Alterations in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia with propofol and sevoflurane

Delta-alpha cross-frequency coupling for different brain regions

Neural interactions occur on different levels and scales. It is of particular importance to understand how they are distributed among different neuroanatomical and physiological relevant brain regions. We investigated neural cross-frequency couplings between different brain regions according to the Desikan-Killiany brain parcellation. The adaptive dynamic Bayesian inference method was applied to EEG measurements of healthy resting subjects in order to reconstruct the coupling functions. It was found that even after averaging over all subjects, the mean coupling function showed a characteristic waveform, confirming the direct influence of the delta-phase on the alpha-phase dynamics in certain brain regions and that the shape of the coupling function changes for different regions. While the averaged coupling function within a region was of similar form, the region-averaged coupling function was averaged out, which implies that there is a common dependence within separate regions across the subjects. It was also found that for certain regions the influence of delta on alpha oscillations is more pronounced and that oscillations that influence other are more evenly distributed across brain regions than the influenced oscillations. When presenting the information on brain lobes, it was shown that the influence of delta emanating from the brain as a whole is greatest on the alpha oscillations of the cingulate frontal lobe, and at the same time the influence of delta from the cingulate parietal brain lobe is greatest on the alpha oscillations of the whole brain.

White-matter degradation and dynamical compensation support age-related functional alterations in human brain

Structural connectivity of the brain at different ages is analyzed using diffusion-weighted magnetic resonance imaging (MRI) data. The largest decrease of streamlines is found in frontal regions and for long inter-hemispheric links. The average length of the tracts also decreases, but the clustering is unaffected. From functional MRI we identify age-related changes of dynamic functional connectivity (dFC) and spatial covariation features of functional connectivity (FC) links captured by metaconnectivity. They indicate more stable dFC, but wider range and variance of MC, whereas static features of FC did not show any significant differences with age. We implement individual connectivity in whole-brain models and test several hypotheses for the mechanisms of operation among underlying neural system. We demonstrate that age-related functional fingerprints are only supported if the model accounts for: (i) compensation of the individual brains for the overall loss of structural connectivity and (ii) decrease of propagation velocity due to the loss of myelination. We also show that with these 2 conditions, it is sufficient to decompose the time-delays as bimodal distribution that only distinguishes between intra- and inter-hemispheric delays, and that the same working point also captures the static FC the best, and produces the largest variability at slow time-scales.

Integrating psychosocial variables and societal diversity in epidemic models for predicting COVID-19 transmission dynamics

During the current COVID-19 pandemic, governments must make decisions based on a variety of information including estimations of infection spread, health care capacity, economic and psychosocial considerations. The disparate validity of current short-term forecasts of these factors is a major challenge to governments. By causally linking an established epidemiological spread model with dynamically evolving psychosocial variables, using Bayesian inference we estimate the strength and direction of these interactions for German and Danish data of disease spread, human mobility, and psychosocial factors based on the serial cross-sectional COVID-19 Snapshot Monitoring (COSMO; N = 16,981). We demonstrate that the strength of cumulative influence of psychosocial variables on infection rates is of a similar magnitude as the influence of physical distancing. We further show that the efficacy of political interventions to contain the disease strongly depends on societal diversity, in particular group-specific sensitivity to affective risk perception. As a consequence, the model may assist in quantifying the effect and timing of interventions, forecasting future scenarios, and differentiating the impact on diverse groups as a function of their societal organization. Importantly, the careful handling of societal factors, including support to the more vulnerable groups, adds another direct instrument to the battery of political interventions fighting epidemic spread.

From Brain-Body Function to Conscious Interactions

In this review, we discuss empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience. First, we motivate the discussion through evidence regarding the dynamic brain. Second, we review different brain-body couplings associated with conscious experience and its potential role in driving brain dynamics. Third, we introduce the machinery of multilayer networks to account for several types of interactions in brain-body systems. Then, a multilayer structure consists of two main generalizations: a formal semantic to study biological systems, and an integrative account for several signatures and models of consciousness. Finally, under this framework, we define composition of layers to account for entangled features of brain-body systems related to conscious experience. As such, a multilayer mathematical framework is highly integrative and thus may be more complete than other models. In this short review, we discuss a variety of empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience.

Normalizing the brain connectome for communication through synchronization

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.

Identifying Cognitive Impairment in Elderly Using Coupling Functions Between Cerebral Oxyhemoglobin and Arterial Blood Pressure

Background

This study aimed to assess brain oxygenation status and cerebral autoregulation function in subjects with cognitive dysfunction.

Methods

The Montreal Cognitive Assessment (MoCA) was applied to divide the subjects into three groups: cognitive impairment (Group CI, 72.50 ± 10.93 y), mild cognitive impairment (Group MCI, 72.02 ± 9.90 y), and normal cognition (Group NC, 70.72 ± 7.66 y). Near-infrared spectroscopy technology and a non-invasive blood pressure device were used to simultaneously measure changes in cerebral tissue oxygenation signals in the bilateral prefrontal lobes (LPFC/RPFC) and arterial blood pressure (ABP) signals from subjects in the resting state (15 min). The coupling between ABP and cerebral oxyhemoglobin concentrations (Δ [O2Hb]) was calculated in very-low-frequency (VLF, 0.02-0.07 Hz) and low-frequency (LF, 0.07-0.2 Hz) bands based on the dynamical Bayesian inference approach. Pearson correlation analyses were used to study the relationships between MoCA scores, tissue oxygenation index, and strength of coupling function.

