Finite element analysis of very large bone models based on micro-CT scans

TL;DR

The paper tackles the challenge of performing anatomically realistic μFE analyses on small-animal bones at near-organ scales using micro-CT data. It delivers an open-source end-to-end framework that combines MIA clustering segmentation, voxel-based meshing in Simpleware, and MFEM-based matrix-free solvers with a voxel-structured multigrid preconditioner to solve extremely large linear-elastic systems. Key findings demonstrate feasibility for models with up to $8\times 10^{8}$ DOFs, show that a $40$ μm voxel size preserves boundary displacements and principal strains with minimal bias while reducing compute cost, and calibrate micron-scale bone properties via DIC to around $21$ GPa, validating the approach against Abaqus. The framework, validated on NZW rabbit femora and optimized for HPC, provides a robust foundation for preclinical assessment of bone mechanics and treatment-related risks, with potential to reduce reliance on animal experiments.

Abstract

High-resolution voxel-based micro-finite element ($μ$FE) models derived from $μ$CT imaging enable detailed investigation of bone mechanics but remain computationally challenging at anatomically relevant scales. This study presents a comprehensive $μ$FE framework for large-scale biomechanical analysis of an intact New Zealand White (NZW) rabbit femur, integrating advanced segmentation, scalable finite element solvers, and experimental validation using predominantly open-source libraries. Bone geometries were segmented from $μ$CT data using the MIA clustering algorithm and converted into voxel-based $μ$FE meshes, which were solved using the open-source MFEM library with algorithms designed for large-scale linear elasticity systems. The numerical solutions were verified by comparing with a commercial finite element solver, and by evaluating the performance of full assembly and element-by-element formulations within MFEM. Models containing over $8\times10^{8}$ DOFs were solved using moderate HPC resources, demonstrating the feasibility of anatomically realistic $μ$FE simulations at this scale. Resolution effects were investigated by comparing models with voxel sizes of 20, 40, and 80 $μ$m, revealing that 40 $μ$m preserves boundary displacement and principal strain distributions with minimal bias while significantly reducing computational cost. Sensitivity analyses further showed that segmentation parameters influence the global mechanical response. Finally, $μ$FE predictions were coupled with Digital Image Correlation measurements on an NZW rabbit femur under compression to calibrate effective bone material properties at the micron scale. The results demonstrate that large-scale, experimentally informed $μ$FE modeling can be achieved using open-source tools, providing a robust foundation for preclinical assessment of bone mechanics and treatment-related risks.

Figures (21)

• Figure 1: NZW rabbit femur sample preparation. The samples were carefully separated from the rest of the rabbit's leg, soft tissue was cleaned, and the samples were mounted into a steel block using PMMA.
• Figure 2: QCT scan of a NZW rabbit femur with slice thickness of 0.67 mm, spacing between slices of 0.33 mm and pixel size of 0.11 × 0.11 $\text{mm}^2$. The same slice of CT scan is presented: top - as received, bottom - after HU thresholding to 750 to match the actual dimensions of the bone. Figure by G. Degabli, 2019 DegabliGal2019FinalBones.
• Figure 3: Mesh and boundary conditions of the L40 and L20 $\mu$FE femur models. The dashed lines at the distal end represent fully constrained boundary conditions, while the arrows (Fz) indicate the applied compressive traction at the femoral head. Insets illustrate the internal trabecular architecture and voxel-based mesh resolution.
• Figure 4: Schematic flow-chart describing the generation of the $\mu$FE model from $\mu$CT scans of a bone.
• Figure 5: Reduced femur model with 72,070 hexahedral elements and associated coarsened voxel hierarchy.