Centre for Health Sciences Research, University of Salford, PO34 Brian Blatchford Building, Manchester, M6 6PU, United Kingdom.
Gait Posture. 2020 Jul;80:318-323. doi: 10.1016/j.gaitpost.2020.06.023. Epub 2020 Jun 20.
The spring-mass model is commonly used to investigate the mechanical characteristics of human running. Underlying this model is the assumption of a linear force-length relationship, during the stance phase of running, and the idea that stiffness can be characterised using a single spring constant. However, it remains unclear whether the assumption of linearity is valid across different running styles.
How does the linearity of the force-length curve vary across a sample of runners and is there an association between force-length linearity and foot-strike index/speed?
Kinematic and kinetic data were collected from twenty-eight participants who ran overground at four speeds. The square of the Pearson's correlation coefficient, R, was used to quantify linearity; with a threshold of R ≥ 0.95 selected to define linear behaviour. A linear mixed model was used to investigate the association between linearity and foot-strike index and speed.
Only 36-46 % of participants demonstrated linear force-length behaviour across the four speeds during the loading phase. Importantly, the linear model showed a significant effect of both foot-strike index and speed on linearity during the loading phase (p = 0.003 and p < 0.001, respectively).
This study showed that the assumption of a linear force-length relationship is not appropriate for all runners. These findings suggest that the use of the spring-mass model, and a constant value of stiffness, may not be appropriate for characterising and comparing different running styles. Given these findings, it may be better to restrict the use of the spring-mass model to individuals who exhibit linear force-length dependence. It would also be appropriate for future studies, characterising stiffness using the spring-mass model, to report data on force-length linearity across the cohort under study.
弹簧质量模型常用于研究人体跑步的力学特性。该模型的基础是假设在跑步的支撑阶段存在线性力-长度关系，并且认为刚度可以用单个弹簧常数来描述。然而，在不同的跑步方式下，线性假设是否成立仍不清楚。
在一组跑步者中，力-长度曲线的线性度如何变化，力-长度线性度与足触地指数/速度之间是否存在关联？
从以四种速度在地面上跑步的二十八名参与者中收集运动学和动力学数据。使用皮尔逊相关系数的平方，R，来量化线性度；选择 R≥0.95 作为线性行为的阈值。使用线性混合模型来研究线性度与足触地指数和速度之间的关联。
只有 36-46%的参与者在加载阶段的四个速度下表现出力-长度的线性行为。重要的是，线性模型显示足触地指数和速度对加载阶段的线性度都有显著影响（p=0.003 和 p<0.001）。
本研究表明，线性力-长度关系的假设并不适用于所有跑步者。这些发现表明，使用弹簧质量模型和恒定的刚度值可能不适于描述和比较不同的跑步方式。鉴于这些发现，限制弹簧质量模型的使用可能更适合于表现出线形力-长度依赖性的个体。未来使用弹簧质量模型来描述刚度的研究也应该报告研究队列中力-长度线性度的数据。
