On the time allometry of co-ordinated rhythmic movements

Moth resonant mechanics are tuned to wingbeat frequency and energetic demands

An insect's wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect's flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.

Elastohydrodynamic Scaling Law for Heart Rates

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

The primacy of rhythm: how discrete actions merge into a stable rhythmic pattern

This study examined how humans spontaneously merge a sequence of discrete actions into a rhythmic pattern, even when periodicity is not required. Two experiments used a virtual throwing task, in which subjects performed a long sequence of discrete throwing movements, aiming to hit a virtual target. In experiment 1, subjects performed the task for 11 sessions. Although there was no instruction to perform rhythmically, the variability of the interthrow intervals decreased to a level comparable to that of synchronizing with a metronome; furthermore, dwell times shortened or even disappeared with practice. Floquet multipliers and decreasing variability of the arm trajectories estimated in state space indicated an increasing degree of dynamic stability. Subjects who achieved a higher level of periodicity and stability also displayed higher accuracy in the throwing task. To directly test whether rhythmicity affected performance, experiment 2 disrupted the evolving continuity and periodicity by enforcing a pause between successive throws. This discrete group performed significantly worse and with higher variability in their arm trajectories than the self-paced group. These findings are discussed in the context of previous neuroimaging results showing that rhythmic movements involve significantly fewer cortical and subcortical activations than discrete movements and therefore may pose a computationally more parsimonious solution. Such emerging stable rhythms in neuromotor subsystems may serve as building blocks or dynamic primitives for complex actions. The tendency for humans to spontaneously fall into a rhythm in voluntary movements is consistent with the ubiquity of rhythms at all levels of the physiological system. NEW & NOTEWORTHY When performing a series of throws to hit a target, humans spontaneously merged successive actions into a continuous approximately periodic pattern. The degree of rhythmicity and stability correlated with hitting accuracy. Enforcing irregular pauses between throws to disrupt the rhythm deteriorated performance. Stable rhythmic patterns may simplify control of movement and serve as dynamic primitives for more complex actions. This observation reveals that biological systems tend to exhibit rhythmic behavior consistent with a plethora of physiological processes.

The impact of speed and time on gait dynamics

To determine the effects of speed on gait previous studies have examined young adults walking at different speeds; however, the small number of strides may have influenced the results. The aim of this study was to investigate the immediate and long-term impact of continuous slow walking on the mean, variability and structure of stride-to-stride measures. Fourteen young adults walked at a constant pace on a treadmill at three speeds (preferred walking speed (PWS), 90% and 80% PWS) for 30 min each. Spatiotemporal gait parameters were computed over six successive 5-min intervals. Walking slower significantly decreased stride length, while stride period and width increased. Additionally, stride period and width variability increased. Signal regularity of stride width increased and decreased in stride period. Persistence of stride period and width increased significantly at slower speeds. While several measures changed during 30min of walking, only stride period variability and signal regularity revealed a significant speed and time interaction. Healthy young adults walking at slower than preferred speeds demonstrated greater persistence and signal regularity of stride period while spatiotemporal changes such as increased stride width and period variability arose. These results suggest that different control processes are involved in adapting to the slower speeds.

Synchrony in Joint Action Is Directed by Each Participant's Motor Control System

In this work, we ask how the probability of achieving synchrony in joint action is affected by the choice of motion parameters of each individual. We use the mirror game paradigm to study how changes in leader's motion parameters, specifically frequency and peak velocity, affect the probability of entering the state of co-confidence (CC) motion: a dyadic state of synchronized, smooth and co-predictive motions. In order to systematically study this question, we used a one-person version of the mirror game, where the participant mirrored piece-wise rhythmic movements produced by a computer on a graphics tablet. We systematically varied the frequency and peak velocity of the movements to determine how these parameters affect the likelihood of synchronized joint action. To assess synchrony in the mirror game we used the previously developed marker of co-confident (CC) motions: smooth, jitter-less and synchronized motions indicative of co-predicative control. We found that when mirroring movements with low frequencies (i.e., long duration movements), the participants never showed CC, and as the frequency of the stimuli increased, the probability of observing CC also increased. This finding is discussed in the framework of motor control studies showing an upper limit on the duration of smooth motion. We confirmed the relationship between motion parameters and the probability to perform CC with three sets of data of open-ended two-player mirror games. These findings demonstrate that when performing movements together, there are optimal movement frequencies to use in order to maximize the possibility of entering a state of synchronized joint action. It also shows that the ability to perform synchronized joint action is constrained by the properties of our motor control systems.

