Investigating a Nonconservative Invariant of Motion in Coordinated Rhythmic Movements

The dimensions of an animal's limbs are fixed, but in locomotion and other rhythmic activities, they oscillated at a number of different frequencies. How might the physical conditions for this frequency variation be characterized? Kugler and Turvey (1987) hypothesized that the conditions might be adiabatic. A rhythmic system undergoes an adiabatic transformation of frequency when the stiffness is changed without a transfer of energy by heating. By standard definitions, adiabatic transformability is achievable only in conservative systems and only at infinitely slow rates of transformation. Kugler and Turvey's (1987) hypothesis extends adiabatic to systems that are dissipative and transformed rapidly by internal sources of energy, such as biological movement systems. Two predictions follow from the hypothesis. The first prediction is that a relation should be obtained in frequency-energy coordinates that has constant slope (Ehrenfest's adiabatic relation, a semipermanent invariant of motion) and an energy intercept less than zero (constant energy dissipation regardless of frequency). The second prediction is that the positive linear relation in frequency-energy coordinates can be satisfied by different relations in period-amplitude coordinates; amplitude increasing, amplitude increasing then decreasing, amplitude decreasing. The predictions were evaluated in four experiments with the same three participants. In each experiment, the rhythmic movement unit was defined by a pendulum of fixed dimensions held in the right hand that was made to oscillate at frequencies in the range 0.6 Hz to 1.8 Hz by the requirement of 1:1 frequency locking with a pendulum of different dimensions held in the other hand. Changes in the period of a pendular rhythmic movement were accompanied by statistically significant changes in the amplitude. Amplitude's systematic dependence on period differed, however, among the three participants in the experiments.     

Extracting Global and Local Dynamics From the Stochastics of Rhythmic Forearm Movements

The authors examined the dynamics governing rhythmic forearm movements that 9 participants performed under a variety of task constraints by using a generic, unbiased analysis technique for extracting the drift coefficients of Fokker-Planck equations from stochastic data. From those coefficients, they reconstructed and analyzed vector fields and phase portraits to identify characteristic, task-dependent kinematic and dynamical features. They first directly estimated the parameters of weakly nonlinear self-sustaining oscillators from the extracted drift coefficients. The estimated parameters that the authors had selected instinctively and then particularized by using averaging methods largely confirmed previously derived limit-cycle models. Next, they ventured beyond limit-cycle models to examine global and local dynamical features that those models cannot adequately address, particularly task-dependent changes in flow strength and curvature and distinct dynamical features associated with flexion and extension. The authors argue that those features should be focal points of researchers' future modeling efforts to formulate a more adequate and encompassing account of the dynamics of rhythmic movement.     

Resonance Tuning in Rhythmic Arm Movements

The hypothesis was tested that the preferred frequency of rhythmic movement corresponds to the resonant frequency of the muscle-limb system, as proposed by the hybrid spring-pendulum model (Kugler Turvey, 1987). In contrast to previous studies, the resonant frequency and stiffness of the system were estimated independently, which permitted quantitative predictions of the preferred frequency to be made. Human subjects (N = 5) were asked to oscillate their forearms in the vertical plane at their preferred frequency under conditions of added mass and external spring loading. Subjects also oscillated their arms at frequencies below and above the preferred frequency, which enabled the investigators to estimate the resonant frequency and stiffness of the elbow joint by using the phase transfer method (Viviani, Soechting, Terzuolo, 1976). The preferred frequency corresponded to the resonant frequency of the muscle-limb system under each condition, as predicted. The oscillation amplitude varied inversely with the preferred frequency, which was also predicted. Finally, the internal joint stiffness was modulated so that it matched the impedance of the external springs but was unaffected by added mass. The results are consistent with an autonomous oscillator model that incorporates proprioception about the dynamics of the periphery.     

Timing and the Control of Rhythmic Upper-Limb Movements

Accurate timing of limb displacement is crucial for effective motor control. The authors examined the effects of movement velocity, duration, direction, added mass, and auditory cueing on timing, spatial, and trajectory variability of single- and multijoint rhythmic movements. During single-joint movements, increased velocity decreased timing and spatial variability, whereas increased movement duration increased timing variability but decreased spatial variability. For multijoint movements, regardless of condition, increasing velocity decreased joint timing, spatial, and trajectory variability, but all hand variabilities were unaffected by velocity, duration, load, or direction. Timing, spatial, and trajectory variability was greater at the shoulder compared with the elbow and minimal at the hand, supporting the notion that reaching movements are planned in hand space as opposed to joint space.     

