally using a lap-shear test specimen (25 mm wide with overlapping length of 12.7 mm, according to ASTM D3163 – 01 [49]) made of a rectangular HA-coated composite plate and a rectangular steel plate bonded together by means of a polyamide-epoxy adhesive (with verified composite–steel adhesion of 30 MPa) as employed elsewhere [46].

2.3 FEA of the biomimetic stem

2.3.1 Finite element model description

A three-dimensional (3D) finite element model was developed to predict the clinical outcome of the new stem (Fig. 3). Femur geometry was obtained from a public web site (BEL repository, see http://www.bio-medtown.org) and is based on Pacific Research Labs’ Sawbones femurs. Structural properties used for trabecular and cortical bone (modelled as linear isotropic and orthotropic materials respectively) are summarized in Table 2. The stem structure is

modelled with quadratic hexahedral elements and a linearly elastic orthotropic material (values used were an average of tension and compression proper-ties: E was set at 25 GPa and n at 0.3).

The stem was implanted with perfect contact (i.e. perfectly matching contact surfaces) between trabe-cular bone and stem (proximal part of the implant) and no contact between cortical bone and stem (distal part of the implant). The bone–implant inter-face is simulated using the previously described sur-face-to-surface contact elements. Both primary (non-osseointegrated case, HA layer is present) and secondary (osseointegrated case, HA layer has been replaced by bone) stem stability were modelled, without press-fit effect, to provide a worst-case sce-nario of poor stem fixation. Parameters used in the contact elements (Table 3) were based on contact elements in study and literature data. Because the interface is between bone and the HA layer of the implants, the same values of parameters can be used for both models. The choice of parameters will be further detailed in the contact elements study result section (section 3.1).

Three static loading conditions were considered: slow walking (1 km/h), stair climbing, and one-leg stance (Table 4), with a distally immobilized femur

Table 3 Numerical values used in the bone–implant interface during simulations

Non-osseointegrated state Osseointegrated state

Normal stiffness, Kn(N/mm)§ 600–1800y 1000–5000z

Tangent stiffness, Kt(N/mm)§ Not relevant 1000*

Static friction coefficient (ms)§ 0.1–0.3 0.2–0.6

Contact cohesion (MPa) 0 15*

Contact algorithm Augmented Lagrangian

*Obtained experimentally from the lap-shear test.

yFrom Bernakiewicz et al. [14], based on experimental tests with composite femurs. zFrom Orlik et al. [15].

§From literature data, mean values.

Fig. 3 Finite element model used in the current study: (a) geometrical model; (b) medial view; (c) fron-tal view. Abductors muscles are represented by a dashed line, hip contact force by a solid line (one-leg stance loading is depicted)

Table 2 Material properties used for cortical and tra-becular bone. Data from reference [38] Trabecular bone material properties

E 0.4 GPa

n 0.3

Cortical bone material properties

Ex 11.5 GPa Ey 11.5 GPa Ez 17.5 GPa nxy 0.3 nyz 0.4 nxz 0.4 Gxy 3.0 GPa Gyz 3.5 GPa Gxz 3.5 GPa

Note: z-axis is parallel to femoral shaft, x- and y-axes are perpen-dicular to femoral shaft.

(see Fig. 3). The walking and stair-climbing load cases represent daily activities. The most severe case, the one-leg stance loading, represents gait in an active healthy individual. All three load cases were simulated on a healthy femur, a femur implanted with a CF/PA12 stem, and a femur implanted with a Ti–6Al–4V solid stem, in order to evaluate the advan-tage of using the biomimetic stem over commonly used Ti–6Al–4V models, and to investigate stress shielding with the composite stem. All loading condi-tions were simulated using hip contact force and abductor muscles force only. Despite the limited clinical relevance of this type of loading [50], these boundary conditions are widely used and well accepted in the literature for THA simulation. A mesh convergence study was conducted on the models: element size was set at 3 mm. The models consist of 33 524 to 61 122 elements and 55 385 to 89 553 nodes (for the healthy femur and Ti–6Al–4V stem respec-tively). The convergence study included analysis of contact parameters such as contact pressure and sliding distance to ensure they were fully converged (i.e. converged to their fourth significant digit).

