A Dynamic Systems Approach to the Effects of Aging

Behavioural Science Section Gerontology 2010;56:335–344 DOI: 10.1159/000262445

Received: January 8, 2009 Accepted: April 30, 2009 Published online: November 26, 2009

A Dynamic Systems Approach to the Effects of Aging on Bimanual Coordination Jean-Jacques Temprado a Sarah Vercruysse a, c Robin Salesse b Eric Berton a a

UMR 6233 ‘Institut des Sciences du Mouvement’ CNRS et Université de la Méditerranée, Marseille, and Centre de Recherche sur la Cognition et l’Apprentissage – UMR 6234 CNRS et Université de Poitiers, Poitiers, France; c Research Center for Neuromotor, Pediatric and Pelvic Rehabilitation, Catholic University of Leuven, Leuven, Belgium b

Key Words Aging ⴢ Bimanual coordination ⴢ Dynamic systems theory

Abstract The present study examined the effects of aging on the execution of a bimanual coordination task in a classical phase transition paradigm in which coordination patterns (inphase and anti-phase) and movement frequency were manipulated. Two groups of adults, the so-called young (average age 26 years) and old (average age 71 years) participants, performed both in-phase and anti-phase patterns at different frequencies. As we expected variability of relative phase was larger for older participants than for younger ones for both the in-phase and the anti-phase coordination patterns. Moreover, phase transitions occurred at lower frequencies for older participants and more transitions were observed for older than for younger participants. Although no specific hypotheses were made about the prominent source(s) of age-related changes in coordination dynamics (i.e., an alteration in the coupling function and/or an increase of the magnitude of noise), our results suggest that these changes might result from increases in the (neural) noise to be found in the (bimanual) action system. Copyright © 2009 S. Karger AG, Basel

© 2009 S. Karger AG, Basel 0304–324X/10/0563–0335$26.00/0 Fax +41 61 306 12 34 E-Mail [email protected] www.karger.com

Accessible online at: www.karger.com/ger

Introduction

It is widely accepted that age-related loss of behavioral adaptability observed in many motor tasks results from a complex interplay of musculoskeletal, cognitive, metabolic and neural subsystems of the organism [1, 2]. Nevertheless, the strategy often adopted in aging research consists of breaking these interactions into simple (linear) and additive causalities, for instance through the evaluation of the alterations of separate subsystems (e.g. somatosensory, cognitive, muscular, etc.) and their deleterious effects on behavioral performance [for an overview, see 3]. Moreover, although the quality of everyday life of older persons depends to a large part on their ability to carry out multi-limb coordination, little is known about the degree to which problems of motor coordination affect the elderly. Indeed, during the last 20 years, attention has mainly been drawn to the effects of aging on posture, gait and uni-manual movements [3; for notable exceptions, see 4–7]. These statements motivated us to investigate the effects of aging on movement coordination in a dynamic systems theory approach. The dynamic systems approach is particularly suitable for investigating the factors underlying the (loss of) adaptability of behavioral and physiological systems [2, Jean-Jacques Temprado UMR 6233 ‘Institut des Sciences du Mouvement’, Université de la Méditerranée Faculté des Sciences du Sport, 163 Avenue de Luminy, BP 910 FR–13288 Marseille Cedex (France) Tel. +33 4 91 172 272, Fax +33 491 172 252, E-Mail jean-jacques.temprado @ univmed.fr