Movement consistency during repetitive tool use action

The consistency and repeatability of movement patterns has been of long-standing interest in locomotor biomechanics, but less well explored in other domains. Tool use is one of such a domain; while the complex dynamics of the human-tool-environment system have been approached from various angles, to date it remains unknown how the rhythmicity of repetitive tool-using action emerges. To examine whether the spontaneously adopted movement frequency is a variable susceptible to individual execution approaches or emerges as constant behaviour, we recorded sawing motion across a range of 14 experimental conditions using various manipulations. This was compared to free and pantomimed arm movements. We found that a mean (SD) sawing frequency of 2.0 (0.4) Hz was employed across experimental conditions. Most experimental conditions did not significantly affect the sawing frequency, signifying the robustness of this spontaneously emerging movement. Free horizontal arm translation and miming of sawing was performed at half the movement frequency with more than double the excursion distance, showing that not all arm movements spontaneously emerge at the observed sawing parameters. Observed movement frequencies across all conditions could be closely predicted from movement time reference data for generic arm movements found in the Methods Time Measurement literature, highlighting a generic biomechanical relationship between the time taken for a given distance travelled underlying the observed behaviour. We conclude that our findings lend support to the hypothesis that repetitive movements during tool use are executed according to generic and predictable musculoskeletal mechanics and constraints, albeit in the context of the general task (sawing) and environmental constraints such as friction, rather than being subject to task-specific control or individual cognitive schemata.

Comparisons of chewing rhythm, craniomandibular morphology, body mass and height between mothers and their biological daughters

OBJECTIVE

To study and compare the relationships between mean chewing cycle duration, selected cephalometric variables representing mandibular length, face height, etc., measured in women and in their teenage or young-adult biological daughters.

DESIGN

Daughters were recruited from local high schools and the University of Michigan School of Dentistry. Selection criteria included healthy females with full dentition, 1st molar occlusion, no active orthodontics, no medical conditions nor medication use that could interfere with normal masticatory motor function. Mothers had to be biologically related to their daughters. All data were obtained in the School of Dentistry. Measurements obtained from lateral cephalograms included: two "jaw length" measures, condylion-gnathion and gonion-gnathion, and four measures of facial profile including lower anterior face height, and angles sella-nasion-A point (SNA), sella-nasion-B point (SNB) and A point-nasion-B point (ANB). Mean cycle duration was calculated from 60 continuous chewing cycles, where a cycle was defined as the time between two successive maximum jaw openings in the vertical dimension. Other variables included subject height and weight. Linear and logistic regression analyses were used to evaluate the mother-daughter relationships and to study the relationships between cephalometric variables and chewing cycle duration.

RESULTS

Height, weight, Co-Gn and Go-Gn were significantly correlated between mother-daughter pairs; however, mean cycle duration was not (r(2)=0.015). Mean cycle duration was positively correlated with ANB and height in mothers, but negatively correlated with Co-Gn in daughters.

CONCLUSIONS

Chewing rate is not correlated between mothers and daughters in humans.

Walking dynamics in preadolescents with and without Down syndrome

BACKGROUND

A force-driven harmonic oscillator (FDHO) model reveals the elastic property of general muscular activity during walking.

OBJECTIVE

This study aimed to investigate whether children with Down syndrome (DS) have a lower K/G ratio, a primary variable derived from the FDHO model, compared with children with typical development during overground and treadmill walking and whether children with DS can adapt the K/G ratio to walking speeds, external ankle load, and a treadmill setting.

DESIGN

A cross-sectional study design was used that included 26 children with and without DS, aged 7 to 10 years, for overground walking and 20 of them for treadmill walking in a laboratory setting.

