The rigidity of the human foot is often described as a feature of our evolution for upright walking and is bolstered by a thick plantar aponeurosis that connects the heel to the toes. Previous descriptions of human foot function consider stretch of the plantar aponeurosis via toe extension (windlass mechanism) to stiffen the foot as it is levered against the ground for push-off during walking. In this study, we applied controlled loading to human feet in vivo , and studied foot function during the push-off phase of walking, with the aim of carefully testing how the foot is tensioned during contact with the ground. Both experimental paradigms revealed that plantar aponeurosis strain via the ‘windlass mechanism' could not explain the tensioning and stiffening of the foot that is observed with increased foot-ground contact forces and push-off effort. Instead, electromyographic recordings suggested that active contractions of ankle plantar flexors provide the source of tension in the plantar aponeurosis. Furthermore, plantar intrinsic foot muscles were also contributing to the developed tension along the plantar aspect of the foot. We conclude that active muscular contraction, not the passive windlass mechanism, is the foot's primary source of rigidity for push-off against the ground during bipedal walking.
Humans choose work-minimizing movement strategies when interacting with compliant surfaces. Our ankles are credited with stiffening our lower limbs and maintaining the excursion of our body's center of mass on a range of surface stiffnesses. We may also be able to stiffen our feet through an active contribution from our plantar intrinsic muscles (PIMs) on such surfaces. However, traditional modelling of the ankle joint has masked this contribution. We compared foot and ankle mechanics and muscle activation on Low, Medium and High stiffness surfaces during bilateral hopping using a traditional and anatomical ankle model. The traditional ankle model overestimated work and underestimated quasi-stiffness compared to the anatomical model. Hopping on a low stiffness surface resulted in less longitudinal arch compression with respect to the high stiffness surface. However, because midfoot torque was also reduced, midfoot quasi-stiffness remained unchanged. We observed lower activation of the PIMs, soleus and tibialis anterior on the low and medium stiffness conditions, which paralleled the pattern we saw in the work performed by the foot and ankle. Rather than performing unnecessary work, participants altered their landing posture to harness the energy stored by the sprung surface in the low and medium conditions. These findings highlight our preference to minimize mechanical work when transitioning to compliant surfaces and highlight the importance of considering the foot as an active, multi-articular, part of the human leg.
Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohm's law in these models, the resulting dispersion relations for the dynamics parallel to the magnetic field, and the implications for numerical simulations. We find that if electron pressure is included in Ohm's law, then both electromagnetic and finite electron mass effects must also be included in order to obtain physical dispersion relations. A simple modification to the plasma vorticity is also found which improves handling of low density regions, of particular relevance to the simulation of the boundary region of magnetised plasmas.
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