Spinal anticipation and cortical correction: coordination of movements (1930).
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Cerebral Cortex↗
Biomedical subjects
P J Beek
Publications and source records attributed to P J Beek.
Distinguishing between the effects of frequency and amplitude on interlimb coupling in tapping a 2:3 polyrhythm.
Rhythmic interlimb coordination is characterized by attraction to stable phase and frequency relations. Sudden, unintended transitions between such coordination patterns have been observed in iso- and multifrequency tasks when movement frequency was gradually increased. These transitions have been accounted for by modeling the two limbs as nonlinearly coupled oscillators. The prevailing form of the coupling function is based on time derivatives, but an alternative formulation can be derived by incorporating time delays. These time delays may be related to the neurophysiological delays associated with the use of kinesthetic afferences. The two ways of deriving coupling functions for interlimb coordination allow for different predictions with respect to the effects of movement frequency and amplitude on the strength of interaction between the limbs. In the current experiment, the effects of amplitude and frequency were dissociated experimentally, so as to arrive at an empirically motivated choice between the two ways of formalizing interlimb coupling. Subjects tapped the polyrhythm 2:3 at five different frequencies under three amplitude conditions. Whereas no effects of amplitude were observed, the strength of interaction between the hands decreased with increasing movement frequency. These results support the time-delay version of the model, in which differential (loss of) stability of coordination modes results from differential dependence on movement amplitude, but overall coupling strength is related reciprocally to movement frequency squared. This version of the model was related tentatively to three proposed aspects of interlimb coordination: (1) neurophysiological delays associated with the use of kinesthetic afferences; (2) rate-dependent decrease in pattern stability; and (3) differential entrainment influences of kinesthetic signals.
Adult↗
Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude?
The coordination of rhythmic movements is characterized by attraction to stable modes as well as by loss of stability due to the manipulation of external control parameters. For isochronous coordination between two oscillating components, frequency-induced transitions from antiphase to inphase coordination are frequently observed. Such transitions have been understood on the basis of a dynamical model, the HKB model, consisting of both a potential function for relative phase and a description of the oscillating limbs in terms of nonlinearly coupled limit cycle oscillators. According to the latter aspect of this model, the loss of stability of the antiphase pattern, which precedes the transition to the inphase pattern, is mediated by the decrease in movement amplitude that occurs when the movement frequency is scaled up. This amplitude-based transition mechanism was examined experimentally in the context of a unimanual tracking task. Subjects were instructed to maintain a prescribed amplitude, while tracking an oscillating visual stimulus in either the inphase or the antiphase mode. Three different movement amplitudes were used to examine the prediction that larger amplitudes lead to more stable coordination. When the frequency of oscillation was gradually increased, transitions from antiphase to inphase coordination were observed in the majority of the trials, despite constant or sometimes even slightly increasing amplitudes. No significant effects of amplitude on pattern stability, as indicated by the variability of relative phase and by the critical frequency, were observed. To the extent that these findings can be generalized beyond the present task domain, they suggest that frequency-induced transitions in coordinated rhythmic movements may not be mediated by a drop in amplitude and that alternative directions in modeling may have to be considered.
Analysis of Variance↗
Evidence for a phase transition in the early development of prehension.
A longitudinal study was conducted to examine the hypothesis that the development of prehension during the first 5 months of life is characterized by the presence of a discontinuous phase transition. Ten infants were observed weekly from 8 to 24 weeks of age. Video recordings were made of movements toward an attractive object which were classified according to two behavioral categories: reaching without grasping and reaching with grasping. The time evolution of the relative incidence of these behavioral categories was analyzed statistically. Evidence was found for a sudden jump from a (developmental) state in which reaching without grasping is predominant to a state in which reaching with grasping is predominant. Evidence was also found for bimodality, inaccessibility, and anomalous variance. In combination, these findings support the hypothesis that the investigated behavioral change constitutes a discontinuous phase transition. The behavioral change in question occurred at the moment in developmental time at which the attractor strength of reaching for objects as such relative to that of other behavioral activities appeared to be increased.
