Neural Cross-Frequency Coupling Functions

The phase coherence of the neurovascular unit is reduced in Huntington's disease

Huntington's disease is a neurodegenerative disorder in which neuronal death leads to chorea and cognitive decline. Individuals with ≥40 cytosine-adenine-guanine repeats on the interesting transcript 15 gene develop Huntington's disease due to a mutated huntingtin protein. While the associated structural and molecular changes are well characterized, the alterations in neurovascular function that lead to the symptoms are not yet fully understood. Recently, the neurovascular unit has gained attention as a key player in neurodegenerative diseases. The mutant huntingtin protein is known to be present in the major parts of the neurovascular unit in individuals with Huntington's disease. However, a non-invasive assessment of neurovascular unit function in Huntington's disease has not yet been performed. Here, we investigate neurovascular interactions in presymptomatic (N = 13) and symptomatic (N = 15) Huntington's disease participants compared to healthy controls (N = 36). To assess the dynamics of oxygen transport to the brain, functional near-infrared spectroscopy, ECG and respiration effort were recorded. Simultaneously, neuronal activity was assessed using EEG. The resultant time series were analysed using methods for discerning time-resolved multiscale dynamics, such as wavelet transform power and wavelet phase coherence. Neurovascular phase coherence in the interval around 0.1 Hz is significantly reduced in both Huntington's disease groups. The presymptomatic Huntington's disease group has a lower power of oxygenation oscillations compared to controls. The spatial coherence of the oxygenation oscillations is lower in the symptomatic Huntington's disease group compared to the controls. The EEG phase coherence, especially in the α band, is reduced in both Huntington's disease groups and, to a significantly greater extent, in the symptomatic group. Our results show a reduced efficiency of the neurovascular unit in Huntington's disease both in the presymptomatic and symptomatic stages of the disease. The vasculature is already significantly impaired in the presymptomatic stage of the disease, resulting in reduced cerebral blood flow control. The results indicate vascular remodelling, which is most likely a compensatory mechanism. In contrast, the declines in α and γ coherence indicate a gradual deterioration of neuronal activity. The results raise the question of whether functional changes in the vasculature precede the functional changes in neuronal activity, which requires further investigation. The observation of altered dynamics paves the way for a simple method to monitor the progression of Huntington's disease non-invasively and evaluate the efficacy of treatments.

Phase autoencoder for limit-cycle oscillators

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and the phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and the phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.

Blood pressure-cerebral oxygen coupling model: A new approach for stroke risk prediction

Stroke is a major cause of death and disability worldwide, but predicting its risk remains challenging. This study aimed to evaluate the cerebral blood flow autoregulation function of subjects with different stroke risk levels and predict their stroke risk. The coupling strength between cerebral oxygen and blood pressure signals was calculated by wavelet analysis and dynamic Bayesian inference and used as a quantitative index of cerebral blood flow autoregulation. A stroke prediction model based on the extreme random tree was constructed using the coupling strength and other data as input features. The results showed that the coupling strength was significantly higher in the high-risk group than the other groups. Moreover, the prediction model achieved an average accuracy of 0.80 across the three groups. The coupling strength of cerebral oxygen and blood pressure can be used as an objective index to predict stroke risk, which has implications for stroke prevention and intervention.

Functional connectivity between the amygdala and prefrontal cortex underlies processing of emotion ambiguity

