Subscribe to RSS
DOI: 10.1055/a-2558-6349
Running critical power modeling: insights into physiological and neuromuscular performance factors

Abstract
This study aims to determine the relationship between the critical power and the work above critical power (W′) with physiological and neuromuscular performance factors. Twenty-one recreational runners, 11 men and 10 women, were tested on three separate occasions spaced by 48–72 hours. In the first testing session, the vertical load–velocity and horizontal force–velocity profiles were determined. In the second testing session, the maximal oxygen uptake, running economy, first and second ventilatory thresholds and maximal aerobic power were determined through a graded exercise test. In the third testing session, the critical power and W′ were determined through two-time trials of 9- and 3-minutes. The critical power was significantly correlated with all physiological factors evaluated (r≥− 0.479; p≤0.028); meanwhile, none were with W′ (r≤0.377; p≥0.092). On the other hand, W′ was positively associated with specific neuromuscular performance factors of the vertical load–velocity (r=0.763; p<0.001; i.e., theoretical maximal vertical velocity) and horizontal force–velocity (r≥0.658; p≤0.001; i.e., theoretical maximal horizontal velocity and maximal power) profiles. The critical power modelling results in a feasible procedure to capture both physiological and neuromuscular performance determinants through the critical power and W′ parameters, respectively.
Publication History
Received: 10 December 2024
Accepted after revision: 13 March 2025
Accepted Manuscript online:
13 March 2025
Article published online:
18 April 2025
© 2025. Thieme. All rights reserved.
Georg Thieme Verlag KG
Oswald-Hesse-Straße 50, 70469 Stuttgart, Germany
-
References
- 1 Stellingwerff T, Bovim IM, Whitfield J. Contemporary nutrition interventions to optimize performance in middle-distance runners. Int J Sport Nutr Exerc Metab 2019; 29 (02) 106-116
- 2 Ingham SA, Whyte GP, Pedlar C, Bailey DM, Dunman N, Nevill AM. Determinants of 800-m and 1500-m running performance using allometric models. Med Sci Sports Exerc 2008; 40 (02) 345-350
- 3 Jones AM, Kirby BS, Clark IE. et al. Physiological demands of running at 2-hour marathon race pace. J Appl Physiol 2021; 130 (02) 369-379
- 4 Souza KM, Vieira G, Baldi MF, Guglielmo LGA, Lucas RD, Denadai BS. Physiological and neuromuscular variables associated to aerobic performance in endurance runners: Effects of the event distance. Rev Bras Med Esporte 2011; 17: 40-44
- 5 Jones AM. A five year physiological case study of an Olympic runner. Br J Sports Med 1998; 32 (01) 39-43
- 6 Grant S, Craig I, Wilson J, Aitchison T. The relationship between 3 km running performance and selected physiological variables. J Sports Sci 1997; 15 (04) 403-410
- 7 Kumagai S, Tanaka K, Matsuura Y, Matsuzaka A, Hirakoba K, Asano K. Relationships of the anaerobic threshold with the 5 km, 10 km, and 10 mile races. Eur J Appl Physiol Occup Physiol 1982; 49 (01) 13-23
- 8 Gómez-Molina J, Ogueta-Alday A, Camara J, Stickley C, Rodríguez-Marroyo JA, García-López J. Predictive variables of half-marathon performance for male runners. J Sports Sci Med 2017; 16 (02) 187-194
- 9 Van Hooren B, Jukic I, Cox M, Frenken KG, Bautista I, Moore IS. The relationship between running biomechanics and running economy: a systematic review and meta-analysis of observational studies. Sports Med 2024; 54: 1269-1316
- 10 Barnes KR, Kilding AE. Running economy: measurement, norms, and determining factors. Sports Med Open 2015; 1: 8
- 11 Paavolainen L, Häkkinen K, Hämäläinen I, Nummela A, Rusko H. Explosive-strength training improves 5-km running time by improving running economy and muscle power. J Appl Physiol 1999; 86: 1527-33
- 12 Houmard JA, Costill DL, Mitchell JB, Park SH, Chenier TC. The role of anaerobic ability in middle-distance running performance. Eur J Appl Physiol Occup Physiol 1991; 62: 40-43
- 13 Cole AS, Woodruff ME, Horn MP, Mahon AD. Strength, power, and aerobic exercise correlates of 5-km cross-country running performance in adolescent runners. Pediatr Exerc Sci 2006; 18 (03) 374-384
- 14 Spurrs RW, Murphy AJ, Watsford ML. The effect of plyometric training on distance running performance. Eur J Appl Physiol 2003; 89: 1-7
- 15 Li F, Newton RU, Shi Y, Sutton D, Ding H. Correlation of eccentric strength, reactive strength, and leg stiffness with running economy in well-trained distance runners. J Strength Cond Res 2021; 35 (06) 1491-1499