Stress shielding in the femur is evaluated using Von Mises stress. A previous study by Terrier et al. [51] has shown that strain energy density-based and Von Mises-based remodelling stimuli lead to similar bone density results; as Von Mises stress is less sen-sitive to contact element artefacts such as faceted geometry, it was chosen as the scalar value used to quantify stress shielding.

3 RESULTS

3.1 Contact element study

3.1.1 Non-osseointegrated case

In the non-osseointegrated case (contact in sliding mode with purely frictional behaviour), two impor-tant parameters were identified: normal rigidity (Kn)

and static friction coefficient (ms), as observed from

the maximum pressure results in Fig. 4. Two values of normal rigidity (1000 and 3000 N/mm3) and static friction coefficients (ms) ranging from 0.1 to 0.6 were

used. Figure 4 shows that pressure first increases as m_sincreases, then stabilizes for m_s˜ 0.2. The use of a higher value for normal rigidity leads to higher pres-sure on the contact surfaces.

Figure 5 represents the maximal calculated micromotions for the same range of ms values. For

ms\0.2, micromotions are very high, but they quickly stabilize into a decreasing asymptotic beha-viour for ms˜ 0.2. Figures 4 and 5 emphasize the

existence of a critical threshold value for ms(0.2 for

the simplified model).

3.1.2 Osseointegrated case

In the osseointegrated case (contact in sticking mode with linear resistance to shear forces), the Table 4 Load cases used in the simulations

Hip contact force (N) Abductor muscle load (N)

FX FY FZ FX FY FZ

Load case 1 (1 km/h walk)y

785 17.5 21850 2471 144 967

Load case 2 (stair climbing)y 1034 906 21866 2375 377 532

Load case 3 (one-leg stance)z

1492 2915 22925 21342 832 2055

Note: z-axis is in the caudal direction and parallel to the medullar canal, x-axis is in the medial direction, and y-axis is in the posterior direction.

yFrom Akay et al. [24]. zFrom Tai et al. [21].

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 5 10 15 20 25 30 35

Static friction coefficient µ_s

Maximal pressure (MPa)

K

n = 1000 N/mm³ K

n = 3000 N/mm³

Fig. 4 Evolution of maximal pressure in the contact elements following an increase in the static fric-tion coefficient, for fixed values of tangent stiff-ness Kt (1000 N/mm3) and contact cohesion

(0 MPa), and two different values of normal stiffness Kn(1000 and 3000 N/mm3)

important parameters identified were contact cohe-sion (b) and tangent rigidity (Kt). Normal stiffness

and static friction coefficient had no impact as tlim

is never reached and contact behaviour remains in sticking mode.

Figure 6 presents the effect of tangential rigidity on shear stress for the osseointegrated case with a contact cohesion set at 60 MPa. This figure shows that contact shear stress is influenced by Ktbut not

by ms. Kt is thus the key parameter to determine

whether the critical value of shear stress (i.e. the bone contact break point) is reached, i.e. if aseptic loosening occurs. Micromotions also remain very low regardless of values used for normal rigidity and friction coefficient: a maximum of approximately 10 mm was reached for all models and loadings.

3.1.3 Resulting bone–implant interface parameters

Three parameters affecting micromotions at the bone–implant interface were determined: normal stiffness Kn, tangent stiffness Kt, and static friction

coefficient ms. Contact cohesion, b, which serves as

a bonding degree, is used to simulate an implant in its osseointegrated state. Values were assigned to Kn

(1000 and 2000 N/mm3 for the non-osseointegrated and osseointegrated states respectively) and ms(0.4)

in agreement with other published values (see Table 3). Kt was experimentally measured from the

lap shear test at 1000 N/mm3 (1016 6 55 N/mm3

over ten cycles) and contact cohesion likewise at 15 MPa (14.5 6 1.2 MPa over two specimens). Those values were used in subsequent simulation runs for both Ti–6Al–4V and CF/PA12 stems.