Processing facial expressions of emotion draws on a distributed brain network. In particular, judging ambiguous facial emotions involves coordination between multiple brain areas. Here, we applied multimodal functional connectivity analysis to achieve network-level understanding of the neural mechanisms underlying perceptual ambiguity in facial expressions. We found directional effective connectivity between the amygdala, dorsomedial prefrontal cortex (dmPFC), and ventromedial PFC, supporting both bottom-up affective processes for ambiguity representation/perception and top-down cognitive processes for ambiguity resolution/decision. Direct recordings from the human neurosurgical patients showed that the responses of amygdala and dmPFC neurons were modulated by the level of emotion ambiguity, and amygdala neurons responded earlier than dmPFC neurons, reflecting the bottom-up process for ambiguity processing. We further found parietal-frontal coherence and delta-alpha cross-frequency coupling involved in encoding emotion ambiguity. We replicated the EEG coherence result using independent experiments and further showed modulation of the coherence. EEG source connectivity revealed that the dmPFC top-down regulated the activities in other brain regions. Lastly, we showed altered behavioral responses in neuropsychiatric patients who may have dysfunctions in amygdala-PFC functional connectivity. Together, using multimodal experimental and analytical approaches, we have delineated a neural network that underlies processing of emotion ambiguity.

Connectivity-based Meta-Bands: A new approach for automatic frequency band identification in connectivity analyses

The majority of electroencephalographic (EEG) and magnetoencephalographic (MEG) studies filter and analyse neural signals in specific frequency ranges, known as "canonical" frequency bands. However, this segmentation, is not exempt from limitations, mainly due to the lack of adaptation to the neural idiosyncrasies of each individual. In this study, we introduce a new data-driven method to automatically identify frequency ranges based on the topological similarity of the frequency-dependent functional neural network. The resting-state neural activity of 195 cognitively healthy subjects from three different databases (MEG: 123 subjects; EEG1: 27 subjects; EEG2: 45 subjects) was analysed. In a first step, MEG and EEG signals were filtered with a narrow-band filter bank (1 Hz bandwidth) from 1 to 70 Hz with a 0.5 Hz step. Next, the connectivity in each of these filtered signals was estimated using the orthogonalized version of the amplitude envelope correlation to obtain the frequency-dependent functional neural network. Finally, a community detection algorithm was used to identify communities in the frequency domain showing a similar network topology. We have called this approach the "Connectivity-based Meta-Bands" (CMB) algorithm. Additionally, two types of synthetic signals were used to configure the hyper-parameters of the CMB algorithm. We observed that the classical approaches to band segmentation are partially aligned with the underlying network topologies at group level for the MEG signals, but they are missing individual idiosyncrasies that may be biasing previous studies, as revealed by our methodology. On the other hand, the sensitivity of EEG signals to reflect this underlying frequency-dependent network structure is limited, revealing a simpler frequency parcellation, not aligned with that defined by the "canonical" frequency bands. To the best of our knowledge, this is the first study that proposes an unsupervised band segmentation method based on the topological similarity of functional neural network across frequencies. This methodology fully accounts for subject-specific patterns, providing more robust and personalized analyses, and paving the way for new studies focused on exploring the frequency-dependent structure of brain connectivity.

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.

Cross-frequency coupling between slow harmonics via the real brainstem oscillators: An in vivo animal study

Brain waves of discrete rhythms (gamma to delta frequency ranges) are ubiquitously recorded and interpreted with respect to probable corresponding specific functions. The most challenging idea of interpreting varied frequencies of brain waves has been postulated as a communication mechanism in which different neuronal assemblies use specific ranges of frequencies cooperatively. One promising candidate is cross-frequency coupling (CFC), in which some neuronal assemblies efficiently utilize the fastest gamma range brain waves as an information carrier (phase-amplitude CFC); however, phase-phase CFC via the slowest delta and theta waves has rarely been described to date. Moreover, CFC has rarely been reported in the animal brainstem including humans, which most likely utilizes the slowest waves (delta and theta ranges). Harmonic waves are characterized by the presence of a fundamental frequency with several overtones, multiples of the fundamental frequency. Rat brainstem waves seemed to consist of slow harmonics with different frequencies that could cooperatively produce a phase-phase CFC. Harmonic rhythms of different frequency ranges can cross-couple with each other to sustain robust and resilient consonance via real oscillators, notwithstanding any perturbations.

