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IntroductionBiomechanical changes due to aging increase the oxygen consumption of walking by over 30%. When this is coupled with reduced oxygen uptake capacity, the ability to sustain walking becomes compromised. This reduced physical activity and mobility can lead to further physical degeneration and mortality. Unfortunately, the underlying reasons for the increased metabolic cost are still inadequately understood. While motion capture systems can measure signals with high temporal resolution, it is impossible to directly characterize the fluctuation of metabolic cost throughout the gait cycle. MethodsTo address this issue, this research focuses on computing the metabolic cost time series from the mean value using two neural-network-based approaches: autoencoders (AEs) and expanders. For the AEs, the encoders are designed to compress the input time series down to their mean value, and the decoder expands those values into the time series. After training, the decoder is extracted and applied to mean metabolic cost values to compute the time series. A second approach leverages an expander to map the mean values to the time series without an encoder. The networks are trained using ten different metabolic cost models generated by a computational walking model that simulates the gait cycle subjected to 35 different robotic perturbations without using experimental input data. The networks are validated using the estimated metabolic costs for the unperturbed gait cycle. ResultsThe investigation found that AEs without tied weights and the expanders performed best using nonlinear activation functions, while the AEs with tied weights performed best with linear activation functions. Unexpectedly, the results show that the expanders outperform the AEs. DiscussionA limitation of this research is the reliance on time series for the initial training. Future efforts will focus on developing methods that overcome this issue. Improved methods for estimating within-stride fluctuations in metabolic cost have the potential of improving rehabilitation and assistive devices by targeting the gait phases with increased metabolic cost. This research could also be applied to expand sparse measurements to locations or times that were not measured explicitly. This application would reduce the number of measurement points required to capture the response of a system.
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This content will become publicly available on November 1, 2026
Natural variability can increase human walking metabolic costs and its implications to simulation-based metabolic estimation
Human walking contains variability due to small intrinsic perturbations arising from sensory or motor noise, or to promote motor learning. We hypothesize that such stride-to-stride variability may increase the metabolic cost of walking over and above a perfectly periodic motion, and that neglecting such variability in simulations may mis-estimate the metabolic cost. Here, we quantify the metabolic estimation errors accrued by neglecting the stride-to-stride variability using human data and a musculoskeletal model by comparing the cost of multiple strides of walking and the cost of a perfectly periodic stride with averaged kinematics and kinetics. We find that using an averaged stride underestimates the cost by approximately 2.5%, whereas using a random stride may mis-estimate the cost positively or negatively by up to 15%, ignoring the contribution of measurement errors to the observed stride-to-stride variability. As a further illustration of the cost increase in a simpler dynamical context, we use a feedback-controlled inverted pendulum walking model to show that increasing the sensory or motor noise increases the overall metabolic cost, as well as the variability of stride-to-stride metabolic costs, as seen with the musculoskeletal simulations. Our work establishes the importance of accounting for stride-to-stride variability when estimating metabolic costs from motion.
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- Award ID(s):
- 2014506
- PAR ID:
- 10652188
- Publisher / Repository:
- Royal Society Publishing
- Date Published:
- Journal Name:
- Journal of The Royal Society Interface
- Volume:
- 22
- Issue:
- 232
- ISSN:
- 1742-5662
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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