Effect of porous orthopaedic implant material and structure on load sharing with simulated bone ingrowth: A finite element analysis comparing titanium and PEEK

Abstract

Osseointegration of load-bearing orthopaedic implants, including interbody fusion devices, is critical to long-term biomechanical functionality. Mechanical loads are a key regulator of bone tissue remodeling and maintenance, and stress-shielding due to metal orthopaedic implants being much stiffer than bone has been implicated in clinical observations of long-term bone loss in tissue adjacent to implants. Porous features that accommodate bone ingrowth have improved implant fixation in the short term, but long-term retrieval studies have sometimes demonstrated limited, superficial ingrowth into the pore layer of metal implants and aseptic loosening remains a problem for a subset of patients. Polyether-ether-ketone (PEEK) is a widely used orthopaedic material with an elastic modulus more similar to bone than metals, and a manufacturing process to form porous PEEK was recently developed to allow bone ingrowth while preserving strength for load-bearing applications. To investigate the biomechanical implications of porous PEEK compared to porous metals, we analyzed finite element (FE) models of the pore structure-bone interface using two clinically available implants with high (> 60%) porosity, one being constructed from PEEK and the other from electron beam 3D-printed titanium (Ti). The objective of this study was to investigate how porous PEEK and porous Ti mechanical properties affect load sharing with bone within the porous architectures over time. Porous PEEK substantially increased the load share transferred to ingrown bone compared to porous Ti under compression (i.e. at 4 weeks: PEEK = 66%; Ti = 13%), tension (PEEK = 71%; Ti = 12%), and shear (PEEK = 68%; Ti = 9%) at all time points of simulated bone ingrowth. Applying PEEK mechanical properties to the Ti implant geometry and vice versa demonstrated that the observed increases in load sharing with PEEK were primarily due to differences in intrinsic elastic modulus and not pore architecture (i.e. 4 weeks, compression: PEEK material/Ti geometry = 53%; Ti material/PEEK geometry = 12%). Additionally, local tissue energy effective strains on bone tissue adjacent to the implant under spinal load magnitudes were over two-fold higher with porous PEEK than porous Ti (i.e. 4 weeks, compression: PEEK = 784 ± 351 microstrain; Ti = 180 ± 300 microstrain; and 12 weeks, compression: PEEK = 298 ± 88 microstrain; Ti = 121 ± 49 microstrain). The higher local strains on bone tissue in the PEEK pore structure were below previously established thresholds for bone damage but in the range necessary for physiological bone maintenance and adaptation. Placing these strain magnitudes in the context of literature on bone adaptation to mechanical loads, this study suggests that porous PEEK structures may provide a more favorable mechanical

1. Introduction

Orthopaedic implants used to treat degenerative joint conditions of the spine, hip, shoulder, and knee bear and transmit substantial mechanical loads during day-to-day activities. To maintain biomechanical function for the patient, implant surfaces must osseointegrate with the adjacent bone tissue so that the bone-implant construct can effectively transfer loads as a cohesive unit (Albrektsson and Johansson, 2001). Loss of osseointegration can cause implant loosening and require revision surgery (Sundfeldt et al., 2006; Branemark, 1983). Several decades ago, stainless steel, cobalt-chromium, tantalum, and titanium implants with texturing or porous surfaces were introduced to permit bone ingrowth into the porous layer and enhance mechanical interlock between the implant and bone (Homsy et al., 1972; Hahn and Palich, 1970; Kienapfel et al., 1999). While the addition of surface texturing and porosity to implants through techniques like bead sintering, fiber metal meshing, and plasma spraying have improved implant fixation in the short term (Kienapfel et al., 1999; Camron et al., 1976; Levine et al., 2006; Sumner et al., 1995), long-term retrieval studies have sometimes demonstrated limited ingrowth into the pore layer of such metal implants and implant loosening remains a significant clinical problem for a subset of patients (Sundfeldt et al., 2006; Bobyn and Engh, 1984; Galante and Jacobs, 1992).

