Changing Complexity and Autocorrelations of Long Time Series Stride
  Interval With Walking Direction and Vestibular Stimulation

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Abstract

Background: It is still unknown if physiological complexity and autocorrelations (AC) of long-range stride interval (SI) time series are related to walking direction (WD) and application of galvanic vestibular stimulation (GVS). Methods and results: The SI fluctuations versus time for 34 healthy people walking 15 minutes on an instrumented treadmill is studied in four conditions: forward walking (FW) without GVS (FW_{S0}) and with GVS (FW_{S+}), and backward walking without GVS (BW_{S0}) and with GVS (BW_{S+}). The time series are then analysed from a spatio-temporal point of view and from a long-range AC point of view: particular attention is paid to the Hurst exponent (\alpha) and to the Minkowski fractal dimension, interpreted as indexes expressing predictability and complexity of the time series respectively. WD has a major impact on the results: walking backward increases spatio-temporal variablility and modifies long-range AC. GVS differently influences FW and BW: It increases the stride width in FW while increasing the mean SI duration in BW. The fractal dimension is always decreased when turning on GVS, but the long-range AC are unchanged. Conclusion: The control condition is typical of a chaotic system exhibiting long-range AC, and the trend of \alpha versus stride amplitude is compatible with a peculiar pendular model of walking. GVS reduced complexity or predictability, depending on WD. During FW walking, GVS reduced complexity, leading to fewer walking adaptability. During BW walking, GVS reduced predictability, leading to a more random walking. The present study thus opens a way to classify walking according to the complexity and predictability of SI time series. Our findings may finally have applications in the field of rehabilitation. They suggest that, in FW, GVS is a relevant tool to work on balance, while in BW, GVS may help to improve the regularity of steps.

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Probing the human vestibular system with galvanic stimulation.

Brian Day, C. Fitzpatrick (2004)

Galvanic vestibular stimulation (GVS) is a simple, safe, and specific way to elicit vestibular reflexes. Yet, despite a long history, it has only recently found popularity as a research tool and is rarely used clinically. The obstacle to advancing and exploiting GVS is that we cannot interpret the evoked responses with certainty because we do not understand how the stimulus acts as an input to the system. This paper examines the electrophysiology and anatomy of the vestibular organs and the effects of GVS on human balance control and develops a model that explains the observed balance responses. These responses are large and highly organized over all body segments and adapt to postural and balance requirements. To achieve this, neurons in the vestibular nuclei receive convergent signals from all vestibular receptors and somatosensory and cortical inputs. GVS sway responses are affected by other sources of information about balance but can appear as the sum of otolithic and semicircular canal responses. Electrophysiological studies showing similar activation of primary afferents from the otolith organs and canals and their convergence in the vestibular nuclei support this. On the basis of the morphology of the cristae and the alignment of the semicircular canals in the skull, rotational vectors calculated for every mode of GVS agree with the observed sway. However, vector summation of signals from all utricular afferents does not explain the observed sway. Thus we propose the hypothesis that the otolithic component of the balance response originates from only the pars medialis of the utricular macula.

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Kinematic variability and local dynamic stability of upper body motions when walking at different speeds.

Jonathan B. Dingwell, Traci L Marin (2005)

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.

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Nonlinear time series analysis of normal and pathological human walking.

Jonathan B. Dingwell, Joseph P. Cusumano (2000)

Characterizing locomotor dynamics is essential for understanding the neuromuscular control of locomotion. In particular, quantifying dynamic stability during walking is important for assessing people who have a greater risk of falling. However, traditional biomechanical methods of defining stability have not quantified the resistance of the neuromuscular system to perturbations, suggesting that more precise definitions are required. For the present study, average maximum finite-time Lyapunov exponents were estimated to quantify the local dynamic stability of human walking kinematics. Local scaling exponents, defined as the local slopes of the correlation sum curves, were also calculated to quantify the local scaling structure of each embedded time series. Comparisons were made between overground and motorized treadmill walking in young healthy subjects and between diabetic neuropathic (NP) patients and healthy controls (CO) during overground walking. A modification of the method of surrogate data was developed to examine the stochastic nature of the fluctuations overlying the nominally periodic patterns in these data sets. Results demonstrated that having subjects walk on a motorized treadmill artificially stabilized their natural locomotor kinematics by small but statistically significant amounts. Furthermore, a paradox previously present in the biomechanical literature that resulted from mistakenly equating variability with dynamic stability was resolved. By slowing their self-selected walking speeds, NP patients adopted more locally stable gait patterns, even though they simultaneously exhibited greater kinematic variability than CO subjects. Additionally, the loss of peripheral sensation in NP patients was associated with statistically significant differences in the local scaling structure of their walking kinematics at those length scales where it was anticipated that sensory feedback would play the greatest role. Lastly, stride-to-stride fluctuations in the walking patterns of all three subject groups were clearly distinguishable from linearly autocorrelated Gaussian noise. As a collateral benefit of the methodological approach taken in this study, some of the first steps at characterizing the underlying structure of human locomotor dynamics have been taken. Implications for understanding the neuromuscular control of locomotion are discussed. (c) 2000 American Institute of Physics.

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Publication date Created: 2017-03-28

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ArXiV ID: 1703.09487

SO-VID: 0cf952bf-2b76-4ad2-9351-2f289aee51eb

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Comments 20 pages, 6 figures

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ScienceOpen disciplines: Medical physics

Changing Complexity and Autocorrelations of Long Time Series Stride Interval With Walking Direction and Vestibular Stimulation

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Most cited references 30

Probing the human vestibular system with galvanic stimulation.

Kinematic variability and local dynamic stability of upper body motions when walking at different speeds.

Nonlinear time series analysis of normal and pathological human walking.

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