Transverse contributions to the longitudinal stiffness of the human foot

TL;DR

The study tests the in vivo contribution of the transverse tarsal arch (TTA) to midfoot stiffness by externally increasing intermetatarsal stiffness with forefoot tape during walking. Using a multi-segment foot model and inverse dynamics in 13 participants, it shows that forefoot taping reduces negative midfoot work by $13.9\%$ and increases sagittal-plane midfoot stiffness by $16.8\%$, without altering TTA curvature. This supports the cross-axis coupling hypothesis in living humans and demonstrates a non-invasive means to modulate foot stiffness without morphologic changes. The findings have potential clinical and athletic applications for managing pathological foot laxity and enhancing performance, while also highlighting the role of stiffness transmission over arch geometry changes.

Abstract

Humans rely on foot stiffness to withstand the propulsive forces of walking and running. Skeletal adaptations that increase foot stiffness include the medial longitudinal arch (MLA) and the transverse tarsal arch (TTA). The TTA has been hypothesized to stiffen the foot through cross-axis coupling of transverse intermetatarsal stiffness with sagittal-plane midfoot stiffness, but this has been tested only in cadaveric specimens. In vivo testing is essential because muscle contraction substantially modulates MLA function and may similarly affect the TTA's cross-axis coupling. Here we provide in vivo evidence for the TTA's contribution to foot stiffness by externally increasing intermetatarsal stiffness and measuring its effects on midfoot elasticity during walking. As predicted by the cross-axis coupling hypothesis, increasing intermetatarsal stiffness with an elastic tape wrapped around the forefoot reduced the energy absorbed in midfoot flattening and increased sagittal-plane midfoot stiffness concomitantly (mean,$\pm$,standard error of the mean (SEM): $13.9\% \pm 3\%$ and $16.8\% \pm 5.8\%$, respectively). However, taping did not change the curvature of the TTA, thereby isolating the effects of cross-axis coupling from morphological changes to the TTA. Thus, forefoot taping modulates midfoot stiffness through cross-axis coupling and could provide a non-invasive means to manage pathological foot flexibility or enhance athletic performance.

Figures (14)

• Figure 1: Cross-axis stiffness coupling hypothesis.a, Increasing the intermetatarsal stiffness using an elastic tape wound around the ball of the foot is predicted to increase the midfoot stiffness due to the TTA's cross-axis coupling. b, Foot model with three hinged rods representing metatarsals. Transverse curvature implies non-parallel hinge axes (dash-dot lines). The transverse curvature in the model is inverted with respect to the curvature in the foot so that gravity can be used as a substitute for ground reaction force at the distal end. c, Frontal view of a physical foot model with a distal bending load. The model shows increasing longitudinal bending stiffness (left-to-right): without any transverse arch, with a transverse arch, with a transverse arch and a distal elastic band to increase the transverse intermetatarsal stiffness (highlighted in red).
• Figure 2: Experimental load-deformation measurements of the foot in walking.a, Subjects walked on a force-measuring treadmill with reflective markers placed on the left foot and leg according to the marker set described in Leardini2007. b, Bony landmarks on the foot define the hindfoot and forefoot segments. Rotational power is the dot product of the midfoot reaction torque with the angular velocity of the forefoot relative to the hindfoot. Translational power is the dot product of the midfoot joint reaction force with the translational velocity of the forefoot relative to the hindfoot. Their sum yields the six degree of freedom power of the midfoot zelik2015aa. Assessment of repeatability of the tape application protocol is reported in figure \ref{['fig:results:supplement:tape stiffness']}, center of pressure trajectories in figure \ref{['fig:results:supplement:COP medio-lateral traces']} and figure \ref{['fig:results:supplement:COP antero-posterior traces']}, ankle angle in figure \ref{['fig:results:supplement:ankle angle traces']}. Motion capture accuracy estimates are reported in table \ref{['table:methods:supplement:calibration']}.
• Figure 3: Change in midfoot work and stiffness during walking.a, Six degrees of freedom midfoot power through stance in the free, taped and control conditions. The net negative work done during stance in the taped condition (shaded region) is smaller than in the free or control conditions. Vertical lines show the instant in stance when the center of pressure crossed the midfoot joint. b, Negative work over stance, normalized by the free condition $(W/W_{\rm free})$ and averaged across all subjects (n = 13). Whiskers show the SEM. c, Sagittal torque at the midfoot joint versus the midfoot deformation angle. Thick lines show the portion of the load-deformation curve used for midfoot stiffness estimation. d, Midfoot stiffness in the free condition relative to the taped and control conditions $(K_{\rm free}/K)$ (n = 13). Whiskers show the SEM. Correlation between work and stiffness is reported in figure \ref{['fig:results:supplement:correlation']}. Data on positive work production and toe angle change between conditions are reported in figure \ref{['fig:results:supplement:push off']} and figure \ref{['fig:results:supplement:toe']}. Data on forefoot width variation through stance are reported in figure \ref{['fig:results:supplement:splay']}. Correlations between forefoot curvature and midfoot work and stiffness are reported in figure \ref{['fig:results:supplement:curvature']}. Individual subject power data are reported in figure \ref{['fig:results:supplement:power traces']}, and torque-angle curves in figure \ref{['fig:results:supplement:moment angle traces']}. Raw data underlying this figure and its supplements are available in figure 3 -- source data 1--7.
• Figure \ref{fig:methods} -- figure supplement 1: Assessment of the tape wrapping protocol.a, Elastic tape was wrapped around two wooden blocks rigidly clamped to a materials testing machine. The blocks were cyclically separated to measure the stiffness of the wrapped tape. b, Force-displacement curves of five samples of the tape were measured to assess the variability in the wrapping protocol. The fifth cycle for each sample is shown here. From 5 repetitions of the wrapping and testing steps, the ratio of the total change in load to the total displacement, or the effective stiffness, is $37.56\,{\rm N/mm} \pm 1.02$ N/mm (mean $\pm$ standard deviation).
• Figure \ref{fig:results} -- figure supplement 1: Correlation between the ratio of negative midfoot work in the tape and free conditions, and ratio of midfoot stiffness in the free and tape conditions.