# Quantifying the local strain energy density distribution in the mouse tibia: the critical role of the loading direction

## TL;DR

This study shows that the direction of force applied to the mouse tibia significantly affects how energy is distributed in the bone, which is important for understanding bone adaptation.

## Contribution

The study introduces a method to quantify how loading direction affects strain energy density in mouse tibiae using micro-FE models.

## Key findings

- Loading directions like θ = 10°, ϕ = 205–210° reduced the top 5% SED values compared to axial loading.
- Other directions, such as θ = 30°, ϕ = 35–50°, increased SED values significantly.
- The mouse tibia showed high sensitivity to loading direction across all tested groups and time points.

## Abstract

Understanding how bone adapts to external forces is fundamental for exploring potential biomechanical interventions against skeletal diseases. This can be studied preclinically, combining in vivo experiments in rodents and in silico mechanoregulation models. While the in vivo tibial loading model is widely used to study bone adaptation, the common assumption of purely axial loading may be a simplification. This study quantifies the effect of the loading direction on the strain energy density (SED) distribution in the mouse tibia, a commonly used input for mechanoregulated bone remodelling models. To achieve this, validated micro-finite element (micro-FE) models were used to test the differences in local SED when the bone was loaded along different loading directions. In vivo micro-computed tomography (micro-CT) images were acquired from the tibiae of eleven ovariectomised mice at 18 weeks old before intervention and at 20 weeks old, after six mice underwent external mechanical loading. Micro-CT-based micro-FE models were generated for each tibia at both time points and loaded with a unit load in each Cartesian direction independently. The results from these unit load models were linearly combined to simulate various loading directions, defined by angles θ (inferior-superior) and ϕ (anterior–posterior). The results revealed a high sensitivity of the mouse tibia to the loading direction across both groups and time points. Several loading directions (e.g., θ = 10°, ϕ = 205–210°) resulted in lower medians of the top 5% SED values compared to those obtained for the nominal axial case (θ = 0°, ϕ = 0°). Conversely, higher values were observed for other directions (e.g., θ = 30°, ϕ = 35–50°). These findings emphasise the importance of considering the loading direction in experimental and computational bone adaptation studies.

The online version contains supplementary material available at 10.1007/s10237-025-02011-z.