title: Modeling of Running Performances in Humans: Comparison of Power Laws and Critical Speed.
abstract: Zinoubi, B, Vandewalle, H, and Driss, T. Modeling of running performances in humans: comparison of power laws and critical speed. J Strength Cond Res 31(7): 1859-1867, 2017-The concepts of power law and critical speed (SCrit) have been applied to the analysis of individual running performances. We have analyzed the results of 2 exceptional runners (Nurmi and Gebrselassie) and 11 physical education students (PESs) who performed 3 exhausting running exercises. Power laws can accurately describe the relationships between exhaustion time (tlim) and distance (Dlim) or speed (S) (Equation is included in full-text article.)in elite runners and PES. However, the validity of the application of power laws must be verified for higher values of tlim in nonelite runners. Exponent γ is close to 1 in elite runners and lower in PESs (from 0.625 to 0.872). The value of SCrit was computed from 2 values of tlim (3-14 minutes; SCrit 3-14) and was expressed as a fraction of maximal aerobic speed (MAS) which was assumed to correspond to the maximal speed that can be sustained over 7 minutes (Equation is included in full-text article.)The individual values of (Equation is included in full-text article.)(0.945 for Gebrselassie, 0.919 for Nurmi, and 0.764 ± 0.078 in PESs) were linearly correlated with γ (r > 0.999) and almost equal to γ (0.952 for Gebrselassie, 0.918 for Nurmi, and 0.779 ± 0.076 for PESs). The same results were observed when SCrit was computed for tlim equal to 6-28 minutes (SCrit 6-28) and MAS was the maximal velocity sustainable during 14 minutes (S14min). The fact that γ is linearly correlated and almost equal to (Equation is included in full-text article.)or (Equation is included in full-text article.)suggests that exponent γ can be considered as an index of aerobic endurance.
authors.affiliation: 1Laboratory CeRSM (EA 2931), Research Center on Sport and Movement; Group of Physiology, Biomechanics and Imagery of Movement; Sciences and Techniques of the Physical and Sporting Activities; University of Paris West Nanterre La Defense, Nanterre, France; and 2Laboratory of Physiology, UFR of Health, Medicine and Human Biology; University of Paris XIII, Bobigny, France.
authors.forename: Badrane
authors.initials: B
authors.lastname: Zinoubi
authors.forename: Henry
authors.initials: H
authors.lastname: Vandewalle
authors.forename: Tarak
authors.initials: T
authors.lastname: Driss
mesh_terms: D000328:Adult; D056352:Athletes; D005221:Fatigue / Q000503:physiopathology; D005260:Female; D006801:Humans; D008297:Male; D008954:Models, Biological; D010101:Oxygen Consumption / Q000502:physiology; D010807:Physical Endurance / Q000502:physiology; D012420:Running / Q000502:physiology*