8–11]. At the core of this approach is the belief that the existence of preferred behavioral states, their stabilization and dissolution emerge from the product of many local interactions that occur within and between the different subsystems and components of the organism, at different levels of organization. Thus, concepts, methods and tools of the dynamic systems theory have been used to capture behavioral patterns resulting from multiple coupling interactions, substantiated by various substrates, that the subsystems actually entertain with each other at the microscopic level [9, 12, 13]. Among a number of domains of application, the dynamic systems approach developed valuable experimental paradigms and models for studying inter-limb coordination [9, 13, 14]. Some of the most promising support for this approach has been shown in bimanual coordination tasks. Bimanual coordination is characterized by two preferred patterns of coordination – in-phase and anti-phase [15]. In the present study, by convention and according to Kelso’s [15] original definition, patterns that result from the simultaneous activation of homologous muscle groups are denoted in-phase (i.e. mirror symmetrical movements with respect to the body midline); while coordination patterns that result from simultaneous activation of non-homologous muscle groups are denoted antiphase (i.e. one limb moves toward the body midline, whereas the other limb moves away from it and vice versa). Numerous works have shown that the in-phase pattern is more stable than the anti-phase pattern, and an unavoidable switch from the latter to the former occurs when oscillation frequency increases beyond a given critical threshold [15–17]. In that case, the increase in oscillation frequency is considered a control parameter that modifies the coordinative behavior captured by the relative phase, so-called order parameter. The behavioral picture of this spontaneous dynamics of bimanual coordination was formalized by Haken et al. [18] through the dynamics of the relative phase between the limbs, seen as self-sustained oscillators linked through a nonlinear coupling function [18, 19]. Such an informational coupling captures the multiple interactions or linkages that the components actually entrain with each other, substantiated through various substrates (neural, musculoskeletal, vascular, etc.) [12, 20]. Behaviorally, coupling manifests in the space of relative phase, allowing the system to adopt but a limited set of stable coordination states. The relative stability of the two patterns may vary as a function of a control parameter (oscillation frequency) that modifies the attraction of the stable states, that is, the ‘force’ that 336

Gerontology 2010;56:335–344

they exert on relative phase toward in-phase or antiphase. A major consequence of the bimanual action system to be subject to coordination dynamics is that stability plays a central role, which is most evident when stability is lost. Specifically, the magnitude of fluctuations of the relative phase quantifies the stability of coordination patterns and determines whether it changes when scaling a control parameter. Theoretically, scaling the control parameter results in a loss of stability, which ultimately may lead to phase transition. Thus, pattern switching is preceded by critical fluctuations, assessed as an increase in the standard deviation of relative phase, as oscillation frequency increases. These fluctuations subsequently decrease after the transition, once the in-phase pattern is adopted [16, 19, 21]. The influence of stochastic fluctuations on bimanual coordination dynamics has been accounted for by Schöner et al. [19], by assuming the existence of a Gaussian white noise process, independent of the scaling of the control parameter (movement frequency). Thus, given a particular noise magnitude, variability of relative phase depends on the coupling strength of coordination patterns, which is modulated by movement frequency. Using this model to investigate how aging – considered as a parameter acting over a long time scale – may affect the bimanual coordination dynamics observable over a short time scale may afford new insights into the study of behavioral adaptability over lifespan. However, this issue has received only limited attention [for a noticeable exception, see 22]. Indeed, most studies on aging and coordination only consisted of describing bimanual performance differences between young and older adults and showed inconsistent results [4, 5, 7]. For instance, Lee et al. [4] showed that older participants were less stable than younger participants for both the in-phase and antiphase patterns. Wishart et al. [7] reported that older participants performed as well as younger participants at all frequencies of an in-phase pattern and at low frequencies of an anti-phase pattern. In this study, age differences only tended to emerge most prominently at high frequencies for the anti-phase pattern. On the other hand, the findings of Serrien et al. [5] suggested that bimanual performance was resistant to age-related deficits for both the in-phase and anti-phase patterns. Greene and Williams [22] briefly reported the results observed in an experiment on bimanual coordination dynamics that is, on pattern stability and changes at different oscillation frequencies. They found that older participants exhibited involuntary transitions from the (more difficult) anti-phase to Temprado /Vercruysse /Salesse /Berton