METHODS

During overground walking, participants walked at 2 speeds: normal and fastest speed. During treadmill walking, participants walked at 75% and 100% of their preferred overground speed. Two load conditions were manipulated for both overground and treadmill walking: no load and an ankle load that was equal to 2% of body mass on each side.

RESULTS

Children with DS showed a K/G ratio similar to that of their healthy peers and increased this ratio with walking speed regardless of ankle load during overground walking. Children with DS produced a lower K/G ratio at the fast speed of treadmill walking without ankle load, but ankle load helped them produce a K/G ratio similar to that of their healthy peers.

LIMITATIONS

The FDHO model cannot specify what muscles are used or how muscles are coordinated for a given motor task.

CONCLUSIONS

Children with DS show elastic property of general muscular activity similar to their healthy peers during overground walking. External ankle load helps children with DS increase general muscular activity and match their healthy peers while walking fast on a treadmill.

The effects of gravity on human walking: a new test of the dynamic similarity hypothesis using a predictive model

The dynamic similarity hypothesis (DSH) suggests that differences in animal locomotor biomechanics are due mostly to differences in size. According to the DSH, when the ratios of inertial to gravitational forces are equal between two animals that differ in size [e.g. at equal Froude numbers, where Froude =velocity2/(gravity × hip height)], their movements can be made similar by multiplying all time durations by one constant, all forces by a second constant and all linear distances by a third constant. The DSH has been generally supported by numerous comparative studies showing that as inertial forces differ (i.e. differences in the centripetal force acting on the animal due to variation in hip heights), animals walk with dynamic similarity. However, humans walking in simulated reduced gravity do not walk with dynamically similar kinematics. The simulated gravity experiments did not completely account for the effects of gravity on all body segments, and the importance of gravity in the DSH requires further examination. This study uses a kinematic model to predict the effects of gravity on human locomotion,taking into account both the effects of gravitational forces on the upper body and on the limbs. Results show that dynamic similarity is maintained in altered gravitational environments. Thus, the DSH does account for differences in the inertial forces governing locomotion (e.g. differences in hip height)as well as differences in the gravitational forces governing locomotion.

Scaling of dynamics in the earliest stages of walking

BACKGROUND AND PURPOSE

Although the description of mature walking is fairly well established, less is known about what is being learned in the process. Such knowledge is critical to the physical therapist who wants to teach children with developmental delays. The purpose of this experiment was to test the notion that learning to walk efficiently involves fine-tuning the body's controllable stiffness (by co-contraction and isometric muscle contractions against gravity) to match (at a 1:1 scaling) the gravitational (pendular) stiffness of the swing leg.

SUBJECTS

The study participants were 7 children with typical development and the newly emerged ability to walk 6 steps without falling (ages 11 months to 1 year 5 months at the onset of walking).

METHODS

Pendular stiffness and spring stiffness were estimated from the equations of motion for a hybrid model with kinematic data as children walked over ground. Testing occurred once per month for the first 7 months of walking.

RESULTS

After the first month of walking, children walked with greater spring stiffness than would be predicted by the model. The ratio began to approach the predicted value (1:1) as the months progressed.

DISCUSSION AND CONCLUSION

The results of this and a previous study of the pendular dynamics of gait suggest that learning to walk is a 2-stage process. The first stage involves the child's discovery of how to conserve energy by inputting a particular muscular force at the correct moment in the cycle. The second stage involves the fine-tuning of the soft-tissue stiffness that takes advantage of the resonance characteristics of tissues. In order to address developmental delays, investigators must discover the dynamic resources used for the activity and attempt to foster their development. A number of interventions that probe this approach are discussed.

Action and perception at the level of synergies

Meeting the challenge of assembling coherent organizations of very many muscles characterizes a functional level of biological movement systems referred to as the level of muscular-articular links or synergies. The present article examines the issues confronting the forming, regulating, and ordering of synergies and the hypothesized principles, both classical and contemporary, which resolve them. A primary goal of the article is to highlight the abstractness of the concepts and tools required to understand the level's action-perception competence. Coverage is given to symmetry groups, task space, order parameters, metastability, biotensegrity, allometric scaling, and impredicative definitions.

