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Intrinsic optical signal (IOS) imaging promises a noninvasive method for objective assessment of retinal function. This study demonstrates concurrent optical coherence tomography (OCT) of amplitude-IOS and phase-IOS changes in human photoreceptors. A new procedure for differential-phase-mapping (DPM) is validated to enable depth-resolved phase-IOS imaging. Dynamic OCT revealed rapid amplitude-IOS and phase-IOS changes, which occur almost right away after the stimulus onset. These IOS changes were predominantly observed within the photoreceptor outer segment (OS), particularly two boundaries connecting to the inner segment and retinal pigment epithelium. The comparative analysis supports that both amplitude-IOS and phase-IOS attribute to transient OS morphological change associated with phototransduction activation in retinal photoreceptors. A simulation modeling is proposed to discuss the relationship between the photoreceptor OS length and phase-IOS changes.

The authors show that neural networks exhibiting noise-induced rhythms, also known as quasi-cycle oscillations, can synchronize through out-of-phase locking depending on the noise intensity and the size of the coupling delay

The population and number dynamics of small mammals in the vicinity of the Torey lakes (Southeast Transbaikalia, Russia) were characterized between 2008 and 2017. The monitoring was carried out against the backdrop of the complete drying out of these largest lakes in the region. The stability of the fauna of small mammals was revealed over an 80-year period, although the structure of communities has changed significantly as a result of changes in moistening of the territory. Xerophilous species of mammals had an advantage in the period of studies in the dry climate phase. Correlation analysis showed a possible link between the population dynamics of some common species of small mammals with the precipitation amount of the current and previous years or with the precipitation amount of some spring (in one case, winter) months.

While the literature has characterized balance control during quasi-static and/or dynamic tasks, comparatively few studies have examined relationships across paradigms. This study investigated whether quiet-stance postural steadiness metrics were associated with reactive control parameters (during both stepping and restabilization phases) following a lean-and-release perturbation. A total of 40 older adults participated. Postural steadiness (center of the pressure range, root mean square, velocity, and frequency) was evaluated in “feet together” and “tandem stance” positions. During the reactive control trials, the step length, step width, movement time, and reaction time were measured, in addition to the postural steadiness variables measured during the restabilization phase following the stepping response. Out of 64 comparisons, only 10 moderate correlations were observed between postural steadiness and reactive spatio-temporal stepping parameters (P ≤ .05, r = −.312 to −.534). However, postural steadiness metrics were associated with the center of pressure velocity and frequency during the restabilization phase of the reactive control trials (P ≤ .02, r = .383 to .775 for velocity and P ≤ .01, r = .386 to .550 for frequency). Although some elements of quasi-static center of pressure control demonstrated moderate associations with dynamic stepping responses, relationships were stronger for restabilization phase dynamics after foot-contact. Future work should examine the potential association between restabilization phase control and older adult fall-risk.

Previous research has shown that feedback evaluation is sensitive to monetary incentive. We investigated whether this sensitivity is driven by motivational salience (the difference between both rewarding and punishing events versus neutral events) or by motivational valence (the difference between rewarding and punishing events). Fifty-seven participants performed a monetary incentive delay task under a gain context, a loss context, and a neutral context with their electroencephalogram recorded. During the time domain, the feedback-related negativity (FRN) showed a motivational salience effect whereas the P3 displayed a reward valence effect. During the time-frequency domain, we observed a motivational salience effect for phase-locked theta power regardless of performance feedback, but a reward valence effect for non-phase-locked theta power in response to unsuccessful feedback. Moreover, we found a reward valence effect for phase-locked delta. These findings thus suggest that the affective modulation on feedback evaluation can be driven either by motivational valence or by motivational salience, which depends on the temporal dynamics (the FRN vs. the P3), the frequency dynamics (theta vs. delta power), as well as the phase dynamics (evoked vs. induced power).