Functional connectivity between the amygdala and prefrontal cortex underlies processing of emotion ambiguity

Processing facial expressions of emotion draws on a distributed brain network. In particular, judging ambiguous facial emotions involves coordination between multiple brain areas. Here, we applied multimodal functional connectivity analysis to achieve network-level understanding of the neural mechanisms underlying perceptual ambiguity in facial expressions. We found directional effective connectivity between the amygdala, dorsomedial prefrontal cortex (dmPFC), and ventromedial PFC, supporting both bottom-up affective processes for ambiguity representation/perception and top-down cognitive processes for ambiguity resolution/decision. Direct recordings from the human neurosurgical patients showed that the responses of amygdala and dmPFC neurons were modulated by the level of emotion ambiguity, and amygdala neurons responded earlier than dmPFC neurons, reflecting the bottom-up process for ambiguity processing. We further found parietal-frontal coherence and delta-alpha cross-frequency coupling involved in encoding emotion ambiguity. We replicated the EEG coherence result using independent experiments and further showed modulation of the coherence. EEG source connectivity revealed that the dmPFC top-down regulated the activities in other brain regions. Lastly, we showed altered behavioral responses in neuropsychiatric patients who may have dysfunctions in amygdala-PFC functional connectivity. Together, using multimodal experimental and analytical approaches, we have delineated a neural network that underlies processing of emotion ambiguity.

Significance Statement

A large number of different brain regions participate in emotion processing. However, it remains elusive how these brain regions interact and coordinate with each other and collectively encode emotions, especially when the task requires orchestration between different brain areas. In this study, we employed multimodal approaches that well complemented each other to comprehensively study the neural mechanisms of emotion ambiguity. Our results provided a systematic understanding of the amygdala-PFC network underlying emotion ambiguity with fMRI-based connectivity, EEG coordination of cortical regions, synchronization of brain rhythms, directed information flow of the source signals, and latency of single-neuron responses. Our results further shed light on neuropsychiatric patients who have abnormal amygdala-PFC connectivity.

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.

A meta-analysis showing improved cognitive performance in healthy young adults with transcranial alternating current stimulation

Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation used for improving cognitive functions via delivering weak electrical stimulation with a certain frequency. This systematic review and meta-analysis investigated the effects of tACS protocols on cognitive functions in healthy young adults. We identified 56 qualified studies that compared cognitive functions between tACS and sham control groups, as indicated by cognitive performances and cognition-related reaction time. Moderator variable analyses specified effect size according to (a) timing of tACS, (b) frequency band of simulation, (c) targeted brain region, and (b) cognitive domain, respectively. Random-effects model meta-analysis revealed small positive effects of tACS protocols on cognitive performances. The moderator variable analyses found significant effects for online-tACS with theta frequency band, online-tACS with gamma frequency band, and offline-tACS with theta frequency band. Moreover, cognitive performances were improved in online- and offline-tACS with theta frequency band on either prefrontal and posterior parietal cortical regions, and further both online- and offline-tACS with theta frequency band enhanced executive function. Online-tACS with gamma frequency band on posterior parietal cortex was effective for improving cognitive performances, and the cognitive improvements appeared in executive function and perceptual-motor function. These findings suggested that tACS protocols with specific timing and frequency band may effectively improve cognitive performances.

Interacting Oscillators with Fluctuating Coupling: Mode Mixing without Cross-Correlations

Coupled oscillators are one of the basic models in nonlinear dynamics. Here, we study numerically and analytically the spectra of two harmonic oscillators with stochastically fluctuating coupling and driving forces reproducing a thermostat. We show that, even at small coupling, vanishing on average, the oscillation spectra exhibit mixing, even though no cross-correlations exists between the oscillators. Our results reveal a new mechanism of mode mixing for stochastically uncorrelated systems that is crucial for analysis of spectra in various systems, from simple liquids to living systems.

Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data

We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial regression and can be solved as a convex optimization problem. The validity of the proposed method is numerically illustrated by using two-dimensional limit-cycle oscillators as examples. As an application, we demonstrate data-driven fast entrainment with amplitude suppression using the optimal periodic input derived from the estimated phase and amplitude functions.