Acquisition of the lateral inconsistency in involuntary behaviour of upper limbs in 12-year-old children during walking at moderate speed

The aim of this work was to investigate possible lateralisation in the behaviour of periodic motion of the human upper limb, during normal walking at a comfortable speed of locomotion. Ten healthy pre-adolescent, strongly right-handed, 12-year-old males participated in the experiment. Participants were walking on a treadmill with a standardised velocity of 1.1m/s (comfortable speed for all of them). A video analysis system with Silicon software was used to synchronically measure various angles of arms and forearms. The initial, final and interim angular positions of both arms and forearms in 10 cycles of each participant were compared in terms of variations (cycle to cycle) between both upper extremities at corresponding phases of each cycle for distal and proximal segments, respectively. We compared the coefficients of variation in relation to the spatial and temporal data of both limbs and their angular velocities. In addition we investigated the level of cycle-to-cycle regularity (constancy) of behaviour in relation to various positions, periods and velocities of movement of upper extremities (specifically arms and forearms) using the Eta non-linear method of correlation. All participants exhibited a lower level of regularity for the distal segments. The spatial and temporal variations in the dominant limb were also greater than the non-dominant limb for all participants. This may be due to a larger contribution from the right-sided muscles that are considered to be the main contributing factor to the motion of the dominant upper limb during walking, rather than simply gravity force acting alone. A possible practical application of this information may be useful in the objective clinical identification of the level of dominance of the upper extremity (arm plus forearm), in addition to 'traditional' handedness.

Convergence of forelimb and hindlimb Natural Pendular Period in baboons (Papio cynocephalus) and its implication for the evolution of primate quadrupedalism

The patterns of muscle mass distribution along the lengths of limbs may have important effects on the mechanics and energetics of quadrupedalism. Specifically, Myers and Steudel (J. Morphol. 234 (1997) 183) have shown that fore- and hindlimb Natural Pendular Periods (NPPs) may affect quadrupedal kinematics and must converge to reduce locomotor energetic costs. This study quantifies patterns of limb mass distribution in a live sample of Papio cynocephalus using limb inertial properties (mass, center of mass, mass moment of inertia, and radius of gyration). These inertial properties are calculated using a geometric modeling technique similar to that of Crompton et al. (Am. J. phys. Anthrop. 99 (1996) 547). The inertial properties in Papio are compared to those of Canis from Myers and Steudel (J. Morphol. 234 (1997) 183). The Papio sample has convergent fore- and hindlimb NPPs. Additionally, these limb NPPs are relatively large compared to those of Canis due to the relatively distally distributed limb mass in the Papio sample (relatively large limb masses, relatively distal centers of mass and radii of gyration, and relatively large limb mass moments of inertia). This relatively distal limb mass appears related to the grasping abilities of their hands and feet. Causal links are explored between limb shape adaptations for grasping hands and feet and the kinematics of primate quadrupedalism. In particular, if primates in general follow Papio's limb mass distribution pattern, then relatively large limb NPPs may lead to the relatively low stride frequencies already documented for primates. The kinematics of primate quadrupedalism appears to have been strongly influenced by both selection for grasping hands and feet and selection for reduced locomotor energetic costs.

Dynamical aspects of learning an interlimb rhythmic movement pattern

Learning a bimanual rhythmic task is explored from the perspective that motor skill acquisition involves the successive reparameterization of a dynamical control structure in the direction of increasing stability, where the intentional process of reparameterization is itself dynamical. Subjects learned to oscillate pendulums held in the right and left hands such that the right hand frequency was twice that of the left (2:1 frequency lock). Over 12 learning sessions of 20 trials each, we interpreted the decreasing fluctuations in the frequency locking to be an index of the increasing concavity of the underlying potential, a measure of stability; the time required to achieve the 2: 1 pattern was interpreted as indexing the relaxation time of an intentional dynamic. Power spectral analyses of the phase velocity ratio exhibited two strategies for acquiring the interlimb movement pattern: (a) adding spectral peaks at integer multiples of the left hand frequency or (b) distributing power across many frequencies in a l/f-like manner. Results are discussed in terms of the promise of a dynamical approach to learning coordinated movements.

