Long range correlations in the stride interval of running
Introduction
Locomotion is a complex act arising from the coordination of multiple mechanisms and couplings of the neuromuscular system, including the motor cortex, cerebellum, basal ganglia and feedback from vestibular, visual and peripheral receptors. It has been shown previously that the stride interval of walking is very stable and subject to only small variations about the mean stride interval (coefficient of variation, CV ∼ 4%), however, the distribution of the stride interval is not normal and appears to be a fractal process [9], [10], [25], [26]. The fluctuations present in the stride interval of human walking are persistent, self-similar and exhibit long range correlations, such that, any given stride interval is dependent on the stride interval at remote previous times, and that the dependence of stride intervals decays in a power law, fractal-like manner with time [9], [10]. Processes with long range dependence are characterized by their autocorrelation function, coupling between points in the time series remains strong as the distance in time between points increases. In the case of human walking, long range correlations in the stride interval have been shown to extend over 1000 s of strides and are robust with respect to walking velocity [10].
Processes with long term correlations or 1/f-like processes have been observed in a number of different systems ranging from physics to sociology [3], [14], [21]. These types of processes are ubiquitous in nature yet they are not easily explained [2], [24]. The key feature of such processes is an inverse power law scaling of fluctuation size with frequency, i.e., small fluctuations occur with high frequency whereas large fluctuations occur with low frequency. In addition to this, 1/f processes are self-similar, in that small irregularities at small time scales have the same statistical properties as large irregularities at large time scales. Thus, the inverse power law scaling of frequency with amplitude is a result of the self-similarity of the fluctuations.
Of particular interest to movement scientists are the long range correlations found in the fluctuations of human movement time series such as the inter-tap interval in synchronization studies, e.g., [4] and the inter-stride interval in human walking, e.g., [9], [10], [25], [26]. The finding that these fluctuations are not random but rather contain structure has led to the idea that investigating this variability may provide insight into how these movements are controlled. For example, Hausdorff et al. have shown that long range correlations in the stride interval of walking break down when subjects walk in time to a metronome [10], indicating that the correlations can be centrally mediated and may originate at or below the level of the spinal cord. Furthermore, the long range correlations have been shown to break down in older adults and in disease states, such as Huntington's [11] due, it is proposed, to a loss of complexity of the neuromuscular system associated with aging and disease. It has also been shown that long range correlations were stronger in young children and decrease across the life span [12].
Of central importance to this paper, is the finding that the long range correlations are stronger at speeds faster and slower than the preferred walking speed [10]. West and Scaffetta successfully modeled these experimental finding of Hausdorff et al. by interpreting slow and fast walking speeds as a “biological stress” that serves to increase the strength of correlation among neuronal centers, and thus increase the strength of the long range correlations [27]. In summary, it can be concluded that the long range correlations that are present in the stride interval of human locomotion are non-trivial and that the strength of the correlations are age, health status and speed dependent.
To further our understanding of the role of long range correlations in control of human locomotion an obvious next step would be to investigate whether these correlations are also present in the stride interval of running. Thus, the aim of the current paper is to examine the 1/f type behavior of the stride interval time series of human running, and how this is influenced by speed. Shik et al. [22] have shown that a decerebrated cat will make the transition from walking to running with either an increase in the amplitude of stimulation delivered to the locomotor region of the mid-brain or an increase in the belt speed of the treadmill the cat moves upon. Thus, it appears that the main difference between walking and running with regard to higher centers of the central nervous system is related to the excitability of the mid-brain. The common core hypothesis of Zehr suggests that rhythmic locomotor tasks such as walking running and swimming share common central neural control mechanisms [30]. Specifically, Zehr has proposed that the same central pattern generators are used in the control of walking and running and it is the reorganization of neural activity which gives rise to the differences between walking and running.
While there are obvious differences between walking and running related to the timing of muscle activations, overall mechanics, and feedback from the periphery, we hypothesize following Zehr [30] that the same basic neural circuitry is used for the generation of walking and running patterns. Consequently, we predict that there will be long range correlations present in the stride interval of running. It is also hypothesized that preferred walking and running speeds are more stable and have greater adaptive capacity than speeds faster or slower than preferred. Previously in walking studies, it has been shown that there is a U-shaped relationship between the strength of the long range correlations in the stride interval time series and speed [10].