the (easier) in-phase pattern at a significantly lower frequency than the younger participants. Detailed information about the methods and measurements used in the experiment of Greene and Williams [22] was unfortunately not available. Thus, aging effects on bimanual coordination dynamics deserved further investigation. The present study addressed this issue by investigating the effects of aging on pattern stability, loss of stability and changes in a bimanual coordination task using a classical phase transition paradigm [15]. As detailed above, two main factors could contribute to altering bimanual coordination pattern stability with aging. The first factor is a change in the coupling strength between the components, which would occur as a result of structural changes of brain connectivity and functional changes of neural crosstalk in the aging brain [23, 24], including time delays of information transmission [25], reduction of attentional capacity [4, 26], and alteration in proprioceptive and visual information processing [5]. In the modeling of bimanual coordination dynamics by Haken et al. [18], inference with regard to changes in coupling strength is usually made on the basis of the magnitude of relative phase variability [19, 27]. Indeed, noise is assumed to be constant and independent of movement frequency. The assumption of noise constancy could however be violated for older participants, making change in noise magnitude the second hypothetical source of alteration of relative phase variability with aging. Indeed, according to the ‘neural noise’ hypothesis [28], it has been suggested that with advanced age, neural noise increases and interferes with the transmission of information within the CNS, leading to random fluctuations in behavioral performance. Thus, an increase in performance variability is a distinguishing marker to age-related alterations in the integrity of the neurobiological mechanisms [29, 30]. Although in the dynamic systems approach no a priori assumption can be made that there is a proportional relationship between neural noise in the system output and the magnitude of variability of relative phase in bimanual performance [31], neural noise can however be considered one of the possible sources of variability of relative phase in bimanual coordination. Hypotheses of the Present Study The present study aimed to test general predictions made with respect to intra-individual variability and its effects on bimanual coordination dynamics with aging. These predictions were the following: (1) variability should be larger for older participants than for younger Aging and Bimanual Coordination

participants for both the in-phase and the anti-phase coordination patterns; (2) more transitions should be observed for older than for younger participants; (3) transitions should occur at lower frequencies for older than for younger participants, and (4) time before transition should be shorter for older than for younger participants. It is noticeable that these predictions did not depend on the origins of intra-individual variability (i.e. an alteration in the coupling function and/or an increase in the magnitude of noise). Participants and Methods A group of 13 younger (6 women and 7 men, mean age 26 8 SD 3.1 years) and a group of 15 older adults (12 women and 3 men, mean age 71 8 SD 5.4 years) volunteered to participate. The older subjects were recruited from the retirement club ‘Maison pour Tous’ in Marseille at which they were engaged in fitness activities twice a week. They lived independently and declared to be in good health. They had no prior experience with the task or the experimental apparatus. Informed consent to participate to the study was obtained from all participants. The protocol was approved by a local ethics committee and has therefore been in accordance with the ethical standards laid down in the Declaration of Helsinki. Apparatus and Task Participants were seated on a chair and leaned with their back against the chair support to prevent shoulder movements. Their upper limbs were placed parallel to each other. Flexion angles of elbows were about 90°. Participants gripped free rotating handles with their fingers flexed thereby allowing them to easily perform pronation-supination movements of the forearms in order to move the handles (fig. 1). The axis of rotation of each handle was positioned between digits III and IV of each hand. Each handle could rotate within a 890° range. This large amplitude range allowed participants to have virtually unrestricted movements of their forearms. Handle movements were recorded at a sampling frequency of 500 Hz using optical coders placed on the axis of rotation of each handle. Participants were requested to perform in-phase and antiphase bimanual coordination patterns by making forearm pronation-supination movements in time with a metronome that prescribed the required frequency in the course of a trial. Frequency was set at 0.5, 1, 1.5, 2 or 2.5 Hz across trials. By convention, patterns resulting from the simultaneous activation of homologous muscles – giving rise to mirror-symmetric movements with respect to body midline – were denoted in-phase. Coordination patterns resulting from simultaneous activation of non-homologous muscles – giving rise to asymmetric movements – were denoted anti-phase (fig. 1). Procedure Before the experiment, participants were informed about the aim and the procedure of the study. Then, a period of familiarization to coordination modes was proposed during which they performed each pattern for 150 s at a freely chosen frequency. Subse-


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Fig. 1. Illustration of hand positions and the direction of their os-

cillations in the two patterns performed by the participants. The in-phase pattern required simultaneous pronation (vs. supination) of both forearms. The anti-phase pattern required pronation (vs. supination) of one forearm coincident with supination (vs. pronation) of the contralateral forearm. The in-phase pattern resulted in mirror-symmetric movements with respect to body midline while the anti-phase pattern resulted in asymmetric movements with respect to body midline.

