Background

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.

Research question

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?

Methods

Kinematic and kinetic data were collected from twenty-eight participants who ran overground at four speeds. The square of the Pearson’s correlation coefficient, R², was used to quantify linearity; with a threshold of R² ≥ 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.

Results

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).

Significance

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.

中文翻译：

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使用弹簧质量模型进行跑步：力长曲线和踩脚模式。

背景

弹簧质量模型通常用于研究人体跑步的机械特性。该模型的基础是在步态站立阶段假设线性力与长度的关系，以及可以使用单个弹簧常数来表征刚度的想法。然而，目前尚不清楚线性假设是否适用于不同的跑步风格。

研究问题

力长曲线的线性度在整个跑步者样本中如何变化，并且力长曲线的线性度和脚踏指数/速度之间有关联吗？

方法

运动和动力学数据是从以四种速度在地面跑过的28位参与者收集的。皮尔逊相关系数R ²的平方用于量化线性度。其中R的阈值² ≥0.95选定以限定线性行为。使用线性混合模型来研究线性与脚踩指数和速度之间的关系。

结果

在装载阶段，只有36–46％的参与者表现出四种速度下的线性力长行为。重要的是，线性模型显示出在装车阶段，脚踩指数和速度都对线性有显着影响（分别为p = 0.003和p <0.001）。

意义

这项研究表明，线性力长关系的假设并不适合所有跑步者。这些发现表明，使用弹簧质量模型以及恒定的刚度值可能不适用于表征和比较不同的行驶方式。鉴于这些发现，最好将弹簧质量模型的使用范围限制为具有线性力长度依赖性的个体。对于使用弹簧质量模型表征刚度的未来研究来说，报告整个研究人群的力长线性数据也很合适。