The functional relationship between long range correlations and gait speed reflects the degree of adaptability in system organization and, at the mid-range (maybe preferred) speed, the stride intervals are less strongly influenced by previous stride intervals. Specifically, we hypothesize that at the preferred running speed (PRS), there will be more available dynamical degrees of freedom. By dynamical degrees of freedom, we refer to the degrees of freedom associated with the attractor dynamics, or the dimensionality of the movement system [6], [8], [17]. An attractor can be viewed as an invariant set of points in state space toward which points in the time series are attracted, in spite of any differences in the initial conditions and the fluctuations that arise over time. Running at slower and faster speeds than the preferred speed will introduce constraints to the task of running that will act to reduce the dimensionality or the dynamical degrees of freedom associated with this task. Thus, we predict that the strength of long range correlations in the stride interval of running will increase at speeds greater and less than the PRS which reflects the increase in the dynamical degrees of freedom at the PRS.
Section snippets
Subjects
Eight female volunteers from The Pennsylvania State University between the ages of 22 years and 31 years of age (average = 24.9 ± 2.0 years) were recruited for the study. The average height and mass of the subjects was 164.6 ± 2.3 cm and 57.8 ± 3.6 kg, respectively. The subjects were recreational runners who ran a minimum of 15 miles/week. All subjects provided informed consent and all procedures were approved by the Institutional Review Board of The Pennsylvania State University.
Apparatus
The apparatus consisted
Results
All subjects were able to complete all of the trials. The average PRS was 10.9 ± 0.9 km/h and ranged from 9.6 km/h to 12.6 km/h. The average number of strides per trial was 659 ± 47, the smallest number of strides in any trial was 561 and the largest 767. There were no significant differences between legs for any of the dependent variables. There was an approximately linear decrease in stride interval with increasing running speed (Fig. 1A), F (4, 28) = 38.70, p < 0.01. Post hoc analysis revealed that
Discussion
Long range correlations (correlations that extend for 1000 s of strides) have been revealed in the stride interval of human walking, e.g., [9], [10]. In this study, we investigated whether these long range correlations were also present in the stride interval time series of running, and, if so, how they are influenced by running speed. We collected 8 min running trials which yielded on average around 660 strides per time series. Thus, the lengths of these time series are within the range
Acknowledgements
The authors would like to thank Nori Okita for his technical support and the anonymous reviewers for their helpful comments.
References (30)
- et al.
Gait instability and fractal dynamics of older adults with a “cautious” gait: why do certain older adults walk fearfully?
Gait Posture
(2005) - et al.
Dimensional change in motor learning
Hum Mov Sci
(2001) - et al.
Allometric control, inverse power laws and human gait
Chaos Solut Fractals
(1999) - et al.
Treadmill versus walkway locomotion in humans: an EMG study
Ergonomics
(1986) How nature works: the science of self organized criticality
(1996)- et al.
Fractal physiology
(1994) - et al.
Long memory processes (1/f type) in human coordination
Phys Rev Lett
(1997) - et al.
Effect of nonstationarities on detrended fluctuation analysis.
Phys Rev E Stat Nonlinear Soft Matter Phys
(2002) - et al.
Probability, random processes, and the statistical description of dynamics
- et al.
Local dynamic stability versus kinematic variability of continuous overground and treadmill walking
J Biomech Eng
(2001)
Advantages of rhythmic movements at resonance: minimal noise, and maximal predictability
J Motor Behav
Is walking a random walk? Evidence for long-range correlations in stride interval of human gait
J Appl Physiol
Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations
J Appl Physiol
Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease
J Appl Physiol
Maturation of gait dynamics: stride-to-stride variability and its temporal organization in children
J Appl Physiol
Cited by (118)
A review of psychological and neuroscientific research on musical groove
2024, Neuroscience and Biobehavioral ReviewsRunning gait produces long range correlations: A systematic review
2023, Gait and PostureIs there any biomechanical justification to use hopping as a return to running test? A cross-sectional study
2023, Physical Therapy in SportLong-range correlations and stride pattern variability in recreational and elite distance runners during a prolonged run
2022, Gait and PostureCitation Excerpt :Consistent with our hypothesis, the results demonstrated that LRCs decreased significantly over the course of the run for all stride parameters in both groups and followed a similar pattern; after initially showing high relative values, α decreased sharply after the first interval and remained stable for the remainder of the run (see Fig. 1). For SL, ST and CT, α was consistent with previous studies [5–8,10,33]. The decrease in α between the first two intervals ranged from 14.4% (SL) to 9.1% (CT), and a similar reduction at an early stage was also reported by Meardon et al. [6].
Gait analysis under the lens of statistical physics
2022, Computational and Structural Biotechnology Journal