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.

Effective brain network analysis in unilateral and bilateral upper limb exercise training in subjects with stroke

PURPOSE

Knowing the patterns of brain activation that occur and networks involved under different interventions is important for motor recovery in subjects with stroke. This study aimed to study the patterns of brain activation and networks in two interventions, affected upper limb side and bilateral exercise training, using concurrent functional near-infrared spectroscopy (fNIRS) imaging.

METHODS

Thirty-two patients in the early subacute stage were randomly divided into two groups: unilateral and bilateral groups. The patients in the unilateral group underwent isokinetic muscle strength training on the affected upper limb side and patients in the bilateral group underwent bilateral upper limb training. Oxyhemoglobin and deoxyhemoglobin concentration changes (ΔHbO₂ and ΔHbR, respectively) were recorded in the ipsilateral and contralateral prefrontal cortex (IPFC and CPFC, respectively) and ipsilateral and contralateral motor cortex (IMC and CMC, respectively) by fNIRS equipment in the resting state and training conditions. The phase information of a 0.01-0.08 Hz fNIRS signal was extracted by the wavelet transform method. Dynamic Bayesian inference was adopted to calculate the coupling strength and direction of effective connectivity. The network threshold was determined by surrogate signal method, the global (weighted clustering coefficient, global efficiency and small-worldness) and local (degree, betweenness centrality and local efficiency) network metrics were calculated. The degree of cerebral lateralization was also compared between the two groups.

RESULTS

The results of covariance analysis showed that, compared with bilateral training, the coupling effect of CMC→IMC was significantly enhanced (p = 0.03); also, the local efficiency of the IMC (p = 0.01), IPFC (p<0.001), and CPFC (p = 0.006) and the hemispheric autonomy index of IPFC (p = 0.007) were significantly increased in unilateral training. In addition, there was a significant positive correlation between the coupling intensity of the inter-hemispheric motor area and the shifted local efficiency.

CONCLUSIONS

The results indicated that unilateral upper limb training could more effectively promote the interaction and balance of bilateral motor hemispheres and help brain reorganization in the IMC and prefrontal cortex in stroke patients. The method provided in this study could be used to evaluate dynamic brain activation and network reorganization under different interventions, thus improving the strategy of rehabilitation intervention in a timely manner and resulting in better motor recovery. This article is protected by copyright. All rights reserved.

Ensemble of coupling forms and networks among brain rhythms as function of states and cognition

The current paradigm in brain research focuses on individual brain rhythms, their spatiotemporal organization, and specific pairwise interactions in association with physiological states, cognitive functions, and pathological conditions. Here we propose a conceptually different approach to understanding physiologic function as emerging behavior from communications among distinct brain rhythms. We hypothesize that all brain rhythms coordinate as a network to generate states and facilitate functions. We analyze healthy subjects during rest, exercise, and cognitive tasks and show that synchronous modulation in the micro-architecture of brain rhythms mediates their cross-communications. We discover that brain rhythms interact through an ensemble of coupling forms, universally observed across cortical areas, uniquely defining each physiological state. We demonstrate that a dynamic network regulates the collective behavior of brain rhythms and that network topology and links strength hierarchically reorganize with transitions across states, indicating that brain-rhythm interactions play an essential role in generating physiological states and cognition.

A Peri-Ictal EEG-Based Biomarker for Sudden Unexpected Death in Epilepsy (SUDEP) Derived From Brain Network Analysis

Sudden unexpected death in epilepsy (SUDEP) is the leading seizure-related cause of death in epilepsy patients. There are no validated biomarkers of SUDEP risk. Here, we explored peri-ictal differences in topological brain network properties from scalp EEG recordings of SUDEP victims. Functional connectivity networks were constructed and examined as directed graphs derived from undirected delta and high frequency oscillation (HFO) EEG coherence networks in eight SUDEP and 14 non-SUDEP epileptic patients. These networks were proxies for information flow at different spatiotemporal scales, where low frequency oscillations coordinate large-scale activity driving local HFOs. The clustering coefficient and global efficiency of the network were higher in the SUDEP group pre-ictally, ictally and post-ictally (p < 0.0001 to p < 0.001), with features characteristic of small-world networks. These results suggest that cross-frequency functional connectivity network topology may be a non-invasive biomarker of SUDEP risk.

