Mass perturbation of a body segment: 2. Effects on interlimb coordination

The shifts in relative phase that are observed when rhythmically coordinated limbs are submitted to asymmetric mass perturbations have typically been attributed to the induced eigenfrequency difference (delta omega) between limbs. Modeling the moving limbs as forced linear oscillators, however, reveals that asymmetric mass perturbations may induce a difference not only in eigenfrequency (i.e., delta omega not equal 0) but also in the covarying low-frequency control gains (i.e., delta k not equal 0). Because the inverse of the low-frequency control gain (k) reflects the level of muscular torque (input) required for a particular displacement from equilibrium (output), asymmetric mass perturbations may result in an imbalance in the muscular torques required for task performance (related to delta k not equal 0). Thus, it is possible that the effects attributed to delta omega were in fact mediated by delta k. In 2 experiments, the authors manipulated delta k and delta omega separately by applying mass perturbations to the lower legs of 9 participants. The relative phasing between the legs was not affected by delta k, but manipulation of delta omega (while delta k remained approximately 0) induced systematic relative phase shifts that were more pronounced for antiphase than for in-phase coordination. That indication that the coordination dynamics is indeed influenced by an imbalance in eigenfrequency is discussed vis-a-vis the question of how such a merely peripheral property may affect the underlying coordination process.     

Mass Perturbation of a Body Segment: I. Effects on Segment Dynamics

Investigators often use mass perturbation of body segments as an experimental paradigm to study movement coordination. To analyze the effect of mass perturbation on small-amplitude oscillations, the authors linearize the equation of motion of a single segment moving in a vertical plane and derive the effect of added mass on the undamped eigenfrequency, the relative damping, and the low-frequency control gain of the segment. Mass addition results in a decrease in both the relative damping and the low-frequency control gain; the undamped eigenfrequency increases for mass addition between the pivot point and R₀ (where R₀ is the length of a point mass pendulum whose undamped eigenfrequency is identical to that of the unperturbed segment), decreases for mass addition beyond R₀, and remains unaffected for mass addition at R₀. For a typical lower leg + foot segment, R₀ is just proximal to the ankle joint. That location may explain the absence of an effect on oscillation frequency in studies in which mass has been added to the ankle. The authors' analysis provides a basis for a more effective application of mass perturbations in future experiments.     

Mass perturbation of a body segment: 1. Effects on segment dynamics

Investigators often use mass perturbation of body segments as an experimental paradigm to study movement coordination. To analyze the effect of mass perturbation on small-amplitude oscillations, the authors linearize the equation of motion of a single segment moving in a vertical plane and derive the effect of added mass on the undamped eigenfrequency, the relative damping, and the low-frequency control gain of the segment. Mass addition results in a decrease in both the relative damping and the low-frequency control gain; the undamped eigenfrequency increases for mass addition between the pivot point and R0 (where R0 is the length of a point mass pendulum whose undamped eigenfrequency is identical to that of the unperturbed segment), decreases for mass addition beyond R0, and remains unaffected for mass addition at R0. For a typical lower leg + foot segment, R0 is just proximal to the ankle joint. That location may explain the absence of an effect on oscillation frequency in studies in which mass has been added to the ankle. The authors' analysis provides a basis for a more effective application of mass perturbations in future experiments.     

Interaction of directional,neuromuscular and egocentric constraints on the stability of preferred bimanual coordination patterns

We investigated how the relative direction of limb movements in external space (iso- and non-isodirectionality), muscular constraints (the relative timing of homologous muscle activation) and the egocentric frame of reference (moving simultaneously toward/away the longitudinal axis of the body) contribute to the stability of coordinated movements. In the first experiment, we attempted to determine the respective stability of isodirectional and non-isodirectional movements in between-persons coordination. In a second experiment, we determined the effect of the relative direction in external space, and of muscular constraints, on pattern stability during a within-person bimanual coordination task. In the third experiment we dissociated the effects on pattern stability of the muscular constraints, relative direction and egocentric frame of reference. The results showed that (1) simultaneous activation of homologous muscles resulted in more stable performance than simultaneous activation of non-homologous muscles during within-subject coordination, and that (2) isodirectional movements were more stable than non-isodirectional movements during between-persons coordination, confirming the role of the relative direction of the moving limbs in the stability of bimanual coordination. Moreover, the egocentric constraint was to some extent found distinguishable from the effect of the relative direction of the moving limbs in external space, and from the effect of the relative timing of muscle activation. In summary, the present study showed that relative direction of the moving limbs in external space and muscular constraints may interact either to stabilize or destabilize coordination patterns.     

