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Including anisotropy in homogenised inverse remodelling algorithms for habitual load case estimation in bone
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DOI：10.1007/s10237-026-02106-1.png)
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Abstract
En 中文
Bone architecture, including local bone volume fraction and fabric anisotropy, is optimised to resist forces and moments induced by long-term average loading patterns. Finite element (FE)-based inverse bone remodelling allows to estimate a habitual load case using high-resolution computed tomography images. Homogenised FE models use less computational resources than micro-FE approaches but have so far been limited to density-based remodelling. This study aims to include fabric anisotropy in homogenised inverse bone remodelling algorithms for the estimation of long-term habitual loading conditions in bone. The newly developed theoretical framework was applied to 24 human distal tibia samples, and the influence of fabric anisotropy, St. Venant effect, and load case complexity on predicted forces, moments and objective function outcomes was analysed. Physiologically plausible forces and moments were obtained for all analysis types. Although the distal tibia is predominantly loaded in axial compression, the inclusion of additional forces and moments improved the optimisation quality by reducing the overall objective function (p < 0.001). In contrast, global optimisation outcomes were not significantly affected by the exclusion of boundary layer elements from the optimisation scheme despite the occurrence of relatively high stress discrepancies in these regions. Including microstructural orientation into the inverse bone remodelling algorithm led to a significant increase in the predicted load magnitude (p < 0.001) and a reduction in objective function values by approximately 50 %, suggesting improved agreement between the predicted load case and bone architecture. These findings underline the relevance of considering both bone volume fraction and fabric anisotropy for habitual load case estimation in bone using homogenized FE.
Keywords:
Load estimation
Inverse remodelling
Homogenised finite element
Anisotropy
Bone
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