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quently, they completed 40 trials of 30-second duration: 20 trials for each pattern that is, 4 trials at each frequency. Participants were given a 30-second rest period between each trial and a break of 10 min after 20 trials. Movements were paced by an auditory metronome delivered via headphone (3.3 kHz square waves, duration 50 ms). Participants were instructed to produce the required pattern as accurately and continuously as possible, carrying out a full movement cycle between 2 subsequent metronome beats. They were also encouraged to keep the rest of their body as stable as possible and their back against the chair support. Moreover, instruction was given to the participants not to resist pattern change (i.e., the socalled ‘do not intervene instruction’) [15], that is, to maintain the initial coordination pattern unless they felt that switching to another pattern would allow the task to be performed more comfortably at the prevailing frequency. Data Analysis Raw data were filtered with a second-order dual-pass Butterworth filter with a cutoff frequency of 8 Hz. The cycle-by-cycle effective movement frequency (averaged across both hands) was computed for each trial together with a frequency deviation score for the pre-transition period. This score reflects the absolute difference between the average within-trial effective frequency and the metronome one. When participants’ effective frequency deviated more than 80.25 Hz of the requested frequency, the trial was then considered as having been performed at the corresponding frequency condition. For instance, if the requested frequency was 2.5 Hz but the actually performed frequency was 2.12 Hz, the trial was considered with the trials performed at 2 Hz. This reorganization enabled determining whether participants succeeded in following the task instruction. Subsequently, it enabled determining the effects of effective frequency on the different coordination variables. In other words, it ensured that other comparisons of outcome variables within a given frequency level were based on an equivalent temporal constraint. The mean amplitude of each hand movement was calculated for each trial (in degrees) and averaged over the 2 hands. Relative phasing between the oscillations of the right and the left hands served as a measure of bimanual coordination. Point estimate relative phase was computed with the right hand as the reference, using a peak-peaking algorithm [32; for a review, see 33] and the following formula:

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Fig. 2. Illustration of the method used to determine the onset of the transition in a representative trial (here, the required pattern was anti-phase at a movement frequency of 2.5 Hz). The posttransition period is illustrated by the grey area. The analyses were only conducted in the pre-transition period. The plain line represents the point estimate relative phase and the dashed line the evolution of the three cycles rolling mean. The onset of the transition corresponds to the time where the rolling mean overpass the 845° criteria represented by the two horizontal plain lines (135° and 225°, respectively).

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t1 t 2

q 360n T with t1 and t2 being the time of maximal right and left phase angles, respectively, and T the period of the right hand. The stability of coordination patterns was assessed by computing: (i) the number of phase transitions; (ii) the time-to-transition, and (iii) the standard deviation of the relative phase in the pre-transition period. To identify phase transitions (i.e. an abrupt switch from one pattern to another), a specific visualization process via a customized graphic interface was employed (fig. 2). Thanks to the interface, the experimenter was informed when the mean value of 3 consecutive cycles of the relative phase was leaving a 845° range around the required phase to perform. Position cursors were then set at the last relative phase value within this range. This value defined the end of the pre-transition period, i.e.

