A Two-Criteria Remodelling Model for Loading-Dependent Morphological Adaptation of Individual Trabeculae

Background: Trabecular-bone adaptation (TBA) continuously reshapes the trabecular-bone (TB) microstructure at the microscale in response to mechanical loading. While organ-scale adaptation has been extensively studied, the mechanisms governing the evolution of individual trabeculae remain inadequately understood. Methods: This study proposes a new remodelling model: under finite remodelling capacity, surface regions that satisfy mechanostat criteria compete for remodelling events according to the spatial non-uniformity of local mechanical stimulus. This model uses a two-criteria remodelling scheme that combines (i) a mechanostat criterion for bone formation and resorption and (ii) a distance-weighted non-uniformity criterion. The model is implemented with a 2D finite-element framework using a USDFLD subroutine in the Abaqus/Standard software package. Idealised X- and I-shaped trabecular geometries are subjected to controlled bending, compression, and shear load cases to examine loading-dependent morphology evolution. Results: Compared with the corresponding one-criterion models, the two-criteria framework produces a lower fraction of active remodelling surface and a more clearly bounded convergence process. The numerical simulations reproduce characteristic plate-like morphologies of trabeculae under bending and rod-like morphologies under compression, while additional variations in thresholds and loading conditions shift the response towards resorption-biased structures. Conclusions: The results indicate that the mechanostat criterion primarily stabilises the global bone mass, whereas the non-uniformity criterion governs where remodelling is preferentially located on the trabecular surface. The proposed framework therefore provides a microscale and mechanistically interpretable basis for analysing loading-dependent morphological adaptation of individual trabeculae.