3.2 Finite element model of titanium and biomimetic stems

3.2.1 Stress shielding

Stress shielding was evaluated in all three load cases, for osseointegrated and non-osseointegrated implants. Figure 7 shows Von Mises stress in the femur for the non-osseointegrated implant interface in the one-leg stance load case. It indicates that the calcar region of the bone undergoes stresses that are higher with the CF/PA12 stem (22 MPa) than with the Ti–6Al–4V stem (11 MPa), but lower than in the healthy femur (33 MPa). The lateral and medial sides of the femur also showed this effect.

Figure 8 shows Von Mises stress in the femur for the osseointegrated implants in the slow walking load case. Stress reduction in the calcar region of the bone with both types of implant is still visible (12 and 8 MPa for CF/PA12 and Ti–6Al–4V, respectively). The remaining bone undergoes similar stress levels for both implants. Load transfer to the bone is altered when compared with the non-implanted femur: the distal femur is subjected to higher stresses on its medial side (27 MPa) rather than its lateral side for both implants, indicating a change in load transfer. 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0 5 10 15 20 25 30 35 40 45 50

Static friction coefficient µ

s Maximal micromotions (µ m) K n = 1000 N/mm³ K n = 3000 N/mm³

Fig. 5 Evolution of maximal micromotions in the con-tact elements following an increase in the static friction coefficient, for fixed values of tangent stiffness Kt(1000 N/mm3) and contact cohesion

(0 MPa) and two different values of normal stiff-ness Kn(1000 and 3000 N/mm3) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2 3 4 5 6 7 8 9 10 11 12 Tangent stiffness Kt (N/mm 3₎

Maximal friction stress (MPa)

µ s = 0,1 µ s = 0,2 µ s = 0,3 µ s = 0,4 µ s = 0,5 µ s = 0,6

Fig. 6 Evolution of the maximal friction stress in the contact elements following an increase of tan-gent stiffness, for fixed values of static friction coefficient (range 0.1–0.6), normal stiffness, and contact cohesion (60 MPa)

Figure 9 represents a comparison between the totally debonded implant and the osseointegrated implant for the stair-climbing load case. Again, the CF/PA12-implanted femur is subjected to higher stresses (27 and 19 MPa in debonded and osseointe-grated states respectively) than its Ti–6Al–4V-implanted counterpart (20 and 16 MPa in debonded and osseointegrated states respectively) on the lat-eral proximal femur. In totally debonded state, the lateral side of the femur experienced the highest loads; in the osseointegrated state, the highest loads were on the medial side of the femur.

In general, stresses were higher for the debonded state compared with the osseointegrated state,

regardless of the load case or stem material used. The highest stress reduction is located in the calcar region. The lateral side of the femur is also less stressed with any type of implant and load case.

3.2.2 Micromotions at bone-implant interface

Figure 10 shows micromotions in the proximal part of the stem for the stair-climbing and one-leg stance load cases (non-osseointegrated state). For the stair-climbing load case, micromotions reach a peak of 124 mm for the composite stem and 85 mm for the Ti–6Al–4V stem; for the one-leg stance load case, the maximal values are 211 mm for the composite stem Fig. 7 Von Mises stress in the proximal femur for one-leg stance loading, non-osseointegrated

implants (Kn= 2000 N/mm, ms= 0.4, Kt= 0 N/mm, b = 0 MPa): (a) healthy femur; (b) CF/

PA12 stem; (c) Ti stem. In the calcar region, stresses reached 33 MPa for the healthy femur, 22 MPa for the CF/PA12-implanted femur, and were as low as 11 MPa for the Ti-implanted femur (the stress concentration zone seen on the abductor crest of the Ti model is the abductors load application point)