- 16 James LP, Talpey SW, Young WB, Geneau MC, Newton RU, Gastin PB. Strength classification and diagnosis: not all strength is created equal. Strength Cond J 2023; 45 (03) 333-341
- 17 Pérez-Castilla A, Ramirez-Campillo R, Fernandes J, García-Ramos A. Feasibility of the 2-point method to determine the load−velocity relationship variables during the countermovement jump exercise. J Sport Health Sci 2023; 12 (04) 544-552
- 18 Pérez-Castilla A, Jukic I, Janicijevic D, Akyildiz Z, Senturk D, García-Ramos A. Load-velocity relationship variables to assess the maximal neuromuscular capacities during the back-squat exercise. Sports Health 2022; 14 (06) 885-893
- 19 Romero-Franco N, Jiménez-Reyes P, Castaño-Zambudio A. et al. Sprint performance and mechanical outputs computed with an iPhone app: Comparison with existing reference methods. Eur J Sport Sci 2017; 17 (04) 386-392
- 20 Gaesser GA, Wilson LA. Effects of continuous and interval training on the parameters of the power-endurance time relationship for high-intensity exercise. Int J Sports Med 1988; 9 (06) 417-421
- 21 Sawyer BJ, Stokes DG, Womack CJ, Morton RH, Weltman A, Gaesser GA. Strength training increases endurance time to exhaustion during high-intensity exercise despite no change in critical power. J Strength Cond Res 2014; 28 (03) 601-609
- 22 Hill DW. The critical power concept: a review. Sports Med 1993; 16: 237-254
- 23 Caswell A. The influence of biological sex, hemoglobin mass, and skeletal muscle characteristics on cycling critical power. University of Calgary; 2023
- 24 Galantine P, Sudlow A, Peyrot N. et al. Force–velocity profile in sprinting: sex effect. Eur J Appl Physiol 2023; 123 (04) 911-921
- 25 Ruiz-Alias SA, Ñancupil-Andrade AA, Pérez-Castilla A, García-Pinillos F. Power or speed: Which metric is more accurate for modelling endurance running performance on track?. Eur J Sport Sci 2024; 24: 1597-1603
- 26 Ruiz-Alias SA, Olaya-Cuartero J, Ñancupil-Andrade AA, García-Pinillos F. 9/3-minute running critical power test: mechanical threshold location with respect to ventilatory thresholds and maximum oxygen uptake. Int J Sports Physiol Perform 2022; 17 (07) 1111-1118
- 27 Dearing CG, Paton CD. Is Stryd critical power a meaningful parameter for runners?. Biol Sport 2023; 40 (03) 657-664
- 28 Pérez-Castilla A, Piepoli A, Delgado-García G, Garrido-Blanca G, García-Ramos A. Reliability and concurrent validity of seven commercially available devices for the assessment of movement velocity at different intensities during the bench press. J Strength Cond Res 2019; 33 (05) 1258-1265
- 29 Guidetti L, Meucci M, Bolletta F, Emerenziani GP, Gallotta MC, Baldari C. Validity, reliability and minimum detectable change of COSMED K5 portable gas exchange system in breath-by-breath mode. PLoS One 2018; 13 (12) e0209925
- 30 Imbach F, Candau R, Chailan R, Perrey S. Validity of the Stryd power meter in measuring running parameters at submaximal speeds. Sports 2020; 8 (07) 103
- 31 Whipp B, Huntsman DS, Storer TW, Lamarra N, Wasserman K. A constant which determines the duration of tolerance to high-intensity work. FASEB J 1982; 41: 1591
- 32 Hopkins WG, Marshall SW, Batterham AM, Hanin J. Progressive statistics for studies in sports medicine and exercise science. Med Sci Sports Exerc 2009; 41: 3-13
- 33 Henneman E. Relation between size of neurons and their susceptibility to discharge. Science 1957; 126 (3287) 1345-1347
- 34 Goulding RP, Burnley M, Wüst R. How priming exercise affects oxygen uptake kinetics: from underpinning mechanisms to endurance performance. Sports Med 2023; 53 (05) 959-976
- 35 Jaén-Carrillo D, Roche-Seruendo LE, Felton L, Cartón-Llorente A, García-Pinillos F. Stiffness in running: a narrative integrative review. Strength Cond J 2021; 43 (02) 104-115
- 36 Bishop D, Jenkins DG. The influence of resistance training on the critical power function & time to fatigue at critical power. Aust J Sci Med Sport 1996; 28 (04) 101-105
- 37 Karsten B, Stevens L, Colpus M, Larumbe-Zabala E, Naclerio F. The effects of a sport-specific maximal strength and conditioning training on critical velocity, anaerobic running distance, and 5-km race performance. Int J Sports Physiol Perform 2016; 11: 80-85
- 38 Ruiz-Alias SA, Ñancupil-Andrade AA, Pérez-Castilla A, García-Pinillos F. Running Critical Power and W’: Influence of the Environment, Timing and Time Trial Order. Int J Sports Med 2024; 45 (04) 309-315
- 39 Ruiz-Alias SA, Ñancupil-Andrade AA, Pérez-Castilla A, García-Pinillos F. Running critical power: between-day, interlimb and interunit reliability. Sports Eng 2024; 27 (01) 10