Transmission of stimulus-locked responses in two coupled phase oscillators

Comparing brain connectivity metrics: a didactic tutorial with a toy model and experimental data

OBJECTIVE

The objective of this paper is to didactically compare resting state connectivity networks computed using two different methods called phase locking value (PLV) and convergent cross-mapping (CCM). PLV is a ubiquitous measure of connectivity in electrophysiological research but is less often applied to fMRI BOLD timeseries since this model-based metric assumes that oscillatory coupling is a sufficient condition for connectivity. Alternatively, CCM is a model-free method, which detects potentially nonlinear causal influences based on the ability to estimate one timeseries with another and does not assume an oscillatory structure.

APPROACH

We use a toy dataset to test the PLV and CCM algorithms under different known synchronization conditions. Additionally, experimental resting state EEG and fMRI datasets are used for comparison.

MAIN RESULTS

The results show that the resting state brain networks computed using both algorithms produce similar results for both resting state EEG and fMRI datasets. For both neuroimaging datasets, the network characteristics follow the same trends and the similarity between the computed networks, for both algorithms, is highly significant.

SIGNIFICANCE

CCM is able to identify low or one-way connection strengths better than PLV but takes exponentially longer to compute. Based on these results, PLV provides a good metric for on-line network identification because it is both computationally fast and an excellent approximation of the network computed with CCM.

Anti-kindling Induced by Two-Stage Coordinated Reset Stimulation with Weak Onset Intensity

Abnormal neuronal synchrony plays an important role in a number of brain diseases. To specifically counteract abnormal neuronal synchrony by desynchronization, Coordinated Reset (CR) stimulation, a spatiotemporally patterned stimulation technique, was designed with computational means. In neuronal networks with spike timing–dependent plasticity CR stimulation causes a decrease of synaptic weights and finally anti-kindling, i.e., unlearning of abnormally strong synaptic connectivity and abnormal neuronal synchrony. Long-lasting desynchronizing aftereffects of CR stimulation have been verified in pre-clinical and clinical proof of concept studies. In general, for different neuromodulation approaches, both invasive and non-invasive, it is desirable to enable effective stimulation at reduced stimulation intensities, thereby avoiding side effects. For the first time, we here present a two-stage CR stimulation protocol, where two qualitatively different types of CR stimulation are delivered one after another, and the first stage comes at a particularly weak stimulation intensity. Numerical simulations show that a two-stage CR stimulation can induce the same degree of anti-kindling as a single-stage CR stimulation with intermediate stimulation intensity. This stimulation approach might be clinically beneficial in patients suffering from brain diseases characterized by abnormal neuronal synchrony where a first treatment stage should be performed at particularly weak stimulation intensities in order to avoid side effects. This might, e.g., be relevant in the context of acoustic CR stimulation in tinnitus patients with hyperacusis or in the case of electrical deep brain CR stimulation with sub-optimally positioned leads or side effects caused by stimulation of the target itself. We discuss how to apply our method in first in man and proof of concept studies.

Behavioral impact of unisensory and multisensory audio-tactile events: pros and cons for interlimb coordination in juggling

Recent behavioral neuroscience research revealed that elementary reactive behavior can be improved in the case of cross-modal sensory interactions thanks to underlying multisensory integration mechanisms. Can this benefit be generalized to an ongoing coordination of movements under severe physical constraints? We choose a juggling task to examine this question. A central issue well-known in juggling lies in establishing and maintaining a specific temporal coordination among balls, hands, eyes and posture. Here, we tested whether providing additional timing information about the balls and hands motions by using external sound and tactile periodic stimulations, the later presented at the wrists, improved the behavior of jugglers. One specific combination of auditory and tactile metronome led to a decrease of the spatiotemporal variability of the juggler's performance: a simple sound associated to left and right tactile cues presented antiphase to each other, which corresponded to the temporal pattern of hands movement in the juggling task. A contrario, no improvements were obtained in the case of other auditory and tactile combinations. We even found a degraded performance when tactile events were presented alone. The nervous system thus appears able to integrate in efficient way environmental information brought by different sensory modalities, but only if the information specified matches specific features of the coordination pattern. We discuss the possible implications of these results for the understanding of the neuronal integration process implied in audio-tactile interaction in the context of complex voluntary movement, and considering the well-known gating effect of movement on vibrotactile perception.