Objective:We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.Material and Methods:In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.Results:Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.Conclusion:Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

First order phase reduced model is a good approximation of the dynamics of forced nonlinear oscillators near its limit cycle. The phase evolution is determined by the unforced frequency, the forcing term, and the phase response curve (PRC). Such models arise in biological oscillations such as in circadian rhythm, neural signaling, heart beat, etc. This technical note focuses on the phase regulation of the circadian rhythm using light intensity as the input. Though the model is simple, the circle topology of the state space needs to be carefully addressed. The most common entrainment method is to use a periodic input, such as in our daily light-dark cycle. We obtain the complete stable entrainment condition based on the entraiment input and the PRC. Motivated by the jet-lag problem, we also consider the minimum time entrainment control to achieve a specified phase shift. Application of the Pontryagin Minimum Principle leads to an efficient solution strategy for the optimal control, without solving the two-point boundary value problem. The optimal control may be further represented as a feedback control law based on the current and desired phases. Our analysis allows the answer to questions such as: When traveling from New York to Paris, is it faster to use light to shift the phase forward by 6 hours or delay the phase by 18 hours? The answer is somewhat counter-intuitive—delaying by 18 hours requires less time. The general answer depends on the light intensity level and the shape of the PRC. PRCs for human and Drosophila from the literature are used to illustrate the results.

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking., Comment: 10 pages, 8 figures

Sensorimotor predictions are essential for adaptive behavior. In natural environments, events that demand sensorimotor predictions unfold across many timescales, and corresponding temporal predictions (either explicit or implicit) should therefore emerge in brain dynamics. Neuronal oscillations are scale-specific processes found in several frequency bands. They underlie periodicity in sensorimotor processing and can represent temporal predictions via their phase dynamics. These processes build upon endogenous neural rhythmicity and adapt in response to exogenous timing demands. While much of the research on periodicity in neural processing has focused on subsecond oscillations, these fast-scale rhythms are in fact paralleled by critical-like, scale-free dynamics and fluctuations of brain activity at various timescales, ranging from seconds to hundreds of seconds. In this review, we put forth a framework positing that critical brain dynamics are essential for the role of neuronal oscillations in timing and that cross-frequency coupling flexibly organizes neuronal processing across multiple frequencies.

A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems.

Already several years ago [3], it was suggested that a laser with optical injection can respond to external perturbations by emitting spikes if the perturbation overcomes a certain threshold, all the spikes being identical to each other, in complete analogy with the behaviour of the simple theta-model neuron [1]. The underlying explanation of this phenomenon lies in the isomorphism between a model of neuron [1] and that of an over-damped oscillator with periodic forcing (often called the Adler equation [2]). The control of these spikes was only achieved recently [5], while their observation goes back to [4]. Although there is an excellent agreement between these observations and the predictions of the reduction to pure phase dynamics of a laser model [3], it was soon noticed that whenever the pure phase dynamics reduction ceases to be valid, more complex dynamical phenomena can take place, leading to multipulse excitability [6]. This has led to the investigation of the behaviour of a semiconductor laser locked to an external forcing in response to external perturbations beyond the simple case of the Adler-like mode. We observe resonator features of the neuron-like system and multi-spike responses. Beyond improving the understanding of the neuron-like excitable dynamics of the laser with injected signal, our aim is to leverage the multipulse excitability and the resonator features of the optical neuron analogue for optical data processing and to provide possible insight about complex solitons interactions in forced oscillatory media [7, 8].

Alpha oscillations are modulated in response to visual temporal and spatial cues, However, the neural response to alerting cues is less explored, as is how this response is affected by healthy aging. Using scalp EEG, we examined how visual cortical alpha activity relates to working memory performance. Younger (20-30 years) and older (60-70 years) participants were presented with a visual alerting cue uninformative of the position or size of a lateralized working memory array. Older adults showed longer response times overall, and reduced accuracy when memory load was high. Older adults had less consistent cue-evoked phase resetting than younger adults, which predicted worse performance. Alpha phase prior to memory array presentation predicted response time, but the relationship between phase and response time was weaker in older adults. These results suggest that changes in alpha phase dynamics, especially prior to presentation of task-relevant stimuli, potentially contribute to age-related cognitive decline.

