The force-driven harmonic oscillator model for energy-efficient locomotion in individuals with transtibial amputation

The force-driven harmonic oscillator (FDHO) model states that the driving force is minimum at the resonant period of an oscillator. By manipulating prosthetic mass, this study explored the compromise of resonant periods between the two legs in persons with unilateral traumatic transtibial amputation (TTA) at self-selected walking velocity (SSWV), with an aim to better understand the energy minimization mechanisms of walking. It was hypothesized that (1) SSWV was the most energy-efficient walking velocity (MEWV), (2) the stride period at SSWV (Ts) is a compromise between the resonant periods of the normal leg (Tn) and the prosthetic leg (Tp) when they are dissimilar. Eight subjects completed multiple-speed treadmill walking tests (at 53, 67, 80, 93, and 107 m/min) according to three mass conditions (60%, 80%, and 100% of the normal leg below-knee mass) in a random order. Oxygen consumption and stride period were measured, and SSWV was empirically determined. The MEWV, the speed with minimum energy expenditure per distance traveled, was derived from quadratic regression, and its stride period (Tm) was estimated. A theoretical compromise period (Tv) between Tn and Tp was predicted by a virtual single pendulum system based on Huygens' Law. Across different mass conditions, comparisons were made among: Ts, Tm, Tv, Tn, and Tp. Results showed that: (1) Ts was significantly different from Tm; (2) Ts was greater than both Tn and Tp; (3) no significant difference was found between Tm and Tn. Implications for amputee rehabilitation in terms of thigh muscle training and prosthesis development were discussed.