{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T21:51:51Z","timestamp":1790718711406,"version":"4.1.0"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:00:00Z","timestamp":1781136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Trail running imposes highly variable biomechanical demands due to steep, irregular terrain that renders flat-road pacing models inadequate. We present a physics-based digital twin that integrates a terrain-adaptive grade-adjusted pace (GAP) model with individualised physiological calibration to predict finish time across heterogeneous trail-running races. The GAP core applies Minetti\u2019s fifth-degree metabolic cost polynomial to map slope-dependent energy cost across the full range of uphill and downhill gradients encountered in trail racing. Segment-by-segment pace is further modulated by an altitude\u2013VO2max correction, a Banister TRIMP-based fatigue term, and a progressive pacing-decay factor. Course-elevation profiles are extracted from 1 Hz barometric altimeter data through a five-step normalisation pipeline. Individual parameters (sustainable VT2 fraction \u03b1; pacing-decay slope \u03bc) were calibrated by grid search against 13 race sessions. A sequential validation across four model-complexity stages showed R2 increasing from 0.763 to 0.905. Leave-one-out cross-validation (n = 13) yielded R2 = 0.864, MAE = 18.2 min, MAPE = 11.1%, and a small positive bias (+2.0 min). The framework demonstrates that integrating biomechanical terrain correction with individual physiological calibration substantially improves race-time prediction for trail running, offering a promising foundation for athlete-specific pre-race simulation.<\/jats:p>","DOI":"10.3390\/s26123731","type":"journal-article","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T01:52:08Z","timestamp":1781229128000},"page":"3731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Physics-Based Digital Twin for Trail Running Race Performance Prediction: A Proof-of-Concept Study"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0588-0871","authenticated-orcid":false,"given":"Diego","family":"Ja\u00e9n-Carrillo","sequence":"first","affiliation":[{"name":"Department of Sport Science, University of Innsbruck, 6020 Innsbruck, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9575-7465","authenticated-orcid":false,"given":"Daniel","family":"Pattis","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University of Innsbruck, 6020 Innsbruck, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s40279-016-0605-y","article-title":"Biomechanics and Physiology of Uphill and Downhill Running","volume":"47","author":"Vernillo","year":"2017","journal-title":"Sports Med."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Perrotin, N., Gardan, N., Lesprillier, A., Le Goff, C., Seigneur, J.-M., Abdi, E., Sanudo, B., and Taiar, R. (2021). Biomechanics of trail running performance: Quantification of spatio-temporal parameters by using low cost sensors in ecological conditions. Appl. Sci., 11.","DOI":"10.3390\/app11052093"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1152\/japplphysiol.01177.2001","article-title":"Energy cost of walking and running at extreme uphill and downhill slopes","volume":"93","author":"Minetti","year":"2002","journal-title":"J. Appl. Physiol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1123\/ijspp.2024-0390","article-title":"Pacing Strategy and Resulting Performance of Elite Trail Runners: Insights From the 2023 World Mountain and Trail Running Championships","volume":"20","author":"Holler","year":"2025","journal-title":"Int. J. Sports Physiol. Perform."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Suter, D., Sousa, C.V., Hill, L., Scheer, V., Nikolaidis, P.T., and Knechtle, B. (2020). Even Pacing Is Associated with Faster Finishing Times in Ultramarathon Distance Trail Running\u2014The \u201cUltra-Trail du Mont Blanc\u201d 2008\u20132019. Int. J. Environ. Res. Public Health, 17.","DOI":"10.3390\/ijerph17197074"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jidovtseff, B., and De Cock, F. (2026). Field-based modelling of segment speed in trail running using GPS and course characteristics. Int. J. Perform. Anal. Sport, 1\u201314.","DOI":"10.1080\/24748668.2026.2651537"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1113\/jphysiol.2007.143834","article-title":"Endurance exercise performance: The physiology of champions","volume":"586","author":"Joyner","year":"2008","journal-title":"J. Physiol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1152\/japplphysiol.00546.2015","article-title":"Energetics of vertical kilometer foot races; is steeper cheaper?","volume":"120","author":"Giovanelli","year":"2016","journal-title":"J. Appl. Physiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"125104","DOI":"10.1016\/j.eswa.2024.125104","article-title":"Digital twins in sport: Concepts, taxonomies, challenges and practical potentials","volume":"258","author":"Fister","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_10","first-page":"1271","article-title":"Digital twins in sports science: Applications for performance enhancement, injury prevention, and rehabilitation through advanced big data analytics and deep learning methodologies\u2014A comprehensive narrative review","volume":"43","author":"Barbaria","year":"2025","journal-title":"Biol. Sport"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1249\/mss.0b013e3181590bc2","article-title":"Assessment of speed and position during human locomotion using nondifferential GPS","volume":"40","author":"Townshend","year":"2008","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1007\/s00421-005-0081-9","article-title":"Linear decrease in and performance with increasing altitude in endurance athletes","volume":"96","author":"Wehrlin","year":"2006","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_13","first-page":"57","article-title":"A systems model of training for athletic performance","volume":"7","author":"Banister","year":"1975","journal-title":"Aust. J. Sports Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1152\/jappl.1991.71.3.1151","article-title":"Optimizing athletic performance by influence curves","volume":"71","author":"Morton","year":"1991","journal-title":"J. Appl. Physiol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1097\/00005768-199602000-00015","article-title":"Modeled responses to training and taper in competitive swimmers","volume":"28","author":"Mujika","year":"1996","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1249\/mss.0b013e31802d3aba","article-title":"Impact of weather on marathon-running performance","volume":"39","author":"Ely","year":"2007","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18433","DOI":"10.3390\/s141018433","article-title":"The effect of different global navigation satellite system methods on positioning accuracy in elite alpine skiing","volume":"14","author":"Gilgien","year":"2014","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1080\/02640414.2015.1022870","article-title":"Energy cost and kinematics of level, uphill and downhill running: Fatigue-induced changes after a mountain ultramarathon","volume":"33","author":"Vernillo","year":"2015","journal-title":"J. Sports Sci."},{"key":"ref_19","first-page":"1353","article-title":"Toward autonomous artificial intelligence agents in sports science: A modular framework for development, validation, and implementation","volume":"43","author":"Dergaa","year":"2026","journal-title":"Biol. Sport"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1007\/s40279-021-01459-0","article-title":"The importance of \u2018durability\u2019 in the physiological profiling of endurance athletes","volume":"51","author":"Maunder","year":"2021","journal-title":"Sports Med."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/12\/3731\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T04:23:03Z","timestamp":1781842983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/12\/3731"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,11]]},"references-count":20,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["s26123731"],"URL":"https:\/\/doi.org\/10.3390\/s26123731","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,11]]}}}