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just before the required relative phase shifted to another stable phase relation. This procedure therefore allowed the experimenter to separate pre- and post-transition regions [for a similar method, see 34]. If no stable pattern was re-attained after leaving the required pattern for more than 45° during at least 3 cycles, the trial was categorized as transition trial [35]. Each participant performed the 10 different conditions 4 times. Thus, for each subject, in each condition, the number of phase transitions was summed (from 0 to 4). Then, this number was transformed into a percentage, which varied from 0 to 100%. The percentage of phase transition was then transformed using a root square arcsine transform to ensure both the homogeneity of the variance and the normality of the error distribution [36]. Time-to-transition was defined as the time between the beginning of one trial and the end of the pre-transition period. For trials in which no transition was observed, this value was set to the total duration of the trial (i.e. 30 s) [for a similar method, see 16]. Variability of coordination patterns was assessed by computing the standard deviation of the relative phase. For the trials in which a transition occurred, variability was calculated for the pre-transition period. The absolute error of the relative phase, that is the unsigned difference between the mean relative phase and the required pattern, was used as an index of accuracy of bimanual coordination. Statistics Movement frequency, variability of the relative phase, absolute error of the relative phase and movement amplitude were subjected to a two-way 2 (group) ! 2 (pattern) ! 5 (frequency) ANOVA with repeated measures on the 2 last factors. The percentage of phase transition and time of pattern maintaining were subjected to a 2 (group) ! 4 (frequency) ANOVA with repeated measures on the last factor. All significant ANOVA effects were further analyzed using Newman-Keuls post-hoc tests. The significance of all statistic tests was 0.05.

Results

served at 2.0 and 2.5 Hz (p ! 0.05). Nevertheless, the deviation from the requested frequency was larger for the older adults than for the younger but only at the higher frequency (2.5 Hz). Overall, for the younger group, all participants were able to perform both the in-phase and anti-phase patterns at the requested frequencies. On the other hand, for the older group, 6 participants (of 15) were unable to perform at 2.5 Hz for the anti-phase pattern and 1 participant was unable to perform at 2.0 Hz. Among these 6 participants, only 3 were unable to perform the higher frequency (2.5 Hz) for the in-phase pattern. Thus, subsequent analyses were carried out with missing values for some participants at 2.0 Hz (1 participant) and 2.5 Hz (6 participants for the anti-phase and 3 participants for the in-phase pattern). Percentage of Phase Transitions No transition was observed for the in-phase pattern either for the older or the younger group. Moreover, no transition was observed at 0.5 Hz for the anti-phase pattern, either for the older or the younger group. The analysis revealed a significant frequency effect (F3, 57 = 45.6, p ! 0.001) and a significant group effect (F1, 19 = 6.5, p ! 0.05). Results showed that the percentage of transition significantly increased with frequency, from 7 (1.0 Hz) to 26% (1.5 Hz), 64 (2 Hz) and 68% (2.5 Hz). Moreover, the percentage of transition was always larger for older participants than for younger participants, whatever the frequency level (fig. 3). A close inspection of the results revealed that at 2.5 Hz older participants were close to the maximum of transition (85%) though the percentage of transition was !60% for the younger participants.

Movement Frequency The analysis revealed a significant main effect of group (F1, 25 = 13.4, p ! 0.01), pattern (F1, 25 = 6.1, p ! 0.05) and frequency (F4, 100 = 61.9, p ! 0.001) and a significant group ! frequency interaction effect (F4, 100 = 8.2, p ! 0.001). Results showed that the deviation of the effective frequency from the requested frequency was higher for the anti-phase mode (0.17 Hz) than for the in-phase mode (0.14 Hz). Post-hoc decomposition of the group ! frequency interaction using the NewmanKeuls test showed that the error significantly increased with frequency for the older group, that is from 1.0 to 1.5, from 1.5 to 2.0 and from 2.0 to 2.5 Hz. For the younger group, no difference was observed between 0.5, 1.0 and 1.5 Hz. On the other hand, error scores observed for these three frequencies were different from those ob-

Time of Pattern Maintaining Analysis was conducted on the time of maintaining the anti-phase pattern for the 4 frequency levels for which phase transitions were observed (i.e., at 1.0, 1.5, 2.0 and 2.5 Hz). This analysis revealed a significant effect of group (F1, 19 = 7.8, p ! 0.05) and frequency (F3, 57 = 30.2, p ! 0.001). Results showed that whatever the frequency level, the time of maintaining the pattern was always longer for younger participants than for older participants. Moreover, the time of maintaining the anti-phase pattern was equivalent at 1.0 and 1.5 Hz but significantly longer than those observed at 2.0 and 2.5 Hz. In addition, the time of maintaining was longer at 2.0 than at 2.5 Hz.

