A Density-Dependent Target Stimulus for Inverse Bone (Re)modeling with Homogenized Finite Element Models

Inverse bone (re)modeling (IBR) can infer physiological loading conditions from the bone microstructure. IBR scales unit loads, imposed on finite element (FE) models of a bone, such that the trabecular microstructure is homogeneously loaded and the difference to a target stimulus is minimized. Micro-FE (mu FE) analyses are typically used to model the microstructure, but computationally more efficient, homogenized FE (hFE) models, where the microstructure is replaced by an equivalent continuum, could be used instead. However, also the target stimulus has to be translated from the tissue to the continuum level. In this study, a new continuum-level target stimulus relating relative bone density and strain energy density is proposed. It was applied using different types of hFE models to predict the physiological loading of 21 distal radii sections, which was subsequently compared to mu FE-based IBR. The hFE models were able to correctly identify the dominant load direction and showed a high correlation of the predicted forces, but mean magnitude errors ranged from - 14.7 to 26.6% even for the best models. While mu FE-based IBR can still be regarded as a gold standard, hFE-based IBR enables faster predictions, the usage of more sophisticated boundary conditions, and the usage of clinical images.

Automated summary

Inverse bone remodeling can infer physiological loading conditions from bone microstructure. Homogenized finite element models can be used as an alternative to micro-structured models to improve computational efficiency. A new continuum-level target stimulus is proposed and applied to predict physiological loading in different models.