Fig. 8 Von Mises stress in the proximal femur for 1 km/h walk loading, completely osseointe-grated implants (Kn= 2000 N/mm, ms= 0.4, Kt= 1000 N/mm, b = 15 MPa): (a) healthy femur;

(b) CF/PA12 stem; (c) Ti stem. In the calcar region, stresses reached 15 MPa for the healthy femur, 12 MPa for the CF/PA12-implanted femur, and 8 MPa for the Ti-implanted femur (the stress concentration zone seen on the abductor crest of the Ti model is the abductors load application point)

and 92 mm for the Ti–6Al–4V stem. For both types of implant, these peak values are contained within a relatively small similar area of the stem surface and most of the proximal stem surface shows micromotions under the osseointegration-required threshold value of 40 mm [13]. The higher values are contained within a small zone for the CF/PA12 stem, but distributed over a wider surface for the Ti–6Al–4V stem.

Table 5 presents the percentages of surface sub-jected to micromotions of the proximal implant sur-faces presented in Fig. 10, allowing for a more quantified evaluation of micromotions at the bone– implant interface. For the one-legged stance load Fig. 10 Anterior view of micromotions at the bone–

implant interface for stair-climbing and one-leg stance loading, non-osseointegrated (Kn=

2000 N/mm, ms= 0.4, Kt= 0 N/mm, b = 0 MPa)

implants: (a) CF/PA12 in stair climbing; (b) Ti in stair climbing; (c) CF/PA12 in one-leg stance; (d) Ti in one-leg stance. For both load cases, the CF/PA12 stem shows higher micro-motions in a small region located proximally (maximum of 124 mm for stair climbing and 211 mm for one-leg stance), whereas the Ti stem shows higher micromotions distributed over its surface (maximum of 85 mm for stair climbing and 92 mm for one-leg stance) Fig. 9 Von Mises stress in the proximal femur for

stair-climbing loading, non-osseointegrated (Kn= 2000

N/mm, ms= 0.4, Kt= 0 N/mm, b = 0 MPa) and

osseointegrated (Kn= 2000 N/mm, ms= 0.4, Kt=

1000 N/mm, b = 15 MPa) case: (a) healthy femur; (b) debonded CF/PA12 stem; (c) debonded Ti stem; (d) osseointegrated CF/PA12 stem; (e) osseointegrated Ti stem. In the calcar region, stresses reached 20 MPa in the healthy femur, 12 MPa in the CF/PA12-implanted femur, and 8 MPa in the Ti-implanted femur (non-osseointe-grated case). In the osseointe(non-osseointe-grated case, stresses in the calcar region are slightly lower for both implants (the stress concentration zone seen on the abductor crest of the Ti model is the abduc-tors load application point)

Table 5 Percentages of surface subjected to micromotions in the titanium and composite stems, for the one-legged stance and stair-climbing load cases

Micromotions Stem model and load case

Ti–6Al–4V stem Composite stem

One-legged stance (%) Stair climbing One-legged stance Stair climbing

< 40 mm 78.3 97.8 73.8 94.9

40\x < 60 mm 11.5 1.1 7.9 3.0

60\x < 100 mm 10.1 1.2 11.5 1.4

100\x <150 mm 0.1 0 3.1 0.6

. 150 mm 0 0 3.7 0

case, the percentage of implant surface subjected to micromotions less than 40 mm is 78.3 per cent for the Ti–6Al–4V stem and 73.8 per cent for the compo-site stem. For the stair-climbing load case, the per-centages are 97.8 per cent for the Ti–6Al–4V stem and 94.9 per cent for the composite stem.

Osseointegrated interfaces lead to very low micromotions in all models and load cases, as expected from a perfectly bonded implant (values below 10 mm).

