A Customized Distribution of the Coefficient of Friction of the Porous Coating in the Short Femoral Stem Reduces Stress Shielding

Abstract

Stress shielding and aseptic loosening have been identified as adverse effects of short-stem total hip arthroplasty resulting in hardware failure. However, there is a gap in research regarding the impact of stress shielding in customized porous coatings. The purpose of this study was to optimize the distribution of the coefficients of friction in the porous coating of a metaphyseal femoral stem to minimize stress shielding. Static structural analysis of an implanted short, tapered-wedge stem with a titanium porous coating was performed with the use of Analysis System Mechanical Software under axial loading. To limit computational time, we randomly sampled only 500 of the possible combinations of coefficients of friction. Results indicate that the coefficient of friction in the distal lateral porous coating significantly affected the mid-distal medial femoral surface and lateral femoral surface. The resultant increased proximal strains resulted from an increased coefficient of friction in lateral porous coating and a reduction in the coefficient of friction in medial mid-distal coating. These findings suggest that a customized porous coating distribution may produce strain patterns that are biomechanically closer to intact bone, thereby reducing stress shielding in short femoral stems.

1. Introduction

Total hip arthroplasty with short femoral stems is an effective treatment for hip osteoarthritis by increasing load distribution in the proximal metaphyseal bone and improving implant fixation and osseointegration [1,2,3,4]. Nevertheless, long-term complications, including aseptic loosening, poor bone ingrowth, and stress shielding, remain a serious impediment leading to hardware failure [5,6,7,8,9,10,11]. While primary stability is crucial for these stems until osseointegration occurs, studies have reported average femoral stem subsidence ranging from 0.39 to 1.04 mm during short-term follow-up [1,3,10].

Prevention of bone mass loss, cortical hypertrophy, and implant subsidence are addressed through alteration of the femoral stem geometry [12,13] or material properties [14,15,16,17,18]. Research using digital image correlation (DIC) and finite element analysis (FEA) [7,19] has shown that even within the same category of short stems, according to the Khanuja classification, differences in load transfer and stress shielding effects can be observed [3,20].

Stems with varying porosities have effectively reduced stress shielding while providing stable implant fixation through bone ingrowth [21,22]. Increasing graded porosity toward the distal end of stems has been found to promote osseointegration and decrease bone resorption [23,24]. Fully porous stems with axially graded stiffness have demonstrated the most significant benefit in minimizing stress shielding [25]. A preliminary FEA study on the distribution of friction coefficients in porous coatings showed a reduction in proximal stress shielding either by lowering friction in medial regions and increasing it distally on the lateral side or by increasing friction proximally while maintaining a value of 1.2 in the middle distal porous coating [26]. Despite these findings, further research on the mechanical behavior of porous coatings with customized friction coefficient distributions remains limited [21].

The purpose of this study was to investigate the distribution of friction coefficients in a porous coating placed on a short metaphyseal femoral stem and to customize it to reproduce the biomechanical behavior of physiological bone in the proximal region.

2. Methods

2.1. FEA Model

In this study, a 3D finite element analysis (FEA) model was developed for a short, tapered-wedge stem (TRI-LOCK Bone Preservation Stem, DePuy Orthopedics, Inc., Warsaw, IN, USA). A porous coating was applied to the proximal 50% of the stem in titanium alloy (Ti6Al4V) called “GRIPTION^®”. The average pore size was 300 μm, volume porosity 63%, and coefficient of friction 1.2, which is required for tissue ingrowth and vascularization, and this highly porous surface is central to tissue integration. Using Computer-Aided Three-dimensional Interactive Application (CATIA V5) software, the stem was implanted into a femur model to improve the accuracy of the simulation and analysis.

This study was based on previous published experimental results from axial load tests of a FEA model, which examined cortical surface strain distribution in both intact and implanted femurs [13,19] (Supplementary Material Figure S1). The materials used in the model included cortical bone and cancellous bone, with Young’s moduli of elasticity set at 16.7 GPa and 155 MPa, respectively, as recommended by Sawbones manufacturers [27,28,29,30,31]. A statistical comparison between the experimental and FEA models was performed at both macroscopic and microscopic levels through strain analysis and the Mann–Whitney/Wilcoxon rank sum test. The results showed no significant differences in strain distribution between the lateral (p = 0.443) and medial (p = 0.160) cortices in the experimental and FEA models, indicating a strong agreement between the two (Supplementary Material Figure S2). To ensure the consistency and accuracy of the test, each simulation was run twice.

