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

Abstract

Purpose 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. Method 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. Results 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). Conclusion Voxel‐based continuum FEA offers surrogate measures of Tb modulus fr...

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“…Recently, emerging whole-body CT scanners have drawn interest as an alternative to HR-pQCT and MRI for in vivo bone micro-imaging at peripheral sites due to their widespread availability in clinical setting, high-resolution, fast scan-speed, and ultra-low radiation (Chen et al 2018 ). In an ex vivo study, (Bauer et al 2014 ) computed failure loads of small cadaveric Tb specimens using CT-based FEA, where bone voxels were separated from marrow by thresholding and a constant Young’s modulus was used for bone voxels in an oriented brick mesh model (Guha et al 2022 ) established a nonlinear continuum FEA method for in vivo ankle CT scans that computes Tb microstructural strength without requiring separation of Tb micro-network from marrow space, while capturing the impacts of micro-distribution of bone mineral on strength. Relaxation of the segmentation of Tb microstructure by Guha et al ’s method allows FEA-based study of bone strength at relatively low-resolution (LR) imaging frequently available in routine clinical scans, while accounting for bone micro-distribution at the level of Tb network.…”

“…A major challenge with CT-based FEA methods emerges due to the wide variation in spatial resolution and other imaging and reconstruction features among different CT scanners along with rapid upgrades in technology causing inconsistency in Tb micro-morphometric measures in multi-site and longitudinal bone studies (Chen et al 2018 ). Although, the paper by (Guha et al 2022 ) demonstrated that their method offers reliable measures of Tb microstructural strength at in vivo peripheral CT imaging, variability of their measures derived from muti-scanner CT images with varying spatial resolution has not yet been established. This paper is aimed to examine the multi-scanner variability of Guha et al ’s Tb FEA measures in an in vivo study.…”

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