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Increased stability of short femoral stem through customized distribution of coefficient of friction in porous coating – Scientific Reports

In this study, 3D FEA models were created, consisting of a short-tapered wedge stem (TRI-LOCK Bone Preservation Stem, DePuy Orthopaedics Inc. Warsaw, IN, USA) made of titanium alloy (Ti6Al4V) with a highly porous coating (“GRIPTION®”) on the proximal 50% portion, implanted in a femur model using CAD software. Its porous coating features an average pore size of 300 μm, which lies within the optimal range for tissue growth into the structure and enables vascularization; an average volume porosity 63% and coefficient of friction (CF) equal to 1.2.

Our study utilized cortical and cancellous bone material with Young’s modulus of elasticity E = 16.7GPa and E = 155 MPa, based on previous data and sawbones’s manufacturers’ suggestions28,29,30,31,32. This study was based on previous published experimental results from an axial load test and validated the FEA model using cortical surface-strain distribution in intact and implanted femurs14,17 (Fig. 1). Strains were examined both macroscopically and microscopically, and statistical comparisons were conducted among the experimental and FEA models. Comparison through Mann–Whitney/Wilcoxon Rank-Sum demonstrated no statistical differences in the distributions of strains in lateral (p = 0.443) and in medial (p = 0.160) cortex between experimental and FEA model, hence the FEA model results coincided to the DIC ones (Supplementary material 1). Verification of consistency and accuracy was assessed by running each simulation twice.

Figure 1
figure 1

(a) Layout of the axial loading experiment of an implanted prothesis in femur (previously published41); (b) Establishment of femoral axis before stabilizing the femur with epoxy distally for the experimental biomechanical study; (c) Loading system configuration (direction of hip and abductors’ forces).

The Analysis System (ANSYS) Mechanical Software was used for the simulation. The implant’s geometry, including the porous coating part was acquired from computed tomography imaging (DICOM files), and converted into .STEP files, with minor modifications in its geometry for adjusting the porous coating for FEA analysis (Fig. 2). The coefficient of friction, influenced by surface roughness, lubrication conditions, temperature, contact pressure; indirectly influences the porosity of Ti6AI4V33,34,35. We used as constants the geometry design of Tri-Lock BPS short stem and the material Ti6Al4V alloy and we examined as variable the distribution of the coefficient of friction of the porous coating under FEA analysis of axial load.

Figure 2
figure 2

Geometry of the computational model. (a) femoral part consisting of cortical bone; (b) proximal femoral area consisting of cancellous bone; (c) femoral prothesis; (d) porous coating part of the stem; (e) loading system configuration (force applied by abductors and hip force); (f) system’s boundaries (fixed support of the distal femoral part).

In ANSYS Workbench 2020 (R2), bone and stem geometries were set in space planes, and material properties were assigned. Contact interfaces between cortical and cancellous bone parts, and between solid stem parts and porous coat were set as bonded; loads were transferred between bonded components through their common interface, and components would never be separated from each other. The interfaces between bone parts and solid stem parts were set as frictionless due to the smooth area of the solid part; however, the contact interfaces between bone parts and porous coat parts; were assigned as frictional based on Coulomb’s Law of Friction.

$${F}_{f}riction le mu* {F}_{n}ormal$$

where, ({F}_{f}riction) is the frictional force; mu (μ) is the coefficient of friction; ({F}_{n}ormal) is the normal force.

The contact parameters were set as the surfaces between the contact body and the target body, the Augmented Lagrange formulation, the penetration tolerance of 10% of underlying elements depth, elastic slip tolerance of 1% of average contact length in pair and normal stiffness equal to 10. The analysis solver was set to detect any deflection and the full Newton–Raphson method was used to update solution until convergence.

During ipsilateral single-limb stance it has been found that the joint-contact force was 2.1 times body weight, and during the stance phase of gait the peak force typically was 2.6 to 2.8 times body weight, allowing the assessment of the structural integrity and loading patterns of the femur under weight-bearing conditions36. During the single leg stance, adductor muscles resist the torques produced by the body weight in order to maintain stability37. Cristofilini et. al.38 presented that the applied hip force should be around 29° to the femoral diaphysis and the abducting force around 40° to the femoral diaphysis. The angle between the joint reaction force combined with the abductor force at the center of the femoral head and the human body’s partial gravity and the vertical line on the ground is 9–12 degrees10. Hence, the study replicated the natural inclination of single-leg stance by fixing the distal femoral end neutral on the sagittal plane and at 11 degrees of adduction in the frontal plane. We applied a hip force of 2471N at 29° to the femoral diaphysis and an abducting force of 1556 N at 40° to the femoral diaphysis based on previous published experiment14 (Fig. 2e,f).

