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

Gill, Niamh; Preece, SJ; Baker, Richard

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, R2
, 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.

• Journal Article Type: Article
• Acceptance Date: Jun 16, 2020
• Online Publication Date: Jun 20, 2020
• Publication Date: 2020-07
• Deposit Date: Jun 22, 2020
• Publicly Available Date: Jun 20, 2021
• Journal: Gait & Posture
• Print ISSN: 0966-6362
• Electronic ISSN: 1879-2219
• Publisher: Elsevier
• Volume: 80
• Pages: 318-323
• DOI: https://doi.org/10.1016/j.gaitpost.2020.06.023
• Publisher URL: https://doi.org/10.1016/j.gaitpost.2020.06.023
• Related Public URLs: http://www.journals.elsevier.com/gait-and-posture/