Lateralized regular spatial patterns in oscillating drawing arm movements of right-handed young women

There is a lacuna in literature with reference to the spatial lateral difference in fast rhythmical movements produced by the whole dominant and nondominant whole arm, where spinal regulation has a significant role. Based on a fast oscillating zigzag drawing task, this study focused on (a) creation of a specific model of the task based on the intermittencies of coupled vectors of the fast motion, (b) identification of the spatial patterns that triggered these vectors, and (c) identification of quantified lateral differences between the spatial rhythmical patterns. 12 strongly right-handed young women performed 9 to 11 trials drawing zigzag lines. Each participant was required to extend her arm and perform this task using the left and right arm selectively on a frontally positioned graphic design system. The spatial patterns produced on each trial were identified in terms of five constant combinations of horizontal (X) and vertical (Y) projections of each line on the zigzag drawings. The dominant arm differed from the nondominant arm in preferred patterns. Because the duration of each line in the zigzag was highly restricted in time, the appearance of the patterns with different block schemes of movement could be explained as being associated with lower levels of the central nervous system. Initiation of fast movement of the total upper arm is probably associated with selection of the block scheme of motor control appropriate to each arm. Each block scheme is grounded on the coupled vectors of motion organised with particular muscle groups. Some block schemes seemed linked specifically to the dominant arm.

The force-driven harmonic oscillator model for energy-efficient locomotion in individuals with transtibial amputation

The force-driven harmonic oscillator (FDHO) model states that the driving force is minimum at the resonant period of an oscillator. By manipulating prosthetic mass, this study explored the compromise of resonant periods between the two legs in persons with unilateral traumatic transtibial amputation (TTA) at self-selected walking velocity (SSWV), with an aim to better understand the energy minimization mechanisms of walking. It was hypothesized that (1) SSWV was the most energy-efficient walking velocity (MEWV), (2) the stride period at SSWV (Ts) is a compromise between the resonant periods of the normal leg (Tn) and the prosthetic leg (Tp) when they are dissimilar. Eight subjects completed multiple-speed treadmill walking tests (at 53, 67, 80, 93, and 107 m/min) according to three mass conditions (60%, 80%, and 100% of the normal leg below-knee mass) in a random order. Oxygen consumption and stride period were measured, and SSWV was empirically determined. The MEWV, the speed with minimum energy expenditure per distance traveled, was derived from quadratic regression, and its stride period (Tm) was estimated. A theoretical compromise period (Tv) between Tn and Tp was predicted by a virtual single pendulum system based on Huygens' Law. Across different mass conditions, comparisons were made among: Ts, Tm, Tv, Tn, and Tp. Results showed that: (1) Ts was significantly different from Tm; (2) Ts was greater than both Tn and Tp; (3) no significant difference was found between Tm and Tn. Implications for amputee rehabilitation in terms of thigh muscle training and prosthesis development were discussed.

Task-effector asymmetries in a rhythmic continuation task

Variability in rhythmic movements has been interpreted as a signature of internal or peripheral noise processes. Grounded in an oscillator interpretation, this study hypothesized that period variability and drift arises from the asymmetry between target period and the limb's intrinsic dynamics. Participants synchronized to 7 target periods, swinging 1 of 3 pendulums in a continuation paradigm; 3 periods were longer, 3 shorter, and 1 identical to the preferred period. Results supported 5 predictions: Drift toward the preferred period was observed that scaled with the asymmetry. Variability was lowest for symmetry conditions and increased with the asymmetry. Variability decreased concomitant with the approach toward the preferred period. Periods exponentially approached the preferred period with positive autocorrelations up to 10 cycles.

Biomechanical Substrates of the Two-point Touch Cane Technique: A Review of Research

This article reviews research on the biomechanical elements related to the most commonly used long cane technique: two-point touch. The use of several natural biomechanical tendencies supports the contention that the technique is inherently efficient.