Results

In the interval VLF, Group CI (p = 0.001) and Group MCI (p = 0.013) exhibited significantly higher coupling strength from ABP to Δ [O2Hb] in the LPFC than Group NC. In the interval LF, coupling strength from ABP to Δ [O2Hb] in the LPFC was significantly higher in Group CI than in Group NC (p = 0.001). Pearson correlation results showed that MoCA scores had a significant positive correlation with the tissue oxygenation index and a significant negative correlation with the coupling strength from ABP to Δ [O2Hb].

Conclusion

The significantly increased coupling strength may be evidence of impaired cerebral autoregulation function in subjects with cognitive dysfunction. The Pearson correlation results suggest that indicators of brain oxygenation status and cerebral autoregulation function can reflect cognitive function. This study provides insights into the mechanisms underlying the pathophysiology of cognitive impairment and provides objective indicators for screening cognitive impairment in the elderly population.

Detection of Cross-Frequency Coupling Between Brain Areas: An Extension of Phase Linearity Measurement

The current paper proposes a method to estimate phase to phase cross-frequency coupling between brain areas, applied to broadband signals, without any a priori hypothesis about the frequency of the synchronized components. N:m synchronization is the only form of cross-frequency synchronization that allows the exchange of information at the time resolution of the faster signal, hence likely to play a fundamental role in large-scale coordination of brain activity. The proposed method, named cross-frequency phase linearity measurement (CF-PLM), builds and expands upon the phase linearity measurement, an iso-frequency connectivity metrics previously published by our group. The main idea lies in using the shape of the interferometric spectrum of the two analyzed signals in order to estimate the strength of cross-frequency coupling. We first provide a theoretical explanation of the metrics. Then, we test the proposed metric on simulated data from coupled oscillators synchronized in iso- and cross-frequency (using both Rössler and Kuramoto oscillator models), and subsequently apply it on real data from brain activity. Results show that the method is useful to estimate n:m synchronization, based solely on the phase of the signals (independently of the amplitude), and no a-priori hypothesis is available about the expected frequencies.

Resting State EEG Directed Functional Connectivity Unveils Changes in Motor Network Organization in Subacute Stroke Patients After Rehabilitation

Brain plasticity and functional reorganization are mechanisms behind functional motor recovery of patients after an ischemic stroke. The study of resting-state motor network functional connectivity by means of EEG proved to be useful in investigating changes occurring in the information flow and find correlation with motor function recovery. In the literature, most studies applying EEG to post-stroke patients investigated the undirected functional connectivity of interacting brain regions. Quite recently, works started to investigate the directionality of the connections and many approaches or features have been proposed, each of them being more suitable to describe different aspects, e.g., direct or indirect information flow between network nodes, the coupling strength or its characteristic oscillation frequency. Each work chose one specific measure, despite in literature there is not an agreed consensus, and the selection of the most appropriate measure is still an open issue. In an attempt to shed light on this methodological aspect, we propose here to combine the information of direct and indirect coupling provided by two frequency-domain measures based on Granger’s causality, i.e., the directed coherence (DC) and the generalized partial directed coherence (gPDC), to investigate the longitudinal changes of resting-state directed connectivity associated with sensorimotor rhythms α and β, occurring in 18 sub-acute ischemic stroke patients who followed a rehabilitation treatment. Our results showed a relevant role of the information flow through the pre-motor regions in the reorganization of the motor network after the rehabilitation in the sub-acute stage. In particular, DC highlighted an increase in intra-hemispheric coupling strength between pre-motor and primary motor areas, especially in ipsi-lesional hemisphere in both α and β frequency bands, whereas gPDC was more sensitive in the detection of those connection whose variation was mostly represented within the population. A decreased causal flow from contra-lesional premotor cortex towards supplementary motor area was detected in both α and β frequency bands and a significant reinforced inter-hemispheric connection from ipsi to contra-lesional pre-motor cortex was observed in β frequency. Interestingly, the connection from contra towards ipsilesional pre-motor area correlated with upper limb motor recovery in α band. The usage of two different measures of directed connectivity allowed a better comprehension of those coupling changes between brain motor regions, either direct or mediated, which mostly were influenced by the rehabilitation, revealing a particular involvement of the pre-motor areas in the cerebral functional reorganization.

Propofol Versus Sevoflurane General Anaesthesia for Selective Impairment of Attention Networks After Gynaecological Surgery in Middle-Aged Women: A Randomised Controlled Trial

PURPOSE

Attention is an essential component of cognitive function that may be impaired after surgery with anaesthesia. Propofol intravenous anaesthesia and sevoflurane inhalational anaesthesia are frequently used in gynaecological surgery. However, which type of anaesthetic has fewer cognitive effects postoperatively remains unclear. We compared the differences in attention network impairment after surgery in women receiving propofol versus sevoflurane general anaesthesia.

PATIENTS AND METHODS

Eighty-three patients with gynaecological diseases who were 40-60 years of age were involved in the study. All patients underwent elective gynaecological surgery under either total intravenous anaesthesia or sevoflurane inhalational anaesthesia, depending on randomisation. The efficiencies of the three attention networks were captured using the attention network test preoperatively and on the 1st and 5th postoperative days.

