ArticleEuropean journal of applied physiology2026
Metabolic energy expenditure during level, uphill, and downhill running.
Article in European journal of applied physiology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- Oxygen uptake on-kinetics during horizontal and uphill treadmill running in moderate- and severe-intensity domains.European journal of applied physiology · 2026Article
- Modeling heart rate (HR) dynamics to reconstruct missing HR data in trail running.BMC sports science, medicine & rehabilitation · 2026Article
Corrections and comments
- Erratum issued
Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
purposeTo extend the Running Energy Expenditure Estimation (RE3) model for predicting metabolic rates during uphill and downhill running as well as to enhance the Hoogkamer-Taboga-Kram (HTK) equation for estimating metabolic rates during level and uphill running.
methodsWe combined running metabolic data from an original dataset (n = 62) with individual subject data from 26 studies (n = 424) and group mean data from 12 studies (n = 187). Using this integrated dataset, we derived a new graded running term for the empirical RE3 model and updated the HTK equation coefficients for level and uphill running. We then compared the accuracy and precision of these new equations with the established American College of Sports Medicine (ACSM) and Minetti et al. equations based on the root-mean-square deviation (RMSD).
resultsAccuracy and precision of estimating level Ṁ were high for the Minetti et al. (RMSD, 1.44 W kg
conclusionThe improved RE3 and HTK equations estimate metabolic rates during level and graded running with improved accuracy and precision. We provide a publicly available web-based metabolic rate calculator that simplifies estimation for researchers, practitioners, and runners alike.
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