Spring Mass Model for Running

NewsBot · Jun 20, 2020

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Using the Spring-Mass Model for Running: Force-Length Curves and Foot-Strike Patterns
NiamhGillStephen J.PreeceRichardBaker
Gait & Posture; 2020

Highlights
•There is a large variability in the shape of the force-length curve.
•Linearity appears to decrease as running speed increased.
•A more forefoot strike pattern is associated with a more linear force-length curve.
•Constant stiffness should be limited to those with a linear force-length behaviour.
•The assumption of a linear force-length curve is not appropriate for all runners.
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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.
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NewsBot · Jun 20, 2020

Related Thread:
Running Energy Cost and Spring-Mass Behavior

NewsBot · Nov 18, 2020

The human foot functions like a spring of adjustable stiffness during running
Nicholas B Holowka et al
J Exp Biol. 2020 Nov 16

Like other animals, humans use their legs like springs to save energy during running. One potential contributor to leg stiffness in humans is the longitudinal arch (LA) of the foot. Studies of cadaveric feet have demonstrated that the LA can function like a spring, but it is unknown whether humans can adjust LA stiffness in coordination with more proximal joints to help control leg stiffness during running. Here, we used 3-D motion capture to record 27 adult participants running on a forceplate-instrumented treadmill, and calculated LA stiffness using beam bending and midfoot kinematics models of the foot. Because changing stride frequency causes humans to adjust overall leg stiffness, we had participants run at their preferred frequency and frequencies 35% above and 20% below preferred to test for similar adjustments in the LA. Regardless of which foot model we used, we found that participants increased LA quasi-stiffness significantly between low and high frequency runs, mirroring changes at the ankle, knee and leg overall. However, among foot models, we found that the model incorporating triceps surae force into bending force on the foot produced unrealistically high LA work estimates, leading us to discourage this modeling approach. Additionally, we found that there was not a consistent correlation between LA height and quasi-stiffness values among the participants, indicating that static LA height measurements are not good predictors of dynamic function. Overall, our findings support the hypothesis that humans dynamically adjust LA stiffness during running in concert with other structures of the leg
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