Using the spring-mass model for running: Force-length curves and foot-strike patterns

Abstract

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, R 2 , was used to quantify linearity; with a threshold of R 2 ≥ 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.

Using statistical parametric mapping to assess the association of duty factor and step frequency on running kinetic

“…This result corroborates the choice made by several authors to use the decompression phase instead of the compression one to calculate the vertical stiffness (Cavagna et al, 1988;Schepens et al, 1998). Deviation from linearity of the force-length relationship among individuals was also reported by Gill et al (2020). Indeed, these authors reported that the linearity of the force-length curve was foot-strike index (foot-strike pattern) dependent and that this curve should be investigated before using the spring-mass model.…”

“…The spring-mass characteristics of the lower limb were assessed by computing the force-length relationship ( Gill et al, 2020 ), i.e., the force vector projected along the leg as function of the leg compression/decompression during stance, and ( Liew et al, 2017 ), calculated using both the compression and decompression of the human body ( Gill et al, 2020 ) and adapted from Liew et al (2017) . More explicitly, compressive ( k leg, comp ) and decompressive ( k leg, decomp ) leg stiffnesses were given by the maximum of the force vector projected along the leg ( F leg,max ) divided by the maximum leg compression ( ∆L comp ) and decompression ( ∆L decomp ) during stance, respectively.…”

“…The linearity of the force-length relationship was quantified using the coefficient of determination ( ) during both leg compression ( ) and decompression ( ). However, the calculation of was modified so that and values were computed by comparing the compression and decompression force-length relationships to the perfectly elastic compression and decompression lines, i.e., linear relations obtained using slopes equal to k leg, comp and k leg, decomp , respectively ( Gill et al, 2020 ). In other words, evaluates how far the force-length relationship is from a linear model obtained using .…”

“…Besides, force related variables that additionally consider the temporal aspect of the running step were also considered because the latter can vary with DF and SF. The third purpose of the present study was to investigate the association of DF and SF on the force-length relationship ( Gill et al, 2020 ) and ( Liew et al, 2017 ).…”

Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

“…This suggests that the mechanical stiffness during braking and propulsion phases does not necessarily have to be the same. To understand the phenomena occurring during running tasks, it seems necessary to determine the mechanical stiffness for both these phases separately [ 154 , 155 ]. Such an approach has been used in a number of studies, although these approaches differ.…”