Frequency detuning of the phase entrainment dynamics of visually coupled rhythmic movements

 An order parameter equation for correlated limb movements was applied to rhythmic coordination between the limbs of two people. The interlimb coordination was established and maintained through vision. Manipulations of frequency competition, coupled frequency, and intended mode (in-phase or anti-phase) produced equilibria and fluctuations in relative phase predicted by the order parameter equation and confirmed originally in within-person coordination. It was concluded that there is an elementary coordination dynamics governing the rhythmic coordination between organisms as well as between components of a single organism. Received: 6 June 1994 / Accepted in revised form: 11 November 1994     

Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity

 Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, anti-phase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed. Received: 12 July 1999 / Accepted in revised form: 14 April 2000     

Relative phase dynamics in perturbed interlimb coordination: the effects of frequency and amplitude

Sch?ner [Sch?ner G (1995) Ecol Psychol 7: 291-314] argued that the relative phase dynamics of rhythmic interlimb coordination may be attributed to the timing level in that the stability properties of the relative phase are largely independent of dynamical principles operating at the goal level, such as those related to the maintenance of a particular amplitude or target position. Yet, according to the coupling functions in the coupled oscillator model proposed by Haken et al. [Haken H, Kelso JAS, Bunz H (1985) Biol Cybern 51: 347-356], the effect of frequency on the stability properties of relative phase is either wholly or partially mediated by frequency-induced changes in amplitude, implying that the relative phase dynamics strongly depends on spatial factors. In order to distinguish between these contrasting interpretations of the organizational principles underwriting the phase dynamics of interlimb coordination, an experiment was conducted in which the effects of frequency and amplitude on the stability of relative phase were separated. Six subjects performed both in-phase and antiphase coordination patterns at seven different frequencies and three different amplitudes. Two measures of pattern stability were used, the standard deviation of relative phase and the exponent of the relaxation process following phasic perturbations of relative phase. According to both measures, pattern stability decreased with increasing frequency, whereas the amplitude manipulation only had a significant effect on the standard deviation of relative phase. This result was interpreted to imply that the organizational principles at the (relative) timing level are affected only moderately by task constraints pertaining to the goal level, and that models of interlimb coordination in which amplitude coupling plays a partial or subordinate role should be preferred above models relying solely on amplitude coupling.     

Effect of hindlimb unloading on interlimb coordination during treadmill locomotion in the rat

Effects of hindlimb unloading on interlimb coordination were examined in adult rats walking on a treadmill at moderate speed. In the first group of animals, the electromyographic activity (EMG) of soleus muscle of both hindlimbs was recorded after 7 and 14 days of unloading. In the second group, the EMG was recorded daily until the 14th day of unloading. The general organization of locomotion was preserved in the two groups whatever the duration of the unloading. The step cycles of the two hindlimbs were always strictly alternating. However, the locomotor pattern was very irregular. A lateral instability was observed. It was accompanied by an abduction of the hindlimbs, and frequent hyperextensions of the ankle when walking. The EMG analysis showed an increase in step cycle duration and in coactivation duration of the soleus muscles (i.e. in the double stance duration). In the rats recorded daily, mean EMG was dramatically reduced the 1st day of unloading, suggesting a decrease in the neural drive. Taken together, these data indicate that 14 days of hindlimb unloading can alter the neuromuscular pattern during locomotion. It is proposed that these changes are related to changes in the peripheral sensory information. Accepted: 29 June 1998     

A coupled oscillator model of disordered interlimb coordination in patients with Parkinson's disease

Coordination between the left and right limbs during cyclic movements, which can be characterized by the amplitude of each limb's oscillatory movement and relative phase, is impaired in patients with Parkinson's disease (PD). A pedaling exercise on an ergometer in a recent clinical study revealed several types of coordination disorder in PD patients. These include an irregular and burst-like amplitude modulation with intermittent changes in its relative phase, a typical sign of chaotic behavior in nonlinear dynamical systems. This clinical observation leads us to hypothesize that emergence of the rhythmic motor behaviors might be concerned with nonlinearity of an underlying dynamical system. In order to gain insight into this hypothesis, we consider a simple hard-wired central pattern generator model consisting of two identical oscillators connected by reciprocal inhibition. In the model, each oscillator acts as a neural half-center controlling movement of a single limb, either left or right, and receives a control input modeling a flow of descending signals from higher motor centers. When these two control inputs are tonic-constant and identical, the model has left-right symmetry and basically exhibits ordered coordination with an alternating periodic oscillation. We show that, depending on the intensities of these two control inputs and on the difference between them that introduces asymmetry into the model, the model can reproduce several behaviors observed in the clinical study. Bifurcation analysis of the model clarifies two possible mechanisms for the generation of disordered coordination in the model: one is the spontaneous symmetry-breaking bifurcation in the model with the left-right symmetry. The other is related to the degree of asymmetry reflecting the difference between the two control inputs. Finally, clinical implications by the model's dynamics are briefly discussed.     