Of the factors that could contribute to loss of implant fixation after surgery, it is well documented that both cortical and trabecular bone remodeling is heavily regulated by the local mechanical stimulus (i.e. stress and strain magnitude) within the tissue. Excessive early loading of implants with poor primary stability prior to osseointegration can cause interfacial micromotion and supraphysiological strains exceeding 30%, stimulating fibrosis on the implant surface and bone-implant instability (Pilliar et al., 1986; Wazen et al., 2013). On the other hand, consistent mechanical loading of implants with sufficient primary stability is critical to bone tissue formation and maintenance (Frost, 1987; Ozcivici et al., 2010; Klosterhoff et al., 2017). The strain magnitude range where bone formation is enhanced is dependent on the maturity of the loaded tissue. For intact bone tissue, experimental studies have established that moderate magnitude strains of 0.1–0.3% (1000–3000 microstrain) promote local bone formation, and reductions in mechanical stimuli drastically increase the likelihood of bone resorption (Rubin and Lanyon, 1985, 1987; Schulte et al., 2013; Bhatia et al., 2015). This strain threshold is slightly higher in healing bone defects, where in vivo models have indicated that direct intramembranous ossification of the defect tissue is predominant at a strain magnitude of approximately 1% (10,000 microstrain) (Miller et al., 2015). When porous metallic implants were first introduced, a number of experimental and computational basic science investigations applied mechanoadaptation principles to implant specific geometries and observed that high stiffness metal implants alter the distribution of strain and shield loads away from bone adjacent to or within the pore structure of the implant, thus reducing mechanical stimuli below physiological levels in some regions (Huiskes et al., 1987, 1992; Guldberg et al., 1997). These findings suggest that sustained implant-mediated stress-shielding can cause bone resorption over extended timescales, and is a feasible mechanistic explanation for clinical observations of long-term bone loss and implant loosening in predictable regions that bear reduced loads after surgery (Engh et al., 1987; Bobyn et al., 1992; Nagels et al., 2003). From a biomechanical perspective, it follows that stress-shielding may be alleviated through two approaches: using materials with a lower intrinsic elastic modulus more similar to bone, or designing implants with less material to reduce the apparent stiffness of the implant in situ. Implants incorporating these design principles may produce a more physiologically favorable mechanical environment for adjacent and ingrown bone to support long-term osseointegration (Bobyn et al., 1992; Sumner and Galante, 1992).

One widely used orthopaedic implant material with promising mechanical properties from a mechanobiological perspective is poly-ether-ether-ketone (PEEK) (Kurtz and Devine, 2007). PEEK comprises the majority of spinal interbody fusion devices (IBD’s, more popularly “cages”) because of its radiolucent imaging characteristics and mechanical properties that are more similar to bone than metals. The reduced elastic modulus of PEEK indicates that it may improve load sharing between the implant and surrounding tissue compared to metals. Concurrently, new metal processing techniques including electron beam and selective laser melting (i.e. 3D-printing) have facilitated the manufacture of titanium implants with highly porous surfaces and architectures mimic trabecular bone (Warnke et al., 2009). However, the effect of these newly developed porous metals and porous polymers on load sharing with ingrown and adjacent bone have not been explicitly compared.

To investigate the biomechanical implications of porous PEEK compared to porous metals like titanium, we analyzed finite element (FE) models generated directly from high-resolution microcomputed tomography (microCT) scans of two clinically available spinal implants with high (> 60%) porosity, one being constructed from PEEK (COHERE®, Vertera Inc., Atlanta, GA) and the other from titanium (Tesera Trabecular Technology™, Renovis®, Redlands, CA). The objective of this study was to investigate how porous PEEK and porous titanium mechanical properties affect load sharing with adjacent bone and the mechanical stimulus transmitted to bone within clinically available porous architectures over time under relevant spinal load magnitudes. To decouple the effect of PEEK and titanium’s intrinsic mechanical properties from differences in the three-dimensional porous architecture of the two different devices, we assigned the mechanical properties of both PEEK and titanium to each of the two porous implant geometries and studied the mechanical environment in all cases under compression, tension, and shear. We hypothesized that the significantly lower elastic modulus of PEEK compared to titanium would increase load sharing with adjacent bone and enhance local strain transfer to bone within the pore layer regardless of pore architecture or level of bone ingrowth.