RESULTS

Both groups of patients showed differences in impairments on the 1st and 5th postoperative days. Pairwise comparisons indicated that the alerting and orienting networks of patients in the propofol group were impaired to a greater extent than those of patients in the sevoflurane group on the 1st postoperative day, while the executive control network was impaired to a lesser extent. On the 5th postoperative day, the alerting networks of both groups recovered to the baseline level. Patients in the propofol group still showed impairment of the orienting network, while patients in the sevoflurane group recovered to baseline. For the executive control network, patients in the sevoflurane group still exhibited more severe impairment than those in the propofol group.

CONCLUSION

In middle-aged women, propofol impaired orienting and alerting networks more than sevoflurane, while sevoflurane showed more residual impairment of the executive control network.

Directional couplings between the respiration and parasympathetic control of the heart rate during sleep and wakefulness in healthy subjects at different ages

Cardiorespiratory interactions are important, both for understanding the fundamental processes of functioning of the human body and for development of methods for diagnostics of various pathologies. The properties of cardiorespiratory interaction are determined by the processes of autonomic control of blood circulation, which are modulated by the higher nervous activity. We study the directional couplings between the respiration and the process of parasympathetic control of the heart rate in the awake state and different stages of sleep in 96 healthy subjects from different age groups. The detection of directional couplings is carried out using the method of phase dynamics modeling applied to experimental RR-intervals and the signal of respiration. We reveal the presence of bidirectional couplings between the studied processes in all age groups. Our results show that the coupling from respiration to the process of parasympathetic control of the heart rate is stronger than the coupling in the opposite direction. The difference in the strength of bidirectional couplings between the considered processes is most pronounced in deep sleep.

Evaluation of Anesthetic Specific EEG Dynamics during State Transitions between Loss and Return of Responsiveness

Purpose: electroencephalographic (EEG) information is used to monitor the level of cortical depression of a patient undergoing surgical intervention under general anesthesia. The dynamic state transitions into and out of anesthetic-induced loss and return of responsiveness (LOR, ROR) present a possibility to evaluate the dynamics of the EEG induced by different substances. We evaluated changes in the EEG power spectrum during anesthesia emergence for three different anesthetic regimens. We also assessed the possible impact of these changes on processed EEG parameters such as the permutation entropy (PeEn) and the cerebral state index (CSI). Methods: we analyzed the EEG from 45 patients, equally assigned to three groups. All patients were induced with propofol and the groups differed by the maintenance anesthetic regimen, i.e., sevoflurane, isoflurane, or propofol. We evaluated the EEG and parameter dynamics during LOR and ROR. For the emergence period, we focused on possible differences in the EEG dynamics in the different groups. Results: depending on the substance, the EEG emergence patterns showed significant differences that led to a substance-specific early activation of higher frequencies as indicated by the “wake” CSI values that occurred minutes before ROR in the inhalational anesthetic groups. Conclusion: our results highlight substance-specific differences in the emergence from anesthesia that can influence the EEG-based monitoring that probably have to be considered in order to improve neuromonitoring during general anesthesia.

Mild poikilocapnic hypoxia increases very low frequency haemoglobin oxygenation oscillations in prefrontal cortex

BACKGROUND

The aim of the study was to investigate the effect of mild cerebral hypoxia on haemoglobin oxygenation (HbO₂), cerebrospinal fluid dynamics and cardiovascular physiology. To achieve this goal, four signals were recorded simultaneously: blood pressure, heart rate / electrocardiogram, HbO₂ from right hemisphere and changes of subarachnoid space (SAS) width from left hemisphere. Signals were registered from 30 healthy, young participants (2 females and 28 males, body mass index = 24.5 ± 2.3 kg/m², age 30.8 ± 13.4 years).

RESULTS

We analysed the recorded signals using wavelet transform and phase coherence. We demonstrated for the first time that in healthy subjects exposed to mild poikilokapnic hypoxia there were increases in very low frequency HbO₂ oscillations (< 0.052 Hz) in prefrontal cortex. Additionally, SAS fluctuation diminished in the whole frequency range which could be explained by brain oedema.

CONCLUSIONS

Consequently the study provides insight into mechanisms governing brain response to a mild hypoxic challenge. Our study supports the notion that HbO₂ and SAS width monitoring might be beneficial for patients with acute lung disease.

A Bridge between the Breath and the Brain: Synchronization of Respiration, a Pupillometric Marker of the Locus Coeruleus, and an EEG Marker of Attentional Control State

Yogic and meditative traditions have long held that the fluctuations of the breath and the mind are intimately related. While respiratory modulation of cortical activity and attentional switching are established, the extent to which electrophysiological markers of attention exhibit synchronization with respiration is unknown. To this end, we examined (1) frontal midline theta-beta ratio (TBR), an indicator of attentional control state known to correlate with mind wandering episodes and functional connectivity of the executive control network; (2) pupil diameter (PD), a known proxy measure of locus coeruleus (LC) noradrenergic activity; and (3) respiration for evidence of phase synchronization and information transfer (multivariate Granger causality) during quiet restful breathing. Our results indicate that both TBR and PD are simultaneously synchronized with the breath, suggesting an underlying oscillation of an attentionally relevant electrophysiological index that is phase-locked to the respiratory cycle which could have the potential to bias the attentional system into switching states. We highlight the LC’s pivotal role as a coupling mechanism between respiration and TBR, and elaborate on its dual functions as both a chemosensitive respiratory nucleus and a pacemaker of the attentional system. We further suggest that an appreciation of the dynamics of this weakly coupled oscillatory system could help deepen our understanding of the traditional claim of a relationship between breathing and attention.