Age Factors↗
Anticipatory postural adjustments before load pickup in a bi-manual whole body lifting task.
Balance regulation and movement control were examined in the context of bi-manual lifting. Subjects picked up a load (20% body mass) after several unloaded cycles using the leg-lift technique. The addition of the load to the body caused the system center of mass to shift forward and thus presented the subject with an expected perturbation of balance. To examine whether the disturbances to balance were counteracted by anticipatory postural adjustments, the last cycle, in which the barbell was grasped and lifted, was compared with the preceding unloaded cycle. Using a global mechanical analysis of the movement, we found that anticipatory postural adjustments were present before load pickup in bi-manual lifting. These anticipatory postural adjustments were characterized by a backward directed horizontal momentum, a backward directed horizontal component of the ground reaction force accompanied with a forward shift of the center of pressure, and a backward shift of the center of mass (CoM). These characteristics could all be understood from the mechanical consideration that adding a load in front of the body induces a forward shift of the CoM. However, major compensations of the position of the CoM were also observed after bar grasp. It is therefore proposed that commands giving rise to postural adjustments are closely tied to commands controlling the ongoing movement. On the basis of this insight the strict dichotomy in the control of posture and movement is being questioned.
Adult↗
Anticipatory postural adjustments in the back and leg lift.
This study examined anticipatory postural adjustments in a dynamic multi-joint action in which a relatively fast voluntary movement is being executed while balance is maintained in the field of gravity. In a bi-manual whole body lifting task, the pickup of the load induces a forward shift in the position of the center of mass, challenging the dynamic balance regulation while simultaneously impeding the ongoing extension movement. We investigated whether anticipatory postural adjustments are an addition to a voluntary motor command or an inherent component of this command. Using a global mechanical analysis of the movement, we found that anticipatory postural adjustments are present in bimanual lifting, both in back lifting and leg lifting, and that lifting technique had a significant influence on the pattern of the adjustments. If the mass of the object was reduced unexpectedly, balance was disturbed in 92% of the mass-reduced trials. These findings suggest that the anticipatory postural adjustments to be performed are specified in advance such that the expected changes in the mechanical interaction with the environment are taken into account. The observations lend support to the hypothesis that the control of the observed anticipatory postural adjustments is an integral part of the control of the lifting movement itself. Consequently, the strict dichotomy in the control of posture and movement is being questioned.
Adult↗
Reading with magnifiers.
The design of low vision aids for partially sighted people, such as magnifiers, is evaluated theoretically in order to identify meaningful directions of research for improving these aids. Both reading with and without a magnifier involves alternating sequences of locating and recognizing textual information. Little is known, however, about these processes in magnifier reading. On the basis of an extensive review of the literature, two topics are identified that stand out as being in need of experimental investigation: (1) the relationship between the (typo)graphical characteristics of printed text and the location and recognition of textual information, and (2) the interplay of location and recognition processes in magnifier reading, including the role of non-visual factors, such as movements of the hand, trunk, head and eyes in this interplay. With regard to the first topic, it is expected that the visibility and, hence, the recognition of textual information by partially sighted people can be improved by matching the fundamental spatial frequencies of graphical structures with the spatial contrast sensitivity of partially sighted people. With regard to the second topic, it is argued that persistent problems in the design of the magnifiers, such as the optimal window size, can only be resolved by studying reading with a magnifier as a (multimodal) perceptual-motor activity.
Data Display↗
Frequency-induced phase transitions in bimanual tapping.