2. Materials and methods

2.1. Imaging

One representative sample of porous PEEK (COHERE®, Vertera Inc., Atlanta, GA) and porous titanium (Ti; Tesera Trabecular Technology™, Renovis®, Redlands, CA) was scanned at a resolution of 17.2 and 24.3 μm, respectively using microCT (microCT 50, Scanco Medical, Brüttisellen, Switzerland). The scanner was set at 90 kVp and 200 μA for Ti, and 55 kVp and 200 μA for PEEK. To characterize the pore morphometrics of each device, the full thickness of the porous structures were manually contoured and a threshold was applied to segment porous PEEK and porous Ti from their respective scan in a similar fashion to previous pore layer characterizations (Evans et al., 2015). Direct distance transformation methods was used to quantify porosity, strut spacing, strut thickness, pore structure depth, and pore interconnectivity (Hildebrand et al., 1999). Mean ± standard deviation, where applicable, of the pore structure morphometrics are reported in Table 1, and statistical differences between porous PEEK and porous Ti were assessed by Student’s t-test. Both materials had high porosity (> 60%) and interconnectivity (> 99.9%). Strut spacing, an estimation of pore size, was twice as large for porous Ti compared to porous PEEK (Ti = 607 ± 277 μm vs. PEEK = 263 ± 73 μm, p < .05), as was strut thickness (Ti = 277 ± 92 μm vs. PEEK = 99 ± 42 μm, p < .05). The pore structure for porous Ti was approximately 50% deeper than porous PEEK (Ti = 1263 ± 93 μm vs. PEEK = 829 ± 100 μm, p < .05). After evaluation, thresholded images of a rectangular portion of each device including the underlying bulk solid were smoothed with a Gaussian filter (sigma=0.8, support=1) and exported as DICOM image stacks for mesh generation. Porous PEEK and porous Ti structures were imaged by scanning electron microscope at 25× and 50×. (Hitachi S-3700N VP SEM, 10 kV, 25 Pa) (Fig. 1).

Table 1.

Mean porous architecture parameters from microCT data presented as mean of one sample of each porous structure, ± standard deviation across the surface of the sample is included where applicable.

	Porous PEEK	Porous Ti
Porosity (%)	71.15%	64.37%
Strut Spacing (μm)	263 ± 73*	607 ± 277
Strut Thickness (μm)	99 ± 42*	277 ± 92
Pore Structure Depth (μm)	829 ± 100*	1263 ± 93
Interconnectivity (%)	99.997%	99.928%

^*, p < .05, PEEK vs. Ti.

Fig. 1.

SEM images of (A, B) PEEK and (C, D) Ti porous structures acquired at 25× and 50× magnifications, respectively. (Scale bars: a, c = 1 mm; b, d = 500 μm).

2.2. Finite element model and convergence analysis

The DICOM images were converted to finite element meshes using Simpleware ScanIP+FE software (Synopsys, Mountain View, CA). A threshold-driven region growing algorithm was used to segment the PEEK and titanium material from the surrounding air. The model geometry was smoothed with a discrete Gaussian filter, and any unconnected fragments were removed. Models were cropped to span approximately 8 pores along an edge, and a rectangular slab of simulated mature bone tissue was abutted to the porous surface. Four layers of tissue for simulating bony ingrowth were then created by dilating the external surface of the porous material by two voxels per layer in all directions (Fig. 2). This resulted in a layer thickness of 52 μm for the PEEK geometry and a layer thickness of 141 μm for the titanium geometry. Each layer was assumed to represent 4 weeks of bony ingrowth, providing an equal number of time steps for both models. As described below, each model’s geometry was used to simulate mechanical behavior using both PEEK and titanium material properties, providing the ability to decouple the influence of the porous architecture and height from the material properties.

Fig. 2.

Finite element models of porous PEEK and titanium were generated from microCT imaging. Rectangular regions of the structures were abutted to a rectangular slab of simulated mature bone tissue. (A, D) Side views of the unmeshed porous structure-bone model and (B, E) isometric views of the porous structure, for PEEK and Ti respectively. (C, F) Bone ingrowth into the pore structure was simulated by dilating the external surface of the porous material in all directions in four discrete layers, each representing 4 weeks of bony ingrowth. Note: PEEK and Ti models are not depicted at same scale.

Bone, PEEK, and Ti were modelled as linear elastic, homogeneous, isotropic solids. Constant mechanical properties were assigned to PEEK (E = 3 GPa, ν = 0.33) and Ti (E = 109 GPa, ν = 0.33) at all modelling time points. At the first modelling time point, simulating the configuration immediately after implantation, the implant material and rectangular bone surface were included. Bone tissue formation within the porous structure was simulated by adding a new layer of bone at each 4-week time step, until the entire pore space was filled. From the second time point on, each layer of new bone tissue was sequentially assigned bone mechanical properties in discrete steps. To simulate mineralization and maturation within each layer of bone over time, microCT mineral density data of tissue ingrowth from a previous in vivo study evaluating porous PEEK in a rat femoral segmental defect was converted to elastic modulus using the relationship of Wagner, et al., (Eq.(1)) where E is elastic modulus (in GPa) and ρ is mineral density (in g/ cc) (Evans et al., 2015; Wagner et al., 2011):

$${\text{log}}_{10}E=-8.58+4.05{\text{ log}}_{10}\left(400/\left(1+\frac{0.504}{\rho }\right)\right)$$ (1)

With each subsequent time point, an additional layer of new tissue was assigned bone properties and previous layers of bone were assigned increased moduli based on the bone layer age progression outlined in Table 2. By 28 weeks (the seventh modelling time point), all four layers of bone are assumed to be fully mineralized and the model has reached a steady-state.

