C. (Lieke) E. Peper

Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces

Abstract Recently, Jirsa et al. and Haken discussed a theory comprising the brain wave equation proposed by Nunez, the Wilson–Cowan/Ermentrout–Cowan model, and Hopfield networks. This theory was applied to model findings obtained in an experiment that relates brain activity and behavior, the so-called Julliard experiment. In previous works of Jirsa et al. and Frank et al. the focus was on the brain wave aspect. Recently, we conducted similar experiments. The results obtained are modeled in this paper in terms of coupled oscillator systems. Coupled oscillator systems are considered to represent the Wilson–Cowan/Ermentrout–Cowan-model aspect of the unifying theory. Building on a model proposed by Haken, Kelso, and Bunz and the theory of weakly coupled oscillators established by Winfree and by Kuramoto, we derive a nonlinear Fokker–Planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments.

Modeling rhythmic interlimb coordination. Beyond the Haken-Kelso-Bunz model

Although the Haken-Kelso-Bunz (HKB) model was originally formulated to account for phase transitions in bimanual movements, it evolved, through experimentation and conceptual elaboration, into a fundamental formal construct for the experimental study of rhythmically coordinated movements in general. The model consists of two levels of formalization: a potential defining the stability properties of relative phase and a system of coupled limit cycle oscillators defining the individual limb movements and their interactions. Whereas the empirical validity of the potential is well established, the validity of the formalization in terms of coupled oscillators is questionable, both with regard to the assumption that individual limb movements are limit cycle oscillators with (only) two active degrees of freedom and with regard to the postulated coupling. To remedy these limitations a more elaborate system of coupled oscillators is outlined, comprising two coupled limit cycle oscillators at the neural level, each of which is coupled to a linearly damped oscillator, representing the end-effectors.

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.

A model for phase transitions in human hand movements during multifrequency tapping

In bimanual tapping, abrupt transitions between frequency ratios were observed when movement frequency was gradually increased. The transition routes showed individual tendencies, not necessarily in agreement with predictions derived from the sine circle map. Therefore, a more detailed theoretical model of coupled oscillators was developed. In the model the interaction function is a polynomial of coupling terms which allow for specific frequency locks. The magnitudes of these coupling terms are related to the amplitude of oscillation and the order of the frequency lock. Because increase in movement frequency is associated with a drop in amplitude, it results in differential loss of stability of the allowed frequency ratios. New frequency-locked states may be attained by detuning the stiffness parameters of the component oscillators. The model accounts for both free-running solutions and individual tendencies in transition routes. The relative weights of the coupling terms are influenced by practice and intention.

Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude?

Abstract. 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.

Motor consequences of experimentally induced limb pain: a systematic review.

Compelling evidence exists that pain may affect the motor system, but it is unclear if different sources of peripheral limb pain exert selective effects on motor control. This systematic review evaluates the effects of experimental (sub)cutaneous pain, joint pain, muscle pain and tendon pain on the motor system in healthy humans. The results show that pain affects many components of motor processing at various levels of the nervous system, but that the effects of pain are largely irrespective of its source. Pain is associated with inhibition of muscle activity in the (painful) agonist and its non‐painful antagonists and synergists, especially at higher intensities of muscle contraction. Despite the influence of pain on muscle activation, only subtle alterations were found in movement kinetics and kinematics. The performance of various motor tasks mostly remained unimpaired, presumably as a result of a redistribution of muscle activity, both within the (painful) agonist and among muscles involved in the task. At the most basic level of motor control, cutaneous pain caused amplification of the nociceptive withdrawal reflex, whereas insufficient evidence was found for systematic modulation of other spinal reflexes. At higher levels of motor control, pain was associated with decreased corticospinal excitability. Collectively, the findings show that short‐lasting experimentally induced limb pain may induce immediate changes at all levels of motor control, irrespective of the source of pain. These changes facilitate protective and compensatory motor behaviour, and are discussed with regard to pertinent models on the effects of pain on motor control.

