Elsevier

Journal of Biomechanics

Volume 49, Issue 14, 3 October 2016, Pages 3306-3312
Journal of Biomechanics

Vertical stiffness and center-of-mass movement in children and adults during single-leg hopping

https://doi.org/10.1016/j.jbiomech.2016.08.014Get rights and content

Abstract

Single-leg hopping in-place can be typically modeled using a spring-mass model. Within this model, the leg acts as a spring whose stiffness can be regulated to hop at different heights and frequencies. The control of vertical stiffness has been shown to be important for running and jumping performance, as well as injury prevention. It is known that adults increase vertical stiffness to hop at frequencies higher than preferred, but it is unknown if children younger than 11 years have a similar ability to control vertical stiffness. Further, little is known about the horizontal movement of the center-of-mass (COM) and foot positioning during hopping in both children and adults. The purpose of this study was to evaluate the validity of the spring-mass model in 5–11 years old children and compare horizontal COM and foot movement between children and adults. We found that single-leg hopping in children generally follows a spring-mass model and children are able to increase vertical stiffness with hopping frequency. Moreover, children demonstrate adult-like control strategies of decreasing the COM range and toe displacement but maintaining the COM positioning with increasing frequency. However, children showed a faster preferred frequency, elevated vertical stiffness normalized by body weight, a greater toe displacement between hops and a greater toe range within a trial. Together, single-leg hopping in place can generally be modeled in 5–11 years old children as a spring-mass model; however, children at this age are still developing their motor ability to control the COM and foot placement during hopping.

Introduction

Hopping is a movement characterized by unperturbed vertical rebounding in-place on a single foot. As for other motor tasks of interest, such as running, hopping can be modeled as a spring-mass model (Blickhan, 1989, Cavagna, 1988, Chang et al., 2008, Farley et al., 1991, Farley and Morgenroth, 1999, Hobara et al., 2010). The spring-mass model describes the relationship of center of mass (COM) displacement and storage and release of elastic energy (Farley et al., 1991). Based on the spring-mass model, a preferred hopping frequency exists at 2.0–2.2 Hz in young adults independent of body mass (Auyang et al., 2009, Farley et al., 1991, Granata et al., 2002), but has not been reported in children younger than 11 years.

To hop outside of the preferred frequency, previous studies have demonstrated that adults manipulate vertical stiffness (commonly used as leg stiffness), the ratio between vertical ground reaction force (GRF) and vertical COM displacement (Austin et al., 2003, Granata et al., 2002, Moran et al., 2013). The ability to adjust vertical stiffness is important to change hopping height, running speed and reduce the risk of injury (Butler et al., 2003). In children aged 4–8 years, vertical stiffness separates developmental levels for single-leg forward hopping (Getchell and Roberton, 1989). In boys aged 11–12 years, vertical stiffness increases with hopping frequency during two-legged hopping in-place (Oliver and Smith, 2010). However, it is not known if vertical stiffness during single-leg hopping in-place can be modeled as a spring-mass model in children younger than 11 years.

In contrast to the numerous studies on vertical stiffness during hopping in-place, little has been reported on horizontal COM movement in both children and adults. Differences in COM movement between the anterior-posterior (AP) and medial-lateral (ML) directions during the stance phase of hopping may illustrate different balance requirements and body control. Horizontal COM movement has been extensively studied in standing, typically demonstrating greater movement in the AP compared to the ML (Gage et al., 2004, Winter et al., 1996). It is reasonable to assume the COM movement during hopping in-place may have a similar pattern to standing given, in both motor tasks, the COM is high above the floor and controlled over a small base of support. Further, little is known on the horizontal COM position in relation to the base of support, which would provide insight into whole-body orientation strategies necessary for balance control.

Unlike standing, hopping in-place is a dynamic task where the foot may land in different places at each hop. Horizontal movement of the foot could be the result of the spring-mass model inertia property and used as a compensatory strategy to correct COM movement. The inability to quickly correct for horizontal foot displacements could result in a larger hopping area or loss of balance. Auyang and Chang (2013) found similar AP foot placement deviations when constraining adult subjects to hop at one frequency within different hopping areas. However, no study has reported the control of horizontal foot placement during hopping at different frequencies in adults or children.

The purpose of this study was to address two research questions. First, does single-leg hopping in children aged 5–11 years follow the spring-mass model, comparable to adults, where vertical stiffness is manipulated to change hopping frequency? Second, do children demonstrate adult-like patterns of horizontal COM trajectory and foot positioning across a range of frequencies? Accordingly, we hypothesized that (a) hopping in children will follow a spring-mass model, and vertical stiffness will increase with hopping frequency, with children showing higher vertical stiffness normalized by bodyweight, (b) horizontal COM movement during stance phase will be greater in the AP direction than the ML and decrease with increasing frequency, with children demonstrating greater COM movement, (c) with increasing frequency, the COM will be positioned closer to the toe with less ML deviation compared to the AP, but children will show a COM position closer to the toe, and (d) AP toe displacement between hops will be greater than in the ML direction, but will decrease with increasing frequency and children will demonstrate greater toe displacement.

Section snippets

Participants

We recruited 17 children aged 5–11 years and 16 young adults. Subjects had no previous or existing medical conditions that prevented them from single-leg hopping for 20 s. Anthropometric measures were collected including height, body-mass and leg length, measured as the distance from the anterior superior iliac spine to the medial condyle of the femur to the medial malleolus of the ankle. This study was approved by the institutional review board at the hosting university. Informed consents were

Results

Three children subjects (aged 5, 6 and 7), and three adult subjects demonstrated no change in hopping frequency across conditions. As the purpose of this study was to investigate how children and adults coordinate hopping at different frequencies, these subjects were excluded from further analysis. Mean (standard deviation) of age, height, body-mass and leg length of the remaining 14 children subjects (9 males and 5 females) were 8.70 (1.81) yrs, 1.34 (0.08) m, 32.97 (7.95) kg, and 0.71 (0.05) m,

Discussion

This study aimed to compare vertical stiffness, estimated from a spring-mass model, and COM movement and positioning, and foot placement between children aged 5–11 years and adults during single-leg hopping in-place. Our results indicated that children at this age range are able to hop outside of their preferred frequency and, somewhat comparable to adults, manipulate absolute vertical stiffness and horizontal COM movement. However, children showed higher vertical stiffness normalized to their

Conflicts of interest statement

There were no conflicts of interest when completing this study.

Acknowledgments

We are grateful to all the children and their families for their participation in this study. Special thanks are due to Elizabeth Mena, Steven Pham and Huaqing Liang for their assistance in data collection and analysis. There was no writing assistance when we prepared for this manuscript.

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