Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling

Osteoporosis is a bone disease associated with enhanced bone loss, microstructural degeneration, and fracture-risk. Finite element (FE) modeling is used to estimate trabecular bone (Tb) modulus from high-resolution three-dimensional (3-D) imaging modalities including micro-computed tomography (CT), magnetic resonance imaging (MRI), and high-resolution peripheral quantitative CT (HR-pQCT). This paper validates an application of voxel-based continuum finite element analysis (FEA) to predict Tb modulus from clinical CT imaging under a condition similar to in vivo imaging by comparing with measures derived by micro-CT and experimental approaches.

Voxel-based continuum FEA methods for CT imaging were implemented using linear and nonlinear models and applied on distal tibial scans under a condition similar to in vivo imaging. First, tibial axis in a CT scan was aligned with the coordinate z-axis at 150 μm isotropic voxels. FEA was applied on an upright cylindrical volume of interests (VOI) with its axis coinciding with the tibial bone axis. Voxel volume, edge, and vertex elements and their connectivity were defined as per the isotropic image grid. A calibration phantom was used to calibrate CT numbers in Hounsfield unit to bone mineral density (BMD) values, which was then converted into calcium hydroxyapatite (CHA) density. Mechanical properties at each voxel volume element was defined using its ash-density defined on CT-derived CHA density. For FEA, the bottom surface of the cylindrical VOI was fixed and a constant displacement was applied along the z-direction at each vertex element on the top surface to simulate a physical axial compressive loading condition. Finally, a Poisson's ratio of 0.3 was applied, and Tb modulus (MPa) was computed as the ratio of average von Mises stress (MPa) of volume elements on the top surface and the applied displacement. FEA parameters including mesh element size, substep number, and different tolerance values were optimized.

CT-derived Tb modulus values using continuum FEA showed high linear correlation with the micro-CT-derived reference values (r ∈ [0.87 0.90]) as well as experimentally measured values (r ∈ [0.80 0.87]). Linear correlation of computed modulus with their reference values using continuum FEA with linear modeling was comparable with that obtained by nonlinear modeling. Nonlinear continuum FEA-based modulus values (mean of 1087.2 MPa) showed greater difference from their reference values (mean of 1498.9 MPa using micro-CT-based FEA) as compared with linear continuum methods. High repeat CT scan reproducibility (intra-class correlation [ICC] = 0.98) was observed for computed modulus values using both linear and nonlinear continuum FEA. It was observed that high stress regions coincide with Tb microstructure as fuzzily characterized by BMD values. Distributions of von Mises stress over Tb microstructure and marrow regions were significantly different (p < 10^-8 ).

Voxel-based continuum FEA offers surrogate measures of Tb modulus from CT imaging under a condition similar to in vivo imaging that alleviates the need for segmentation of Tb and marrow regions, while accounting for bone distribution at the microstructural level. This relaxation of binary segmentation will extend the scope of FEA application to assess mechanical properties of bone microstructure at relatively low-resolution imaging.