A new conceptual model of asymmetry in motor performance for bidimensional fast-oscillating movements in selected variants of performance

Spatial characteristics and lateral differences between two upper extremities were investigated in unilateral graphical tasks involving fast oscillating movements in the vertical plane based on the model of restricted (less than 10 degrees) horizontal abduction adduction in the shoulder joint. The spatial locations of reversal points were used to identify two groups of motor performance: with big angles and gross vertical vectors (stretched accordion group), and small projectile angles with small vertical vectors (compressed accordion group). Both groups appeared in right and left arm performance. The former group had a strong pattern of distribution of big and small projectile angles which reflects a particular variant of execution with a significant difference between angles and intermittent big and small angles (BB). Two other variants of execution relating to specific angular patterns of performance were identified in the compressed accordion group: one (Bs) showed a big difference between big and small angles but without intermittance; the other (ss) had only small differences between magnitudes of angles. The Bs variant of execution was observed only in left-handed performance, whilst ss was typical of both extremities. The performances affiliated to the stretched accordion group with the BB variant of execution mostly operated with reciprocal cooperation between alterations of X and Y vectors for the right arm. Performance related to the same group with the Bs variant of execution used concurrent collaboration involving alteration of these vectors for the left arm. The compressed accordion group which deployed the ss variant of execution mostly displayed concurrent alteration of vectors irrespective of the side of performance. It is suggested that the spatial movement strategies might reflect several different schemes of motor control wherein coupling of oscillators controls vertical and horizontal movements. It is also proposed that specific subunits of the functional system of nervous elements responsible for the expression of spatial derivatives of motor programmes may exist at lower levels of the CNS and might be initiated by the left brain or by the cooperative activity of the left and right hemispheres.

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.

Level of gymnastic skill as an intrinsic constraint on postural coordination

In this study, we considered the interacting effects of expertise in gymnastics, the type of support surface and the required frequency of head movement on the emergence of postural modes of coordination. A group of elite female gymnasts and a control group of non-gymnasts were asked to track the fore-aft motion of a target with their heads. Two support surface conditions (a balance beam vs the floor) were crossed with four frequencies of target motion. The relative phase between the angular motion of the ankles and hips was analysed. Two stable patterns emerged: an in-phase mode and an anti-phase mode, with the hip-ankle relative phase close to 0 degrees and 180 degrees, respectively. Increasing target frequency produced a change from in-phase to anti-phase coordination, in conditions where no instructions were given to the participants (Experiment 1) as well as in those where participants were instructed to maintain an in-phase mode for as long as possible (Experiment 2). This change, however, occurred earlier for the non-gymnasts than for the gymnasts. We conclude that 0 degrees and 180 degrees are two stable postural coordination modes, that expertise in gymnastics leads to a functional modification of existing patterns of coordination, and that expertise in general can be considered an intrinsic constraint on coordination.

The Timing of Intralimb Coordination

The authors examined the manner in which self-selected movement frequencies are impacted upon by repeated engagement in an intralimb coordination task and by alterations in the inertial characteristics of the limb. Twelve healthy adult volunteers rhythmically flexed and extended their elbow and wrist joints at a comfortable self-established frequency in 1 of 2 modes of coordination (in-phase and antiphase), while grasping 1 of 3 weighted dowels (no-weight condition [0.03 kg], light weight condition [0.5 kg], heavy weight condition [1.0 kg]). The movement frequencies adopted by subjects on the 3rd of 3 weekly sessions, following more than 120 experimental trials, were appreciably higher than those obtained during an initial session. The addition of mass to the system had an inconsistent influence upon the preferred frequency of movement. When subjects' limbs were loaded with what was deemed to be a light weight (0.5 kg), the movement frequencies that were adopted were indistinguishable from those selected when there was no (0.03 kg) loading of the limbs. In contrast, when subjects' limbs were loaded with a relatively heavy weight (1 kg), the resulting self-selected movement frequencies were reliably lower than when there was no loading of the limbs. The adopted frequency of movement was also influenced in a reliable fashion by the mode of coordination in which the movements were prepared. Those results are discussed with reference to mechanical and neuromuscular constraints on coordination dynamics.