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Fig. 4. Average standard deviation of the relative phase (in degrees) computed for older and younger participants at the different movement frequencies.

Variability of Relative Phase The analysis revealed a significant group effect (F1, 16 = 6.5, p ! 0.05), pattern effect (F1, 16 = 41.9, p ! 0.001), frequency effect (F4, 68 = 5.9, p ! 0.001) and a frequency ! pattern interaction effect (F4, 64 = 4.4, p ! 0.01). Results showed that whatever the frequency and the pattern, the older participants were more variable than the younger participants (19.2 and 15.8°, respectively). Post-hoc decomposition of the interaction effect carried out with the Newman-Keuls test showed that the anti-phase pattern was significantly more variable than the in-phase pattern for both groups, but only at the 2 higher frequency levels (2.0 and 2.5 Hz). Moreover, variability of the anti-phase pattern increased at the 2 higher frequency levels (2.0 and 2.5 Hz) with respect to 0.5, 1.0 and 1.5 Hz. On the other hand, no effect of frequency was observed for the in-phase pattern for both groups (fig. 4).

anti-phase pattern was significantly larger than that observed for the in-phase pattern for both groups, but only at the 2 higher frequency levels (2.0 and 2.5 Hz). Moreover, for the anti-phase pattern the error increased at the 2 higher frequency levels (2.0 and 2.5 Hz) with respect to 0.5, 1.0 and 1.5 Hz. On the other hand, no effect of frequency was observed for the in-phase pattern for both groups.

Absolute Error of Relative Phase The analysis revealed a significant group effect (F1, 16 = 4.7, p ! 0.05), pattern effect (F1, 16 = 14.0, p ! 0.01), a significant frequency effect (F4, 64 = 12.3, p ! 0.001) and a frequency ! pattern interaction effect (F4, 64 = 2.9, p ! 0.05). Results showed that the error observed for the older participants was larger than the error observed for the younger participants (15.5 and 10°, respectively), independent of pattern and frequency. Post-hoc decomposition of the interaction effect carried out with the Newman-Keuls test showed that the error observed for the 340


Amplitude The analysis revealed a significant effect of frequency (F4, 64 = 18.2, p ! 0.001). Post-hoc decomposition carried out with the Newman-Keuls test showed that movement amplitude decreased at the higher frequencies (150 and 131° at 2.0 and 2.5 Hz, respectively) with respect to the 3 other frequencies, which exhibited equivalent amplitude of movement (176, 174 and 170° at 0.5, 1 and 1.5 Hz, respectively). No significant difference was found between the 2 groups.

Discussion

The present study attempted to bridge the gap between two issues which until now have been rather isolated, namely age-related alterations in the neurobehavioral system and the dynamic theory of coordination pattern. Using a classical phase transition paradigm in bimanual coordination, the connection between the two approaches was made through the notion of intra-individual variTemprado /Vercruysse /Salesse /Berton

