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Effect of Hopping Frequency on Bilateral Differences in Leg Stiffness

Hiroaki Hobara, Koh Inoue, and Kazuyuki Kanosue

Understanding the degree of leg stiffness during human movement would provide important information that may be used for injury prevention. In the current study, we investigated bilateral differences in leg stiffness during one-legged hopping. Ten male participants performed one-legged hopping in place, matching metronome beats at 1.5, 2.2, and 3.0 Hz. Based on a spring-mass model, we calculated leg stiffness, which is defined as the ratio of maximal ground reaction force to maximum center of mass displacement at the middle of the stance phase, measured from vertical ground reaction force. In all hopping frequency settings, there was no significant difference in leg stiffness between legs. Although not statistically significant, asymmetry was the greatest at 1.5 Hz, followed by 2.2 and 3.0 Hz for all dependent variables. Furthermore, the number of subjects with an asymmetry greater than the 10% criterion was larger at 1.5 Hz than those at 2.2 and 3.0 Hz. These results will assist in the formulation of treatment-specific training regimes and rehabilitation programs for lower extremity injuries.

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A Comparison of Computation Methods for Leg Stiffness During Hopping

Hiroaki Hobara, Koh Inoue, Yoshiyuki Kobayashi, and Toru Ogata

Despite the presence of several different calculations of leg stiffness during hopping, little is known about how the methodologies produce differences in the leg stiffness. The purpose of this study was to directly compare K leg during hopping as calculated from three previously published computation methods. Ten male subjects hopped in place on two legs, at four frequencies (2.2, 2.6, 3.0, and 3.4 Hz). In this article, leg stiffness was calculated from the natural frequency of oscillation (method A), the ratio of maximal ground reaction force (GRF) to peak center of mass displacement at the middle of the stance phase (method B), and an approximation based on sine-wave GRF modeling (method C). We found that leg stiffness in all methods increased with an increase in hopping frequency, but K leg values using methods A and B were significantly higher than when using method C at all hopping frequencies. Therefore, care should be taken when comparing leg stiffness obtained by method C with those calculated by other methods.

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Differences in Spring-Mass Characteristics Between One- and Two-Legged Hopping

Hiroaki Hobara, Yoshiyuki Kobayashi, Emika Kato, and Toru Ogata

Although many athletic activities and plyometric training methods involve both unilateral and bilateral movement, little is known about differences in the leg stiffness (K leg) experienced during one-legged hopping (OLH) and two-legged hopping (TLH) in place. The purpose of this study was to investigate the effect of hopping frequencies on differences in K leg during OLH and TLH. Using a spring-mass model and data collected from 17 participants during OLH and TLH at frequencies of 2.0, 2.5, and 3.0 Hz, K leg was calculated as the ratio of maximal ground reaction force (F peak) to the maximum center of mass displacement (ΔCOM) at the middle of the stance phase measured from vertical ground reaction force. Both K leg and F peak were found to be significantly greater during TLH than OLH at all frequencies, but type of hopping was not found to have a significant effect on ΔCOM. These results suggest that K leg is different between OLH and TLH at a given hopping frequency and differences in K leg during OLH and TLH are mainly associated with differences in F peak but not ΔCOM.

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Normative Spatiotemporal Parameters During 100-m Sprints in Amputee Sprinters Using Running-Specific Prostheses

Hiroaki Hobara, Wolfgang Potthast, Ralf Müller, Yoshiyuki Kobayashi, Thijs A. Heldoorn, and Masaaki Mochimaru

The aim of this study was to develop a normative sample of step frequency and step length during maximal sprinting in amputee sprinters. We analyzed elite-level 100-m races of 255 amputees and 93 able-bodied sprinters, both men and women, from publicly-available Internet broadcasts. For each sprinter’s run, the average forward velocity, step frequency, and step length over the 100-m distance were analyzed by using the official record and number of steps in each race. The average forward velocity was greatest in able-bodied sprinters (10.04 ± 0.17 m/s), followed by bilateral transtibial (8.77 ± 0.27 m/s), unilateral transtibial (8.65 ± 0.30 m/s), and transfemoral amputee sprinters (7.65 ± 0.38 m/s) in men. Differences in velocity among 4 groups were associated with step length (able-bodied vs transtibial amputees) or both step frequency and step length (able-bodied vs transfemoral amputees). Although we also found that the velocity was greatest in able-bodied sprinters (9.10 ± 0.14 m/s), followed by unilateral transtibial (7.08 ± 0.26 m/s), bilateral transtibial (7.06 ± 0.48 m/s), and transfemoral amputee sprinters (5.92 ± 0.33 m/s) in women, the differences in the velocity among the groups were associated with both step frequency and step length. Current results suggest that spatiotemporal parameters during a 100-m race of amputee sprinters is varied by amputation levels and sex.

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Amputee Locomotion: Ground Reaction Forces During Submaximal Running With Running-Specific Prostheses

Brian S. Baum, Hiroaki Hobara, Yoon Hyuk Kim, and Jae Kun Shim

Individuals with lower extremity amputation must adapt the mechanical interactions between the feet and ground to account for musculoskeletal function loss. However, it is currently unknown how individuals with amputation modulate three-dimensional ground reaction forces (GRFs) when running. This study aimed to understand how running with running-specific prostheses influences three-dimensional support forces from the ground. Eight individuals with unilateral transtibial amputations and 8 control subjects ran overground at 2.5, 3.0, and 3.5 m/s. Ten force plates measured GRFs at 1000 Hz. Peak and average GRFs and impulses in each plane were compared between limbs and groups. Prosthetic limbs generated reduced vertical impulses, braking forces and impulses, and mediolateral forces while generating similar propulsive impulses compared with intact and control limbs. Intact limbs generated greater peak and average vertical forces and average braking forces than control subjects’ limbs. These data indicate that the nonamputated limb experiences elevated mechanical loading compared with prosthetic and control limbs. This may place individuals with amputation at greater risk of acute injury or joint degeneration in their intact limb. Individuals with amputation adapted to running-specific prosthesis force production limitations by generating longer periods of positive impulse thus producing propulsive impulses equivalent to intact and control limbs.

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A Comparison of Vertical Stiffness Values Calculated from Different Measures of Center of Mass Displacement in Single-Leg Hopping

Kurt L. Mudie, Amitabh Gupta, Simon Green, Hiroaki Hobara, and Peter J. Clothier

This study assessed the agreement between Kvert calculated from 4 different methods of estimating vertical displacement of the center of mass (COM) during single-leg hopping. Healthy participants (N = 38) completed a 10-s single-leg hopping effort on a force plate, with 3D motion of the lower limb, pelvis, and trunk captured. Derived variables were calculated for a total of 753 hop cycles using 4 methods, including: double integration of the vertical ground reaction force, law of falling bodies, a marker cluster on the sacrum, and a segmental analysis method. Bland-Altman plots demonstrated that Kvert calculated using segmental analysis and double integration methods have a relatively small bias (0.93 kN⋅m–1) and 95% limits of agreement (–1.89 to 3.75 kN⋅m–1). In contrast, a greater bias was revealed between sacral marker cluster and segmental analysis (–2.32 kN⋅m–1), sacral marker cluster and double integration (–3.25 kN⋅m–1), and the law of falling bodies compared with all methods (17.26–20.52 kN⋅m–1). These findings suggest the segmental analysis and double integration methods can be used interchangeably for the calculation of Kvert during single-leg hopping. The authors propose the segmental analysis method to be considered the gold standard for the calculation of Kvert during single-leg, on-the-spot hopping.