The Foot's Arch and the Energetics of Human Locomotion

Abstract

The energy-sparing spring theory of the foot's arch has become central to interpretations of the foot's mechanical function and evolution. Using a novel insole technique that restricted compression of the foot's longitudinal arch, this study provides the first direct evidence that arch compression/recoil during locomotion contributes to lowering energy cost. Restricting arch compression near maximally (~80%) during moderate-speed (2.7 ms(-1)) level running increased metabolic cost by + 6.0% (p < 0.001, d = 0.67; unaffected by foot strike technique). A simple model shows that the metabolic energy saved by the arch is largely explained by the passive-elastic work it supplies that would otherwise be done by active muscle. Both experimental and model data confirm that it is the end-range of arch compression that dictates the energy-saving role of the arch. Restricting arch compression had no effect on the cost of walking or incline running (3°), commensurate with the smaller role of passive-elastic mechanics in these gaits. These findings substantiate the elastic energy-saving role of the longitudinal arch during running, and suggest that arch supports used in some footwear and orthotics may increase the cost of running.

Figure 1

(a) Maximum arch compression (mm; mean ± S.E.M.) relative to arch height at minimal shoe-only level running initial foot contact. (b) Estimated elastic energy (J kg⁻¹, mean ± S.E.M.) returned from the arch of the foot in one step. *indicates significantly different (p < 0.05) to the minimal shoe-only trial in the same condition, ^indicates significant difference between the half arch insole (HAI) and full arch insole (FAI) (level running only).

Figure 2

(a) Experimentally observed and (b) model-predicted percent change in the gross metabolic cost of locomotion (mean ± S.E.M.) from the minimal shoe-only to insole trial across walking, level running and incline running conditions. FAI = full arch insole, HAI = half arch insole. * indicates significant (p < 0.05) increase in metabolic energy cost [(a) experimental, (b) modeled] between the minimal shoe-only and insole trial within the same condition.

Figure 3

Right foot medial view illustrating (a) foot marker positions used to compute foot and arch kinematics. The white markers are physical reflective markers, the large red circles are pointed landmarks and the small red circles represent the computed joint centers. The inset illustrates the virtual landmarks relative to the skeleton, the sole axis and the navicular displacement measure. The inset figure was generated using OpenSim 3.0 (https://simtk.org/home/opensim), freely available open source musculoskeletal modeling software⁴². (b) example of the arch compression-restricting insole; image displayed is the Full Arch Insole (FAI); photograph by S.M.S. (c) Footwear illustrating marker ‘windows’, the insole marker and weight pouch used for matching total shoe and insole weight; photograph by S.M.S. MP1 = first metatarsophalangeal joint, MP5 = fifth metatarsophalangeal joint.

Figure 4

(a) Arch elastic strain energy – ankle compressive load relationship adapted from Ker et al. used to estimate arch strain energy from the participant’s maximum ankle joint compressive load (see Online Supplementary Material). (b) Subject specific load-displacement curve used to predict stored arch elastic energy during different conditions from measured arch compression. The subject-specific load-displacement curve was established using the maximum arch compression from the participant’s trials and the corresponding ankle compressive load, and by adjusting the optimized control point so that the area under the curve (elastic energy storage) matched the estimated energy storage from (a).