Desynchronizing anti-resonance effect of m: n ON-OFF coordinated reset stimulation

This computational study is devoted to the optimal parameter calibration for coordinated reset (CR) stimulation, a stimulation technique suggested for an effective desynchronization of pathological neuronal synchronization. We present a detailed study of the parameter space of the CR stimulation method and show that CR stimulation can induce cluster states, desynchronization and oscillation death. The stimulation-induced cluster states (at CR offset) cause the longest desynchronizing post-stimulus transients, which constitute an essential part of the CR stimulation effect. We discover a desynchronization-related anti-resonance response of the stimulated oscillators induced by a periodic ON-OFF CR stimulation protocol with m cycles ON stimulation followed by n cycles OFF stimulation. The undesired collective oscillations are effectively desynchronized if the stimulation is administered at resonant frequencies of the controlled ensemble, which is in complete contrast to the typical effect of the usual periodic forcing.

Optimal information transfer in the cortex through synchronization

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.

Different brain areas are involved in any cognitive task. This implies that information has to be transmitted between different brain areas. Recent experimental results suggest that synchronization plays a crucial role in information exchange between cortical areas. They show that synchronization is capable of rendering network connections effective or ineffective. We study this hypothesis using a neurodynamical model and present results suggesting that both phase and strength of neuronal oscillations in the gamma frequency band influence amount and speed of information transport. We conclude that neuronal synchronization is crucial for information transmission and therefore might even have behavioral relevance.

Dynamic Causal Models for phase coupling

This paper presents an extension of the Dynamic Causal Modelling (DCM) framework to the analysis of phase-coupled data. A weakly coupled oscillator approach is used to describe dynamic phase changes in a network of oscillators. The use of Bayesian model comparison allows one to infer the mechanisms underlying synchronization processes in the brain. For example, whether activity is driven by master-slave versus mutual entrainment mechanisms. Results are presented on synthetic data from physiological models and on MEG data from a study of visual working memory.

swLORETA: a novel approach to robust source localization and synchronization tomography

Standardized low-resolution brain electromagnetic tomography (sLORETA) is a widely used technique for source localization. However, this technique still has some limitations, especially under realistic noisy conditions and in the case of deep sources. To overcome these problems, we present here swLORETA, an improved version of sLORETA, obtained by incorporating a singular value decomposition-based lead field weighting. We show that the precision of the source localization can further be improved by a tomographic phase synchronization analysis based on swLORETA. The phase synchronization analysis turns out to be superior to a standard linear coherence analysis, since the latter cannot distinguish between real phase locking and signal mixing.

Amplitude and phase dynamics associated with acoustically paced finger tapping

To gain insight into the brain activity associated with the performance of an acoustically paced synchronization task, we analyzed the amplitude and phase dynamics inherent in magnetoencephalographic (MEG) signals across frequency bands in order to discriminate between evoked and induced responses. MEG signals were averaged with respect to motor and auditory events (tap and tone onsets). Principal component analysis was used to compare amplitude and phase changes during listening and during paced and unpaced tapping, allowing a separation of brain activity related to motor and auditory processes, respectively. Motor performance was accompanied by phasic amplitude changes and increased phase locking in the beta band. Auditory processing of acoustic stimuli resulted in a simultaneous increase of amplitude and phase locking in the theta and alpha band. The temporal overlap of auditory-related amplitude changes and phase locking indicated an evoked response, in accordance with previous studies on auditory perception. The temporal difference of movement-related amplitude and phase dynamics in the beta band, on the other hand, suggested a change in ongoing brain activity, i.e., an induced response supporting previous results on motor-related brain dynamics in the beta band.

