Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks
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 a...
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Frontiers Media S.A.
2025-06-01
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| Series: | Frontiers in Bioengineering and Biotechnology |
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| author | Manal Mustafa Alex C. Dzewaltowski Alex C. Dzewaltowski Philippe Malcolm Keegan J. Moore Keegan J. Moore |
| author_facet | Manal Mustafa Alex C. Dzewaltowski Alex C. Dzewaltowski Philippe Malcolm Keegan J. Moore Keegan J. Moore |
| author_sort | Manal Mustafa |
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| description | 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. |
| format | Article |
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| institution | OA Journals |
| issn | 2296-4185 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Bioengineering and Biotechnology |
| spelling | doaj-art-8ebcc6f1645f48b5b73167ed1531ed8f2025-08-20T02:09:24ZengFrontiers Media S.A.Frontiers in Bioengineering and Biotechnology2296-41852025-06-011310.3389/fbioe.2025.15790851579085Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networksManal Mustafa0Alex C. Dzewaltowski1Alex C. Dzewaltowski2Philippe Malcolm3Keegan J. Moore4Keegan J. Moore5Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, United StatesDepartment of Biomechanics, University of Nebraska Omaha, Omaha, NE, United StatesScholl College of Podiatric Medicine, Rosalind Franklin University of Medicine and Science, North Chicago, IL, United StatesDepartment of Biomechanics, University of Nebraska Omaha, Omaha, NE, United StatesDepartment of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, United StatesDaniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, United StatesIntroductionBiomechanical 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.https://www.frontiersin.org/articles/10.3389/fbioe.2025.1579085/fullwalkingbiomechanicsenergeticsmachine learningsystem identification |
| spellingShingle | Manal Mustafa Alex C. Dzewaltowski Alex C. Dzewaltowski Philippe Malcolm Keegan J. Moore Keegan J. Moore Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks Frontiers in Bioengineering and Biotechnology walking biomechanics energetics machine learning system identification |
| title | Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks |
| title_full | Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks |
| title_fullStr | Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks |
| title_full_unstemmed | Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks |
| title_short | Estimating within-stride metabolic cost from stride-average data using autoencoders and expander networks |
| title_sort | estimating within stride metabolic cost from stride average data using autoencoders and expander networks |
| topic | walking biomechanics energetics machine learning system identification |
| url | https://www.frontiersin.org/articles/10.3389/fbioe.2025.1579085/full |
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