Tetrahedral microFE models of human trabecular bone can be a valid alternative to voxel-based hexahedral models: A comparative study using an open-source workflow

This study tested whether tetrahedral micro Finite Element (microFE) models can be a computationally lighter alternative to gold-standard voxel-based hexahedral models to evaluate trabecular bone biomechanics from microCT images.
A three-step verification process of tetrahedral models was performed by: (i) checking volumetric accuracy against hexahedral models (ii) performing a convergence analysis on the maximum element size, (iii) comparing results to full resolution hexahedral models in terms of apparent elastic modulus (Eapp) and peak strain.
The open-source software Ciclope was extended by adding quadratic elements and support for a high-performance parallel solver for hexahedral models, and used to generate microFE models of 38 human trabecular specimens.
Volumetric accuracy of tetrahedral meshes could be kept within 2 %.
Quadratic tetrahedra showed robust convergence while linear tetrahedra converged with residual differences >3 % of Eapp at the finest mesh refinement.
Both linear and quadratic tetrahedra were strongly correlated (R2 > 0.99) to hexahedra in terms of Eapp.
Quadratic tetrahedra with median element edge of three voxel size and four-fold computational weight reduction approximated hexahedral-based Eapp in the range 0–2 %, while linear tetrahedra overestimated Eapp over 5%.
Peak minimum principal strains were similar to hexahedral models (−0.6 ± 1.4 % for linear and 1.3 ± 0.4 % for quadratic tetrahedra), but median strains differed non negligibly (8.5 ± 3.1 % for linear and 3.5 ± 1.5 % for quadratic tetrahedra).
In summary: (i) coarse linear tetrahedral models may be sufficient for comparative/ranking purposes on specimens elasticity while quadratic tetrahedra should be adopted when targeting absolute values of Eapp; (ii) tetrahedral and hexahedral models may be interchangeable to determine peak strains.