The authors analyzed computed tomography (CT) shoulder scans of patients scheduled to receive TSA, and selected 5 shoulders that represent a wide spectrum of size, sex and age, known to denote bone quality (Kirchhoff et al., 2012). The selection comprised 2 women (aged 82 and 87; head diameters 55 and 47 mm) and 3 men (aged 56, 59, and 73; head diameter 63, 49, and 59 mm). The number of subjects included in this study was comparable to those of other FEA studies investigating stress distribution within the humerus (Chevalier et al., 2016; Quental et al., 2012; Razfar et al., 2016). The DICOM images were processed using 3D SolidWorks® (Dassault Systèmes, Waltham, MA, USA) to form 3-dimensional (3D) solid models of the proximal humerus. Separate 3D models of the cortical and trabecular bones were created using combinations of automatic threshold-based segmentation and visual distinctions. Under the supervision of two orthopedic surgeons (JG, AG), humeral head resections were simulated as would be done during TSA. All patients had provided written informed consent for the use of their images and data for research and publishing purposes.
Computer models of 3 generic implants were created based on three design concepts: (A) predominantly oval (Ascend Flex, Wright-Tornier, Montbonnot, France), (B) semi-angular (ISA Onlay, Move-Up, Alixan, France), and (C) predominantly angular (Equinox, Exactech Inc., Gainesville, FL, USA) (Fig. 1). The stems were designed with the same neck-shaft angle (132.5°), head offset (6.2 mm), and humeral head geometry, but differed in the proximal metaphyseal area with different fillet radii of the supero-lateral edge: 8.6 mm (predominantly oval), 3.1 mm (semi-angular) and 1.1 mm (predominantly angular). The humeral heads were designed with a radius-to-height ratio of 1.00:0.76. The coefficient of friction assigned to the proximal grit-blasted metaphyseal region was 0.63, while that assigned to the cylindrical polished diaphyseal region was 0.4 (Grant et al., 2007; Kuiper & Huiskes, 1996; Razfar et al., 2016). Each humeral stem model was created in 9 sizes, increasing by increments of 2 mm in the antero-posterior (AP) direction and increments of 1 mm in the medio-lateral (ML) direction.
To re-create surgical placement in a repeatable manner across all models, anatomic landmarks were used as reference points, such that the native and prosthetic head centers have the same 3D coordinates, and the stem is aligned with the diaphyseal axis. Stem sizing was established by selecting the component that makes contact with the cortical diaphysis (oversized), one increment smaller (normosized), and two increments smaller (undersized). After implant positioning and sizing, all model components were transferred from SolidWorks to ADAMS (Adams, MSC Software Corporation, Santa Ana, CA) (Fig. 2). Bone was meshed using an average of 2 mm (maximum value) quadratic tetrahedral elements, based on mesh convergence analysis. The reliability of our model was confirmed using convergence testing. Careful mesh planning ensured that identical mesh parameters could be used for different implant geometries to allow comparisons of Von Mises stresses in different regions.
In agreement with previous studies, cortical bone was modeled as a homogeneous isotropic material with a Young’s modulus of 20 GPa and Poisson’s ratio 0.3 (Bayraktar et al., 2004; Rho et al., 1993). For trabecular bone, the Young’s modulus was applied on an element-by-element basis and calculated using corresponding CT densities, as described previously (Austman et al., 2009; Carter & Hayes, 1977; Leung et al., 2009; Morgan et al., 2003; Schileo et al., 2008; Taddei et al., 2006). The density-modulus relationship chosen for this study, which was reported by Morgan et al. (Morgan et al., 2003), is specific to trabecular bone:
$$ \mathrm{Equation}\ 1:\mathrm{E}=8920{\uprho}^{1.83} $$
Where E is Young’s modulus and ρ is the apparent bone density, calculated from Hounsfield Units.
All implant components were meshed using appropriately sized quadratic tetrahedral elements, and assigned properties of titanium (Ti6Al4V) (E = 115 GPa, ν = 0.31). To render our results comparable to the study of Razfar et al. (Razfar et al., 2016), the same force magnitude was applied, assuming a median mass of 88.3 kg for all patients, at a single abduction angle of 45°. The resultant force vector was therefore: Fx 160 N, Fy -440 N, Fz -210 N.
Finite element analyses (FEA) were performed with the humerus rigidly constrained at its distal end. To simulate the joint reaction force acting on the humerus, a load was directed from the joint surface toward the center of the humeral head, according to in vivo implant data (Fig. 3). A total of 20 analyses were performed using 4 FEA models (1 intact humerus + 3 implanted humeri) for each of the 5 subjects. To quantify changes in the proximal humerus after TSA, mean bone stresses were compared for the implanted versus intact humerus at 3 transverse sections: proximal (15 mm below head center), middle (40 mm below head center), and distal (65 mm below head center). Torsional stability was assessed by measuring the maximum angular displacement of the stem, defined as the angle (degrees) through which the stem moves around the diaphyseal axis.
