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
Density-modulus relationships are often used to map the mechanical properties of bone based on CT- intensity in finite element models (FEMs). Although these relationships are thought to be site-specific, relationships developed for alternative anatomic locations are often used regardless of bone being modeled. Six relationships are commonly used in finite element studies of the shoulder; however, the accuracy of these relationships have yet to be compared. This study compares each of these six relationships ability to predict apparent strain energy density (SEDapp) in trabecular bone cores from the glenoid. Quantitative-CT (QCT) (0.625 mm isotropic voxels), and µ-CT scans (0.032 mm isotropic voxels) were obtained for fourteen cadaveric scapulae (7 male, 7 female). Micro finite element models (µ-FEMs) were created from 98 virtual ‘cores’ using direct conversion to hexahedral elements. Two µ-FEM cases were considered: homogeneous tissue modulus of 20 GPa, and heterogeneous tissue modulus scaled by CT intensity of the µ-CT images (196 models). Each µ- FEM model was compressively loaded to 0.5% apparent strain and apparent strain energy density (SEDapp) was calculated. Additionally, each of the six density-modulus relationships were used to map heterogeneous material properties to co- registered QCT-derived models (588 models in total). The loading and boundary conditions were replicated in the QCT-FEMs and the SEDapp was calculated and compared to the µ-FEM SEDapp. To account for more samples than donors, restricted maximum likelihood estimation (REML) linear regression compared µ-FEM SEDapp and QCT-FEM SEDapp for each relationship.Introduction
Methods