The implant geometry was acquired from computed tomography imaging (DICOM files) and converted into .STEP files, and the porous coating on the femoral stem was refined for FEA with minor adjustments to ensure precision. The coefficient of friction, influenced by factors such as surface roughness, lubrication, temperature, and contact pressure, indirectly affected the porosity of the titanium alloy (Ti6Al4V) [32,33,34]. With the design of the Tri-Lock BPS short stem and the Ti6Al4V alloy set as constants, the study focused on varying the distribution of the coefficients of friction within the porous coating. The distribution of the coefficients of friction was examined under different axial loading conditions in the FEA model to assess its impact on biomechanical performance, particularly in terms of load transfer and stress shielding.

In the ANSYS Mechanical Software Workbench 2020 (R2), the bone and stem geometries were placed within space planes and assigned particular material properties. The contact interfaces between cortical and cancellous bone parts and between solid stem parts and the porous coat were set as bonded. The interfaces between the bone parts and solid stem parts were set as frictionless due to the smooth area of the solid part; on the contrary, the contact interfaces between the porous coating and the bone were modeled as frictional, according to Coulomb’s law of friction (Equation (1)).

$$F_{f}riction \le mu\ast F_{n}ormal$$

(1)

where $F_{f}riction$ is the frictional force; mu (μ) is the coefficient of friction; and $F_{n}ormal$ is the normal force.

Surfaces between the contact body and the target body were the contact parameters specified with the augmented lagrange formulation for the contacts. A penetration tolerance of 10% of element depth and an elastic slip tolerance of 1% average contact length allowed for slight movement without losing contact. A normal stiffness factor of 10 was applied to control contact stiffness. The analysis solver was set to detect any deflections, and the Newton-Raphson method was used to improve the solution until convergence to obtain accurate and stable results.

During an ipsilateral single-limb stance, the joint contact force is approximately 2.1 times the body weight, with peak forces ranging from 2.6 to 2.8 times the body weight. These forces evaluate the femur’s structural integrity and loading patterns under weight-bearing conditions during the stance phase of walking [35]. The adductor muscles counteract the torques generated by body weight to maintain stability [36]. According to Cristofilini et al. [37], the hip force should be applied at approximately 29° to the femoral diaphysis. In comparison, the abducting force should be used at about 40° to the femoral diaphysis.

The joint reaction force and abductor force angle at the femoral head center axis, relative to the body’s partial gravity and vertical ground line, ranged between 9 and 12 degrees [9]. In the study, the distal femoral end was positioned neutrally on the sagittal plane and angled 11 degrees in adduction on the frontal plane, replicating the natural inclination during a single-leg stance. Previously published data indicated a hip force of 2471 N applied at a 29° angle to the femoral diaphysis and an abducting force of 1556 N applied at a 40° angle to the femoral diaphysis [19] (Supplementary Material Figure S3).

Meshes of more than 2,196,924 nodes with either tetrahedral or hexahedral elements per model were used for FEA discretization. Body sizing was applied to specific mesh regions, providing smoother transitions between grading and a more refined mesh. An edge length of 2 mm was used at the cancellous and cortical bone interfaces. However, the porous coating and bone interfaces were set at an edge length of 0.5 mm, previously demonstrated in other studies to be adequate for mesh convergence and the fine distribution of material so that differentiation between cortical and cancellous bone areas can be adequately made [38,39]. Surface mesh density and element size were controlled by face sizing, which sharpened areas containing complex geometry and bone components. This resulted in a mesh comprising 1,526,318 elements, with an aspect ratio of 1.8506 ± 1.3451 and an element quality of 0.84239 ± 0.10224 (Supplementary Material Figure S4).

The behavior of the femoral stem under axial loading was analyzed through simulation using a static structural nonlinear analysis to determine strain distribution, displacement, and deformation. Biomechanical studies of the proximal femur have proposed that the difference in surface strain is an appropriate proxy for stress shielding [16,40]. Two paths were defined with 142 measurement points each to measure the principal maximal and minimal strains in the medial and lateral cortex. The points were set at 20 mm intervals from the proximal medial and lateral areas, up to a maximum distance of 140 mm, corresponding to Gruen zones 1 to 7 {M1, M2, M3, M4, M5, M6, M7, L1, L2, L3, L4, L5, L6, and L7} (Figure 1) [41].