Phase-entrainment dynamics of visually coupled rhythmic movements

Do interlimb rhythmic coordinations between individuals exhibit the same relations among the same observable quantities as interlimb rhythmic coordination within an individual? The 1∶1 frequency locking between the limbs of two people was investigated using a paradigm in which each person oscillated a hand-held pendulum, achieving and maintaining the mutual entrainment through vision. The intended coordination was antiphase, φ=π, and the difference between the uncoupled eigenfrequencies, Δω, was manipulated through differences in the lengths of the two pendulums. The mean phase relation and its variance for visually coupled coordinations differing in Δω were predicted by an order parameter equation developed by Haken et al. (1985) and Schöner et al. (1986) for the relative phase of correlated movements of limb segments. Specifically, the experiment revealed that: (1) the deviation of φ from π increased with increasing deviation of Δω from 0; and (2) fluctuations in φ increased with increasing deviation of Δω from 0. With deviations of Δω from 0, new peaks were added at higher harmonics in φ's power spectrum. These results were in agreement with previous research on the stable states of interlimb coordination within a person, mediated by mechanoreceptive rather than photoreceptive mechanisms. Additionally, they were in agreement with previous research on phase transitions in interlimb coordination which have been shown to conform to the same order parameter dynamics whether the coupling be mechanoreceptively or photoreceptively based. It was suggested that phase entrainment in biological movement systems may abide by dynamical principles that are indifferent to the details of the coupling.     

The effects of rhythmic sensory cues on the temporal dynamics of human gait

Walking is a complex, rhythmic task performed by the locomotor system. However, natural gait rhythms can be influenced by metronomic auditory stimuli, a phenomenon of particular interest in neurological rehabilitation. In this paper, we examined the effects of aural, visual and tactile rhythmic cues on the temporal dynamics associated with human gait. Data were collected from fifteen healthy adults in two sessions. Each session consisted of five 15-minute trials. In the first trial of each session, participants walked at their preferred walking speed. In subsequent trials, participants were asked to walk to a metronomic beat, provided through visually, aurally, tactile or all three cues (simultaneously and in sync), the pace of which was set to the preferred walking speed of the first trial. Using the collected data, we extracted several parameters including: gait speed, mean stride interval, stride interval variability, scaling exponent and maximum Lyapunov exponent. The extracted parameters showed that rhythmic sensory cues affect the temporal dynamics of human gait. The auditory rhythmic cue had the greatest influence on the gait parameters, while the visual cue had no statistically significant effect on the scaling exponent. These results demonstrate that visual rhythmic cues could be considered as an alternative cueing modality in rehabilitation without concern of adversely altering the statistical persistence of walking.     

Neuroimaging coordination dynamics in the sport sciences

Key methodological issues for designing, analyzing, and interpreting neuroimaging experiments are presented from the perspective of the framework of Coordination Dynamics. To this end, a brief overview of Coordination Dynamics is introduced, including the main concepts of control parameters and collective variables, theoretical modeling, novel experimental paradigms, and cardinal empirical findings. Basic conceptual and methodological issues for the design and implementation of coordination experiments in the context of neuroimaging are discussed. The paper concludes with a presentation of neuroimaging findings central to understanding the neural basis of coordination and addresses their relevance for the sport sciences. The latter include but are not restricted to learning and practice-related issues, the role of mental imagery, and the recovery of function following brain injury.     

Behavioral impact of unisensory and multisensory audio-tactile events: pros and cons for interlimb coordination in juggling

Recent behavioral neuroscience research revealed that elementary reactive behavior can be improved in the case of cross-modal sensory interactions thanks to underlying multisensory integration mechanisms. Can this benefit be generalized to an ongoing coordination of movements under severe physical constraints? We choose a juggling task to examine this question. A central issue well-known in juggling lies in establishing and maintaining a specific temporal coordination among balls, hands, eyes and posture. Here, we tested whether providing additional timing information about the balls and hands motions by using external sound and tactile periodic stimulations, the later presented at the wrists, improved the behavior of jugglers. One specific combination of auditory and tactile metronome led to a decrease of the spatiotemporal variability of the juggler''s performance: a simple sound associated to left and right tactile cues presented antiphase to each other, which corresponded to the temporal pattern of hands movement in the juggling task. A contrario, no improvements were obtained in the case of other auditory and tactile combinations. We even found a degraded performance when tactile events were presented alone. The nervous system thus appears able to integrate in efficient way environmental information brought by different sensory modalities, but only if the information specified matches specific features of the coordination pattern. We discuss the possible implications of these results for the understanding of the neuronal integration process implied in audio-tactile interaction in the context of complex voluntary movement, and considering the well-known gating effect of movement on vibrotactile perception.     

