Persistent and anti-persistent pattern in stride-to-stride variability of treadmill walking: Influence of rhythmic auditory cueing
Highlights
► We studied statistical persistence of Stride Time (ST), Stride Length (SL) and Stride Speed (SS). ► When walking on a treadmill, ST and SL are persistent, while SS is anti-persistent. ► When rhythmic auditory cueing (metronome) is added, SL, ST and SS are anti-persistent. ► A model based on the redundancy theory in the movement control is proposed. ► The goal function constraining both ST and SS lead to a concomitant anti-persistence of SL, ST and SS.
Introduction
Human walking associates the goal of forward progression with the need for a safe motion. A continuous balance control is required to prevent falling. In addition, an efficient postural control keeps the body upright and a fine motor control ensures a safe foot clearance and a soft heel contact (Winter, Patla, & Frank, 1990). These tasks result from complex dynamic sensorimotor interactions. At the spinal level, neural circuitry (Central Pattern Generator) generates the basic locomotor pattern, under the control of various descending pathways (Rossignol, Dubuc, & Gossard, 2006). Visual, auditory and vestibular sensory inputs, as well as afferences from muscles and skin, constitute inputs for feedback and feedforward mechanisms that constantly adapt locomotion to the environment. This multi-level neural control system produces a highly consistent walking pattern. In steady conditions, kinetics, kinematics and muscular activity appear to remain relatively constant from one stride to the next (Hausdorff, 2007). However, small residual stride-to-stride fluctuations occur as the result of internal, neuromuscular noise and small adaptations to the changing environment (such as, for instance, irregularities of the walking surface).
Because an healthy gait mainly consists in maintaining steady speed, Stride Length (SL), Stride Time (ST) and the resulting Stride Speed (SS = SL/ST) can be viewed as “final output” of the multi-dimensional neuromuscular control system, which integrates the result of the different sensory-motor processes. Thus, the analysis of SL, ST and SS could theoretically provide insight into the neurophysiological organization of the motor control and into the regulation of the entire locomotor system (Hausdorff, 2007). For instance, it has been observed that the ratio between step length (SL) and step frequency (SF), or Walk Ratio, is constant over a large range of walking speed (Terrier & Schutz, 2003). In other words, in a physiological range of speeds around preferred walking speed, a linear relationship exists between SL and SF. It seems that this combination of ST and SL is related to energy expenditure optimization (Terrier and Schutz, 2003, Zarrugh et al., 1974). This automated/involuntary adaptation could result from the interaction from lower-level pattern generating mechanism with the dynamical movement context (Zijlstra, Rutgers, Hof, & van Weerden, 1995); furthermore, it has been suggested that interactions between basal ganglia and supplementary motor area could provide the correct stride length and cadence for optimal efficiency (Egerton, Danoudis, Huxham, & Iansek, 2011). Conversely, when a step-by-step control is needed, either in term of ST modulations (i.e., controlling cadence) or SL modulations (i.e., controlling step length), specific supraspinal mechanisms have been suspected, (Zijlstra et al., 1995), possibly implying premotor cortex and supplementary motor area (Halsband, Ito, Tanji, & Freund, 1993).
The synchronization of body movements to external rhythms (auditory-motor coordination) is a remarkable ability of the human brain (Repp, 2005, Zatorre et al., 2007). Step time modulations driven by rhythmic auditory cueing have been studied in the context of different clinical disorders, such as head injuries, Parkinson’s disease or stroke (Lim et al., 2005). It can induce a substantial beneficial effect on gait performance (Lim et al., 2005, Nieuwboer et al., 2007). Rhythmic auditory stimuli may be efficient because they would stimulate an intact auditory-motor system. For instance, in Parkinson’s disease, it is thought that this strategy enables the use of a functional auditory-motor circuit instead of relying on impaired motor control implying affected basal ganglia.
Understanding stride-to-stride control requires quantifying not only average magnitudes of variations across strides (for instance Standard Deviation, SD), but also the specific temporal sequencing of those variations. In the mid 90’s, it has been suggested that successive stride durations (i.e. time series of ST) during walking presented a typical structure over time, characterized by the presence of statistical persistence (Delignières and Torre, 2009, Hausdorff et al., 1995, Hausdorff et al., 1996). In addition to ST, Terrier et al. described persistent patterns in SL and SS during long duration overground walking (Terrier, Turner, & Schutz, 2005). “Persistence” means that deviations are statistically more likely to be followed by subsequent deviations in the same direction (i.e., persist across subsequent data points). Conversely, “anti-persistence” means that deviations in one direction are statistically more likely to be followed by subsequent deviations in the opposite direction.