Laterally focused attention modulates asymmetric coupling in rhythmic interlimb coordination

Peters (J Motor Behav 21:151-155, 1989; Interlimb coordination: neural, dynamical and cognitive constraints, Academic, Orlando, pp 595-615, 1994) suggested that expressions of handedness in bimanual coordination may be reflections of an inherent attentional bias. Indeed, previous results indicated that focusing attention on one of the limbs affected the relative phasing between the limbs in a manner comparable to the effects of hand dominance. The present study extended the comparison between the effects of attentional focus and handedness by testing their impact on the interactions between the limbs. Both left-handed and right-handed participants performed rhythmic bimanual coordination tasks (in-phase and antiphase coordination), while directing attention to either limb. Using brief mechanical perturbations, the degree to which the limbs were influenced by each other was determined. The results revealed that the non-dominant limb was more strongly affected by the dominant limb than vice versa and that, in line with Peters' proposition, this handedness-related asymmetry in coupling strength was reduced when attention was focused on the non-dominant limb, thereby highlighting the potential relation between inherent (handedness-related) asymmetries and voluntary attentional asymmetries. In contrast to previous findings, the (commonly observed) phase lead of the dominant limb was attenuated (rather than accrued) when attention was focused on this limb. This unexpected result was explained in terms of the observed attention-related difference in amplitude between the limbs.     

Dissociation of muscular and spatial constraints on patterns of interlimb coordination

Interlimb coordination is subject to constraints. One major constraint has been described as a tendency for homologous muscle groups to be activated simultaneously. Another has been described as a biasing of limb segments to movement in the same direction. In 2 experiments, the 2 constraints were placed in opposition: In-phase or antiphase contraction of homologous muscles of contralateral limbs produced movement that was spatially antiphase or in-phase, respectively. Probability distributions of relative phase were obtained under manipulations of phase detuning and movement speed. They revealed that the equilibrium and stability of coordination were related, respectively, to spatial relative phase and muscular relative phase. Previously observed spatial and muscular constraints reflect a (possibly very general) factorization of attractor location and attractor strength in the dynamics of interlimb coordination.     

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     

Catching With Both Hands: An Evaluation of Neural Cross-Talk and Coordinative Structure Models of Bimanual Coordination

Kelso, Southard, and Goodman (1979) and Marteniuk and MacKenzie (1980) have each proposed a different theoretical model for bimanual coordination. In the model of Kelso et al., a close temporal relationship between the hands in a bimanual task is predicted, even when each hand is required to move different distances. In Marteniuk and MacKenzie's model, separate motor commands are issued so that each limb will arrive simultaneously at the specified movement endpoint, leading to low temporal associations between limbs. In most previous work on bimanual coordination, manual aiming tasks with differing constraints have been used by subjects in individual studies. In this study, the usefulness of existing models for predicting performance in a real-world catching task in which the required movement pattern was constrained by ball flight characteristics was examined. Eleven university students caught tennis balls with both hands in the following 3 conditions: Condition 1. Ball projected to the right shoulder area (left hand moved a greater distance than the right); Condition 2. Ball projected to center of the chest area, (both hands moved same distance); and Condition 3. Ball projected to left shoulder area (right hand moved a greater distance). Kinematic data (time to peak velocity, movement initiation time) indicating significant cross-correlations between the left and right limbs in all 3 conditions concurred with the data of Kelso et al. (1979) on manual aiming. Timing appeared to be an essential variable coordinating bimanual interceptive actions. Although the limbs moved at different speeds when each was required to move different distances, times to peak velocity showed strong associations, suggesting the presence of a coordinative structure.     

A symmetric and an asymmetric model for the equal-sensation function in olfaction

Data from various intramodel matching experiments in olfaction were analyzed with regard to a symmetric and an asymmetric model for the equal-sensation function. The asymmetric model was discussed in relation to the symmetric model. In all, 11 equal-sensation functions were investigated, and of these 9 were with different pairs of odorants. The following odorants were investigated: hydrogen sulfide, pyridine, dimethyl disulfide, and five odorants obtained by different combustion procedures of animal manure. It was found that the equal-sensation function can be written in the following asymmetric form: $$\varphi _i = b_{ik} \lambda \cdot \varphi _k ^{b_{ik} } ,\psi _i = \psi _k $$ or symmetric form: $$\varphi _i = C^{I - b_{ik} } \cdot \varphi _k ^{b_{ik} } ,\psi _i = \psi _k ,$$ where ?_i and ?_k are stimuli expressed in multiples of respective absolute thresholds, λ and C are general constants invariant of experimental matching method and matched attribute (perceived unpleasantness or intensity). The constants λ and C were calculated both for group data and individual data. The asymmetric form of the equal-sensation function was interpreted in terms of relativity and the symmetric form in terms of measurement.     