Towards new concepts for a biological neuroscience of consciousness

In the search for a sound model of consciousness, we aim at introducing new concepts: closure, compositionality, biobranes and autobranes. This is important to overcome reductionism and to bring life back into the neuroscience of consciousness. Using these definitions, we conjecture that consciousness co-arises with the non-trivial composition of biological closure in the form of biobranes and autobranes: conscious processes generate closed activity at various levels and are, in turn, themselves, supported by biobranes and autobranes. This approach leads to a non-reductionist biological and simultaneously phenomenological theory of conscious experience, giving new perspectives for a science of consciousness. Future works will implement experimental definitions and computational simulations to characterize these dynamical biobranes interacting.

Intermittent Sequential Pneumatic Compression Improves Coupling between Cerebral Oxyhaemoglobin and Arterial Blood Pressure in Patients with Cerebral Infarction

This study aims to explore the effect of intermittent sequential pneumatic compression (ISPC) intervention on the coupling relationship between arterial blood pressure (ABP) and changes in oxyhaemoglobin (Δ [O₂Hb]). The coupling strength between the two physiological systems was estimated using a coupling function based on dynamic Bayesian inference. The participants were 22 cerebral infarction patients and 20 age- and sex-matched healthy controls. Compared with resting state, the coupling strength from ABP to Δ [O₂Hb] oscillations was significantly lower in the bilateral prefrontal cortex (PFC), sensorimotor cortex (SMC), and temporal lobe cortex (TLC) during the ISPC intervention in cerebral infarction patients in interval II. Additionally, the coupling strength was significantly lower in the bilateral SMC in both groups in interval III. These findings indicate that ISPC intervention may facilitate cerebral circulation in the bilateral PFC, SMC, and TLC in cerebral infarction patients. ISPC may promote motor function recovery through its positive influences on motor-related networks. Furthermore, the coupling between Δ [O₂Hb] and ABP allows non-invasive assessments of autoregulatory function to quantitatively assess the effect of rehabilitation tasks and to guide therapy in clinical situations.

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on a group of 20 healthy volunteers (12 females and 8 males; BMI =22.1±3.2 kg/m2; age 25.3±7.9 years). We analysed the recorded signals with a wavelet transform. For the first time, a method based on dynamical Bayesian inference was used to detect the effective phase connectivity and the underlying coupling functions between the SAS and BP signals. There are several new findings. Slow breathing with or without resistance increases the strength of the coupling between the respiratory and cardiac components of both measured signals. We also observed increases in the strength of the coupling between the respiratory component of the BP and the cardiac component of the SAS and vice versa. Slow breathing synchronises the SAS oscillations, between the brain hemispheres. It also diminishes the similarity of the coupling between all analysed pairs of oscillators, while inspiratory resistance partially reverses this phenomenon. BP–SAS and SAS–BP interactions may reflect changes in the overall biomechanical characteristics of the brain.

Directed Connectivity Analysis of the Neuro-Cardio- and Respiratory Systems Reveals Novel Biomarkers of Susceptibility to SUDEP

Sudden unexpected death in epilepsy (SUDEP) is the leading cause of epilepsy-related mortality and its pathophysiological mechanisms remain unknown. Goal: We set to record and analyze for the first time concurrent electroencephalographic (EEG), electrocardiographic (ECG), and unrestrained whole-body plethysmographic (Pleth) signals from control (WT - wild type) and SUDEP-prone mice (KO- knockout Kcna1 animal model). Methods: Employing multivariate autoregressive models (MVAR) we measured all tri-organ effective directional interactions by the generalized partial directed coherence (GPDC) in the frequency domain over time (hours). Results: When compared to the control (WT) animals, the SUDEP-prone (KO) animals exhibited (p < 0.001) reduced afferent and efferent interactions between the heart and the brain over the full frequency spectrum (0-200Hz), enhanced efferent interactions from the brain to the lungs and from the heart to the lungs at high (>90 Hz) frequencies (especially during periods with seizure activity), and decreased feedback from the lungs to the brain at low (<40 Hz) frequencies. Conclusions: These results show that impairment in the afferent and efferent pathways in the holistic neuro-cardio-respiratory network could lead to SUDEP, and effective connectivity measures and their dynamics could serve as novel biomarkers of susceptibility to SUDEP and seizures respectively.

Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered-measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.

Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators

Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive-repulsive interactions as well as the hybrid model of coexisting attractive-repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive-repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Synchronization transitions caused by time-varying coupling functions

Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Transmission time delays organize the brain network synchronization

The timing of activity across brain regions can be described by its phases for oscillatory processes, and is of crucial importance for brain functioning. The structure of the brain constrains its dynamics through the delays due to propagation and the strengths of the white matter tracts. We use self-sustained delay-coupled, non-isochronous, nonlinearly damped and chaotic oscillators to study how spatio-temporal organization of the brain governs phase lags between the coherent activity of its regions. In silico results for the brain network model demonstrate a robust switching from in- to anti-phase synchronization by increasing the frequency, with a consistent lagging of the stronger connected regions. Relative phases are well predicted by an earlier analysis of Kuramoto oscillators, confirming the spatial heterogeneity of time delays as a crucial mechanism in shaping the functional brain architecture. Increased frequency and coupling are also shown to distort the oscillators by decreasing their amplitude, and stronger regions have lower, but more synchronized activity. These results indicate specific features in the phase relationships within the brain that need to hold for a wide range of local oscillatory dynamics, given that the time delays of the connectome are proportional to the lengths of the structural pathways. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Alteration of coupling between brain and heart induced by sedation with propofol and midazolam

For a comprehensive understanding of the nervous system, several previous studies have examined the network connections between the brain and the heart in diverse conditions. In this study, we identified coupling between the brain and the heart along the continuum of sedation levels, but not in discrete sedation levels (e. g., wakefulness, conscious sedation, and deep sedation). To identify coupling between the brain and the heart during sedation, we induced several depths of sedation using patient-controlled sedation with propofol and midazolam. We performed electroencephalogram (EEG) spectral analysis and extracted the instantaneous heart rate (HR) from the electrocardiogram (ECG). EEG spectral power dynamics and mean HR were compared along the continuum of sedation levels. We found that EEG sigma power was the parameter most sensitive to changes in the sedation level and was correlated with the mean HR under the effect of sedative agents. Moreover, we calculated the Granger causality (GC) value to quantify brain-heart coupling at each sedation level. Additionally, the GC analysis revealed noticeably different strengths and directions of causality among different sedation levels. In all the sedation levels, GC values from the brain to the heart (GCb→h) were higher than GC values from the heart to the brain (GCh→b). Moreover, the mean GCb→h increased as the sedation became deeper, resulting in higher GCb→h values in deep sedation (1.97 ± 0.18 in propofol, 2.02 ± 0.15 in midazolam) than in pre-sedation (1.71 ± 0.13 in propofol, 1.75 ± 0.11 in midazolam; p < 0.001). These results show that coupling between brain and heart activities becomes stronger as sedation becomes deeper, and that this coupling is more attributable to the brain-heart direction than to the heart-brain direction. These findings provide a better understanding of the relationship between the brain and the heart under specific conditions, namely, different sedation states.

Limb linkage rehabilitation training-related changes in cortical activation and effective connectivity after stroke: A functional near-infrared spectroscopy study

Stroke remains the leading cause of long-term disability worldwide. Rehabilitation training is essential for motor function recovery following stroke. Specifically, limb linkage rehabilitation training can stimulate motor function in the upper and lower limbs simultaneously. This study aimed to investigate limb linkage rehabilitation task-related changes in cortical activation and effective connectivity (EC) within a functional brain network after stroke by using functional near-infrared spectroscopy (fNIRS) imaging. Thirteen stroke patients with either left hemiparesis (L-H group, n = 6) and or right hemiparesis (R-H group, n = 7) and 16 healthy individuals (control group) participated in this study. A multichannel fNIRS system was used to measure changes in cerebral oxygenated hemoglobin (delta HbO₂) and deoxygenated hemoglobin (delta HHb) in the bilateral prefrontal cortices (PFCs), motor cortices (MCs), and occipital lobes (OLs) during (1) the resting state and (2) a motor rehabilitation task with upper and lower limb linkage (first 10 min [task_S1], last 10 min [task_S2]). The frequency-specific EC among the brain regions was calculated based on coupling functions and dynamic Bayesian inference in frequency intervals: high-frequency I (0.6-2 Hz) and II (0.145-0.6 Hz), low-frequency III (0.052-0.145 Hz), and very-low-frequency IV (0.021-0.052 Hz). The results showed that the stroke patients exhibited an asymmetric (greater activation in the contralesional versus ipsilesional motor region) cortical activation pattern versus healthy controls. Compared with the healthy controls, the stroke patients showed significantly lower EC (p < 0.025) in intervals I and II in the resting and task states. The EC from the MC and OL to the right PFC in interval IV was significantly higher in the R-H group than in the control group during the resting and task states (p < 0.025). Furthermore, the L-H group showed significantly higher EC from the MC and OL to the left PFC in intervals III and IV during the task states compared with the control group (p < 0.025). The significantly increased influence of the MC and OL on the contralesional PFC in low- and very-low-frequency bands suggested that plastic reorganization of cognitive resources severed to compensate for impairment in stroke patients during the motor rehabilitation task. This study can serve as a basis for understanding task-related reorganization of functional brain networks and developing novel assessment techniques for stroke rehabilitation.

Nonautonomous driving induces stability in network of identical oscillators

Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous perturbation is a good candidate for stabilizing complex dynamics, we consider a network of identical phase oscillators driven by an oscillator with a slowly time-varying frequency. We investigate both the short- and long-term stability of the synchronous solutions of this nonautonomous system. For attractive couplings we show that the region of stability grows as the amplitude of the frequency modulation is increased, through the birth of an intermittent synchronization regime. For repulsive couplings, we propose a control strategy to stabilize the dynamics by altering very slightly the network topology. We also show how, without changing the topology, time-variability in the driving frequency can itself stabilize the dynamics. As a byproduct of the analysis, we observe chimeralike states. We conclude that time-variability-induced stability phenomena are also present in networks, reinforcing the idea that this is a quite realistic scenario for living systems to use in maintaining their functioning in the face of ongoing perturbations.