As in human locomotion, it has been observed in many other physiological time series that the current value possesses the memory of preceding values. This phenomenon – referred alternatively to as long-range correlations, long-term memory, long-range dependence, fractal process or 1/f noise – has been identified in a number of systems and situations, such as heartbeat time series or in the time intervals produced in finger tapping (Diniz et al., 2011). An unified theory explaining this widespread characteristic in physiological processes is still to be built (Diniz et al., 2011). One explanation could be that fractal processes are a natural outcome of complex self-organized systems, emerging from cooperation between their components acting at different space or time scales. Furthermore, it has been proposed that this fractal-like structure was related to the high adaptability of healthy individuals (Goldberger et al., 2002). Conversely, breakdown of the fractal-like structure (i.e., the emergence of more uncorrelated time series) has been associated with various diseases (Goldberger et al., 2002, Hausdorff et al., 1998, Hausdorff et al., 1997, Peng, Havlin et al., 1995b). It was claimed that the loss of statistical persistence would be related to decreased adaptability of neural structures and looser cortical control.
Concerning human gait, methodological issues have questioned the existence of true long-range correlations in ST time series (Maraun, Rust, & Timmer, 2004). On the other hand, a study confirmed the presence of long-range correlations in gait signals by using an alternative statistical approach (Delignières & Torre, 2009). Moreover, it has been suggested that the purported long-range correlations may not require complex central nervous system control mechanisms, but might be due instead to the inherent biomechanical structure of the system (Gates, Su, & Dingwell, 2007). The paradigm of statistical persistence as an index of healthy systems – and its corollary associating uncorrelated pattern with diseases – has also been challenged: indeed, when healthy individuals walked following the cadence of a metronome, ST exhibited either uncorrelated (Hausdorff et al., 1996) or anti-persistent pattern (Delignières and Torre, 2009, Terrier et al., 2005). It has also been suggested that cautious gait could influence persistent patterns (Herman, Giladi, Gurevich, & Hausdorff, 2005). Furthermore, by analyzing the persistence of ST, SL and SS in treadmill walking, a recent study (Dingwell and Cusumano, 2010, Dingwell et al., 2010) found not only that SL and ST exhibited strong statistical persistence, but also that SS exhibited anti-persistent dynamics. The authors suggested that statistical anti-persistence emerges from stride-to-stride fluctuations because of increased central control. Deviations in SS are followed by rapid corrections in order to follow the treadmill speed. However, a slight but repeated over-correction leads to an anti-persistent dynamics.
In view of the results in the literature, an evident research question arises: what happens when treadmill and metronome are used simultaneously? The objective of the present study was therefore to analyze the interactions between two constraints: treadmill, which imposes a constant speed, and rhythmic auditory cueing, which imposes a constant cadence. We assessed, in healthy individuals, statistical persistence (or anti-persistence) in times series of SL, ST and SS by using Detrended Fluctuation Analysis (DFA) at preferred speed as well as at low and high speed, with and without rhythmic auditory cueing. We tested the hypothesis, that only gait variables directly relevant to achieving the task goal (speed and cadence constraints) would exhibit statistical anti-persistence.
Section snippets
Participants
Twenty healthy subjects (10 females, 10 males) participated in the study. Based on preliminary interviews, we ensured that they did not exhibit any orthopedic problems or other health issues that could influence their gait. They were recruited in the Sion area (South-west Switzerland). The participants’ characteristics were (mean (SD): age 36 yr (11), body mass 71 kg (15), and height 171 cm (9). The average Body Mass Index (BMI) was 24 (4), what is close to the average BMI of the Swiss population
Results
Fig. 1 shows the range of speeds chosen by the participants for each condition and the corresponding Walk Ratio (i.e., the ratio between step length and cadence). WR is constant across speeds, with a slight tendency of higher WR at low speed condition. Fig. 2 shows the extent of the data for stride-to-stride variability, expressed as coefficient of variation (CV, i.e., standard deviation/mean × 100). Both conditions are presented: treadmill only (top) and treadmill combined with auditory cueing
Discussion
By using an instrumented treadmill, we measured the length and duration of gait cycles at 3 walking speeds (slow, preferred, fast) and two conditions (without and with rhythmic auditory cueing). We observed that auditory cueing induced a decrease in the variability of ST and SL (lower CV), especially at low speed. Treadmill induced anti-persistent dynamics in the time series of SS, but preserved the persistence of ST and SL. On the contrary, all the three parameters were anti-persistent under
Author contributions
P.T. designed and performed the experiment, analyzed the data and wrote the article. O.D. supervised the study, gave conceptual advice, and edited the manuscript.
Acknowledgments
The authors thank Mr Philippe Kaesermann for the loan of the instrumented treadmill, and the anonymous reviewers for their constructive remarks. The study was supported by the Swiss accident insurance company SUVA, which is an independent, non-profit company under public law. The IRR (Institute for Research in Rehabilitation) is supported by the State of Valais and the City of Sion.
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