Vivien Marmelat

Persistent fluctuations in stride intervals under fractal auditory stimulation

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

Predicting the biological variability of environmental rhythms: Weak or strong anticipation for sensorimotor synchronization?

The internal processes involved in synchronizing our movements with environmental stimuli have traditionally been addressed using regular metronomic sequences. Regarding real-life environments, however, biological rhythms are known to have intrinsic variability, ubiquitously characterized as fractal long-range correlations. In our research we thus investigate to what extent the synchronization processes drawn from regular metronome paradigms can be generalized to other (biologically) variable rhythms. Participants performed synchronized finger tapping under five conditions of long-range and/or short-range correlated, randomly variable, and regular auditory sequences. Combining experimental data analysis and numerical simulation, we found that synchronizing with biologically variable rhythms involves the same internal processes as with other variable rhythms (whether totally random or comprising lawful regularities), but different from those involved with a regular metronome. This challenges both the generalizability of conclusions drawn from regular-metronome paradigms, and recent research assuming that biologically variable rhythms may trigger specific strong anticipatory processes to achieve synchronization.

Theoretical and methodological issues in serial correlation analysis.

In this chapter, we present some theoretical and methodological problems related to the analysis of serial correlations in experimental data. A very common observation in behavioral and physiological experiments is the presence of long-range correlations in time series. In this case, the current observation seems to keep the memory of a large set of previous observations. This kind of process has been referred to as long-range dependence, long-term memory, fractal correlation, or 1/f noise. There is now a general agreement for considering long-range correlations as reflecting the complexity of the system, defined as the flexible and adaptable coordination between its multiple components and subsystems. Long-range correlations are supposed to sign an optimal compromise between order and disorder; order reflecting a too strict and rigid coordination and disorder the absence of coordination. Long-range correlations are considered the signature of health and adaptability, and deviations towards order and disorder have been described in elderly or pathological populations. As such, the detection of long-range correlations and the assessment of their alteration in specific populations or situations appear as an important scientific goal.

How to Sync to the Beat of a Persistent Fractal Metronome without Falling Off the Treadmill

In rehabilitation, rhythmic acoustic cues are often used to improve gait. However, stride-time fluctuations become anti-persistent with such pacing, thereby deviating from the characteristic persistent long-range correlations in stride times of self-paced walking healthy adults. Recent studies therefore experimented with metronomes with persistence in interbeat intervals and successfully evoked persistent stride-time fluctuations. The objective of this study was to examine how participants couple their gait to a persistent metronome, evoking persistently longer or shorter stride times over multiple consecutive strides, without wandering off the treadmill. Twelve healthy participants walked on a treadmill in self-paced, isochronously paced and non-isochronously paced conditions, the latter with anti-persistent, uncorrelated and persistent correlations in interbeat intervals. Stride-to-stride fluctuations of stride times, stride lengths and stride speeds were assessed with detrended fluctuation analysis, in conjunction with an examination of the coupling between stride times and stride lengths. Stride-speed fluctuations were anti-persistent for all conditions. Stride-time and stride-length fluctuations were persistent for self-paced walking and anti-persistent for isochronous pacing. Both stride times and stride lengths changed from anti-persistence to persistence over the four non-isochronous metronome conditions, accompanied by an increasingly stronger coupling between these gait parameters, with peak values for the persistent metronomes. These results revealed that participants were able to follow the beat of a persistent metronome without falling off the treadmill by strongly coupling stride-length fluctuations to the stride-time fluctuations elicited by persistent metronomes, so as to prevent large positional displacements along the treadmill. For self-paced walking, in contrast, this coupling was very weak. In combination, these results challenge the premise that persistent metronomes in gait rehabilitation would evoke stride-to-stride dynamics reminiscent of self-paced walking healthy adults. Future studies are recommended to include an analysis of the interrelation between stride times and stride lengths in addition to the correlational structure of either one in isolation.

Relative Roughness: An Index for Testing the Suitability of the Monofractal Model

Fractal analyses have become very popular and have been applied on a wide variety of empirical time series. The application of these methods supposes that the monofractal framework can offer a suitable model for the analyzed series. However, this model takes into account a quite specific kind of fluctuations, and we consider that fractal analyses have been often applied to series that were completely outside of its relevance. The problem is that fractal methods can be applied to all types of series, and they always give a result, that one can then erroneously interpret in the context of the monofractal framework. We propose in this paper an easily computable index, the relative roughness (RR), defined as the ratio between local and global variances, that allows to test for the applicability of fractal analyses. We show that RR is confined within a limited range (between 1.21 and 0.12, approximately) for long-range correlated series. We propose some examples of empirical series that have been recently analyzed using fractal methods, but, with respect to their RR, should not have been considered in the monofractal model. An acceptable level of RR, however, is a necessary but not sufficient condition for considering series as long-range correlated. Specific methods should be used in complement for testing for the effective presence of long-range correlations in empirical series.

Multifractal signatures of complexity matching

The complexity matching effect supposes that synchronization between complex systems could emerge from multiple interactions across multiple scales and has been hypothesized to underlie a number of daily-life situations. Complexity matching suggests that coupled systems tend to share similar scaling properties, and this phenomenon is revealed by a statistical matching between the scaling exponents that characterize the respective behaviors of both systems. However, some recent papers suggested that this statistical matching could originate from local adjustments or corrections, rather than from a genuine complexity matching between systems. In the present paper, we propose an analysis method based on correlation between multifractal spectra, considering different ranges of time scales. We analyze several datasets collected in various situations (bimanual coordination, interpersonal coordination, and walking in synchrony with a fractal metronome). Our results show that this method is able to distinguish between situations underlain by genuine statistical matching and situations where statistical matching results from local adjustments.