Coupling strength in tapping a 2:3 polyrhythm

The effects of tempo and role (fast vs. slow hand) on the reciprocal interaction (strength of coupling) between two hands tapping a 2:3 polyrhythm were examined from the perspective of nonlinear oscillator theory. A measure of the degree of harmonicity was developed, based on the relative contribution of the tapping frequency to the power spectrum of the limit cycle phase angle of each individual hand. On the assumption of fixed coefficients of the dissipative terms in the component oscillators, comparison of unimanual and bimanual performance with respect to this measure allowed for examination of the effects of the experimental conditions on the strength of the coupling. Five right-handed skilled drummers performed the 2:3 polyrhythm at several tempos and with both hand arrangements (i.e., either the preferred or the non-preferred hand tapped the faster cadence). The analysis revealed an inverse relation between tempo and coupling strength, and a larger influence of the fast hand on the slow hand than vice versa. No differences were observed between the two hand arrangements. The theoretical implications of these results were discussed in relation to similar and dissimilar findings in the literature.

Prospective control of manual interceptive actions: comparative simulations of extant and new model constructs

Two prospective controllers of hand movements in catching-both based on required velocity control-were simulated. Under certain conditions, this required velocity control led to overshoots of the future interception point. These overshoots were absent in pertinent experiments. To remedy this shortcoming, the required velocity model was reformulated in terms of a neural network, the Vector Integration To Endpoint model, to create a Required Velocity Integration To Endpoint model. Addition of a parallel relative velocity channel, resulting in the Relative and Required Velocity Integration To Endpoint model, provided a better account for the experimentally observed kinematics than the existing, purely behavioral models. Simulations of reaching to intercept decelerating and accelerating objects in the presence of background motion were performed to make distinct predictions for future experiments.

Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account

Based on recent brain-imaging data and congruent theoretical insights, a dynamical model is derived to account for the patterns of brain activity observed during stable performance of bimanual multifrequency patterns, as well as during behavioral instabilities in the form of phase transitions between such patterns. The model incorporates four dynamical processes, defined over both motor and premotor cortices, which are coupled through inhibitory and excitatory inter- and intrahemispheric connections. In particular, the model underscores the crucial role of interhemispheric inhibition in reducing the interference between disparate frequencies during stable performance, as well as the failure of this reduction during behavioral transitions. As an aside, the model also accounts for in- and antiphase preferences during isofrequency movements. The viability of the proposed model is illustrated by magnetoencephalographic signals that were recorded from an experienced subject performing a polyrhythmic tapping task that was designed to induce transitions between multifrequency patterns. Consistent with the model’s dynamics, contra- and ipsilateral cortical areas of activation were frequency- and phase-locked, while their activation strength changed markedly in the vicinity of transitions in coordination.

Unilateral versus bilateral upper limb exercise therapy after stroke: A systematic review

OBJECTIVE To compare the effects of unilateral and bilateral training on upper limb function after stroke with regard to two key factors: severity of upper limb paresis and time of intervention post-stroke. DESIGN Systematic review and meta-analysis of randomized controlled trials. METHODS Two authors independently selected trials for inclusion, assessed the methodological quality and extracted data. Study outcomes were pooled by calculating the (standardized) mean difference ((S)MD). Sensitivity analyses for severity and time of intervention post-stroke were applied when possible. RESULTS All 9 studies involving 452 patients showed homogeneity. In chronic patients with a mild upper limb paresis after stroke a marginally significant SMD for upper limb activity performance (SMD 0.34; 95% confidence interval): 0.04-0.63), and marginally significant MDs for perceived upper limb activity performance (amount of use: MD 0.42; 95% confidence interval: 0.09-0.76, and quality of movement: MD 0.45; 95% confidence interval: 0.12-0.78) were found in favour of unilateral training. All other MDs and SMDs were non-significant. CONCLUSION Unilateral and bilateral training are similarly effective. However, intervention success may depend on severity of upper limb paresis and time of intervention post-stroke.