In dry conditions, Ti6Al4V has a moderate coefficient of friction of about 0.4 to 0.6. However, when the femoral stem is implanted in the femur, the conditions of lubrication may vary due to blood and the properties of the cancellous bone. Moreover, the current market model, “model zero”, has a porous coating with one of the highest coefficients of friction, equal to 1.2, which, as discussed, may result in stress shielding in some femoral areas; thus a higher coefficient may be required. Increasing the coefficient of friction too much may result in higher stress concentrations at the interface and interfere with dynamic loading. Therefore, we decided to investigate a model with a distribution of coefficients of friction between 0.5 and 1.5. On the medial (I1, I2, I3, I4, and I5) and lateral (O1, O2, O3, O4, and O5) sides, the porous coating was segmented into 10 regions of height 2 mm. Seven possible values in the range {0.5, 0.7, 0.9, 1.1, 1.2, 1.3, and 1.5} were used for each region, except for O1, of which the value was fixed to 1.2 due to the meshing complication in that part of the porous coating. To measure this region, researchers put a metallic rod on the lateral side of the greater trochanter secured with epoxy glue to simulate the hip abductor muscles. All models were then compared to the ‘model zero’, which had a constant coefficient of friction of 1.2 across the porous coating.

2.2. Statistical Analysis

In this analysis, a finite set of constants {0.5, 0.7, 0.9, 1.1, 1.2, 1.3, and 1.5} was applied to nine variables {O2, O3, O4, O5, I1, I2, I3, I4, and I5}, while the value of O1 remained fixed. This configuration created a 79-node network with over 40 million unique nodes. Due to the complexity of the FEA model and its numerous parameters, testing all possible combinations was impractical. To manage this, 500 random pairs of samples were generated using a uniform random sampling of rows without replacement; as a consequence, we assure that all statistics of the variables O and I were comparably equal (mean and SD, as well as median and quartiles), and all variables O and I were mutually pairwise uncorrelated. The statistical analysis was performed using R software (R version 4.1.2) and the RStudio IDE (RStudio “Ghost Orchid”) development environment.

To achieve 12 hits, we have analyzed 500 different combinations of coefficients of friction in the porous coating area. A “hit” was defined as meeting the following criteria with a statistically significant difference compared to the “model zero” (p < 0.05): four proximal conditions required an increase in strain in the proximal femoral regions (M1, M2, L1, and L2), while eight distal conditions required a decrease in strain in the distal areas (M4, M5, M6, M7, L4, L5, L6, and L7). The goal was to achieve a total of 12 hits across these conditions.

Each experiment produced a set of values that defined a nonparametric distribution based on Shapiro–Wilk test, which was run for composite normality, and the data were found to be non-normal. Therefore, a comparison of paired data (M1, M2, M4, M5, M6, M7, L1, L2, L4, L5, L6, and L7) was conducted with Wilcoxon’s signed-rank test, and the correlation of paired data was assessed with Spearman correlation to analyze monotonic relationships of femur regions with friction coefficients. The median of the “model zero” values minus the values of the examined models are expressed as paired differences.

The strongest relationships were found in the 80–100% range, according to Spearman’s correlation analysis, which also showed differing degrees of significance throughout other ranges. Three categories were used to classify correlation strength: very weak (0–19%), moderate (40–59%), and strong (60–79%). The same pattern was seen in the absolute correlation values, which ranged from extremely low (0–19%) to moderate (40–59%) and strong (60–79%). According to these findings, some variables showed only weak correlations, while others showed stronger ones, giving a complete picture of the interactions between the variables in the dataset. We identified statistically significant absolute correlations (greater than 8.5 percent) in our sample of 500 combinations. Regression analysis was conducted to explore the relationship between the independent variable (coefficient of friction) and the dependent variables (each femoral area) and to determine how combined changes influenced the outcomes. Additionally, for the cases where the number of satisfied conditions in areas M1, M2, M4, M5, M6, M7, L1, L2, L4, L5, L6, and L7 was from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12} simultaneously, Poisson count regression was used to predict the increased strains in all of these areas at the same time.