Stimulus-locked responses of two phase oscillators coupled with delayed feedback

For a system of two phase oscillators coupled with delayed self-feedback we study the impact of pulsatile stimulation administered to both oscillators. This system models the dynamics of two coupled phase-locked loops (PLLs) with a finite internal delay within each loop. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. Remarkably, for large coupling strength the two PLLs are completely desynchronized. We study stimulus-locked responses emerging in the different dynamical regimes. Simple phase resets may be followed by a response clustering, which is intimately connected with long poststimulus resynchronization. Intriguingly, a maximal perturbation (i.e., maximal response clustering and maximal resynchronization time) occurs, if the system gets trapped at a stable manifold of an unstable saddle fixed point due to appropriately calibrated stimulus. Also, single stimuli with suitable parameters can shift the system from a stable synchronized state to a stable desynchronized state or vice versa. Our result show that appropriately calibrated single pulse stimuli may cause pronounced transient and/or long-lasting changes of the oscillators' dynamics. Pulse stimulation may, hence, constitute an effective approach for the control of coupled oscillators, which might be relevant to both physical and medical applications.

Binding of movement, sound and touch: multimodal coordination dynamics

Very little is known about the coordination of movement in combination with stimuli such as sound and touch. The present research investigates the hypothesis that both the type of action (e.g., a flexion or extension movement) and the sensory modality (e.g., auditory or tactile) determine the stability of multimodal coordination. We performed a parametric study in which the ability to synchronize movement, touch and sound was explored over a broad range of stimulus frequencies or rates. As expected, synchronization of finger movement with external auditory and tactile stimuli was successfully established and maintained across all frequencies. In the key experimental conditions, participants were instructed to synchronize peak flexion of the index finger with touch and peak extension with sound (and vice-versa). In this situation, tactile and auditory stimuli were delivered counter-phase to each other. Two key effects were observed. First, switching between multimodal coordination patterns occurred, with transitions selecting one multimodal pattern (flexion with sound and extension with touch) more often than its partner. This finding indicates that the stability of multimodal coordination is influenced by both the type of action and the stimulus modality. Second, at higher rates, transitions from coherent to incoherent phase relations between touch, movement and sound occurred, attesting to the breakdown of multimodal coordination. Because timing errors in multimodal coordination were systematically altered when compared to unimodal control conditions we are led to consider the role played by time delays in multimodal coordination dynamics.

Estimation of the transmission time of stimulus-locked responses: modelling and stochastic phase resetting analysis

A model of two coupled phase oscillators is studied, where both oscillators are subject to random forces but only one oscillator is repetitively stimulated with a pulsatile stimulus. A pulse causes a reset, which is transmitted to the other oscillator via the coupling. The transmission time of the cross-trial (CT) averaged responses, i.e. the difference in time between the maxima of the CT averaged responses of both oscillators differs from the time difference between the maxima of the oscillators' resets. In fact, the transmission time of the CT averaged responses directly corresponds to the phase difference in the stable synchronized state with integer multiples of the oscillators' mean period added to it. With CT averaged responses it is impossible to reliably estimate the time elapsing, owing to the stimulus' action being transmitted between the two oscillators.

Transmission of stimulus-locked responses in two oscillators with bistable coupling

Numerous electroencephalography (EEG) and magnetoencephalography (MEG) studies aim at identifying the chronological order of activation of brain areas. This paper demonstrates that the timing sequence obtained with the gold standard for EEG/MEG analysis (averaging across trials) may not correlate at all with the actual transmission of a stimulus' effect within a pathway formed by connected brain areas. This is shown by studying transmission of stimulus-locked responses in a model that shares basic features with stimulated neuronal rhythms: in two phase oscillators with bistable coupling and noise one oscillator is stimulated. The model presents a mechanism that causes a response clustering, i.e., a switching between two different responses across trials, without extinction of the averaged response (calculated over all trials). Transmission times are calculated for all trials as well as for the two clusters separately with standard averaged responses and with a stochastic phase resetting analysis. The stochastic phase resetting analysis provides reliable estimates of the transmission time. In contrast, transmission times calculated by averaging across trials correspond to the phase difference in the different stable synchronized states (when calculated for the two clusters separately) or their weighted superposition (when calculated over all trials). The standard method does not detect the time elapsing during the transmission of the stimulus' action. The results presented here call into question many findings reported in the evoked response literature.