A comparison of density-modulus relationships used in finite element modeling of the shoulder.

Subject- and site-specific modeling techniques greatly improve the accuracy of computational models derived from clinical-resolution quantitative computed tomography (QCT) data. The majority of shoulder finite element (FE) studies use density-modulus relationships developed for alternative anatomical locations. As such, the objectives of this study were to compare the six most commonly used density-modulus relationships in shoulder finite element (FE) studies. To achieve this, ninety-eight (98) virtual trabecular bone cores were extracted from uCT scans of scapulae from 14 cadaveric specimens (7 male; 7 female). Homogeneous tissue moduli of 20 GPa, and heterogeneous tissue moduli scaled by CT-intensity were considered. Micro finite element models (µ-FEMs) of each virtual core were compressively loaded to 0.5% apparent strain and apparent strain energy density (SEDapp ) was collected. Each uCT virtual core was then co-registered to clinical QCT images, QCT-FEMs created, and each of the 6 density-modulus relationships applied (6 × 98 = 588 QCT-FEMs). The loading and boundary conditions were replicated and SEDapp was collected and compared to µ-FEM SEDapp . When a homogeneous tissue modulus was considered in the µ-FEMs, SEDapp was best predicted in QCT-FEMs with the density-modulus relationship developed from pooled anatomical locations (QCT-FEM SEDapp  = 0.979µ-FEM SEDapp  + 0.0066, r2  = 0.933). A different density-modulus relationship best predicted SEDapp (QCT-FEM SEDapp  = 1.014µ-FEM SEDapp  + 0.0034, r2  = 0.935) when a heterogeneous tissue modulus was considered. This study compared density-modulus relationships used in shoulder FE studies using an independent computational methodology for comparing these relationships.