3. Results

All the models produced different strains from “intact bone” (p < 0.05); however, no models satisfied ten or more out of the 12 conditions (p < 0.05) (Figure 2). The 17 models that satisfied nine out of the 12 conditions (increased strains in M1, M2, and L1 and decreased strains in M5, M6, M7, L4, L6, and L7) followed a similar pattern of friction coefficient distributions. An increased coefficient of friction was observed in lateral areas (O2, O3, O4, and O5) and in proximal medial areas (I1 and I2), while the coefficients in mid-medial areas (I3 and I4) varied. In the distal medial area, the coefficient of friction was stable (I5 = 1.2) (

Table 1. Models (rows) with their combinations of coefficients of friction (columns) that had differences (p < 0.05) in proximal medial areas (M1 and M2), proximal lateral area L1 and distal medial and lateral areas (M5, M6, M7, L4, L6, and L7) but not in M4 or L5.

Models	O1	O2	O3	O4	O5	I1	I2	I3	I4	I5
59	1.2	1.5	1.5	1.2	1.2	1.5	1.5	0.5	1.2	1.2
66	1.2	1.5	1.3	1.2	1.2	1.5	1.5	0.5	1.2	1.2
77	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.5	1.2	1.2
119	1.2	1.5	1.3	0.9	0.9	1.5	1.5	0.5	1.3	1.2
121	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.5	0.5	1.2
122	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.5	0.7	1.2
123	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.5	0.9	1.2
124	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.5	1.1	1.2
127	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.5	0.5	1.2
128	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.5	0.7	1.2
129	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.5	0.9	1.2
130	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.5	1.1	1.2
151	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.7	0.5	1.2
152	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.7	0.7	1.2
153	1.2	1.5	1.3	1.3	1.3	1.5	1.5	0.7	0.9	1.2
157	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.7	0.5	1.2
158	1.2	1.5	1.3	1.5	1.5	1.5	1.5	0.7	0.7	1.2

).

The regression analysis revealed a negative linear relationship between the coefficients of friction in the lateral porous coating (O2, O3, O4, and O5) and the differences in the strains from “model zero” in the proximal femoral areas (M1 and L1), in the mid-medial femoral areas (M3 and M4), and in the distal lateral femoral areas (L5 and L7) (

Table 2. Regression of the independent variables of the coefficients of friction (O2, O3, O4, O5, I1, I2, I3, I4, and I5) and the dependent variables of the femoral areas (M1, M2, M3, M4, M5, M6, M7, L1, L2, L3, L4, L5, L6, and L7) expressed by the difference between $M{1}_{model0}-M{1}_{modelX}$. A p value ≤ 0.05 (bold) was considered to indicate statistical significance. Beta is the estimated change in the coefficient of friction.

