Methods

Mechanical testing of human tibial trabecular bone was done under uniaxial and confined compression configurations. We examined 62 human trabecular bone samples taken from 8 different cadaveric tibiae to obtain all the required parameters defining the CFM, dependent on local bone mineral density (BMD). The derived constitutive rule was subsequently applied using an in-house subroutine to the FE models of the bone specimens, to compare the model predictions against the experimental results.

Methods

Using a six-camera motion capture system, synchronized force plates, and 45 optical markers placed on 6 different subjects, data was recorded for three different activities: walking at a comfortable speed, chair rise, and stair climbing.

Musculoskeletal models, using the Twente Lower Extremity Model 2.0 implemented in the AnyBody modeling System™ (AnyBody Technology A/S, Aalborg, Denmark; figure1), were used to determine the hip joint forces. Hip forces for the subject with the lowest and highest peak force, as well as averaged hip forces were then applied to an FE model of a modular taper connection (Biomet Type-1 taper with a Ti6Al4V Magnum +9 mm adaptor; Figure 2). During the FE simulations, the taper geometry was updated iteratively to account for material removal due to wear. The wear depth was calculated based on Archard's Law, using contact pressures, micromotions, and a wear factor, which was determined from accelerated fretting experiments.

Methods

An FE model was developed in which the geometry can be updated to account for material removal due to wear. In this model the geometry was updated based on Archard's Law, using contact pressures, micromotions and a wear factor, which was determined based on accelerated fretting experiments. The linear wear was calculated using H=k*p*S. Where H is the linear wear depth in mm, k is a wear factor (mm³/Nmm), p is the contact pressure (MPa) and S is the sliding distance (mm). 10 million cycles were simulated using 50 virtual steps. Using this scaling and the measured volumetric wear from the experiments a wear factor of 2.7*10⁻⁵ was applied.

Based on general manufacturing tolerances the resulting mismatch in taper angles were determined to be ± 1.26°. Using this mismatch a tip fit (figure 1a) and base fit (Figure 1b) model were created. In combination with a perfect fit, meaning no mismatch, and two different assembly forces of 4 kN and 15 kN, 6 different situations were studied.

Method

Experimental test: An accelerated fretting screening test was developed that consistently reproduced fretting wear features observed in retrievals. Biomet Type-1 (4°) tapers and +9 mm offset adaptors were assembled with a 4 kN force (N=3). A custom head fixture was used to create an increased offset and torque. The stems were potted in accordance with ISO 7206–6:2013. The set-up was submerged in a 37°C PBS solution with a pH adjusted to 3 using HCL and NaCl concentration of 90gl⁻¹. The components were cyclically loaded between 0.4 – 4 kN for 10 million cycles. After completion, the volumetric and linear wear was measured using a Talyrond-585 roundness measurement machine.

FE model: This was created to match the experimental set up (Figure 1). Taper geometry and experimental material data were obtained from the manufacturer (Zimmer Biomet). The coefficient of friction of the studied combination of components was based on previous experiments (Bitter, 2016). After each change in load the geometry was updated by moving nodes inwards perpendicular to the taper surface. Archard's Law (Archard, 1953) was used to calculate the wear with the following equation: H=k*p*S. Where H is the linear wear depth in mm, k is a wear factor (mm³/Nmm), p is the contact pressure (MPa) and S is the sliding distance (mm). The 10 million experimental cycles were simulated using a range of 5 to 200 computational cycles. For this purpose, the wear factor (k) was scaled for each simulation to match the volumetric wear found in the experiments.

Methods

Experimental test set-up: An accelerated wear test was developed that consistently reproduced fretting wear features observed in retrievals. Biomet stems with smooth 4° Type-1 tapers were combined with Ti6Al4V Magnum +9 mm adaptors using a 2 or 15 kN assembly force. The head was replaced with a custom head fixture to increase the offset and apply a torque at the taper interface. The stems were potted according to ISO 7206-6:2013. The set-up was submerged in a test medium containing PBS and 90gl-1 NaCl. The solution was pH adjusted to 3 using HCl and maintained at 37°C throughout the tests. For each assembly case, n=3 tests were cyclically loaded between 0.4–4 kN for 10 Million cycles. Volumetric wear measurements were performed using a Talyrond-365 roundness measurement machine. The FE model was created to replicate the experimental set up. Geometries and experimental material data were obtained from the manufacturer (Biomet). The same assembly forces of 2 and 15 kN were applied, and the same head fixture was used for similar offset and loading conditions. The 4 kN load was applied at the same angles in accordance with ISO 7206-6:2013. Micromotions and contact pressures were calculated, and based on these a wear score was determined by summation over all contact points.

Materials and methods

Models of the Biomet Type-1 taper, a 60 mm head and a taper adaptor were created. These models were meshed with a mesh size based on a mesh density convergence study. Internal mesh coarsening was applied to reduce computational cost.

Elastic-plastic material properties based on tensile tests were assigned to all titanium components. The contact conditions used in the FE analyses were validated against push-on and pull-off experiments, resulting in a coefficient of friction of 0.5.

To analyze micromotions at the taper-adaptor connection, the models were loaded with 2300N (ISO 7206-4) and 5340N (ISO 7206-6), after being assembled with 2-4-15 kN, axially and under a 30º angle. This ISO standard is commonly used to determine endurance properties of stemmed femoral components.

Micromotions and contact pressures were analyzed by scoring them to an average micromotion and average contact pressure for the surface area in contact.

Materials and methods

We created a model of a BIOMET Type-1 taper and an adapter that is typically used for larger heads.

Titanium alloy material properties were assigned to both components, and frictional contact (μ = 0.5) was simulated between the adapter and the taper.

To ensure that the model accurately represented the contact mechanics, we first simulated experiments in which the head was assembled on the taper in a load-controlled manner, at different load (4 and 15 kN), after which it was disassembled axially. The disassembly loads predicted by the FEA simulations were then compared to the experimental values.

After ensuring a correct prediction of the disassembly loads, we used various impaction loads (2, 4, and 15 kN) to assemble the taper, after which a 2.3 kN load (ISO 7206-4) was applied to the adapter/taper assembly. This loading regime is commonly used to determine endurance properties of stemmed femoral components. Under these loading conditions, we then analyzed the contact stresses and micromotions, and the effect of impaction load on these quantities.