Table 2.

Temporal progression of mechanical properties assigned to bone ingrowth on a layer-wise basis.

Bone Layer Age (weeks)	Mineral Density (mg/cc)	Young’s Modulus (GPa)	Poisson’s Ratio
4	572	7	0.3
8	829	13	0.3
12	882	15	0.3
16	983	17	0.3
20	983	17	0.3
24	983	17	0.3
28	983	17	0.3

Models were meshed with linear 4-node tetrahedrons using ScanIP +FE’s adaptive meshing algorithm, which refines the mesh in areas of high curvature while allowing coarser elements in areas of lower curvature. A convergence study was run to determine the appropriate mesh sizes for the PEEK and titanium models. The reaction force required to produce 0.5% compressive strain was used as a metric for convergence, as this value provides a measure of overall model stiffness. As a second mesh quality criterion, it was also required that each layer of bone be at least two elements thick. Meshes that included the first two layers of bone tissue were refined until the reaction force changed by less than 1%. Meshes ranging in size from 644,291 elements and 116,726 nodes to 2017,244 elements and 377,981 nodes were tested. The final mesh for the PEEK geometry with full bone ingrowth had 184,652 nodes and 1028,771 elements with an edge size ranging from 45 to 110 μm. The final mesh for the titanium geometry with full bone ingrowth had 172,396 nodes and 962,821 elements with an edge size ranging from 158 to 387 μm.

2.3. Load sharing studies

Once the mesh geometry and mechanical properties were established, the portion of load carried by either the bone or the implant was evaluated under compressive, tensile, or shear load. Compression simulations were conducted at all 7 time points described in Table 2, and shear and tension cases were analyzed at the first and last time points (4 and 28 weeks). For all three load cases, a displacement equivalent boundary condition of 0.5% global strain was applied to the top surface of PEEK or Ti. In compression at the initial time point, contact constraints were enforced at the interface between bone and the porous surface (μ = 0.2, (Sampaio et al., 2016)), where no bone ingrowth had occurred. Perfect bonding between surfaces was assumed for time points thereafter. To simulate unconfined compression, the bottom surface of the bone was fixed in the up/down direction (normal to the porous surface). The sides of the implant and bone were constrained to remain planar, accounting for the fact that the model represents a small segment sample of the bone-implant interface confined within a larger system. In tension, the planar constraints were applied to the sides of the model, the bottom of the bone surface was fixed in the up/down direction, and perfect bonding between surfaces was assumed for all time points. For shear simulations, the planar constraints were applied to the sides of the models, the bottom surface of the bone was fixed in all directions to prevent lateral rigid body movement, and perfect bonding between all layers was assumed at all time points. The resultant loads to reach 0.5% global strain are reported in Supplementary Tables 1–3.

To decouple the effects of pore architecture from the effect of elastic modulus, simulations were also analyzed where PEEK’s mechanical properties were applied to the porous Ti geometry and titanium’s mechanical properties were applied to the PEEK geometry at 4 and 28 weeks. Load share for each component was defined as the total force carried by the cross-section of either component (implant or bone) at the midpoint of the pore layer.

2.4. Bone tissue strain studies

Linear transformations were performed to determine strain values subjected to 5 MPa of applied stress for compressive, tensile, and shear cases. The principal strains at the centroid of each element within Layer 1 were computed to isolate the mechanical environment within the first layer of bone ingrowth adjacent to the implant surface. Using the de-finition of Mikić and Carter (Eq. (2)), the average energy effective strain $(\overline{\epsilon })$ was computed for each element to obtain a scalar representation of the overall triaxial strain state of each element where ε_I,ε_II and ε_III the principal strains and ν is Possion’s ratio):

$$\overline{\epsilon }=\sqrt{(1-\nu )\left({\epsilon }_I^2+{\epsilon }_{II}^2+{\epsilon }_{III}^2\right)+2\nu \left({\epsilon }_I{\epsilon }_{II}+{\epsilon }_{II}{\epsilon }_{III}+{\epsilon }_I{\epsilon }_{III}\right)}$$ (2)