	M1		M2		M3		M4		M5		M6		M7
	Beta	p Value	Beta	p Value	Beta	p Value	Beta	p Value	Beta	p Value	Beta	p Value	Beta	p Value
O2	−0.47	<0.001	−0.02	0.439	−0.14	0.002	−0.06	0.001	0.02	<0.001	0.04	<0.001	−0.01	0.242
O3	−0.39	<0.001	0.06	0.058	−0.62	<0.001	−0.17	<0.001	0.03	<0.001	0.05	<0.001	−0.01	0.211
O4	−0.48	<0.001	0.21	<0.001	−3.77	<0.001	−1.06	<0.001	0.11	<0.001	0.07	<0.001	0.01	0.053
O5	−0.27	<0.001	0.05	0.074	−1.85	<0.001	−0.50	<0.001	0.07	<0.001	0.04	<0.001	0.003	0.684
I1	−0.34	<0.001	−0.04	0.118	0.13	0.006	0.04	0.018	0.004	0.291	0.06	<0.001	−0.02	<0.001
I2	0.06	0.137	0.38	<0.001	0.19	<0.001	0.06	<0.001	0.01	0.034	0.05	<0.001	−0.02	0.002
I3	0.96	<0.001	1.42	<0.001	0.48	<0.001	0.13	<0.001	0.01	0.069	−0.01	0.090	0.01	0.018
I4	1.22	<0.001	0.59	<0.001	0.61	<0.001	0.15	<0.001	0.00	0.259	−0.01	0.192	0.02	<0.001
I5	−0.22	<0.001	−1	<0.001	0.87	<0.001	0.26	<0.001	0.01	0.004	0.03	0.002	−0.003	0.713
	L1		L2		L3		L4		L5		L6		L7
	Beta	p value	Beta	p value	Beta	p value	Beta	p value	Beta	p value	Beta	p value	Beta	p value
O2	−0.48	<0.001	2.49	<0.001	0.99	<0.001	−0.03	0.247	0.00	0.853	0.01	<0.001	−0.02	<0.001
O3	0.16	<0.001	1.95	<0.001	1.87	<0.001	−0.04	0.164	−0.04	0.001	0.01	<0.001	−0.02	<0.001
O4	−1.43	<0.001	4.77	<0.001	7.53	<0.001	0.00	0.934	−0.43	<0.001	0.08	<0.001	−0.01	<0.001
O5	−0.69	<0.001	−0.76	<0.001	1.82	<0.001	−0.17	<0.001	−0.16	<0.001	0.06	<0.001	0.00	0.145
I1	0.17	<0.001	−0.11	0.037	−0.11	0.149	−0.07	0.008	0.01	0.473	0.01	0.008	−0.02	<0.001
I2	0.18	<0.001	0.21	<0.001	0.04	0.608	−0.27	<0.001	0.04	0.003	−0.01	0.002	−0.02	<0.001
I3	0.06	0.010	1.13	<0.001	0.54	<0.001	−1.29	<0.001	0.24	<0.001	−0.08	<0.001	−0.02	<0.001
I4	−0.02	0.372	0.97	<0.001	0.81	<0.001	−1.38	<0.001	0.26	<0.001	−0.09	<0.001	−0.02	<0.001
I5	0.10	<0.001	0.52	<0.001	1.16	<0.001	−1.72	<0.001	0.34	<0.001	−0.11	<0.001	−0.04	<0.001

).

The coefficients of friction in the lateral porous coating (O2, O3, O4, and O5) were positively correlated with the differences in strain from “model zero” in the distal medial area (M5 and M6), proximal and mid-lateral femoral areas (L2 and L3), and distal lateral femoral area (L6). Regarding the coefficients of friction in the medial porous coating (I1, I2, I3, I4, and I5), there were positive correlations with the differences in strains from “model zero” in almost all femoral areas but in the distal and mid-lateral femoral areas (L4, L6, and L7). The proximal medial porous coating (I1 and I2) was negatively correlated with the difference in strain in the proximal medial femoral area (M1) and distal medial femoral area (M7). The distal medial porous coat (I5) was negatively correlated with the difference in strain in the proximal medial areas (M1 and M2).

These relationships between the differences in strains from “model zero” in the femoral areas and the coefficients of friction resulted in the following observations. A greater coefficient of friction in the medial porous coating (I2, I3, and I4) decreased the strains in the distal and mid-medial femoral areas (M4, M5, M6, and M7) and in the distal lateral femoral area (L5). At the same time, lower values resulted in increased strains in proximal femoral areas (M1, M2, L1, and L2) and decreased strains in the distal and mid-lateral femoral areas (L4 and L7). A greater coefficient of friction in the proximal and distal medial porous coatings (I1 and I5) increased the strains in the proximal femoral areas (M1, M2, and L2) and decreased the strains in the distal medial and lateral femoral areas (M4, M5, M6, and L5). However, the lower values of the coefficients of friction in the proximal and distal medial porous coatings (I1 and I5) resulted in increased strains in the proximal lateral femoral areas (L1 and L2) and decreased strains in the distal lateral femoral areas (L4 and L7). Regarding the coefficients of friction in the lateral porous coating (O2, O3, O4, and O5), higher values resulted in increased strains in proximal femoral areas (M1 and L1) and decreased strains in distal femoral areas (M5, M6, and L6).

Spearman’s correlation analysis revealed that the coefficient of friction in the distal lateral porous coating (O4 and O5) strongly or very strongly negatively correlated with the difference in strain from “model zero” in the mid-medial femoral areas (M3 and M4), the proximal lateral femoral area (L1), and the distal lateral femoral area (L5) (

Table 3. Spearman’s correlation analysis for coefficients of friction and differences in strains in femoral areas. (Strong or very strong correlations are in bold). Note that an absolute correlation of more than 8.5% is statistically significant in the given sample.