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.

Morphological conservation of limb natural pendular period in the domestic dog (Canis familiaris): implications for locomotor energetics

For better understanding of the links between limb morphology and the metabolic cost of locomotion, we have characterized the relationships between limb length and shape and other functionally important variables in the straightened forelimbs and hindlimbs of a sample of 12 domestic dogs (Canis familiaris). Intra-animal comparisons show that forelimbs and hindlimbs are very similar (not significantly different) in natural pendular period (NPP), center-of-mass, and radius of gyration, even though they differ distinctly in mass, length, moment-of-inertia, and other limb proportions. The conservation of limb NPP, despite pronounced dissimilarity in other limb characteristics, appears to be the result of systematic differences in shape, forelimbs tending to be cylindrical and hindlimbs conical. Estimating limb NPP for other species from data in the literature on segment inertia and total limb length, we present evidence that the similarity between forelimbs and hindlimbs in NPP is generally true for mammals across a large size range. Limbs swinging with or near their natural pendular periods will maximize within-limb pendular exchange of potential and kinetic energy. As all four limbs of moderate- and large-size animals swing with the same period during walking, maximal advantage can be derived from the pendular exchange of energy only if forelimbs and hindlimbs are very similar in NPP. We hypothesize that an important constraint in the evolution of limb length and shape is the locomotor economy derived from forelimbs and hindlimbs of similar natural pendular period.

Spatial coordination in a bimanual task related to regular switching of movement vectors

The spatial aspect of cooperation between the two upper extremities was investigated using a bimanual task involving drawing simultaneous zig-zag lines on a vertical surface. In 62 trials by 31 strongly right-handed subjects three performance types were identified; Type I involved alternation of dominance in sideways and vertical movement components, in Type II a constant vertical movement was superimposed upon sideways movement, and Type III showed no consistent pattern across the two hands. These performance types differed significantly on the measure of spatial coordination, with Type I having the best, and Type III the poorest. These results suggest that on this bimanual task better spatial symmetry in limb movement is achieved when both hands employ similar within-hand strategies, involving switching between vectors for all muscle groups.

Lateralized spatial strategies in oscillating drawing movements

Kinematic characteristics and lateral differences between two upper extremities were investigated in a unimanual graphic task involving fast and precise oscillating movements on the vertical plane. The spatial locations of sequential reversal points were used to calculate the pairs of angles, relative to the horizontal axis. The point biserial coefficient of correlation was used to analyze the difference between big and large angles and their sequence in each pair. Three main groups (A, B, and C) of performance models were distinguished in 132 tests by 33 strongly right-handed male subjects. Group A showed strong variation in vertical movement, Group B covariation in vertical and horizontal vectors, while Group C reflected independent variation of both vertical and horizontal directions. It is suggested that the movement strategies might reflect three different models of motor control involving coupling of an oscillator controlling pools of motoneurons which regulates horizontal movements with an oscillator controlling vertical movement (Groups A + B) or with nonoscillating control signal (Group B). It is argued that Group A represents the simplest strategy and only performance Type A met by the left hand.

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

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.

Self-Optimization of Walking in Nondisabled Children and Children With Spastic Hemiplegic Cerebral Palsy

Children voluntarily adopt a frequency and movement pattern for walking. The force-driven harmonic oscillator (FDHO) model was used in this study for accurate prediction of the preferred walking frequency of nondisabled children and children with spastic hemiplegic cerebral palsy. Four potential optimality criteria with which the preferred walking pattern was forced to comply were examined: minimization of physiological costs, maximization of mechanical energy conservation, minimization of asymmetry in lower limb movements and minimization of variability of interlimb and intralimb coordination. Age and gender-matched nondisabled children (n = 6) and children with spastic hemiplegic cerebral palsy (n = 6) were tested under six frequency conditions of walking at a constant speed on a treadmill. For the nondisabled children, the results indicated that their preferred walking frequency could be accurately predicted by the FDHO model. They freely adopted a walking pattern that minimized physiological costs, asymmetry, and variability of inter- and intralimb coordination. For the children with spastic hemiplegic cerebral palsy, the prediction of preferred overground walking frequency required that the FDHO model be modified to account for muscle mass and leg length discrepancies between limbs and increased stiffness. Most of the children achieved the same optimality goals as the nondisabled when walking at the preferred frequency. However, the children were found to use different mechanisms to attain these goals: for example, a steeper increase observed in physiological cost at higher frequencies; a lowered center of gravity of the body, which allowed for angular symmetry; and greater variability of between-joint coordination in the nonaffected limb and less variability in the affected limb.