2.5. Statistical analysis of tissue strain distribution

In addition to observing the effect of porous PEEK and porous Ti on the average strain within the adjacent ingrown bone, we also investigated the effects of the porous material on the spatial distribution of strains transmitted throughout the adjacent tissue layer for each loading mode and at early and late time points. The standard deviation, median, 1st quartile, 3rd quartile, and interquartile range were computed for porous PEEK and porous Ti in each loading case at 4 and 28 weeks. These descriptive metrics are presented in Table 3. The distribution of energy effective strain throughout the tissue layer was also analyzed by computing the standardized skewness and standardized kurtosis. In all cases, both metrics were found to greatly exceed the standard thresholds for normality (± 2), indicating the spatial distribution of strain in the tissue layer deviated significantly from a normal distribution and consequently, parametric statistical evaluation techniques were not valid. Instead, non-parametric Mann-Whitney U tests were used to assess pairwise differences in the median strain between porous PEEK and porous Ti in each loading case at 4 and 28 weeks. In addition, Kolmogorov-Smirnov tests were used to evaluate if there were differences in the shape of the energy effective strain distribution between PEEK and Ti. Thus, a significant result indicated that strains were distributed differently throughout the tissue layer in porous PEEK and porous Ti structures. StatGraphics Centurion software (v16, Statpoint Technologies Inc, The Plains, VA) was used for statistical analyses and p < .05 was defined as a statistically measurable difference. Data are presented as median ± standard deviation unless otherwise indicated.

Table 3.

Descriptive statistics for the distribution of energy effective strain in Layer 1 of bone ingrowth. Mann-Whitney U tests indicated the median strain for porous PEEK was significantly higher than porous Ti at both 4 and 28 weeks under compression, tension, and shear, indicating that tissue ingrowth into Ti was more strain-shielded. Kolmogorov-Smirnov tests indicated that the distribution of bone tissue strain with porous Ti was significantly different than the distribution with porous PEEK.

Material	Time (weeks)	Average (μstrain)	Standard Deviation (μstrain)	1st Quartile (μstrain)	Median (μstrain)	3rd Quartile (μstrain)	Interquartile Range (μstrain)	Mann-Whitney U Test (PEEK vs. Ti)	Kolmogorov-Smirnov Test (PEEK vs. Ti)
Compression
PEEK	4	816	351	604	784	985	381	*, p < .05	*, p < .05
Ti	4	304	300	103	180	377	274
PEEK	28	315	88	260	298	346	86	*, p < .05	*, p < .05
Ti	28	132	49	94	121	167	73
Tension
PEEK	4	835	359	618	802	1008	390	*, p < .05	*, p < .05
Ti	4	311	308	106	184	387	281
PEEK	28	317	88	262	300	349	87	*, p < .05	*, p < .05
Ti	28	133	50	95	122	168	74
Shear
PEEK	4	1663	714	1219	1639	2044	825	*, p < .05	*, p < .05
Ti	4	528	487	211	328	630	419
PEEK	28	587	186	462	563	679	217	*, p < .05	*, p < .05
Ti	28	225	93	157	208	281	124

3. Results

3.1. Load sharing studies

To evaluate the proportion of load transferred to bone within the porous structure, the percent of total load within the middle cross-section of the porous structure was computed under compression, tension, and shear loading. In addition to analyzing the load shared by the porous PEEK and porous Ti implants, the mechanical properties of each material were switched to provide a direct comparison of the effect of material irrespective of pore architecture. In total, load sharing was evaluated under 34 model scenarios. Under compressive loading in the PEEK model, bone began to bear the majority of load (66.5%) at the onset of mineralization along the implant surface at 4 weeks (Fig. 3). On the other hand, bone within the pore layer of the Ti implant only carried (12.7%) of the load at 4 weeks. Bone maturation altered load distribution to a greater extent in porous Ti between 4 and 28 weeks (additional 29.5% load share transferred to bone) compared to porous PEEK (15.8% additional load share transferred to bone). In both models, the load distribution asymptotically approached a steady-state, with almost no changes in proportions between 16 and 28 weeks. The equilibrium load carried by mineralized bone at full ingrowth was82.3% for porous PEEK and 42.2% for porous Ti.

Fig. 3.

Time evolution of load sharing of (A) porous Ti and (B) porous PEEK under compressive loading.

In addition to compression, porous PEEK substantially increased the load share transferred to the bone within the pores compared to porous Ti under both tensile and shear loading (Fig. 4A–B). Ingrown tissue bore the majority of the load within the central cross-section of the porous structure in all cases with porous PEEK, whereas porous Ti carried the majority of the load even after the pores were completely filled with mature bone tissue. Applying PEEK mechanical properties to the Ti implant pore geometry and vice versa demonstrated that the observed increases in load sharing with porous PEEK were primarily due to PEEK material properties instead of pore architecture (Fig. 4C–D). Pore architecture has a relatively small and variable effect on the degree of load sharing. For example, porous PEEK geometry increased load share carried by bone under shear, but porous Ti geometry increased load share carried by bone under compression. Bone maturation over time had the largest effect on load sharing under compression, whereas tension and shear had slightly smaller effects.