The role of segmental mass and moment of inertia in dynamic-contact task construction

The authors examined whether differences between children and adults in the application of muscle forces during a dynamic-contact task (cycling) can be attributed to children's relatively lower segmental mass and moment of inertia. They examined pedal-force construction as adults and younger and older children (n = 7 in each group), with and without mass added to their limbs, pedaled an appropriately scaled bicycle ergometer. When mass was added to their limbs, children adjusted muscular forces on the pedal in a way that began to approach the pattern demonstrated by adults. Because age, neuromotor maturation, and motor experience were held constant, it seems plausible that by 6 to 8 years of age, and perhaps younger, physical size and growth limit children's production of adult-like muscle forces on the pedal.     

Interlimb coordination in prosthetic walking: effects of asymmetry and walking velocity

The present study focuses on interlimb coordination in walking with an above-knee prosthesis using concepts and tools of dynamical systems theory (DST). Prosthetic walkers are an interesting group to investigate from this theory because their locomotory system is inherently asymmetric, while, according to DST, coordinative stability may be expected to be reduced as a function of the asymmetry of the oscillating components. Furthermore, previous work on locomotion motivated from DST has shown that the stability of interlimb coordination increases with walking velocity, leading to the additional expectation that the anticipated destabilizing effect of the prosthesis-induced asymmetry may be diminished at higher walking velocities. To examine these expectations, an experiment was conducted aimed at comparing interlimb coordination during treadmill walking between seven participants with an above-knee prosthesis and seven controls across a range of walking velocities. The observed gait patterns were analyzed in terms of standard gait measures (i.e., absolute and relative swing, stance and step times) and interlimb coordination measures (i.e., relative phase and frequency locking). As expected, the asymmetry brought about by the prosthesis led to a decrease in the stability of the coordination between the legs as compared to the control group, while coordinative stability increased with increasing walking velocity in both groups in the absence of a significant interaction. In addition, the 2:1 frequency coordination between arm and leg movements that is generally observed in healthy walkers at low walking velocities was absent in the prosthetic walkers. Collectively, these results suggest that both stability and adaptability of coordination are reduced in prosthetic walkers but may be enhanced by training them to walk at higher velocities.     

Coordination dynamics of learning and transfer across different effector systems

If different effector systems share a common task-specific coordination dynamics, transfer and generalization of sensorimotor learning are predicted. Subjects learned a visually specified phase relationship with either the arms or the legs. Coordination tendencies in both effector systems were evaluated before and after practice to detect attractive states of the coordination dynamics. Results indicated that learning a novel relative phase with a single effector system spontaneously transferred to the other, untrained effector system. Transfer was revealed not only as improvements in performance but also as modifications of each system's initial (prelearning) coordinative landscape. What is learned, appears to be a high-level but neurally instantiated dynamic representation of skilled behavior that proves to be largely effector independent, at least across anatomically symmetric limbs.     

Bimanual circle drawing in children with spastic hemiparesis: effect of coupling modes on the performance of the impaired and unimpaired arms

The present study examined the effect of interlimb coupling on the performance of the impaired and unimpaired arm in children with spastic hemiparesis during bimanual circle drawing. The following questions were addressed: (1) does coupling positively influence the performance of the impaired arm compared to single-hand performance and (2) is such an effect dependent on mode of coordination (i.e., symmetric versus asymmetric). Twelve children with spastic hemiparesis produced circle drawings on a digitizer under different task conditions. Spatiotemporal characteristics and quality of movement of pen trajectories of the individual limbs as well as interlimb relative phase were analysed. Coupling in a symmetric coordination mode resulted in a decrease of temporal variability and an increase of smoothness of circle drawing movements in the impaired arm compared to single-handed performance. Coupling in an asymmetric coordination mode resulted in an increase of spatial and temporal variability in the unimpaired arm. It is concluded that coupling may enhance the performance of the impaired arm in children with spastic hemiparesis, but only during symmetric bimanual coordination. A possible underlying neural mechanism that might explain these findings is discussed.     

Spontaneous transitions and symmetry: Pattern dynamics in human four-limb coordination

Transitions between the coordinative patterns of rhythmically moving human arms and legs were studied to test the predictions of a four-component model (Schöner, Jiang and Kelso, 1990). Based upon results from previous two-component experiments (Kelso and Jeka, 1992), three assumptions were made about the four-limb system: (1) all limb pairs produce stable in-phase and anti-phase patterns; (2) the coupling between homologous limbs (i.e., right and left arms or right and left legs) is appreciably stronger than the coupling between nonhomologous limbs (i.e., arm and leg); and (3) right-left symmetry. An analysis of a four-component model (Jeka, Kelso and Kiemel, 1993) led to the prediction of four attracting invariant circles, each with two stable patterns in the state space of four-limb dynamics. In an experiment to test this prediction, subjects were required to cycle all four limbs in one of the eight patterns to the beat of an auditory metronome whose frequency was systematically increased. All subjects demonstrated spontaneous transitions corresponding to pathways along the invariant circles. Pre-transition relative phase variability increased with required frequency up to the transition, suggesting that loss of pattern stability induced the observed transitions. Thus, despite a large number of potential transitions, differential coupling between limb pairs and symmetry of the pattern dynamics restricts the behavior of the human four-limb system to a limited area of its state space.     

