A comparison of modeling approaches when estimating tibial loading during running with different foot strike patterns

Foot strike can alter internal tibial loading, a mechanical factor linked to tibial stress injury. Participant-specific models are essential for evaluating these loads, but detailed tibial geometry typically requires medical imaging. Open-source statistical shape modeling (SSM) enables geometric reconstruction of the tibia from external landmarks without imaging. However, the reconstruction accuracy achievable using only four anatomical markers commonly used in motion capture, relative to imaging-based reference geometries, is unknown. It also remains unclear whether simplified 2D beam theory and detailed 3D finite element analyses produce consistent internal tibial loading responses across altered running conditions. This study (1) quantified reconstruction errors using a 4-marker SSM configuration; and (2) evaluated the consistency of tibial loading estimates across modeling approaches under different foot strike conditions.

An open-source anatomical dataset (n = 35) was used to assess reconstruction accuracy between 4- and 9-marker SSM configurations under varying principal component constraints, relative to MRI-based reference geometries, using the Jaccard index and surface error metrics. A 4-marker SSM approach generated tibial geometries for participants (n = 18) who completed running trials at 4.0 m ⋅ s^-1 under habitual and imposed rearfoot and forefoot strike conditions. Muscular forces were estimated using static optimization. Tibial stress and strain were estimated using 2D beam theory and 3D finite element analysis (FEA) with identical loading inputs. Friedman tests with Wilcoxon post hoc tests and Bonferroni correction (p _corr < 0.05) were used for comparisons, and Spearman's correlation assessed tibial length agreement.

The 4-marker configuration showed a 17.1% lower Jaccard index than the 9-marker configuration. Reconstructed tibial lengths correlated with marker-based measurements (Spearman's ρ = 0.670, p = 0.002), with a mean absolute error of 13.8 mm and a 1.3% average length difference. During imposed forefoot striking, peak anterior tibial stress increased by 17.0% (2D) and 18.8% (3D) relative to habitual rearfoot striking. Participant-specific percentage changes were directionally consistent across methods, with a mean absolute between-method difference of 5.3%.

Relative changes in internal tibial loading showed consistent directional trends between approaches across foot strike conditions, indicating that simplified 2D beam theory may provide a practical alternative for estimating within-participant or within-group changes in healthy runners when medical imaging is unavailable.