University of North Texas, Kinesiology, Health Promotion and Recreation, Denton 76203, USA.
Int J Sports Med. 2011 Jul;32(7):519-22. doi: 10.1055/s-0031-1275298. Epub 2011 May 11.
The purpose of this study was to evaluate the effect of using different mathematical models to describe the relationship between treadmill running speed and time to exhaustion. All models generated a value for an aerobic parameter (critical speed; S (critical)). 35 university students performed 5-7 constant-speed 0%-slope treadmill tests at speeds that elicited exhaustion in ∼3 min to ∼10 min. Speed and time data were fitted using 3 models: (1) a 2-parameter hyperbolic model; (2) a 3-parameter hyperbolic model; and (3) a hybrid 3-parameter hyperbolic+exponential model. The 2-parameter model generated values for S (critical) (mean (± SD): 186 ± 33 m·min (-1)) and anaerobic distance capacity (ADC; 251 ± 122 m) with a high level of statistical certainty (i.e., with small SEEs). The 3-parameter models generated parameter estimates that were unrealistic in magnitude and/or associated with large SEEs and little statistical certainty. Therefore, it was concluded that, for the range of exercise durations used in the present study, the 2-parameter model is preferred because it provides a parsimonious description of the relationship between velocity and time to fatigue, and it produces parameters of known physiological significance, with excellent confidence.
本研究旨在评估使用不同数学模型来描述跑步机跑步速度与力竭时间之间关系的效果。所有模型都生成了一个有氧参数（临界速度；S(critical)）的值。35 名大学生在坡度为 0%的跑步机上进行了 5-7 次等速测试，这些测试的速度在大约 3 分钟到大约 10 分钟内会让人筋疲力尽。速度和时间数据使用 3 种模型进行拟合：（1）双参数双曲线模型；（2）三参数双曲线模型；和（3）混合三参数双曲线+指数模型。双参数模型生成的临界速度（S(critical)）（平均值（±SD）：186 ± 33 m·min(-1)) 和无氧距离能力（ADC；251 ± 122 m）的数值具有较高的统计可信度（即，SEE 较小）。三参数模型生成的参数估计值在数量上不切实际，并且/或者与较大的 SEE 和较小的统计可信度相关。因此，结论是，对于本研究中使用的运动持续时间范围，双参数模型是首选，因为它提供了速度和疲劳时间之间关系的简洁描述，并且产生了具有已知生理意义的参数，具有极佳的置信度。