	O2	O3	O4	O5	I1	I2	I3	I4	I5
M1	−39.51%	−25.77%	−26.79%	−18.24%	−33.81%	−13.15%	57.54%	52.62%	−18.35%
M2	−12.95%	−3.57%	4.69%	6.71%	−6.31%	9.99%	77.31%	34.71%	−43.57%
M3	1.14%	−5.72%	−86.5%	−63.05%	−3.81%	3.49%	15.63%	10.34%	10.05%
M4	0.11%	−5.94%	−85.55%	−61.23%	−3.57%	3.69%	15.29%	8.86%	10.68%
M5	15.59%	16.28%	73.19%	56.87%	20.65%	19.27%	−5.39%	8.16%	15.23%
M6	40.45%	33.32%	37.35%	23.36%	54.27%	50.4%	−18.2%	4.56%	27.05%
M7	−19.65%	−14.65%	7.45%	3.94%	−27.98%	−23.9%	15.18%	11.67%	−9.35%
L1	−15.34%	11.99%	−85.24%	−60.95%	−0.07%	6.97%	9.24%	−1.13%	1.16%
L2	47.61%	39.43%	71.89%	7.12%	26.29%	29.95%	4.34%	22.41%	23.48%
L3	12.41%	20.19%	91.66%	45.31%	16.34%	15.98%	−3.41%	14.57%	21.88%
L4	−3.45%	−6.25%	−8.43%	−2.04%	−17.84%	−32.95%	−47.31%	−59.96%	−59.44%
L5	3.29%	0.3%	−60.8%	−44.19%	3.62%	15.88%	35.07%	36.57%	36.11%
L6	5.36%	1.31%	42.83%	44.3%	1.71%	−14.67%	−43.89%	−48.01%	−44.61%
L7	−41.05%	−36.75%	−17.08%	2.11%	−56.12%	−64.59%	−9.84%	−37.86%	−54.81%

).

However, the distal lateral porous coating (O4 and O5) was strongly or very strongly positively correlated with the differences in strains from “model zero” in the distal medial femoral area (M5) and proximal and mid-lateral femoral areas (L2 and L3) (Figure 3 and Figure 4). Thus, the lower values in the distal lateral porous coating (O4 and O5) resulted in decreased strains in distal femoral areas (M3, M4, and L5) and increased strains in the proximal lateral femoral area (L2). In comparison, the higher values in the distal lateral porous coating (O4 and O5) increased the strains in the proximal lateral femoral area (L1). They decreased the strains in the distal medial femoral area (M5) and mid-lateral femoral area (L2).

The presence of a medial porous coating in I3 was strongly correlated with the difference in strain from “model zero” in the proximal medial femoral area (M2); hence, a decrease in the medial porous coating (I3) could increase the strain in the medial femoral area (M2). The coefficient of friction in the proximal medial porous coating (I2) was strongly negatively correlated with the difference in strain from “model zero” in the distal lateral femoral area (L7); thus, lower values of the coefficient of friction in the proximal medial porous coating (I2) resulted in decreased strain in the distal lateral femoral area (L7).

Poisson count regression analysis of the number of successful conditions (increased strains in M1, M2, L1, L2, and decreased strains in M4, M5, M6, M7, L4, L5, L6, and L7) had positive coefficients of friction for proximal lateral porous coating (O2) and distal lateral porous coating (O5), and negative coefficients of friction for mid-distal porous coating (O4, I3, and I4) (

Table 4. Poisson’s count regression analysis of successful conditions (increased strains in M1, M2, L1, and L2 and decreased strains in M4, M5, M6, M7, L4, L5, L6, and L7) and coefficients of friction. A p value ≤ 0.05 (bold) was considered to indicate statistical significance. Beta is the estimated change in the coefficient of friction.

Predictor	Successful Conditions (Increased Strains in M1, M2, L1, and L2 and Decreased Strains in M4, M5, M6, M7, L4, L5, L6, and L7)
	Beta	p Value
O2	0.16	0.013
O3	−0.02	0.729
O4	−0.16	0.018
O5	0.19	0.004
I1	0.03	0.679
I2	0.02	0.791
I3	−0.54	0.000
I4	−0.26	0.000
I5	0.03	0.690

).