Fig. 4.

Load sharing between bone and implant under compression, tension, and shear at 4 and 28 weeks for (A) Ti geometry/Ti material (B) PEEK geometry/PEEK material (C) PEEK geometry/Ti material (D) Ti geometry/PEEK material. The majority of the load is carried by the bone with PEEK, and the majority of the load is carried by the implant with Ti, regardless of loading direction, level of ingrowth, or pore structure.

3.2. Bone tissue strain studies

To provide a direct comparison of local tissue strains within porous PEEK and porous Ti at physiological loads, strains from the aforementioned displacement boundary condition simulations were linearly transformed to compute strains under a 5 MPa distributed pressure applied to the top surface of each model, corresponding to a substantial loading event (Chatham et al., 2017). After linear transformation, the energy effective strain at the centroid of each finite element in Layer 1 of the bone ingrowth was computed. Initial analyses of standardized skewness and standardized kurtosis of strain within the tissue layer in all models indicated that local strains were not normally distributed throughout the tissue. Therefore, non-parametric statistical procedures were used to evaluate the differential effects of porous PEEK and porous Ti on strain throughout the Layer 1. Mann-Whitney U tests indicated the median strain for porous PEEK was significantly higher than porous Ti at both 4 and 28 weeks under compression, tension, and shear (Table 3). In compression, the average energy effective strain versus time for all bone in Layer 1 under compression is depicted in Fig. 5. The strain transferred to bone adjacent to porous PEEK is over two-fold higher than bone on porous Ti at each time point. As would be expected, the maximum tissue strains occur at 4 weeks when maturity and volume of the bone ingrowth is lowest (PEEK = 784 ± 351 microstrain; Ti = 180 ± 300 microstrain, p < .05). As additional bone is formed and mineral density increases, the strain in the tissue asymptotically approaches equilibrium where full ingrowth is assumed (PEEK: = 298 ± 88 microstrain; Ti = 121 ± 49 microstrain, p < .05). A similar substantial effect of PEEK mechanical properties was also observed in compression, tension, and shear at both 4 and 28 weeks, even when PEEK’s mechanical properties were applied to the Ti geometry and vice versa (Fig. 6). In all loading modes and time points, PEEK amplified transmission of strain to adjacent bone by over two-fold compared to Ti.

Fig. 5.

Mean energy effective strain in Layer 1 of bone ingrowth versus time under compressive loading for Ti and PEEK implants.

Fig. 6.

Mean energy effective strain in Layer 1 of bone ingrowth under (A) compression (B) tension (C) and shear at 4 and 28 weeks. All combinations of pore structure and material property are depicted.

3.3. Tissue strain distribution

In addition to observing differences in the average strain transferred to the tissue between PEEK and Ti, we were interested in differences in the distribution of strains throughout the tissue. Interestingly, Kolmogorov-Smirnov tests indicated that the distribution of strain with porous Ti was significantly different than the distribution with porous PEEK (Table 3). Exemplary strain distributions at 4 and 28 weeks under compression are depicted in Fig. 7. Heavily skewed distributions were observed throughout each model, and in particular were observed in Ti at 4 weeks, where the majority of the tissue experienced strains below 200 microstrain but some elements experienced higher local strains. These data indicate that the reduced elastic modulus of PEEK not only increases strain transfer to adjacent bone relative to Ti, but also distributes mechanical stimuli differently.

Fig. 7.

Histograms and distribution curves depicting relative frequency of energy effective strain on a per element basis in compression (A) at 4 weeks and (B) at 28 weeks.