Linear and nonlinear stiffness and friction in biological rhythmic movements

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.

The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period

Human leg swinging is modeled as the harmonic motion of a hybrid mass-spring pendulum. The cycle period is determined by a gravitational component and an elastic component, which is provided by the attachment of a soft-tissue/muscular spring of variable stiffness. To confirm that the stiffness of the spring changes with alterations in the inertial properties of the oscillator and that stiffness is relevant for the control of cycle period, we conducted this study in which the simple pendulum equivalent length was experimentally manipulated by adding mass to the ankle of a comfortably swinging leg. Twenty-four young, healthy adults were videotaped as they swung their right leg under four conditions: no added mass and with masses of 2.27, 4.55, and 6.82kg added to the ankle. Strong, linear relationships between the acceleration and displacement of the swinging leg within subjects and conditions were found, confirming the motion's harmonic nature. Cycle period significantly increased with the added mass. However, the observed increases were not as large as would be predicted by the induced changes in the gravitational component alone. These differences were interpreted as being due to increases in the active muscular stiffness. Significant linear increases in the elastic component (and hence stiffness) were demonstrated with increases in the simple pendulum equivalent length in 20 of the individual subjects, with r2 values ranging between 0.89 and 0.99. Significant linear relationships were also demonstrated between the elastic and gravitational components in 22 subjects, with individual r2 values between 0.90 and 0.99.(ABSTRACT TRUNCATED AT 250 WORDS)

Energetic Cost and Stability During Human Walking at the Preferred Stride Velocity

The possibility that preferred modes of locomotion emerge from dynamical and optimality constraints and the energetic and dynamical constraints on preferred and predicted walking frequency are explored in this article. Participants were required to walk on a treadmill at their preferred frequency, at a frequency predicted as the resonance of a hybrid pendulum-spring model of the legs, and at frequencies +/-15%, +/-25%, +/-35% of the predicted frequency. Walking at the preferred and predicted frequencies resulted in minimal metabolic costs and maximal stability of the head and joint actions. Mechanical energy conservation was constant across conditions. The head was more stable than the joints. The joints appeared to be in service of the head in maintaining a stable trajectory. The major findings of this study suggest a complementary relationship between energetic (physiological) and stability constraints in the adoption of a preferred frequency of walking. Multiple subsystems may be involved in constraining observed macroscopic behavior in intact biological systems. The approach and results of the study imply that a useful tack in understanding how dynamical control structures arise is to study the potential criteria that serve to act as constraints on skilled movement patterns in unimpaired and impaired populations.

Feedforward postural adjustments in a simple two-joint synergy in patients with Parkinson's disease

Patients with Parkinson's disease, age-matched controls and young control subjects performed discrete elbow or wrist movements in a sagittal plane under the instruction to move one of the joints "as fast as possible." Relative stability of the other, postural joint was comparable in all 3 groups, while movement time was the highest in the patients and the lowest in young controls. Typically, EMG patterns in both muscle pairs acting at the joints demonstrated a commonly observed "tri-phasic" pattern. A cross-correlation analysis of the EMGs confirmed virtually simultaneous bursts in the wrist and elbow flexors and in the wrist and elbow extensors. In all 3 groups, there were no signs of anticipatory activation of postural muscles in about 90% of movements. We consider postural anticipation not a separate process, but a separate peripheral pattern of a single control process that may involve a number of joints and muscles. We conclude that the postural deficits in Parkinson's disease are not related to a basic deficit in the ability to generate feedforward postural adjustments but to other factors that may include the specificity of maintaining the vertical posture in the field of gravity.