Multi-electrode recordings of local field potentials (LFPs) provide the opportunity to investigate the spatiotemporal organization of neural activity on the scale of several millimeters. In particular, the phases of oscillatory LFPs allow studying the coordination of neural oscillations in time and space and to tie it to cognitive processing. Given the computational roles of LFP phases, it is important to know how they relate to the phases of the underlying current source densities (CSDs) that generate them. Although CSDs and LFPs are distinct physical quantities, they are often (implicitly) identified when interpreting experimental observations. That this identification is problematic is clear from the fact that LFP phases change when switching to different electrode montages, while the underlying CSD phases remain unchanged. In this study we use a volume-conductor model to characterize discrepancies between LFP and CSD phase-patterns, to identify the contributing factors, and to assess the effect of different electrode montages. Although we focus on cortical LFPs recorded with two-dimensional (Utah) arrays, our findings are also relevant for other electrode configurations. We found that the main factors that determine the discrepancy between CSD and LFP phase-patterns are the frequency of the neural oscillations and the extent to which the laminar CSD profile is balanced. Furthermore, the presence of laminar phase-differences in cortical oscillations, as commonly observed in experiments, precludes identifying LFP phases with those of the CSD oscillations at a given cortical depth. This observation potentially complicates the interpretation of spike-LFP coherence and spike-triggered LFP averages. With respect to reference strategies, we found that the average-reference montage leads to larger discrepancies between LFP and CSD phases as compared with the referential montage, while the Laplacian montage reduces these discrepancies. We therefore advice to conduct analysis of two-dimensional LFP recordings using the Laplacian montage. RH and GD were funded by the European Research Council (Advanced Grant DYSTRUCTURE No. 295129), the Spanish Research Project PSI2013-42091-P, the CONSOLIDER-INGENIO 2010 Program CSD2007-00012, and the FP7-ICT Brainscales (269921). XA and PV are supported by the European Research Council's CDAC project: “The Role of Consciousness in Adaptive Behavior: A Combined Empirical, Computational and Robot based Approach” (ERC-2013- ADG 341196).

Cerebral palsy (CP) includes a broad range of disorders, which can result in impairment of posture and movement control. Brain-computer interfaces (BCIs) have been proposed as assistive devices for individuals with CP. Better understanding of the neural processing underlying motor control in affected individuals could lead to more targeted BCI rehabilitation and treatment options. We have explored well-known neural correlates of movement, including event-related desynchronization (ERD), phase synchrony, and a recently-introduced measure of phase dynamics, in participants with CP and healthy control participants. Although present, significantly less ERD and phase locking were found in the group with CP. Additionally, inter-group differences in phase dynamics were also significant. Taken together these findings suggest that users with CP exhibit lower levels of motor cortex activation during motor imagery, as reflected in lower levels of ongoing mu suppression and less functional connectivity. These differences indicate that development of BCIs for individuals with CP may pose additional challenges beyond those faced in providing BCIs to healthy individuals.

Alpha-frequency band (8-14 Hz) oscillations are among the most salient phenomena in human electroencephalography (EEG) recordings and yet their functional roles have remained unclear. Much of research on alpha oscillations in human EEG has focused on peri-stimulus amplitude dynamics, which phenomenologically support an idea of alpha oscillations being negatively correlated with local cortical excitability and having a role in the suppression of task-irrelevant neuronal processing. This kind of an inhibitory role for alpha oscillations is also supported by several functional magnetic resonance imaging (fMRI) and trans-cranial magnetic stimulation (TMS) studies. Nevertheless, investigations of local and inter-areal alpha phase dynamics suggest that the alpha-frequency band rhythmicity may play a role also in active task-relevant neuronal processing. These data imply that inter-areal alpha phase synchronization could support attentional, executive, and contextual functions. In this review, we outline evidence supporting different views on the roles of alpha oscillations in cortical networks and unresolved issues that should be addressed to resolve or reconcile these apparently contrasting hypotheses.

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both. We would like to thank Mark Woolrich for his contribution to data acquisition and analysis and the fruitful discussion about interpretation of our findings. We received the following funding: GD, RT: ERC Advanced Grant: DYSTRUCTURE (n. 295129), GD: Spanish Research Project PSI2013-42091-P, Human Brain Project, and FP7-ICT BrainScales (269921). MLK: ERC Consolidator Grant CAREGIVING (n. 615539) and Center for Music in the Brain/Danish National Research Foundation (DNRF117). AD, BP: H2020-MSA-ITN COSMOS (n. 642563).