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
Scott W. Ducharme and Richard E.A. van Emmerik
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.
Edited by Thomas Rowland
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.
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
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.
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.
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.
Tiago M. Barbosa, Wan Xiu Goh, Jorge E. Morais and Mário J. Costa
The aim was to examine the variation of linear and nonlinear proprieties of the behavior in participants with different levels of swimming expertise among the four swim strokes. Seventy-five swimmers were split into three groups (highly qualified experts, experts and nonexperts) and performed a maximal 25m trial for each of the four competitive swim strokes. A speed-meter cable was attached to the swimmer’s hip to measure hip speed; from which speed fluctuation (dv), approximate entropy (ApEn) and fractal dimension (D) variables were derived. Although simple main effects of expertise and swim stroke were obtained for dv and D, no significant interaction of expertise and stroke were found except in ApEn. The ApEn and D were prone to decrease with increasing expertise. As a conclusion, swimming does exhibit nonlinear properties but its magnitude differs according to the swim stroke and level of expertise of the performer.
Dorina Ianc, Carmen Serbescu, Marius Bembea, Laurent Benhamou, Eric Lespessailles and Daniel Courteix
We investigated the effects of calcium supplementation and physical practice on the bone ultrasound properties and trabecular microarchitecture in children. 160 children aged 8−11 were randomly allocated to active or nonactive groups and to receive either a calcium-phosphate or a placebo powder for 6 months. Skeletal status was assessed using an ultrasound technique, which measures the speed of sound (Ad-SoS, m/s) at the phalanx. Bone microarchitecture was characterized by fractal analysis measured on calcaneus radiographs and the result expressed as the Hmean parameter, that has been shown to a good reliability of the bone texture quality. After 6 months, the calcium group had significantly gained Ad-SoS compared to the placebo group (P = 0.01) and Hmean increase was greater in the active than the nonactive group (P < 0.05). Exercise and calcium supplementation had a differential effect on the bone tissue, calcium being rather linked to a systemic effect whereas exercise has acted better onto the skeletal stressed site.