The stability of bimanual performance of the frequency ratios 3:8 and 5:8 was examined from the perspective of the sine circle map and the associated Farey mode-locking hierarchy. By gradually increasing movement frequency, abrupt transitions from the initial frequency ratios to other frequency ratios were induced. In general, transitions occurred to frequency ratios that were near the initial frequency ratio but lower in the Farey ordering, and, hence, of higher stability in the sine circle map. A fair percentage of these transitions were to unimodularly related ratios. The transition routes from 3:8 and 5:8 remained largely unaffected by extensive practice of the lower-order ratios 2:5 and 3:5. Collectively, these results suggest that (i) bimanual tapping occurs in a domain in which frequency-locked states either overlap or are located sufficiently close to each other to make stochastic switching possible (coupling parameter K > 1 or close to 1); (ii) the overall stability of these frequency-locked states decreases as movement frequency increases (due to a decrease in K); and, consequently, (iii) the probability of transitions to nearby frequency ratios increases as movement frequency increases, due to the differential stability of the frequency locks.
Acoustic Stimulation↗
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.
Adult↗
Temporal patterning in cascade juggling.
A key variable in cascade juggling is the proportion of time that a juggler holds onto a juggled object during a hand cycle, that is, the time from catch to throw in relation to the time from catch to catch. Space-time constraints and principles of frequency locking suggest 3/4 as the primary ratio and 2/3 and 5/8 as the most accessible options. In 5 experiments, object number, mass, and type (ball or scarf) were manipulated together with the frequency at which the objects were juggled. With 5 or 7 balls, the ratio was 3/4, independent of frequency. With 3 balls, the ratio decreased with frequency, with 3/4, 2/3, and 5/8 tending to predominate independently of the force variations induced by variation in object mass. With 3 scarves, ratios varied inversely with frequency and often exceeded 3/4. Implications for a dynamical theory of juggling were discussed with the issue of relative timing in coordination and the manipulation of task constraints as an experimental strategy.
Attention↗
Biomechanics of competitive front crawl swimming.
Essential performance-determining factors in front crawl swimming can be analysed within a biomechanical framework, in reference to the physiological basis of performance. These factors include: active drag forces, effective propulsive forces, propelling efficiency and power output. The success of a swimmer is determined by the ability to generate propulsive force, while reducing the resistance to forward motion. Although for a given competitive stroke a range of optimal stroking styles may be expected across a sample of swimmers, a common element of technique related to a high performance level is the use of complex sculling motions of the hands to generate especially lift forces. By changing the orientation of the hand the propulsive force acting on the hand is aimed successfully in the direction of motion. Furthermore, the swimming velocity (v) is related to drag (A), power input (Pi, the rate of energy liberation via the aerobic/anaerobic metabolism), the gross efficiency (eg), propelling efficiency (ep), and power output (Po) according to: [formula; see text] Based on the research available at present it is concluded that: (a) drag in groups of elite swimmers homogeneous with respect to swimming technique is determined by anthropometric dimensions; (b) total mechanical power output (Po) is important since improvement in performance is related to increased Po. Furthermore, it shows dramatic changes with training and possibly reflects the size of the 'swimming engine'; (c) propelling efficiency seems to be important since it is much higher in elite swimmers (61%) than in triathletes (44%); and (d) distance per stroke gives a fairly good indication of propelling efficiency and may be used to evaluate individual progress in technical ability.
Arm↗
Dynamical substructure of coordinated rhythmic movements.
A coordinated rhythmic movement pattern is a dynamical activity involving many hidden layers of rhythmic subtasks. To investigate this dynamical substructure, spectroscopic concepts and methods were applied to an interlimb rhythmic movement task requiring 1:1 frequency locking of two hand-held pendulums in 180 degrees phase relation. The pendulums could be of identical or very different dimensions, thereby providing different values of the ratio omega of uncoupled frequencies. Analyses focused on the power spectrum of continuous relative phase as a function of variation in omega. Predictions were derived from the theories of mode locking and fractal time. Experimental results were in agreement with theoretical expectations and were discussed in terms of the possible recruiting of rhythmic subtasks in the assembling of interlimb absolute coordination, the interdependence of these subtasks, and the general dynamical principles that relate coordinative processes occurring at different length and time scales.
Adult↗