ability of performance, which is considered a prominent marker of aging and plays a central role in coordination dynamics. Accordingly, the general prediction was that coordination patterns should be more variable for older participants than for younger participants. Moreover, it was predicted that such variability would affect bimanual coordination dynamics, that is the number of phase transitions from the anti-phase to the in-phase pattern and the time of maintaining the anti-phase pattern. First of all, it was noticeable that both older and younger participants performed the requested coordination patterns with equivalent movement amplitude. This observation ensured that other comparisons of outcome variables within a given frequency level or coordination pattern were based on an equivalent spatial constraint. The absence of difference between movement amplitude between younger and older adults suggested that participants respected the given instruction, that is ‘carrying out a full movement cycle between two subsequent metronome beats’. The price to pay for keeping amplitude constant seemed to be a decrease in movement frequency, at least at the higher frequency. Such a result is consistent with the age-related general slowing down currently observed in various cognitive and motor tasks [37]. It also suggests that changes in pattern stability observed at the different frequencies did not result from a change in bimanual coupling strength that would be mediated by a decrease in movement amplitude. Indeed, according to the HKB model [18], the eventual loss of stability of the anti-phase mode with increasing frequency would result from the drop in amplitude. In this respect, it is of particular importance that movement amplitude remained equivalent between the 2 groups. Indeed, given the equivalent spatial constraints, a difference in pattern stability between the 2 groups might likely result from inherent (e.g. alteration of neural connections or time delays) [23, 25] rather than strategic changes in coupling strength and/or enhancement of neural noise with aging. On the other hand, the error of the relative phase was larger for the older than for the younger participants. Although such a decrease in pattern accuracy (i.e. coordination performance) was not surprising, this result suggests that asymmetry between the 2 hands changed with aging, thereby leading to a larger shift in relative phase [38]. Previous studies on bimanual coordination stressed the difficulty of older participants to perform coordination patterns at high oscillation frequencies [4, 7]. Con-

sistent results were observed in the present study. Indeed, deviation of the requested frequency was larger for older participants. Moreover, 6 of the 15 older participants failed to perform the anti-phase pattern at 2.5 Hz. However, only 3 of them were unable to perform the in-phase pattern at the highest movement frequency (2.5 Hz). This result suggested that the limits in movement frequency observed for older participants were, at least in part, taskdependent. Since the 2 coordination patterns differed with respect to the timing of muscle group activation (i.e. simultaneous activation of homologous versus non-homologous muscle groups), it is tempting to conclude that neuromuscular constraints play a prominent role in the age-related slowing down of movement execution. However, the 2 patterns also differed with respect to spatial constraints (i.e. mirror-symmetric versus asymmetric movement with respect to body midline), which are currently considered prominent constraints on bimanual coordination [39, 40]. Thus, further experiments are necessary to determine the respective role of neuromuscular and spatial constraints in the slowing down of movement execution during aging. As expected, the results of the present study showed that variability of relative phase was larger for the older participants than that observed for the younger participants for both the in-phase and the anti-phase pattern. Moreover, differences of performance variability between older and younger participants were independent of movement frequency. These results are consistent with those observed by Lee et al. [4], thereby confirming the general observation made in a variety of tasks that variability of behavioral performance increases with aging [2, 29, 30]. On the other hand, they differ from those observed in other studies suggesting that bimanual performance was resistant to age-related deficits for both the in-phase and the anti-phase pattern [5] or, at least, that age differences in relative phase variability only emerged at high frequencies for the anti-phase pattern [7]. Theoretically, differences in relative phase variability between older and younger participants observed in bimanual coordination could result from a decrease in coupling strength and/or an increase in stochastic noise. Such hypotheses are consistent with previous works suggesting that, with aging, neural noise increases [28, 30] and coupling functions between the subsystems and components of the organism are altered [2, 10]. Although in the present experiment no specific hypotheses were made about the prominent source(s) of age-related changes in coordination dynamics, our results however afford insights into the respective evolution of coupling