A new Modelling Framework to Study Time-Varying Directional Brain-Heart Interactions: Preliminary Evaluations and Perspectives

We propose a novel modelling framework to study non-stationary, directional brain-heart interplay in a time varying fashion. Considering electroencephalographic (EEG) signals and Heart Rate Variability (HRV) series as inputs, a new multivariate formulation is derived from proper coupling functions linking cortical electrical activity and heartbeat dynamics generation models. These neural-autonomic coupling rules are formalised according to the current knowledge on the central autonomic network and fully parametrised in adaptive coefficients quantifying the information outflow from-brain-to- heart as well as from-heart-to-brain. Such coefficients can be effectively estimated by solving the model inverse problem, and profitably exploited for a novel assessment of brain-heart interactions. Here we show preliminary experimental results gathered from 27 healthy volunteers undergoing significant sympatho-vagal perturbations through cold-pressor test and discuss prospective uses of this novel methodological frame- work. Specifically, we highlight how the directional brain-heart coupling significantly increases during prolonged baroreflex elicitation with specific time delays and throughout specific brain areas, especially including fronto-parietal regions and lateralisation mechanisms in the temporal cortices.

Continuous wavelet transform in the study of the time-scale properties of intracranial pressure in hydrocephalus

Normal pressure hydrocephalus (NPH) encompasses a heterogeneous group of disorders generally characterized by clinical symptoms, ventriculomegaly and anomalous cerebrospinal fluid (CSF) dynamics. Lumbar infusion tests (ITs) are frequently performed in the preoperatory evaluation of patients who show NPH features. The analysis of intracranial pressure (ICP) signals recorded during ITs could be useful to better understand the pathophysiology underlying NPH and to assist treatment decisions. In this study, 131 ICP signals recorded during ITs were analysed using two continuous wavelet transform (CWT)-derived parameters: Jensen divergence (JD) and spectral flux (SF). These parameters were studied in two frequency bands, associated with different components of the signal: B₁(0.15-0.3 Hz), related to respiratory blood pressure oscillations; and B₂ (0.67-2.5 Hz), related to ICP pulse waves. Statistically significant differences (p < 1.70 × 10^-3, Bonferroni-corrected Wilcoxon signed-rank tests) in pairwise comparisons between phases of ITs were found using the mean and standard deviation of JD and SF. These differences were mainly found in B₂, where a lower irregularity and variability, together with less prominent time-frequency fluctuations, were found in the hypertension phase of ITs. Our results suggest that wavelet analysis could be useful for understanding CSF dynamics in NPH.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Phase-lags in large scale brain synchronization: Methodological considerations and in-silico analysis

Architecture of phase relationships among neural oscillations is central for their functional significance but has remained theoretically poorly understood. We use phenomenological model of delay-coupled oscillators with increasing degree of topological complexity to identify underlying principles by which the spatio-temporal structure of the brain governs the phase lags between oscillatory activity at distant regions. Phase relations and their regions of stability are derived and numerically confirmed for two oscillators and for networks with randomly distributed or clustered bimodal delays, as a first approximation for the brain structural connectivity. Besides in-phase, clustered delays can induce anti-phase synchronization for certain frequencies, while the sign of the lags is determined by the natural frequencies and by the inhomogeneous network interactions. For in-phase synchronization faster oscillators always phase lead, while stronger connected nodes lag behind the weaker during frequency depression, which consistently arises for in-silico results. If nodes are in anti-phase regime, then a distance π is added to the in-phase trends. The statistics of the phases is calculated from the phase locking values (PLV), as in many empirical studies, and we scrutinize the method’s impact. The choice of surrogates do not affects the mean of the observed phase lags, but higher significance levels that are generated by some surrogates, cause decreased variance and might fail to detect the generally weaker coherence of the interhemispheric links. These links are also affected by the non-stationary and intermittent synchronization, which causes multimodal phase lags that can be misleading if averaged. Taken together, the results describe quantitatively the impact of the spatio-temporal connectivity of the brain to the synchronization patterns between brain regions, and to uncover mechanisms through which the spatio-temporal structure of the brain renders phases to be distributed around 0 and π.

Trial registration: South African Clinical Trials Register: http://www.sanctr.gov.za/SAClinicalbrnbspTrials/tabid/169/Default.aspx, then link to respiratory tract then link to tuberculosis, pulmonary; and TASK Applied Sciences Clinical Trials, AP-TB-201-16 (ALOPEXX): https://task.org.za/clinical-trials/.

Functional connectivity, and in particular, phase coupling between distant brain regions may be fundamental in regulating neuronal processing and communication. However, phase relationships between the nodes of the brain and how they are confined by its spatio-temporal structure, have been mostly overlooked. We use a model of oscillatory dynamics superimposed on the space-time structure defined by the connectome, and we analyze the possible regimes of synchronization. Limitations of data analysis are also considered and we show that the choice of the significance threshold for coherence does not essentially impact the statistics of the observed phase lags, although it is crucial for the right detection of statistically significant coherence. Analytical insights are obtained for networks with heterogeneous time-delays, based on the empirical data from the connectome, and these are confirmed by numerical simulations, which show in- or anti-phase synchronization depending on the frequency and the distribution of time-delays. Phase lags are shown to result from inhomogeneous network interactions, so that stronger connected nodes generally phase lag behind the weaker.