Task-Dependent Compensatory Responses to Perturbations Applied During Rhythmic Movements in Humans

Modulation of the responses to perturbation applied during different phases of three rhythmic movements in humans—running, cycling, and hopping—was studied. The perturbation was an electrical stimulus. The results showed gating and modulation of the responses in both ipsi-and contralateral limb muscles. The responses during running and cycling were only excitatory in nature, while during hopping an inhibitory response was observed. These responses were not correlated with the normal activity during the movement. The latency of the response in general was not altered for different stimulation phases. The alterations in the step cycle demonstrated overt behavioral changes due to the responses. There were differences between the responses observed during these movements and walking. In running, the major adaptation to perturbations appears to be in the contralateral side as seen in the changes in the step cycle. During cycling (except for one phase) and hopping, the same set of muscles was activated in response to perturbation. This represents a simplifying strategy in response organization. The dependency of the response on the task characteristics, postural stability requirement, and external constraints imposed on the subject is discussed. These studies provide insights into task-dependent strategies adopted by the nervous system to meet unexpected perturbation during rhythmic movement in humans.     

Diffusive,Synaptic, and Synergetic Coupling: An Evaluation Through In-Phase and Antiphase Rhythmic Movements

The in-phase and antiphase patterns of interlimb l:1 frequency locking were contrasted with respect to models of coordination dynamics in biological movement systems that are based on diffusive coupling, synaptic coupling, and synergetic principles. Predictions were made from each model concerning the stable relative phase phi between the rhythmic units, its standard deviation SDphi and the self-chosen coupled frequency omegasubc;. The experimental task involved human subjects oscillating two handheld pendulums either in-phase or antiphase. The eigenfrequencies of the two hand-pendulum systems were manipulated by varying the length and mass of each pendulum individually. Relative to an eigenfrequency difference of Delta equal to zero, |Deltaomega| > 0 displaced phi from phi = 0 and phi = pi, and amplified SDphi. omegasubc; decreased with |Deltaomega|. Both the displacement of phi and SDphi were greater in the antiphase mode. Additionally, the displacement of phi increased more sharply with |Delta| for antiphase than for in-phase coordination. In contrast, omegasubc; was identical for the two coordination modes. Of the models of interlimb coordination dynamics, the synergetic model was the most successful in addressing the pattern of dependencies of phi and SDphi. The specific forms of the functions relating omegasubc; and phi to Deltaomega pose challenges for all three models, however     

Advantages of Rhythmic Movements at Resonance: Minimal Active Degrees of Freedom,Minimal Noise,and Maximal Predictability

Using time delay embedding, the authors applied phase space reconstruction to the time series of rhythmic movements of a hand-held pendulum. Subjects (N = 6) produced the manual oscillations about the wrist at the pendulum's resonant frequency and at a higher and a lower frequency. The number of active degrees of freedom required to capture the dynamics of the rhythmic behavior was 3 for the resonant frequency and 4 for each of the nonresonant frequencies. The residual high-dimensional noise was similarly lowest for the resonant frequency. Whereas 33% and 20%, respectively, of the vectors in the phase spaces of the dynamics higher and lower than resonance were unpredictable, only 12% were unpredictable at resonance. Finally, the predictability of the evolving dynamics extended farther into the future for oscillations at the resonant frequency. At resonance, the prediction horizon was 5 times farther than the prediction horizon for the higher than resonance behavior and 2.5 times farther than that for the lower than resonance behavior. The results suggest that, in pendular oscillations of a limb or limb segment, attunement of the central nervous system to the resonant frequency minimizes the variables to be controlled and maximizes the predictability of the rhythmic movement's chaotic dynamics.     

Conditioning and the Coordination of Movements

(Krech, D., and Crutchfield, R. S. Theory and Problems of Social Psychology. New York: McGraw-Hill, 1948. Pp. 639.) Reviewed by Gwynne Nettler     

Visual Feedback and Positioning Movements

Subjects (n = 60) performed both the reproduction and learning of a linear positioning movement under one of five visual feedback conditions. Results from two experiments indicated that visual cues from the task display augmented information available from visual feedback of the movement per se. Extraneous cues from the task display have clearly confounded the manipulation of visual feedback in previous positioning studies. When these cues are eliminated, visual distance information seems more useful than visual location information.     