Inter-individual variability in the upper-lower limb breaststroke coordination

The aim of the present study was to examine inter-individual variability in upper-lower limb breaststroke coordination. First, inter-individual variability was compared between recreational and comparative swimmers. Second, as recreational swimmers revealed more variable inter-limb coordination than competitive swimmers, inter-individual variability was assessed among recreational swimmers to identify coordination profiles. The elbow-knee continuous relative phase (CRP) was used to analyze upper-lower limbs coupling during a breaststroke cycle. Twenty-four recreational and twenty-four competitive swimmers swam 25 m at 80% of their maximal speed. Underwater and aerial side views were mixed and genlocked. Angular position, velocity and CRP were calculated for the knee and elbow joints by digitizing body markers from the side view. The kinematics of three cycles were filtered, averaged and normalized in terms of percentage of total cycle duration. The topography of the mean CRP curve of the recreational swimmers resembled a ‘W-shape’, whereas an ‘inverse U-shape’ was seen in the competitive swimmers. However, higher inter-individual variability was observed among the recreational swimmers than among the competitive swimmers (38.1° vs. 19.4°; p < .05), suggesting that several profiles of inter-limb coordination may exist in recreational swimmers. Coordination profiling showed that three clusters could classify the recreational swimmers.     

Symmetry axiom of Haken–Kelso–Bunz coordination dynamics revisited in the context of cognitive activity

We present an axiomatic derivation of a model proposed by Haken, Kelso, and Bunz (1985) that describes dynamical aspects of the rhythmic coordination between two limbs. Elaboration of this model has included a symmetry parameter that captures the coordination consequences of an inherent or imposed frequency difference between the limbs. We modified one of the axioms involved in the model derivation, a symmetry axiom, in order to incorporate a new symmetry parameter. This new parameter defines a shift between (a) the laboratory coordinate system, in which the behavior is observed, and (b) a second, postulated coordinate system. It is this second coordinate system, in which the relevant state dynamics is assumed to take place and in which the state dynamics evolves under the impact of an attractor. The state dynamics as described in the attractor coordinate system is then mapped by means of the new symmetry parameter to the laboratory coordinate system. We discuss analytically the bifurcation diagram of the model and determine main effects and interaction effects of manipulations related to the symmetry parameters and related to the mode of coordination (in-phase and anti-phase). The theoretical results are brought to bear on the challenging experimental observation that concurrent cognitive activity (counting, encoding, retrieving, sentence analysis) changes the location of the bimanual coordination attractor but not its strength. The theoretical results suggest that cognitive activity may have the effect it has because it shifts the attractor coordinate system relative to the laboratory coordinate system.     

On the concept of language in some recent theories of meaning

The work on this paper was done in the research project V ra begrepp om spr k supported byHumanistisk-samhälls-vetenskapliga forskningsr det. I am indebted to Per Martin-Löf, Hans Ruin, Pär Segerdahl, and Sven Öhman for valuable comments on a previous version of this paper. Thanks to the comments of the anonymous referee I was able to improve some formulations in the paper.     

Eye Movements in Strategic Choice

In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level‐k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance‐solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level‐k and cognitive hierarchy models do not. © 2015 The Authors. Journal of Behavioral Decision Making published by John Wiley & Sons Ltd.     

The role of ability and effort in attributions for sport achievement1

In an initial attempt to assess the applicability of Weiner's (1972) attribution model to sport-related behavior, the effects of ability (high versus low), effort (high versus low) and outcome (success versus failure) on causal attributions were investigated. After riding a bicycle ergometer, subjects were asked to attribute the cause of their increased or decreased performance to ability, effort, task difficulty and/or luck. The results indicated that successful outcomes were attributed to both ability and effort and that unsuccessful outcomes were attributed to a lack of ability but not a lack of effort. While the task was seen as easier following success, the perception of low effort mediated this relationship. The results were interpreted to support a situationally specific conceptualization of sport achievement. First, whereas a motivational bias appears to preclude low ability attributions in intellectual pursuits, such is not the case with a novel physical task contingent on strength and muscular endurance. It was suggested that physiologically related ability may be viewed as relatively unstable. Second, relative to intellectual tasks, sport-related effort may be more salient and more quantifiable and may exert a greater influence on subsequent attributions for sport achievement. Finally, support was obtained for the assertions that affect is codetermined by both effort and ability and that expectancy discrepant performance is accounted for largely by perceptions of task difficulty.