Alteration in Brain Functional and Effective Connectivity in Subjects With Hypertension

To reveal the physiological mechanism of the cognitive decline in subjects with hypertension, the functional connectivity (FC) was assessed by using the wavelet phase coherence (WPCO), and effective connectivity (EC) was assessed by using the coupling strength (CS) of near-infrared spectroscopy (NIRS) signals. NIRS signals were continuously recorded from the prefrontal cortex, sensorimotor cortex, and occipital lobes of 13 hypertensive patients (hypertension group, 70 ± 6.5 years old) and 16 elderly healthy subjects (control group, 71 ± 5.5 years old) in resting and standing periods. WPCO and CS were calculated in four frequency intervals: I, 0.6–2; II, 0.145–0.6; III, 0.052–0.145; and IV, 0.021–0.052 Hz. CS quantifies coupling amplitude. In comparison with the control group, the hypertension group showed significantly decreased (p < 0.05) WPCO and CS in intervals III and IV and in the resting and standing states. WPCO and CS were significantly decreased in the resting state compared with those in the standing state in the hypertension group (p < 0.05). Decreased WPCO and CS indicated a reduced network interaction, suggesting disturbed neurovascular coupling in subjects with hypertension. Compared with the control group, the hypertension group showed significantly lower Mini-Mental State Examination (MMSE) (p = 0.028) and Montreal Cognitive Assessment (MoCA) scores (p = 0.011). In the hypertension group, correlation analysis showed that WPCO and CS were significantly positively correlated with MMSE and MoCA scores, respectively. These findings may provide evidence of impaired cognitive function in hypertension and can enhance the understanding on neurovascular coupling.

Coupling of respiration and attention via the locus coeruleus: Effects of meditation and pranayama

The locus coeruleus (LC) has established functions in both attention and respiration. Good attentional performance requires optimal levels of tonic LC activity, and must be matched to task consistently. LC neurons are chemosensitive, causing respiratory phrenic nerve firing to increase frequency with higher CO₂ levels, and as CO₂ level varies with the phase of respiration, tonic LC activity should exhibit fluctuations at respiratory frequency. Top-down modulation of tonic LC activity from brain areas involved in attentional regulation, intended to optimize LC firing to suit task requirements, may have respiratory consequences as well, as increases in LC activity influence phrenic nerve firing. We hypothesize that, due to the physiological and functional overlaps of attentional and respiratory functions of the LC, this small neuromodulatory nucleus is ideally situated to act as a mechanism of synchronization between respiratory and attentional systems, giving rise to a low-amplitude oscillation that enables attentional flexibility, but may also contribute to unintended destabilization of attention. Meditative and pranayama practices result in attentional, emotional, and physiological enhancements that may be partially due to the LC's pivotal role as the nexus in this coupled system. We present original findings of synchronization between respiration and LC activity (via fMRI and pupil dilation) and provide evidence of a relationship between respiratory phase modulation and attentional performance. We also present a mathematical dynamical systems model of respiratory-LC-attentional coupling, review candidate neurophysiological mechanisms of changes in coupling dynamics, and discuss implications for attentional theory, meditation, and pranayama, and possible therapeutic applications.

Alterations in the coupling functions between cerebral oxyhaemoglobin and arterial blood pressure signals in post-stroke subjects

Cerebral autoregulation (CA) is the complex homeostatic regulatory relationship between blood pressure (BP) and cerebral blood flow (CBF). This study aimed to analyze the frequency-specific coupling function between cerebral oxyhemoglobin concentrations (delta [HbO₂]) and mean arterial pressure (MAP) signals based on a model of coupled phase oscillators and dynamical Bayesian inference. Delta [HbO₂] was measured by 24-channel near-infrared spectroscopy (NIRS) and arterial BP signals were obtained by simultaneous resting-state measurements in patients with stroke, that is, 9 with left hemiparesis (L–H group), 8 with right hemiparesis (R–H group), and 17 age-matched healthy individuals as control (healthy group). The coupling functions from MAP to delta [HbO₂] oscillators were identified and analyzed in four frequency intervals (I, 0.6–2 Hz; II, 0.145–0.6 Hz; III, 0.052–0.145 Hz; and IV, 0.021–0.052 Hz). In L–H group, the CS from MAP to delta [HbO₂] in interval III in channel 8 was significantly higher than that in healthy group (p = 0.003). Compared with the healthy controls, the coupling in MAP→delta [HbO₂] showed higher amplitude in interval I and IV in patients with stroke. The increased CS and coupling amplitude may be an evidence of impairment in CA, thereby confirming the presence of impaired CA in patients with stroke. In interval III, the CS in L–H group from MAP to delta [HbO₂] in channel 16 (p = 0.001) was significantly lower than that in healthy controls, which might indicate the compensatory mechanism in CA of the unaffected side in patients with stroke. No significant difference in region-wise CS between affected and unaffected sides was observed in stroke groups, indicating an evidence of globally impaired CA. These findings provide a method for the assessment of CA and will contribute to the development of therapeutic interventions in stroke patients.

