Beam theory and finite element approaches to modelling the stresses in the second metatarsal during running

Abstract

Stress fracture of the second metatarsal is a problematic injury amongst runners, requiring long recovery times. The physiological mechanisms by which a stress fracture may develop are reasonably well understood, however there is poorer understanding of the training variables which may lead to increased risk of injury. This is compounded by the difficulty of directly measuring metatarsal stress. The aims of this thesis were to develop both 2D beam theory and 3D finite element models with participant-specific parameters to investigate the stresses experienced by the second metatarsal during running. The models would be used to answer an applied question regarding the differences in second metatarsal stress between rearfoot (RF) runners and non-rearfoot (NRF) runners. A single data set was collected consisting of 20 runners, including 12 habitual rearfoot and 8 habitual non-rearfoot strikers. Synchronised force, pressure and kinematic data were collected during barefoot running (3.6 ms-1) in addition to three plane magnetic resonance data of the right second metatarsal of each participant. The first modelling study developed and evaluated a 2D beam theory model incorporating vertical and horizontal ground reaction forces under the metatarsal head and toe and utilising participant-specific geometrical information from magnetic resonance images. Peak stress and input variables were compared between RF and NRF groups and statistical parametric mapping analysis allowed comparison of the stress time histories between groups. Results demonstrated that ground reaction forces under the metatarsal head were greater in the NRF group at the time of peak stress, but that peak stress did not differ between groups. The SPM analysis found greater stress in the NRF group during early stance. The second modelling study developed and evaluated a 3D finite element model, incorporating distributed loading and soft tissue effects between the metatarsal head and the ground. A two-part metatarsal bone consisting of trabecular and cortical layers was reconstructed from magnetic resonance images, in addition to the soft tissues surrounding the metatarsal bone. Three time points during stance were analysed; maximum braking (minimum horizontal ground reaction forces), maximum vertical ground reaction force, and maximum propulsion (maximum horizontal ground reaction forces). Maximum von Mises stress and input variables were compared between groups at all three time points. Results showed that vertical ground reaction forces under the metatarsal head were greater in NRF runners at all time points, but stress did not differ between groups at any time. When using the two models the same overall findings were observed, suggesting that external forces do not represent internal loading well. The magnitudes of stress were not different between groups at the time of peak stress (2D model) or the times of maximum braking, maximum vertical ground reaction force or maximum propulsion (3D model), suggesting that habitual foot strike modality does not affect the risk of stress fracture via this mechanism.