4 DISCUSSION

The numerical investigation of the biomimetic stem performance using the previously validated finite element method [40] showed significant differences in the stress distribution between the CF/PA12 com-posite and Ti–6Al–4V implants. Higher micromo-tions levels were reported for the composite stem, but their dependence on contact element para-meters that had not been experimentally evaluated was demonstrated.

The contact element study yielded four important parameters: tangent and normal rigidity, static fric-tion coefficient, and contact cohesion. Normal rigidity and static friction coefficient are recognized in the lit-erature as two governing parameters of the overall behaviour of contact elements used as a bone– implant interface [14, 15]. To the authors’ knowledge, most studies do not mention contact cohesion and disregard tangent rigidity since they only focus on primary implant stability. In this case, osseointegra-tion has not occurred and fricosseointegra-tion holds the implant in place. In the case where secondary stability is mod-elled, mechanical interlock holds the implant in place and offers a resistance to shear forces. Surface-to-surface elements based on classic frictional contact mechanics reproduce well the experimentally obser-ved behaviour for primary stability; use of contact cohesion allows for modelling of the secondary stabi-lity by creating a linear resistance to shear forces.

Micromotions distributions at the bone–implant interface showed higher maximal values for the composite stem than for the Ti–6Al–4V stem. Other authors have come to the same conclusions, numeri-cally and clininumeri-cally [9, 11]. However, micromotions obtained in the present study do not exceed the threshold limit of osseointegration on most of the composite stem surface, even though a worst-case fixation scenario was simulated. Furthermore, the anatomical stem shape used in the present study is known to be non-optimal for micromotions at the bone–implant interface. Other cross-sectional geo-metrical shapes (rectangular or tapered implants

with rounded edges in particular) are known to be more stable because of increased torsional stability [52] attributed to increased local contact pressures. It would therefore seem possible for the composite stem to achieve stable fixation over a sizeable por-tion of its surface, leading to acceptable secondary (long-term) stability and a clinically stable implant. These results will need to be verified on smaller implant size, and on other types of implants.

Obtaining secondary stability is more challenging, however, since bone ingrowth modelling is involved. Some authors have proposed an approach based on evolution of contact parameters [15] that effectively reduces micromotions over time, but still relies on mechanical contact and interlocking without adhe-sion. Others [11] use an approach based on conti-nuum damage mechanics (CDM) and an ‘interface bonding degree’ that seems to produce accurate results. This approach requires iterative simulation and is less interesting from a computing costs per-spective. The use of contact cohesion as a bonding degree allowed the implementation of a simpler, computationally efficient approach that can be used in a static simulation to obtain preliminary results very quickly.

The HA layer of the biomimetic implant upon which the modelling of the bone implant is based will disappear over time as it is slowly absorbed by the surrounding bone tissue. However, the present team showed in two animal studies [42, 43] that the composite exhibited bone apposition at least as good as that obtained on textured Ti–6Al–4V and cell penetration in the implant surface, and therefore seems appropriate for osseointegration. The animal study on rats [43] also suggested that the purposely generated particulate debris did not prevent bone apposition or induce osteolysis, at least in the short time period considered (7 weeks). However, a long-term animal study will be necessary to alleviate osteolysis concerns and to assess the long-term bio-compatibility of the biomimetic material wear deb-ris, as well as wear resistance studies on the material itself. Micromotions will persist even in a well-osseointegrated implant, and wear particles are likely to be produced by friction with a non-osseoin-tegrated section of the implant surface.

The numerical evaluation of the new biomimetic stem performance revealed significant changes in bone stress distribution. The changes were most obvious in the one-legged stance load case because of the higher magnitudes in load levels, but the same trends could be observed in all three load cases. The calcar region is noticeably more stressed in the CF/PA12-implanted femur, osseointegrated or not. The proximal lateral side of the femur also

shows a stress increase, albeit the change is much less drastic. The composite stem does not restore the natural stress state found in the healthy femur, but appears to keep a healthier (higher) level of stress in the proximal femur, preventing, or at least limiting, bone remodelling. These results are in accordance with clinical studies on preservation of bone stock with isoelastic stems [4, 53], and with the Epoch composite stem, a polymer stem with an internal metallic backbone [54].