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strength and noise magnitude in bimanual coordination across lifespan. First of all, for the in-phase pattern, relative phase variability did not increase with frequency for older participants. This result has already been observed in previous studies on bimanual coordination in young healthy adults [15, 41]. According to the modeling of Haken et al. [18], it suggests that an increase in frequency neither changed the magnitude of noise present in the system nor the coupling strength [42]. These results are of importance for the existing knowledge in the domain of aging. On the one hand, they confirm that the inphase pattern is resistant to destabilization by augmenting frequency, even for older participants [5]. On the other hand, they provide new evidence in the persisting debate concerning the effect of the amount of force required to perform a movement on motor variability (be it of central and/or peripheral origin) for older people [29, 43]. Indeed, our results suggest that, at least in the present task situation, a frequency-induced increase in the amount of force required to perform hand movements did not change (neural) noise and, consequently, behavioral variability. On the basis of the results observed for the in-phase pattern, one can suggest that, for the antiphase pattern, coupling strength was not significantly affected by aging. Indeed, in such a case, since noise magnitude remained constant across movement frequencies, one should observe a larger effect of frequency on relative phase variability for older participants than for younger participants (i.e., an interactive effect of aging and frequency). Taken together, in showing that relative phase variability was not modified by frequency for the in-phase pattern and that older participants were more variable than younger participants by about the same difference for both patterns and for all movement frequencies, our results suggest that only the noise present in the system was affected by aging. Results observed for the absolute error of relative phase are consistent with this interpretation. Indeed, we observed an increase in asymmetry between the 2 hands for older participants. According to the HKB model [18], these findings suggest that the detuning parameter (i.e. an index of the difference between the oscillators’ eigenfrequencies) changed with aging. Such an increase in asymmetry between the 2 hands could be (one of) the source(s) of the difference in pattern stability between young and older participants. Such a hypothesis is consistent with the results observed by Richardson et al. [42] using cross-recurrence quantification analysis. They showed that modulations in frequency detuning between oscillatory hands influenced the magnitude of internal fluctuations and 342


consequently relative phase variability. According to Richardson et al. [42], one could speculate that changes in frequency detuning resulted in rescaling of the magnitude of the perturbation process (i.e. noise) inherent to inter-limb coordination. This ‘task-specific’ interpretation of variability difference suggests that different sources of fluctuations might contribute to the increase in age-related differences in relative phase variability that is not only an increase in the magnitude of neural noise. As predicted, more phase transitions were observed for older participants than for younger participants, even at lower frequencies (e.g. 1 and 1.5 Hz). These results are consistent with those reported by Greene and Williams [22]. As a consequence of the general increase in the number of phase transitions, the percentage of pattern switching observed at 2.5 Hz for the 9 older participants able to perform the requested frequency was close to the maximum (85%), suggesting that older participants approached their limit in the capacity of maintaining the anti-phase coordination pattern. It was also observed that the time of maintaining the anti-phase pattern within a trial was shorter for older than for younger participants. Thus, our results showed that alterations in the neurobehavioral system of older participants considerably limited their capacity to maintain the required coordination at moderate and high movement frequencies. However, the bimanual coordination dynamics of older and younger participants obeyed the same general trend, though older participants were more variable, less symmetric and more sensitive to the destabilizing effect of the control parameter (movement frequency). By no doubt, these modifications resulted from alterations in the neuromusculoskeletal system with age. However, the question remains how the coalition of neuromuscular, cognitive, sensory or biomechanical factors changes with age. Further studies are necessary to investigate this issue. A potential limitation to the current study lies in the global inclusion criterion of ‘good health’ adopted to select participants. Good health was attested by the participation, at least twice a week, in physical fitness and walking activities organized for independently living elderly people by our partner association. Although this criterion guaranteed that participants had neither serious cognitive nor motor acute disabilities, minor chronic disabilities, not declared by participants at the time of experiment, could have marginally biased the result of the present experiment.


Conclusion

One of the important challenges for movement scientists concerned with aging is the need to provide a coherent account of behavioral (loss of) adaptability across the lifespan. The present study addressed this issue in a bimanual coordination task by bridging the gap between age-related variability and its effect on coordinated behavior through the use of a framework rooted in self-or-

ganization theories and non-linear dynamic systems. Results suggested that this approach is promising and might help to better understanding how the alterations in the neurobehavioral system, at different levels of organization, may affect behavioral dynamics and movement performance. The question remains, however, of whether and in which conditions inter-limb coupling strength would be altered with aging. This issue will be explored in further studies.

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