4. Discussion

Our findings indicate that increasing the coefficient of friction in the proximal and distal lateral porous coatings (O2 and O5) and decreasing it in the mid-distal porous coating (O4, I3, and I4) can produce strain patterns biomechanically closer to those of intact bone. The 17 models that achieved increased strains in the proximal medial areas (M1, M2) and proximal lateral area (L1), along with decreased strains in the distal medial and the lateral regions (M5, M6, M7, L4, L6, and L7), demonstrated higher coefficients of friction in the lateral porous coating and proximal medial porous coating. The coefficients of friction in the distal lateral porous coating (O4 and O5) had a significant impact on the mid-distal medial femoral area (M3, M4, and M5), the proximal and mid-lateral femoral areas (L1, L2, and L3), and the distal lateral femoral area (L5). A reduced coefficient of friction in the mid-medial porous coating (I3) led to increased strain in the proximal medial femoral area (M2). In contrast, a lower coefficient of friction in the proximal medial porous coating (I2) resulted in decreased strain in the distal lateral femoral area (L7).

The primary limitation of our analysis was the disparity between the simulation environment and real clinical conditions. Each model was run twice to ensure accuracy, yielding 100% interobserver consistency. However, our analysis was static, meaning the effect of dynamic loading on osteocyte stimulation was not considered in this study. Another limitation was the model simplification for computational efficiency, which may have impacted the results. Future research should explore multiscale models to understand load transfer patterns and bone growth better. Additionally, the lack of clinical studies on these constructs and the response of the proposed stems to bone tissue limits the scope of our conclusions.

Further testing of 3D-printed porous stems under axial loading is necessary to investigate their fatigue limits and bone interaction, which will be addressed in a future project. Moreover, due to the optimized distribution of the coefficient of friction in the porous coating, the porosity of the femoral stems in this study was discrete and adjusted for biomechanical performance. This differs from the graded porous femoral stems with discrete or continuous distributions found in the literature [21]. Nonetheless, the optimized porosity distribution in our study appeared to perform better biomechanically. In this work, we analyzed the spatial distribution of the coefficient of friction at the coating of a tapered and short Ti6Al4V femoral stem. Future work should concentrate on defining the correlation of porosity and the coefficient of friction for Ti6Al4V. This could be achieved by using microscale simulations or executing detailed experiments.

One of the main limitations of the model design is the heterogeneity in mesh density across different surfaces and the use of both tetrahedral and hexahedral elements at the complex interfaces in the proximal regions of the porous coating, which could lead to unrealistic results. Future studies could benefit from testing less angled areas to improve accuracy. Additionally, the influence of contact parameters on the results must be explored further through parametric studies. Another limitation of the experimental technique is that only surface strain could be measured, even though bone resorption is a consequence of stress shielding. The interface between the proximal lateral area L1 and the coefficient of friction in O1 was not analyzed due to contact inconsistencies between elements in the greater trochanter area, caused by the specific lamina used in the experiment; thus, we were unable to assess changes in strains produced in L1. Finally, the study’s use of sawbone cortical and homogeneous cancellous properties rather than the heterogeneous properties of real femurs was another limitation aimed at simplifying the FEA simulation.

Surface coatings have been used in orthopedic implants for over 40 years to promote osseointegration. Yet, clinical and biomechanical studies have shown that stress shielding remains an issue in short, tapered-wedge stems [1,11,42]. Current stems with porous coatings exhibit several intrinsic shortcomings, such as poor adherence to the substrate, inconsistent layer thickness, and insufficient thickness to support effective bone tissue ingrowth and achieve optimal biomechanical compatibility [43]. The introduction of additive manufacturing technology now allows for the production of functionally graded stems [16,18,23], with pores arranged according to the stress distribution on the stem to optimize mechanical performance [21]. While several fully porous stems with customized designs are discussed in the literature, no studies have specifically investigated the design of “customized” non-graded porous coatings that offer optimal mechanical and biological adaptation to meet individual patient needs [21,23,25,44]. Therefore, this study focused on analyzing the distribution of friction coefficients in porous coatings on short, tapered-wedge metaphyseal femoral stems.

