Subject-specific finite element models (FEMs) allow for a variety of biomechanical conditions to be tested in a highly repeatable manner. Accuracy of FEMs is improved by mapping density using quantitative computed tomography (QCT) and choosing a constitutive relationship relating density and mechanical properties of bone. Although QCT-derived FEMs have become common practice in contemporary computational studies of whole bones, many density-modulus relationships used at the whole bone level were derived using mechanical loading of small trabecular or cortical bone cores. These cores were mechanically loaded to derive an apparent modulus, which is related to each core's mean apparent or ash density. This study used these relationships and either elemental or nodal material mapping strategies to elucidate optimal methods for scapular QCT-FEMs. Six cadaveric scapulae (3 male; 3 female; mean age: 68±10 years) were loaded within a micro-CT in a custom CT-compatible hexapod robot Pre- and post-loaded scans were acquired (spatial resolution = 33.5 µm) and DVC was used to quantify experimental full-field displacements (BoneDVC, Insigneo) (Figure 1).. Experimental reaction forces applied to the scapulae were measured using a 6-DOF load cell. FEMs were derived from corresponding QCT scans of each cadaver bone. These models were mapped with one of fifteen density-modulus relationships and elemental or nodal material mapping strategies. DVC-derived BCs were imposed on the QCT-FEMs using local displacement measurements obtained from the DVC algorithm. Comparisons between the empirical and computational models were performed using resultant reaction loads and full-field displacements (Figure 2).Introduction
Methods
Mechanical properties mapping based on CT-attenuation is the basis of finite element (FE) modeling with heterogeneous materials and bone geometry defined from clinical-resolution CT scans. Accuracy between empirical and computational models that use constitutive equations relating CT-attenuation to bone density are well described, but material mapping strategy has not gained similar attention. As such, the objective of this study was to determine variations in the apparent modulus of trabecular bone cores mapped with various material mapping strategies, using a validated density-modulus relationship and co-registered µFEMs as the gold standard. Micro-CT images (isotropic 32 µm) were used to create µFEMs from glenoid trabecular bone cores of 14 cadaveric scapula. Each µFEM was loaded in unconstrained compression to determine the trabecular core apparent modulus (Eapp). Quantitative CT (QCT) images (isotropic 0.625 mm) were subsequently acquired and co-registered QCT-FEMs created for each of the 14 cores. The QCT-FEMs were meshed with either linear hexahedral (HEX8), linear tetrahedral (TET4), or quadratic tetrahedral (TET10) elements at 3 mesh densities (0.3125 mm, 0.46875 mm, 0.625 mm). Three material mapping strategies were used to apply heterogeneous element-wise (element-averaging of the native HU field (Mimics V.20, Materialise, Leuven BE)) or nodal (tri-linear interpolation of HU Field or E Field (Matlab V. R2017a, Natick, RI, USA)) material properties to the QCT FEMs. Identical boundary conditions were used and Eapp between the µFEMs and QCT-FEMs was compared (Figure 1). The QCT density of each hexahedral mesh with element size equal to voxel dimensions was used to compare the QCT density mapping between tetrahedral meshes and material mapping strategy.INTRODUCTION
METHODS
Mechanical property relationships used in the computational modeling of bones are most often derived using mechanical testing of normal cadaveric bone. However, a significant percentage of patients undergoing joint arthroplasties exhibit some form of pathologic bone disease, such as osteoarthritis. As such, the objective of this study was to compare the micro-architecture and apparent modulus (Eapp) of humeral trabecular bone in normal cadaveric specimens and bone extracted from patients undergoing total shoulder arthroplasty. Micro-CT scans were acquired at 20 µm spatial resolution for humeral heads from non-pathologic cadavers (n=12) and patients undergoing total shoulder arthroplasty (n=10). Virtual cylindrical cores were extracted along the medial-lateral direction. Custom-code was used to generate micro finite element models (µFEMs) with hexahedral elements. Each µFEM was assigned either a homogeneous tissue modulus of 20 GPa or a heterogeneous tissue modulus scaled by CT- intensity. Simulated compression to 0.5% apparent strain was performed in the medial-lateral direction. Morphometric parameters and apparent modulus-bone volume fraction relationships were compared between groups.Introduction
Methods