Pattern switching in human multilimb coordination dynamics

A relative phase model of four coupled oscillators is used to interpret experiments on the coordination between rhythmically moving human limbs. The pairwise coupling functions in the model are motivated by experiments on two-limb coordination. Stable patterns of coordination between the limbs are represented by fixed points in relative phase coordinates. Four invariant circles exist in the model, each containing two patterns of coordination seen experimentally. The direction of switches between two four-limb patterns on the same circle can be understood in terms of two-limb coordination. Transitions between patterns in the human four-limb system are theoretically interpreted as bifurcations in a nonlinear dynamical system.     

Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study

Obstacle avoidance during locomotion is essential for safe, smooth locomotion. Physiological studies regarding muscle synergy have shown that the combination of a small number of basic patterns produces the large part of muscle activities during locomotion and the addition of another pattern explains muscle activities for obstacle avoidance. Furthermore, central pattern generators in the spinal cord are thought to manage the timing to produce such basic patterns. In the present study, we investigated sensory-motor coordination for obstacle avoidance by the hindlimbs of the rat using a neuromusculoskeletal model. We constructed the musculoskeletal part of the model based on empirical anatomical data of the rat and the nervous system model based on the aforementioned physiological findings of central pattern generators and muscle synergy. To verify the dynamic simulation by the constructed model, we compared the simulation results with kinematic and electromyographic data measured during actual locomotion in rats. In addition, we incorporated sensory regulation models based on physiological evidence of phase resetting and interlimb coordination and examined their functional roles in stepping over an obstacle during locomotion. Our results show that the phase regulation based on interlimb coordination contributes to stepping over a higher obstacle and that based on phase resetting contributes to quick recovery after stepping over the obstacle. These results suggest the importance of sensory regulation in generating successful obstacle avoidance during locomotion.     

The functional importance of rhythmic activity in the brain

Oscillations in brain activity have long been known, but many fundamental aspects of such brain rhythms, particularly their functional importance, have been unclear. As we review here, new insights into these issues are emerging from the application of intervention approaches. In these approaches, the timing of brain oscillations is manipulated by non-invasive brain stimulation, either through sensory input or transcranially, and the behavioural consequence then monitored. Notably, such manipulations have led to rapid, periodic fluctuations in behavioural performance, which co-cycle with underlying brain oscillations. Such findings establish a causal relationship between brain oscillations and behaviour, and are allowing novel tests of longstanding models about the functions of brain oscillations. VIDEO ABSTRACT:     

The Rho/Rac-family guanine nucleotide exchange factor VAV-1 regulates rhythmic behaviors in C. elegans

Rhythmic behaviors are a fundamental feature of all organisms. Pharyngeal pumping, the defecation cycle, and gonadal-sheath-cell contractions are three well-characterized rhythmic behaviors in the nematode C. elegans. The periodicities of the rhythms range from subsecond (pharynx) to seconds (gonadal sheath) to minutes (defecation). However, the molecular mechanisms underlying these rhythmic behaviors are not well understood. Here, we show that the C. elegans Rho/Rac-family guanine nucleotide exchange factor, VAV-1, which is homologous to the mammalian Vav proto-oncogene, has a crucial role in all three behaviors. vav-1 mutants die as larvae because VAV-1 function is required in the pharynx for synchronous contraction of the musculature. In addition, ovulation and the defecation cycle are abnormal and arrhythmic. We show that Rho/Rac-family GTPases and the signaling molecule inositol triphosphate (IP(3)) act downstream of VAV-1 signaling and that the VAV-1 pathway modulates rhythmic behaviors by dynamically regulating the concentration of intracellular Ca(2+).     

Mechanism of neuronal coordination of the rhythmic activities of developing flight muscles and a neurosecretory cell population in the silkmoth, Bombyx mori

Ultradian rhythmic firing activity (period of 40-90 min) of a population of neurosecretory cells (NSCs) producing FXPRLamide peptides in the subesophageal ganglion (SG) of the silkmoth, Bombyx mori, is closely coordinated with periodically occurring electrical activity of developing flight muscles (FMs) during metamorphosis. To examine neuronal mechanisms and pathways that mediate the coordination of the NSC and flight motor systems, the ventral nerve cord (VNC) or circumesophageal connectives were transected. Transection of the VNC between the SG and thoracic ganglia greatly shortened the period of activity rhythm of the FMs (5-15 min) with no effect on the rhythmicity of NSCs. Bilateral transsection of the circumesophageal connectives between the brain and SG abolished the rhythmic activity of NSCs, thereby suggesting that the coordination of the two systems may be mediated by a common oscillatory mechanism in the brain. Further, bisection of the brain in the midline failed to abolish the ultradian rhythmicity of FMs. Thus, each brain hemisphere may have an ultradian oscillator that activates the NSC system in the SG, and modulates the short-period oscillation of the flight motor system located in the thoracic ganglia.