Effective Connectivity in Response to Posture Changes in Elderly Subjects as Assessed Using Functional Near-Infrared Spectroscopy

This study aims to assess the posture-related changes in frequency-specific effective connectivity (EC) in elderly subjects by coupling function measured using functional near-infrared spectroscopy (fNIRS). The fNIRS signals were continuously recorded from the bilateral prefrontal cortex (PFC), motor cortex (MC), and occipital lobe (OL) in 17 healthy elderly and 19 healthy young subjects during sitting and standing states. EC was calculated based on Dynamic Bayesian inference in one low frequency interval I: 0.052–0.145 Hz and one very low frequency interval II: 0.021–0.052 Hz. Results show that in response to posture change, the coupling strength significantly increased in interval I of the young group from right PFC to MC (p < 0.05). Meanwhile, the coupling strength of the elderly group was significantly increased in interval II from the left PFC to right PFC (p = 0.008) and to left MC (p = 0.031) in the standing state as compared with that in the sitting state. Compared with that of the young group, the coupling strength of the elderly group was significantly decreased (p < 0.05) between the right PFC and left PFC in interval I and from PFC and OL to MC in interval II during the sitting state. The decreased EC in interval I was also positively correlated with cognitive scores in the elderly group. In addition, the coupling strength from MC to PFC in interval II during standing state was significantly increased in elderly subjects as compared with that in the young group. These results revealed the age-related changes in reorganization of interregional interactions for different postures. These findings may provide evidence of impaired cognitive function in the elderly and can deepen the understanding on age-related changes in neurovascular coupling.

A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data

Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillators, the dynamics of neural synchronization can be described theoretically using a phase oscillator model. We propose an estimation method to identify the phase oscillator model from real data of cross-frequency synchronized activities. The proposed method can estimate the coupling function governing the properties of synchronization. Furthermore, we examine the reliability of the proposed method using time-series data obtained from numerical simulation and an electronic circuit experiment, and show that our method can estimate the coupling function correctly. Finally, we estimate the coupling function between EEG oscillation and the speech sound envelope, and discuss the validity of these results.

In this paper, we propose an estimation method to identify a dynamical system from rhythmic time-series data. Rhythmic activities have been observed frequently and are synchronized in various fields, and synchronization is an important topic in nonlinear science. It is well known that such synchronization can be described theoretically by a phase oscillator model under the condition that the rhythmic activities can be considered weakly coupled limit-cycle oscillators. Based on this theory, we propose a method to identify the interaction between rhythmic activities as a network of phase oscillators. A practical advantage of the proposed method is that, without detailed modeling, we can extract the phase oscillator model directly from time-series data. For the above theoretical and practical reasons, this method can be applied to rhythmic data from a wide range of fields. In this study, we have focused on human brain activities in which electroencephalography (EEG) signals are often synchronized with each other and with external periodic stimuli. We demonstrate that the proposed method can successfully estimate the interaction between EEG activity and speech rhythm. Consequently, the proposed method can reveal the role of neural synchronization.

Neural Cross-Frequency Coupling Functions

Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics-strength and form-are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

EEG artifacts reduction by multivariate empirical mode decomposition and multiscale entropy for monitoring depth of anaesthesia during surgery

Electroencephalography (EEG) has been widely utilized to measure the depth of anaesthesia (DOA) during operation. However, the EEG signals are usually contaminated by artifacts which have a consequence on the measured DOA accuracy. In this study, an effective and useful filtering algorithm based on multivariate empirical mode decomposition and multiscale entropy (MSE) is proposed to measure DOA. Mean entropy of MSE is used as an index to find artifacts-free intrinsic mode functions. The effect of different levels of artifacts on the performances of the proposed filtering is analysed using simulated data. Furthermore, 21 patients' EEG signals are collected and analysed using sample entropy to calculate the complexity for monitoring DOA. The correlation coefficients of entropy and bispectral index (BIS) results show 0.14 ± 0.30 and 0.63 ± 0.09 before and after filtering, respectively. Artificial neural network (ANN) model is used for range mapping in order to correlate the measurements with BIS. The ANN method results show strong correlation coefficient (0.75 ± 0.08). The results in this paper verify that entropy values and BIS have a strong correlation for the purpose of DOA monitoring and the proposed filtering method can effectively filter artifacts from EEG signals. The proposed method performs better than the commonly used wavelet denoising method. This study provides a fully adaptive and automated filter for EEG to measure DOA more accuracy and thus reduce risk related to maintenance of anaesthetic agents.

Heterogeneity of time delays determines synchronization of coupled oscillators

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

Uncovering brain-heart information through advanced signal and image processing

Through their dynamical interplay, the brain and the heart ensure fundamental homeostasis and mediate a number of physiological functions as well as their disease-related aberrations. Although a vast number of ad hoc analytical and computational tools have been recently applied to the non-invasive characterization of brain and heart dynamic functioning, little attention has been devoted to combining information to unveil the interactions between these two physiological systems. This theme issue collects contributions from leading experts dealing with the development of advanced analytical and computational tools in the field of biomedical signal and image processing. It includes perspectives on recent advances in 7 T magnetic resonance imaging as well as electroencephalogram, electrocardiogram and cerebrovascular flow processing, with the specific aim of elucidating methods to uncover novel biological and physiological correlates of brain-heart physiology and physiopathology.