FEA discretization was performed using meshes of over 2,196,924 nodes of tetrahedral or hexahedral elements per model. Body sizing was used to refine the mesh in certain regions and to apply grading for smoother transitions. The edge length was 2 mm for cancellous and cortical bone interfaces and 0.5 mm for porous coat and bone interfaces, which is known from previous studies to be sufficient for mesh convergence and fine material distribution that can differentiate cortical and cancellous bone areas39,40. Face sizing was used to manage mesh density, element size on surfaces and refine mesh in areas with intricate geometry and bone components, resulting in 1,526,318 elements, aspect ratio 1.8506 ± 1.3451 and element quality 0.84239 ± 0.10224 (Fig. 3).

Figure 3
figure 3

Mesh construct (a) of the implanted stem in femur; (b) of the proximal part of the femur; (c) of the entire prothesis; (d) of the solid part of femoral stem; (e) of the porous coating part. Paths designed in lateral (f) and medial (g) cortex to measure strain distribution.

A static structural nonlinear analysis was used to simulate the femoral stem’s behavior under axial loading, providing information on strain distribution, displacement and deformation. Biomechanical studies of proximal femur proposed that the difference of the surface strain is an appropriate proxy for stress shielding20. Thus, two paths were designed for measurements, with principal maximal and minimal strains measured in the medial and lateral cortex, respectively (142 points each) (Fig. 3f,g). The measurements in the two paths were separated every 20 mm until a maximum of 40 mm in the proximal medial and lateral areas {M1, M2, L1, L2}, respectively, which corresponded to Gruen zones 1 and 7 (Fig. 4)42.

Figure 4
figure 4

Porous coating medial (I1, I2, I3, I4, I5) and lateral areas (O1, O2, O3, O4, O5). Medial (M1, M2, M3, M4, M5, M6, M7) and lateral (L1, L2, L3, L4, L5, L6, L7) path measurements. Gruen zones (G1, G2, G3, G4, G5, G6, G7).

Ti6AI4V has a moderate friction coefficient in dry conditions, falling between 0.4 and 0.6. The current market model, “model zero”, has a friction coefficient of 1.2 and a relative density of 63% of the porous coat. So, friction coefficients between 0.5 and 1.5 were used in research models. The porous coat was separated into 10 areas of height 2 mm in the medial (I1, I2, I3, I4, I5) and lateral (O1, O2, O3, O4, O5) (Fig. 4). Each of them could take seven values in the domain {0.5, 0.7, 0.9, 1.1, 1.2, 1.3, 1.5}, but the O1 was decided to remain stable (CF = 1.2) due to the complex geometry and meshing of that area of the porous coat and due to the fact that in the experiment a metallic rod was attached to the lateral aspect of the greater trochanter, using epoxy glue, to simulate the hip abductor muscles, so measurements could not be taken into account. All models were compared with “model zero”, which was defined as the model with CF = 1.2 in all areas of the porous coat.

Statistical analysis

The discrete set contained 7 values {0.5, 0.7, 0.9, 1.1, 1.2, 1.3, 1.5} assigned to 9 variables {O2, O3, O4, O5, I1, I2, I3, I4, I5}, with O1 remaining stable, creating a grid of 79 nodes (more than 40 million). The FEA model’s complexity made it impossible to run all combinations. To ensure computational feasibility, 500 combinations were randomly sampled without replacement, and conditions were met for the experiment to be accurate due to common summary statistics (means, medians, quartiles) and no strong correlations between the nine variables, mutually pairwise. Data analysis was performed in R και RStudio.

Each experiment resulted in a set of values that defined a non-parametric distribution (according to the Shapiro–Wilk test) requiring non-parametric descriptive and inferential statistics. Wilcoxon’s signed-rank test was used to compare the paired values of each of the areas M1, M2, L1 and L2, while Spearman’s correlation test assessed monotonic relationships between femur areas and friction coefficients. Differences (paired) were expressed as the median of subtracting the “model zero” values minus the examined model values.

The absolute correlation ranged from very weak (0–19%) to moderate (40–59%) to strong (60–79%), with Spearman’s correlation being most significant at 80–100%. In our 500 samples, an absolute correlation of more than 8.5% was defined as statistically significant. Regression analysis examined the relationship between the independent variables of the coefficient of friction and the dependent variable of each femoral area and defined the way in which combined changes influenced each outcome. Lastly, Poisson count regression was utilized to predict the increased strains in areas M1, M2, L1, L2 simultaneously (number of satisfied conditions could be in {0, 1, 2, 3, 4}), within the combinations of friction coefficients.