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Fractal Dynamics, Variability, and Coordination in Human Locomotion

Scott W. Ducharme and Richard E.A. van Emmerik

related to aging and disease. In the second section, we provide an overview of past and current research on coordination dynamics that demonstrates the functional role of variability in human locomotion. Next, the major section of this paper addresses the concept of fractals that has provided new insights

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The Validity of Gait Variability and Fractal Dynamics Obtained From a Single, Body-Fixed Triaxial Accelerometer

Dylan Kobsar, Chad Olson, Raman Paranjape, and John M. Barden

A single triaxial accelerometer has the ability to collect a large amount of continuous gait data to quantitatively assess the control of gait. Unfortunately, there is limited information on the validity of gait variability and fractal dynamics obtained from this device. The purpose of this study was to test the concurrent validity of the variability and fractal dynamic measures of gait provided by a triaxial accelerometer during a continuous 10 minute walk in older adults. Forty-one healthy older adults were fitted with a single triaxial accelerometer at the waist, as well as a criterion footswitch device before completing a ten minute overground walk. The concurrent validity of six outcome measures was examined using intraclass correlation coefficients (ICC) and 95% limits of agreement. All six dependent variables measured by the accelerometer displayed excellent agreement with the footswitch device. Mean parameters displayed the highest validity, followed by measures of variability and fractal dynamics in stride times and measures of variability and fractal dynamics in step times. These findings suggest that an accelerometer is a valid and unique device that has the potential to provide clinicians with valid quantitative data for assessing their clients’ gait.

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Human Movement Variability and Aging

Nicholas Stergiou, Jenny A. Kent, and Denise McGrath

An optimal level of variability enables us to interact adaptively and safely to a continuously changing environment, where often our movements must be adjusted in a matter of milliseconds. A large body of research exists that demonstrates natural variability in healthy gait (along with variability in other, healthy biological signals such as heart rate) and a loss of this variability in aging and injury, as well as in a variety of neurodegenerative and physiological disorders. We submit that this field of research is now in pressing need of an innovative “next step” that goes beyond the many descriptive studies that characterize levels of variability in various patient populations. We need to devise novel therapies that will harness the existing knowledge on biological variability and create new possibilities for those in the grip of disease. We also propose that the nature of the specific physiological limitation present in the neuromuscular apparatus may be less important in the physiological complexity framework than the control mechanisms adopted by the older individual in the coordination of the available degrees of freedom. The theoretical underpinnings of this framework suggest that interventions designed to restore healthy system dynamics may optimize functional improvements in older adults. We submit that interventions based on the restoration of optimal variability and movement complexity could potentially be applied across a range of diseases or dysfunctions as it addresses the adaptability and coordination of available degrees of freedom, regardless of the internal constraints of the individual.

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Relating Metabolic Rate to Body Size, Cont’d: The Fascinating World of Fractals

Edited by Thomas Rowland

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The Effect of Cryotherapy Application to the Knee Joint on Dynamic Postural Stability

Karl Fullam, Brian Caulfield, Garrett F. Coughlan, Wayne McNulty, David Campbell, and Eamonn Delahunt

distance measures. The kinetic dependent variable of interest for the present study was the mean fractal dimension (FD). FD describes the activity of the sensorimotor system in organizing available afferents 25 and the extent to which persons utilize the base of support available to them. 26 FD has been

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Nonlinear Analyses Distinguish Load Carriage Dynamics in Walking and Standing: A Systematic Review

Kolby J. Brink, Kari L. McKenzie, and Aaron D. Likens

classes of nonlinear analyses reviewed in this manuscript. As a preview, our review of the literature only returned a few methods within the context of load carriage. For that reason, we focus on methods that characterize time series properties such as predictability (eg, entropy), complexity (eg, fractal

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Stable and Unstable Load Carriage Effects on the Postural Control of Older Adults

Gregory S. Walsh, Daniel C. Low, and Marco Arkesteijn

can be magnified by unstable loads, 3 providing insight into the mechanisms of postural control adopted by older adults when perturbed. Nonlinear measures of postural sway complexity, such as the fractal dimension, can elucidate the neuromuscular control mechanisms 13 , 14 adopted when the system is

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Oscillating in Synchrony with a Metronome: Serial Dependence, Limit Cycle Dynamics, and Modeling

Kjerstin Torre, Ramesh Balasubramaniam, and Didier Delignières

We analyzed serial dependencies in periods and asynchronies collected during oscillations performed in synchrony with a metronome. Results showed that asynchronies contain 1/f fluctuations, and the series of periods contain antipersistent dependence. The analysis of the phase portrait revealed a specific asymmetry induced by synchronization. We propose a hybrid limit cycle model including a cycle-dependent stiffness parameter provided with fractal properties, and a parametric driving function based on velocity. This model accounts for most experimentally evidenced statistical features, including serial dependence and limit cycle dynamics. We discuss the results and modeling choices within the framework of event-based and emergent timing.

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Long-Range Correlations and Complex Regulation of Pacing in Long-Distance Road Racing

Olaf Hoos, Tobias Boeselt, Martin Steiner, Kuno Hottenrott, and Ralph Beneke


To analyze time-domain, spectral, and fractal properties of speed regulation during half-marathon racing.


In 21 male experienced runners, high-resolution data on speed (V), stride frequency (SF), and stride length (SL) were assessed during half-marathon competition (21,098 m). Performance times, timeand frequency-domain variability, spectral-scaling exponent (beta), and fractal dimension (FD) of V, SF, and SL were analyzed.


V of 3.65 ± 0.41 m/s, SF of 1.41 ± 0.05 Hz, and SL of 2.58 ± 0.25 m occurred with higher (P < .05) individual variability in V and SL than in SF. Beta and FD were always 1.04–1.88 and 1.56–1.99, respectively. Beta and FD differed (P < .05) in SF and SL compared with V and were correlated in V and SL (r = .91, P < .05). Spectral peaks of V, SF, and SL occurred at wavelengths of 3–35 min, and those of V and SL were interrelated (r = .56, P < .05). Mean SF and mean SL were significantly correlated with performance (r = .59 and r = .95, P < .05). SL accounted for 84% ± 6% and SF for 16% ± 6% of speed variability.


The observed nonrandom fluctuations in V, SF, and SL correspond to nonstationary fractional Brownian motion with inherent long-range correlations. This indicates a similar complex regulation process in experienced runners that is primarily mediated via SL.

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Changes of Postural Steadiness Following Use of Prefabricated Orthotic Insoles

Hamid Bateni

Orthoses are designed to assist a malaligned foot in adapting to the environment and reduce the frequency of injury. Literature is divided on the benefits of orthotics insoles for postural stability. The current study was conducted to determine the effect of prefabricated orthotic arch supports on postural stabilization. Twelve healthy young adults participated in this study and were tested with and without prefabricated orthotics. Different variables were computed from movement of center of pressure (COP) during orthotic use as suggested in the literature. The mean position of COP was significantly shifted forward and toward the dominant side. Neither the COP movement nor the velocity changes following the use of orthotics revealed significant differences. Mediolateral range of COP movement and the 95% confidence circle area of sway was significantly reduced (P = .022 and 0.048 respectively), but changes in 95% confidence circle and ellipse areas of fractal dimension were not significant (P = .053 and P = .057 respectively). In conclusion, orthotic insoles significantly improved postural sway initially by reducing mediolateral range of postural sway and 95% confidence circle area of sway at the cost of increased fractal dimension area variables and power.