Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

Fu, Chunjiang; Suzuki, Yasuyuki; Morasso, Pietro; Nomura, Taishin

doi:10.1007/s00422-020-00816-y

Cited by 8 publications

(18 citation statements)

References 49 publications

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“…Our model reproduced the statistical persistence in stride intervals. A lack of phase resetting induced a loss of statistical persistence, as observed in Fu et al (2020). Furthermore, we clarified the mechanisms responsible for changes in this statistical property caused by phase resetting based on the phase response characteristics.…”

Section: Introductionmentioning

confidence: 70%

“…In particular, because the feedforward torques ( 9) and (10) were simply composed of a sinusoidal wave, the gait speeds of our model were slower than those of healthy adults (Figure 2). In addition, although statistical persistence could be associated with low gait stability (low convergence speed to the limit cycle) (Ahn and Hogan, 2013;Fu et al, 2020), our model had higher stability than that of complicated models due to its simplicity. The high stability of our model with phase resetting might have caused the scaling exponent α to be ∼ 0.6, which is smaller than that (∼ 1) in healthy adults (Hausdorff et al, 1995).…”

Section: Limitations Of Our Model and Future Workmentioning

confidence: 86%

“…However, sensory feedback is crucial for producing adaptive locomotor behavior. To investigate the contribution of CPGs to adaptive locomotion in humans, various oscillator models, such as the van der Pol oscillator (Dutra et al, 2003 ; West and Scafetta, 2003 ), Matsuoka oscillator (Matsuoka, 1987 ; Taga et al, 1991 ; Taga, 1995a , b ; Ogihara and Yamazaki, 2001 ; Hase et al, 2003 ; Kim et al, 2011 ), and phase oscillator (Yamasaki et al, 2003 ; Aoi et al, 2010 , 2019 ; Dzeladini et al, 2014 ; Aoi and Funato, 2016 ; Fu et al, 2020 ; Tamura et al, 2020 ; Owaki et al, 2021 ), have been developed.…”

Section: Methodsmentioning

confidence: 99%

“…Cutaneous feedback has been observed to contribute to phase shift and rhythm resetting behavior (Duysens, 1977 ; Schomburg et al, 1998 ). Phase resetting has thus been modeled so that the oscillator phase is reset based on foot contact information (Yamasaki et al, 2003 ; Aoi et al, 2010 ; Aoi and Funato, 2016 ; Fu et al, 2020 ; Tamura et al, 2020 ). In this study, we used the following relationship at touchdown:

where ϕ 0 is a constant.…”

Section: Methodsmentioning

confidence: 99%

“…It has also been hypothesized that the statistical persistence in stride intervals emerges through complex interactions during walking. Fu et al ( 2020 ) integrated a biomechanical model composed of seven rigid links with a CPG model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, to reproduce statistical persistence. They showed that a lack of phase resetting induces a loss of statistical persistence.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study

Okamoto

Obayashi²,

Kokubu³

et al. 2022

Front. Neural Circuits

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Stride intervals in human walking fluctuate from one stride to the next, exhibiting statistical persistence. This statistical property is changed by aging, neural disorders, and experimental interventions. It has been hypothesized that the central nervous system is responsible for the statistical persistence. Human walking is a complex phenomenon generated through the dynamic interactions between the central nervous system and the biomechanical system. It has also been hypothesized that the statistical persistence emerges through the dynamic interactions during walking. In particular, a previous study integrated a biomechanical model composed of seven rigid links with a central pattern generator (CPG) model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, and suggested that phase resetting contributes to the statistical persistence in stride intervals. However, the essential mechanisms remain largely unclear due to the complexity of the neuromechanical model. In this study, we reproduced the statistical persistence in stride intervals using a simplified neuromechanical model composed of a simple compass-type biomechanical model and a simple CPG model that incorporates only phase resetting and a feedforward controller. A lack of phase resetting induced a loss of statistical persistence, as observed for aging, neural disorders, and experimental interventions. These mechanisms were clarified based on the phase response characteristics of our model. These findings provide useful insight into the mechanisms responsible for the statistical persistence of stride intervals in human walking.

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Section: Introductionmentioning

confidence: 70%

Section: Limitations Of Our Model and Future Workmentioning

confidence: 86%

Section: Methodsmentioning

confidence: 99%

where ϕ 0 is a constant.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study

Okamoto

Obayashi²,

Kokubu³

et al. 2022

Front. Neural Circuits

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Long term correlation and inhomogeneity of the inverted pendulum sway time-series under the intermittent control paradigm

Tigrini

Verdini

Fioretti

et al. 2022

Communications in Nonlinear Science and Numerical Simulation

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Smartphone usage during walking decreases the positive persistency in gait cycle variability

Yano,

Nakamura,

Suzuki

et al. 2024

Sci Rep

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Gait cycle variability during steady walking, described by the stride interval time series, has been used as a gait-stability-related measure. In particular, the positive persistency in the stride intervals with 1/f-like fluctuation and reduction of the persistency are the well-documented metrics that can characterize gait patterns of healthy young adults and elderly including patients with neurological diseases, respectively. Here, we examined effects of a dual task on gait cycle variability in healthy young adults, based on the mean and standard deviation statistics as well as the positive persistency of the stride intervals during steady walking on a treadmill. Specifically, three gait conditions were examined: control condition, non-cognitive task with holding a smartphone in front of the chest using their dominant hand and looking fixedly at a blank screen of the smartphone, and cognitive motor task with holding a smartphone as in the non-cognitive task and playing a puzzle game displayed on the smartphone by one-thumb operation. We showed that only the positive persistency, not the mean and standard deviation statistics, was affected by the cognitive and motor load of smartphone usage in the cognitive condition. More specifically, the positive persistency exhibited in the control and the non-cognitive conditions was significantly reduced in the cognitive condition. Our results suggest that the decrease in the positive persistency during the cognitive task, which might represent the deterioration of healthy gait pattern, is caused endogenously by the cognitive and motor load, not necessarily by the reduction of visual field as often hypothesized.

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Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

Cited by 8 publications

References 49 publications

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study

Long term correlation and inhomogeneity of the inverted pendulum sway time-series under the intermittent control paradigm

Smartphone usage during walking decreases the positive persistency in gait cycle variability

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