Compared to homogeneous porous structures, functionally graded stems with axial orientation have been shown to reduce stress shielding in the proximal-medial femur [25]. Axially graded stems with a stiffer proximal end were particularly effective at minimizing stress shielding and generating less micromotion [24]. In a related study, axially graded stems with increasing porosity, based on a sigmoid function from top to bottom, demonstrated that those with greater proximal stiffness could reduce bone–implant interface micromotion more effectively than homogeneous porous stems [45]. Another study found that axial grading with increased distal porosity better balanced interfacial micromotion and load sharing [23]. Our findings indicate that increasing the friction coefficient in a proximal porous coating leads to greater proximal strain, suggesting that increasing proximal porosity could reduce stress shielding by redistributing forces at the porous coating–femur interface. However, we also observed that increasing the coefficient of friction in the distal porous coating (O5 and I5) improved biomechanical performance.

The local density of the femoral stem is adjustable at the concept level to minimize stress shielding, showing a 78% and 40% reduction in bone loss volume for an optimized fully porous femoral stem in Gruen zones 6 and 7, respectively [16]. Additive manufacturing offers a significant advantage in allowing customized implants tailored for optimal mechanical and biological adaptation to patient needs [21]. Electron beam melting is used to manufacture optimized porous coatings of Ti6Al4V with varying friction coefficients in specific regions by controlling the powder deposition or changing energy input in the additive manufacturing process [46,47]. Although tantalum foam porous coatings have been shown to decrease bone resorption, their homogeneous pore distribution has resulted in increased interfacial stresses [48,49,50]. The FEA showed that there is a significant relationship between these specific models and the coefficient of friction, with high strains in the proximal medial areas M1 and M2 and lateral area L1, and least in the distal medial and the lateral areas M5, M6, M7, L4, L6, and L7, respectively. In detail, the augmentation of the coefficient of friction in the O2, I1, and I2 regions improved the contact forces between the porous coating and the bones. This increased the friction at the bone–implant interface, meaning that there were higher strains on areas at the implementation site. These results propose that the distribution of friction rate within the implant design can dictate the load transfer and strain pattern, thereby enhancing the general biomechanical value. However, decreasing the coefficient of friction in the middle and distal porous coatings decreased the forces between the porous coating and bone interfaces, decreasing strains and transferring load to more proximal areas where strain increased. Therefore, customizing the lateral and medial femoral areas can effectively reduce stress shielding.

Successful integration of an implant within tissue depends on both mechanical and biological integration and is vital for short- and long-term surgical outcomes [51]. Adjusting the porous coating properties could control the instability of the stem [23]. Customizing the porosity of the femoral stem based on the bone quality of each patient could perform stable primary arthroplasties and decrease the risk of complications. Future work should focus on functional analysis to investigate the dynamic structure of customized stems, on 3D printing of these constructs, and biomechanical testing through axial and torsional loading tests to investigate the mechanical properties in vitro and later in clinical studies. Moreover, clinical studies should be conducted to evaluate the quality of osteoarthritic or osteoporotic bone and design customized stems that match these properties and create an interface that could create a better biomechanical environment.

Short, tapered-wedge stems achieve fixation at the metaphyseal–diaphyseal junction, where the femur’s medullary cavity narrows, as well as at the proximal part of the diaphysis, providing a three-point fixation in the sagittal plane [52]. Studies examining the fitting regions of tapered-wedge short stems have shown that mediolateral fitting with calcar loading is the optimal method for securing these stems [53,54,55]. Our findings confirmed that the proximal lateral and mid-distal medial and lateral regions of the porous coating significantly impact strain distribution. Additionally, we observed that the coefficients of friction in the mid-distal lateral porous coating (O4 and O5) had a strong influence on the mid-distal medial femoral area (M3, M4, and M5), the proximal and mid-lateral femoral regions (L1, L2, and L3), and the distal lateral femoral area (L5).

5. Conclusions

Results indicate that strains biomechanically closer to intact bone could be obtained if coefficients of friction in proximal and distal porous coatings increase and by decreasing friction in the mid-distal porous coating. The coefficients of the proximal lateral and medial midline and lateral porous coatings influence the strain distribution, confirming the three-point fixation of tapered wedge stems. We suggest a customized femoral stem could result in a better biomechanical interface between the bone and the stem. A customized porous distribution could reduce stress shielding in short femoral stems.