Abstract
INTRODUCTION
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.
METHODS
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.
RESULTS
For tetrahedral meshes the mean QCT density error was 2.4±2.7%, 4.3±4.4%, and 1.6±2.5%, for tetrahedral mesh densities of 0.3125, 0.46875, and 0.625 mm, respectively. Nodal material mapping differs by TET4 and TET10 and therefore for tri-linear interpolation the QCT density error was 0.4±1.6%, 3.5±3.3%, and 2.0±2.2%, for TET4 mesh densities of 0.3125, 0.46875, and 0.625 mm, respectively. The errors were −0.6±1.4%, 2.0±1.4%, 0.2±1.9% for TET10 mesh densities of 0.3125, 0.46875, and 0.625 mm, respectively. Percentage errors in Eappas a function of bone volume fraction (BV/TV) by material mapping strategy were lowest for HEX8 QCT-FEMs mapped with element-based HU (MIMICS). This was also the best mapping strategy for both TET4 and TET10 QCT-FEMs. The node-based material mapping using the HU field was best for TET4 QCT-FEMs with 0.625 mm elements. The node-based E field mapping had the lowest errors for TET10 QCT-FEMs but had greater errors than the other two mapping strategies for all element types (Figure 2).
DISCUSSION
This study compared material mapping strategy, element type, and element density in QCT-FEMs compared to co-registered µFEMs. It was found that QCT-FEMs with hexahedral elements most closely match µFEMs when element averaging of the native HU field is used. This mapping strategy also showed relatively lower errors with linear and quadratic tetrahedral elements compared to node-based material mapping strategies. If modeling parameters are carefully considered when developing QCT-FEMs, models have the potential to accurately replicate micro-level trabecular bone apparent properties.
For any figures or tables, please contact the authors directly.