4. Discussion

The objective of this study was to evaluate the effect of PEEK and Ti mechanical properties on the degree of load sharing with bone ingrowth into two clinically available highly porous implant architectures. Porous metal implants have been used in orthopaedic procedures for decades to enhance primary stability upon surgical implantation and to facilitate long-term mechanical interlock of the implant via bone ingrowth into the pores (Homsy et al., 1972; Bobyn and Engh, 1984; Matassi et al., 2013). However, limited (1.6–16.1%), superficial ingrowth into the outermost 500 μm of the pore structure has been observed in long-term retrieval analyses of metal implants (Sumner et al., 1995; Hanzlik et al., 2015, 2016, 2013), and retrospective studies have reported that aseptic loosening is the primary reason for approximately 52–55%, 29–30%, 38–40%, and 68% of revision surgeries for hip, ankle, knee, and shoulder arthroplasty procedures, respectively (Ulrich et al., 2008; Sadoghi et al., 2013; Deshmukh et al., 2005; Khan et al., 2016; Labek et al., 2013). While numerous mechanisms including transport limitations, implant wear, and micromotion can inhibit osseointegration, stress shielding in initially well fixed implants remains a significant clinical concern because conventional metals possess an elastic modulus much higher than bone, and predictable bone loss or hypertrophy have been observed for decades after hardware is implanted in regions where strain is reduced or increased, respectively (Bobyn et al., 1992; Nagels et al., 2003). From a mechanical standpoint, there are two methods to improve stiffness matching of orthopaedic implants: reducing the amount of material used to construct the implant, thereby reducing its apparent stiffness, or fabricating the implant from a material with a lower elastic modulus. Highly porous 3D-printed Ti has been proposed as an approach to increase porosity (from 30% to 50% to 60–70%) and generate architectural and mechanical properties more similar to bone, but the intrinsic elastic modulus of Ti is still substantially higher than bone (Klosterhoff et al., 2017; Matassi et al., 2013; Ryan et al., 2008). The ability to form porosity into PEEK, a significantly more compliant polymeric material widely used for orthopaedic implants, has recently been developed and deployed for use in cervical spinal fusion procedures, but the mechanical environment produced within the porous structure has not been evaluated (Evans et al., 2015; Torstrick et al., 2017).

In this study, high-resolution FE models of the porous implant-bone interface revealed that porous PEEK substantially increased load sharing with bone inside the pore structure compared to porous Ti in compression, tension, and shear. Importantly, the influence was demonstrated to be mediated primarily by differences in intrinsic elastic moduli between PEEK and Ti, as PEEK was observed to increase load sharing by at least 38% irrespective of the pore structure architecture or the level of bone ingrowth. The importance of load sharing is a fundamental aspect of bone physiology and is clearly established in the bone (re)modelling literature, where removal of sufficient mechanical stimulation results in rapid bone loss, a phenomenon designated as “disuse-mode remodeling” by Frost (Frost, 2001). Much research has been devoted to quantifying what constitutes a sufficient mechanical stimulus and detailed experimental and computational analyses of mechanical loading models have demonstrated that the effect of mechanical stimuli is mediated at the local tissue level in a magnitude and cycle number dependent manner (Ozcivici et al., 2010; Rubin and Lanyon, 1987; Schulte et al., 2013; Bhatia et al., 2015). A study on the human distal radius reported that local energy effective strain magnitudes in the range of 1000–2000 microstrain for 50 cycles a day, 3 days a week can increase local bone formation, which corroborated earlier, similar findings on cortical bone in the turkey ulna (Rubin and Lanyon, 1985; Bhatia et al., 2015). On the low-magnitude high-frequency end of the spectrum, an axial strain threshold as low as 70 microstrain at 30 Hz, similar to those produced by skeletal muscle contractions, can maintain bone mass (Qin et al., 1998). Interestingly, a similar non-linear daily strain history was reported to be conserved in weight-bearing and non-weightbearing bone sites across multiple species (Fritton et al., 2000). Thus, it appears that bone quality and mass is maintained in part by a basal level of mechanical stimulus across a range of magnitudes.