Some limitations remain in the current study. One of these is the fact that nearly ideal contact sur-faces were used to model the contact between stem and bone in both the non-osseointegrated and osseointegrated cases, and that the area of contact might be largely overestimated compared to real clinical situations. Only one implant size was used. This could affect micromotions results. Also, a com-posite femur was used, meaning inter-patient varia-bility is not accounted for in the current study. The HA layer will disappear over time, possibly leading to increased wear particle production in areas not covered by bone.

The stress distribution observed when the stem is modelled as perfectly osseointegrated changes from the one observed when it is modelled as debonded. However, bone remodelling takes place concur-rently with osseointegration, altering stress distribu-tion even further. Thus, osseointegradistribu-tion of the implant could be either prevented or promoted at different locations. Bone remodelling and stem osseointegration should be accounted for simulta-neously in an iterative loading scheme to provide some insights to this question.

Bone remodelling simulations of the CF/PA12-implanted femur should also be performed to address the issues raised by the non-negligible lev-els of interface micromotions and changing stress distributions. These simulations should include a stress-sensitive bone–implant interface capable of adapting to altered stress levels and micromotions in order to allow progressive implant osseointegra-tion as well as aseptic loosening. Other implant shapes should also be investigated, as a geometric optimization of the biomimetic stem could reduce micromotions and help promote osseointegration. Further finite element models should use computed tomography (CT) scan-based femurs rather that composite femur models.

Finally, more animal and biological studies need to be conducted to assess the long-term bioactivity of wear debris from the composite stem, as well as mechanical testing with cadaver bones and fatigue strength testing of the stem, particularly of smaller implant sizes.

5 CONCLUSIONS

The finite element method was used to make a pre-liminary assessment of the performance of a new bio-mimetic femoral stem based on CF/PA12 composite. The bone–implant interface was first investigated and a modelling technique was developed to simulate pri-mary and secondary stability. Stress shielding and bone–implant interface micromotions were evaluated based on this improved interface model.

Although stress shielding was significantly reduced in the CF/PA12-implanted femur compared to the Ti–6Al–4V-implanted femur, it was not com-pletely eliminated. Since the THA procedure involves osteotomy at the femoral neck, loads that were transferred through the subchondral trabecular bone in the healthy hip are now transferred through the stem and shaft of the femur. Thus a certain amount of stress shielding and bone remodelling cannot be avoided, but the use of a biomimetic stem appears to reduce the phenomenon considerably.

Micromotions levels remained a valid concern with the composite stem; depending on the load case used, they can reach a maximal value above the threshold for osseointegration. However, only a small area of the stem surface was subjected to those higher micromotions. Also, it should be remembered that the geometric shape of the implant is non-optimal and likely to have produced higher micromotions than other, more optimized types of implants. Osseointegration would therefore seem possible on most of the stem surface, leading to a clinically stable implant.

FUNDING

This work was supported by the Natural Sciences and Engineering Research Council of Canada. CONFLICT OF INTEREST

None of the authors has financial or personal rela-tionships with other people or organizations that could inappropriately influence or bias the currently presented work.

Ó_{Authors 2011}

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Notation

b contact cohesion

Ex,y,z material modulus of elasticity (in x,

y, and z directions)

FX,Y,Z load applied (in x, y, and z

directions)

Gxy, yz, xz material modulus of shear (in xy, yz,

and xz directions)

Kn contact stiffness in normal direction

Kt contact stiffness in tangential

direction

P contact pressure

un contact penetration distance

uy,z contact slip distance in y and z

directions

m_s static friction coefficient

nxy, yz, xz material Poisson’s ratio (in xy, yz,

and xz directions)

tlim limit value of tangential contact

stress

ty,z tangential contact stresses (y and z

directions)