Dataset Information

Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal.

ABSTRACT: Understanding how humans walk on a surface that can move might provide insights into, for instance, whether walking humans prioritize energy use or stability. Here, motivated by the famous human-driven oscillations observed in the London Millennium Bridge, we introduce a minimal mathematical model of a biped, walking on a platform (bridge or treadmill) capable of lateral movement. This biped model consists of a point-mass upper body with legs that can exert force and perform mechanical work on the upper body. Using numerical optimization, we obtain energy-optimal walking motions for this biped, deriving the periodic body and platform motions that minimize a simple metabolic energy cost. When the platform has an externally imposed sinusoidal displacement of appropriate frequency and amplitude, we predict that body motion entrained to platform motion consumes less energy than walking on a fixed surface. When the platform has finite inertia, a mass- spring-damper with similar parameters to the Millennium Bridge, we show that the optimal biped walking motion sustains a large lateral platform oscillation when sufficiently many people walk on the bridge. Here, the biped model reduces walking metabolic cost by storing and recovering energy from the platform, demonstrating energy benefits for two features observed for walking on the Millennium Bridge: crowd synchrony and large lateral oscillations.

SUBMITTER: Joshi V

PROVIDER: S-EPMC4309130 | biostudies-literature | 2015 Feb

REPOSITORIES: biostudies-literature

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Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal.

Joshi Varun V Srinivasan Manoj M

Proceedings. Mathematical, physical, and engineering sciences 20150201 2174

Understanding how humans walk on a surface that can move might provide insights into, for instance, whether walking humans prioritize energy use or stability. Here, motivated by the famous human-driven oscillations observed in the London Millennium Bridge, we introduce a minimal mathematical model of a biped, walking on a platform (bridge or treadmill) capable of lateral movement. This biped model consists of a point-mass upper body with legs that can exert force and perform mechanical work on t ...[more]

PMID: 25663810

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Project description:The temporal dynamics of stride-to-stride fluctuations in steady-state walking reveal important information about locomotor control and can be quantified using so-called fractal analyses, notably the detrended fluctuation analysis (DFA). Gait dynamics are often collected during treadmill walking using 3-D motion capture to identify gait events from kinematic data. The sampling frequency of motion capture systems may impact the precision of event detection and consequently impact the quantification of stride-to-stride variability. This study aimed i) to determine if collecting multiple walking trials with different sampling frequency affects DFA values of spatiotemporal parameters during treadmill walking, and ii) to determine the reliability of DFA values across downsampled conditions. Seventeen healthy young adults walked on a treadmill while their gait dynamics was captured using different sampling frequency (60, 120 and 240 Hz) in each condition. We also compared data from the highest sampling frequency to downsampled versions of itself. We applied DFA to the following time series: step length, time and speed, and stride length, time and speed. Reliability between experimental conditions and between downsampled conditions were measured with 1) intraclass correlation estimates and their 95% confident intervals, calculated based on a single-measurement, absolute-agreement, two-way mixed-effects model (ICC 3,1), and 2) Bland-Altman bias and limits of agreement. Both analyses revealed a poor reliability of DFA results between conditions using different sampling frequencies, but a relatively good reliability between original and downsampled spatiotemporal variables. Collectively, our results suggest that using sampling frequencies of 120 Hz or 240 Hz provide similar results, but that using 60 Hz may alter DFA values. We recommend that gait kinematics should be collected at around 120 Hz, which provides a compromise between event detection accuracy and processing time.

Project description:Variability is ubiquitous in human movement, arising from internal and external noise, inherent biological redundancy, and from the neurophysiological control actions that help regulate movement fluctuations. Increased walking variability can lead to increased energetic cost and/or increased fall risk. Conversely, biological noise may be beneficial, even necessary, to enhance motor performance. Indeed, encouraging more variability actually facilitates greater improvements in some forms of locomotor rehabilitation. Thus, it is critical to identify the fundamental principles humans use to regulate stride-to-stride fluctuations in walking. This study sought to determine how humans regulate stride-to-stride fluctuations in stepping movements during treadmill walking. We developed computational models based on pre-defined goal functions to compare if subjects, from each stride to the next, tried to maintain the same speed as the treadmill, or instead stay in the same position on the treadmill. Both strategies predicted average behaviors empirically indistinguishable from each other and from that of humans. These strategies, however, predicted very different stride-to-stride fluctuation dynamics. Comparisons to experimental data showed that human stepping movements were generally well-predicted by the speed-control model, but not by the position-control model. Human subjects also exhibited no indications they corrected deviations in absolute position only intermittently: i.e., closer to the boundaries of the treadmill. Thus, humans clearly do not adopt a control strategy whose primary goal is to maintain some constant absolute position on the treadmill. Instead, humans appear to regulate their stepping movements in a way most consistent with a strategy whose primary goal is to try to maintain the same speed as the treadmill at each consecutive stride. These findings have important implications both for understanding how biological systems regulate walking in general and for being able to harness these mechanisms to develop more effective rehabilitation interventions to improve locomotor performance.

Dataset Information

Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal.

Publications

Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal.

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