Force and Timing Variability in Rhythmic Unimanual Tapping

In 3 experiments the interdependencies between timing and force production in unimanual paced and self-paced rhythmic tapping tasks were examined as participants (N = 6 in each experiment) tapped (a) to 1 of 3 target periods (333 ms, 500 ms, and 1,000 ms), while they simultaneously produced a constant peak force (PF) over a 50-s trial; (b) to produce 1 of 3 target forces (5, 10, and 15 N) at their preferred frequency, while keeping their rhythm as invariant as possible; and (c) to all combinations of target force and period. The results showed that (a) magnitudes of force and period were largely independent; (b) variability in timing increased proportionally with tapping period, and the variability in force increased with peak force; (c) force variability decreased at faster tapping rates; and (d) timing variability decreased with increasing force levels, (e) Analysis of tap-to-tap variability revealed adjustments over sequences of taps and an acceleration in the tapping rate in unpaced conditions. The interdependencies of force and time are discussed with respect to the challenges they provide for an oscillator-based account.     

Eye Movements and Spontaneous Eye-blink Rate

Le système vestibulo-oculomoteur est très fragile. L'altéation de son fonctionnement résulte d'une intoxication chronique ou aiguē provenant de drogues ou d'agents neurotoxiques. L'augmentation du taux de battement des paupières est un indice d'irritations sensorielles. Aussi bien les techniques d'enregistrement des mouvements de l'oeil que plusieurs tests concernant les systèmes optico-moteur et vestibulo-oculomoteur sont examinés a partir de leurs applications en médecine du travail.
The vestibulo-oculomotor system is very sensitive to injury. Impairment of its function has been described as an effect of chronic or acute intoxication with drugs or neurotoxic agents. An increase in eye-blink rate indicates sensory irritations. Eye-movement recording techniques as well as several tests of the opto-motor and the vestibule-oculomotor system are outlined and reviewed with regard to their applications in occupational medicine.     

Rhythmic groups and subjective chunks in memory for melodies

Memory for brief melodic phrases was tested using a short-term recognition-memory paradigm. The five-note phrases were rhythmically separated from each other and presented in lists four phrases in length. A single five-note test item followed each list and either corresponded rhythmically to one of the phrases as presented in the list (within items) or to the last three notes of one phrase and the first two notes of the next (across items). Within items were easier than across items. Slow presentation (3 notes/sec) was slightly easier than fast (6 notes/see). The J-shaped serial position curve typical of short-term memory for verbal material was obtained. The results support the position that rhythmic grouping of input determines subjective chunking and memory storage, facilitating the recognition of test items chunked in the same way as list items.     

The Attention Demands of Movements

The probe technique has been employed extensively to measure the attention demands of movement control. Inherent in any RT paradigm is the potential confounding effect of anticipation. Experiment 1 studied this problem by varying probe frequency (or, conversely, catch-trial frequency) for three independent groups of subjects performing the same movement. Probe frequencies of one-third and two-thirds produced V-shaped curves of probe RT plotted against probe position within the movement, while a three-thirds condition was described by a negatively sloped linear function. Because of the different shaped curves it was recommended that a two-thirds frequency be adopted by all researchers in this area. Experiments 2 and 3 looked at the effects of movement length and movement time on the attention demands of movement. Shorter (11-cm) movements were more attention demanding in the middle of the movement than the longer (50-cm) movements, but movement time had no effect.     

Planning and Preparing Expected and Unexpected Movements

Using variations of the movement precue method, this study sought to define the operational characteristics of motoric decisions that govern the planning and preparation of arm, direction, and extent of movement. Experiment 1 examined how these parameters are programmed when the precue method does not confound motoric and nonmotoric decision processes. Experiment 2 examined how an already planned and prepared response is modified (reprogrammed) when an unexpected response must be executed in its place. The collective results of both experiments demonstrated that (a) these parameters were planned and prepared in a specific order; knowledge about direction was necessary for the programming of arm or extent, (b) arm and extent were reprogrammed independently from direction but changes in direction caused all parameters to be reprogrammed, and (c) programming and reprogramming processes operated in a parallel mode when two or more parameters were involved. The results also showed that these parameters were organized within a hierarchical structure. The present findings were discussed in relation to those reported in previous precue studies and existing models of response programming.     

Influence of Rhythmic Sensory Stimuli Upon the Heart-Rate

Eighteen retarded adults, divided into three groups equated for IQ, MA, and number conservation performance, received addition-subtraction and reversibility training under either cognitive-conflict or nonconflict conditions, or received no training. Under cognitive-conflict, transformation of one of two sets of discrete elements produced a perceptual illusion, and the addition-subtraction and reversibility operations applied to that set produced conflict between its length and density. Under nonconflict, simultaneous application of the operations to both sets avoided such conflict. Both training groups made significant gains from pretest and significantly exceeded controls in posttest number conservation (ps < .05). Lack of differential gains by the training groups suggested that cognitive conflict is not essential to induce number conservation.