Predicting the minimal energy costs of human walking.

Preferred stride frequency (PSF) of human walking has been shown to be predictable as the resonant frequency of a force-drive harmonic oscillator (FDHO). The purpose of this study was to determine whether walking at the PSF and FDHO leads to minimal metabolic and mechanical costs. Subjects walked on a level treadmill at the PSF, FDHO, and frequencies above and below. Effects of stride length (SL) and speed (S) were assessed by two conditions, one in which SL was constant and the other in which S was constant. The predictability of PSF from resonance was replicated. Walking at the PSF and FDHO frequencies resulted in metabolic costs which were not significantly different (P greater than 0.05). A U-shaped oxygen consumption curve was observed with the minimum at the PSF and FDHO conditions when S was constant. A two-component curve in which a breakpoint was observed was found in the SL constant condition. A significant increase in metabolic cost was observed above the PSF/FDHO (P less than 0.01). Internal work (power) values were not significantly different between walking frequencies for the S constant condition. In the SL constant condition, internal work values showed linear increases as frequency increased. It was concluded that PSF of walking arises from the interface of the resonance properties of the limbs as oscillators and the tendency of biological systems to self-optimize.