Undoubtedly, an orthopaedic implant experiences both relatively infrequent, high-magnitude strain events, and persistent low-magnitude postural adjustments throughout each day, and it can be approximated that the dynamic strains transferred to the tissue under each cycle is proportional to the stiffness of the implant. Thus, relative differences in structural and mechanical properties between implants play an important role in the mechanical environment they produce in adjacent bone. To assess the local mechanical stimulus transmitted to the bone within the porous structures in this study, we computed the energy effective strain (Mikić and Carter, 1995), a scalar description of the overall strain state, within the adjacent layer of bone tissue when a 5 MPa stress was placed on the implant. This stress corresponds to five-fold higher than the peak von Mises stress at the vertebral end plate-cage interface prior to bone ingrowth in a posteriorly instrumented lumbar spine of an adult standing up from a chair, as predicted by an experimentally validated FE model (Chatham et al., 2017). PEEK was observed to increase the local strain by at least two-fold in compression, tension, and shear, regardless of the pore architecture or level of bone ingrowth. In compression at the initial 4 week time point where strains are highest, porous PEEK produced 784 ± 351 microstrain and porous Ti produced 180 ± 300 microstrain. In the context of bone adaptation, the strains produced in bone tissue within porous Ti corresponded with disuse-mode remodeling, whereas porous PEEK produced a more favorable mechanical environment for bone formation and maintenance (Bhatia et al., 2015). Importantly, the strains produced by the porous PEEK remained below thresholds where fracture, fatigue failure, or inhibition of new bone formation can occur (5000–10,000 microstrain) (Miller et al., 2015; Morgan and Keaveny, 2001; Carter et al., 1981). As maturation of the tissue in the pore layer was incrementally simulated to reach 100% ingrowth, strains decreased asymptotically to 298 ± 88 microstrain for PEEK and 121 ± 49 microstrain for Ti. At this point, the literature indicates that the mechanical environment in both implants is more in the range of increased risk of resorption (Bhatia et al., 2015). However, it is important to note that 100% ingrowth of full mature bone is not observed clinically in short-term studies on metal implants, where ingrowth levels varying anywhere from 10% to 50% are observed (Jensen et al., 2005). Furthermore, as mentioned previously, long-term retrieval studies have reported substantially less ingrowth in porous metals, between 1.6% and 16.1%, suggesting that bone resorption may occur within porous metal structures over time (Sumner et al., 1995; Hanzlik et al., 2015, 2016, 2013). In this regard, the final time point model scenario represents a theoretical lower limit on tissue strain under loading. Thus, the model demonstrates that the beneficial mechanobiological aspects of PEEK relative to Ti are conserved across a wide range of bone ingrowth levels, and that the mechanical environment produced by porous PEEK is favorable for bone maintenance at realistic levels of ingrowth. As mentioned earlier, mechanical stimulation for either Ti or PEEK could be increased by thinning struts or increasing pore size even further to reduce the apparent stiffness of pore structure, but it important to note that the correlation between porosity and stiffness and strength is non-linear at high porosities, as extremely thin struts make structures vulnerable to buckling failure and mechanical properties decrease rapidly at very high porosities (Gibson and Ashby, 1999). Further increases in porosity to Ti structures may close the gap in load sharing with PEEK, but porosities exceeding 70% could rapidly degrade implant mechanical strength and would warrant experimental testing.

As with any computational study, this analysis was conducted under several assumption and has some limitations. In the majority of simulations, the tissue was assumed to be bonded to the implant and translational movement between the implant and adjacent bone are neglected. This approach was selected because we chose to target analysis on the mechanical environment produced in porous structures where primary stability was achieved during surgical implantation and initial tissue ingrowth had occurred, which represents the desired surgical technique and actual situation in the majority of procedures. On the other hand, high magnitude interfacial micromotion (> 150 μm) generating shear strains exceeding 30% at very early time points can result in fibrosis and loss of implant fixation (Pilliar et al., 1986; Wazen et al., 2013). This implant behavior represents a different theoretical framework requiring a separate modelling approach from the investigation presented here, which could warrant targeted analysis in future studies of porous Ti and porous PEEK. Additionally, bone growth kinetics and mechanical properties were assumed to be spatially homogeneous in a layer-wise fashion throughout the pore layer, where the actual ingrowth process in vivo is spatiotemporally heterogeneous. This simplification was incorporated so that the mechanical properties at any given cross section of the model were similar between the two different pore structures. Additionally, the elastic modulus assigned to each layer of tissue accounted for tissue mineral density from in vivo data of tissue within the PEEK pore structure in a rat femoral defect model (Evans et al., 2015). Regardless of the osseointegration kinetics, the findings of this study suggest that PEEK enhances load transfer to ingrown tissue across a range of ingrowth levels and within two different porous architectures. A single stress magnitude of 5 MPa in uniaxial compression, tension, and shear was chosen for the tissue strain analysis in this study, which corresponds to a substantial load on a posteriorly instrumented lumbar interbody fusion device with no bone ingrowth (Chatham et al., 2017). Finally, linear elastic behavior was applied in consideration of the goal of this study: to capture relative differences in the mechanical environment produced by Ti and PEEK under normal physiological implant loads.

To summarize, porous PEEK was found to increase load sharing with adjacent bone compared to porous Ti, whereas porous Ti produced tissue strains that have been implicated in increasing the risk of bone resorption, regardless of the two pore architectures or levels of bone ingrowth investigated. The results of this study suggest that the lower intrinsic elastic modulus in porous PEEK structures may provide a more favorable mechanical environment for bone formation and maintenance under spinal load magnitudes than currently available porous 3D-printed Ti.