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.

Spatiotemporal dynamics of maximal and minimal EEG spectral power

Oscillatory neural activities are prevalent in the brain with their phase realignment contributing to the coordination of neural communication. Phase realignments may have especially strong (or weak) impact when neural activities are strongly synchronized (or desynchronized) within the interacting populations. We report that the spatiotemporal dynamics of strong regional synchronization measured as maximal EEG spectral power-referred to as activation-and strong regional desynchronization measured as minimal EEG spectral power-referred to as suppression-are characterized by the spatial segregation of small-scale and large-scale networks. Specifically, small-scale spectral-power activations and suppressions involving only 2-7% (1-4 of 60) of EEG scalp sites were prolonged (relative to stochastic dynamics) and consistently co-localized in a frequency specific manner. For example, the small-scale networks for θ, α, β1, and β2 bands (4-30 Hz) consistently included frontal sites when the eyes were closed, whereas the small-scale network for γ band (31-55 Hz) consistently clustered in medial-central-posterior sites whether the eyes were open or closed. Large-scale activations and suppressions involving over 17-30% (10-18 of 60) of EEG sites were also prolonged and generally clustered in regions complementary to where small-scale activations and suppressions clustered. In contrast, intermediate-scale activations and suppressions (involving 7-17% of EEG sites) tended to follow stochastic dynamics and were less consistently localized. These results suggest that strong synchronizations and desynchronizations tend to occur in small-scale and large-scale networks that are spatially segregated and frequency specific. These synchronization networks may broadly segregate the relatively independent and highly cooperative oscillatory processes while phase realignments fine-tune the network configurations based on behavioral demands.

Addressing indirect frequency coupling via partial generalized coherence

Distinguishing between direct and indirect frequency coupling is an important aspect of functional connectivity analyses because this distinction can determine if two brain regions are directly connected. Although partial coherence quantifies partial frequency coupling in the linear Gaussian case, we introduce a general framework that can address even the nonlinear and non-Gaussian case. Our technique, partial generalized coherence (PGC), expands prior work by allowing pairwise frequency coupling analyses to be conditioned on other processes, enabling model-free partial frequency coupling results. By taking advantage of recent advances in conditional mutual information estimation, we are able to implement our technique in a way that scales well with dimensionality, making it possible to condition on many processes and produce a partial frequency coupling graph. We analyzed both linear Gaussian and nonlinear simulated networks. We then performed PGC analysis of calcium recordings from mouse olfactory bulb glomeruli under anesthesia and quantified the dominant influence of breathing-related activity on the pairwise relationships between glomeruli for breathing-related frequencies. Overall, we introduce a technique capable of eliminating indirect frequency coupling in a model-free way, empowering future research to correct for potentially misleading frequency interactions in functional connectivity analyses.

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.

Cross-Frequency Power-Power Coupling Analysis: A Useful Cross-Frequency Measure to Classify ICA-Decomposed EEG

Magneto-/Electro-encephalography (M/EEG) commonly uses (fast) Fourier transformation to compute power spectral density (PSD). However, the resulting PSD plot lacks temporal information, making interpretation sometimes equivocal. For example, consider two different PSDs: a central parietal EEG PSD with twin peaks at 10 Hz and 20 Hz and a central parietal PSD with twin peaks at 10 Hz and 50 Hz. We can assume the first PSD shows a mu rhythm and the second harmonic; however, the latter PSD likely shows an alpha peak and an independent line noise. Without prior knowledge, however, the PSD alone cannot distinguish between the two cases. To address this limitation of PSD, we propose using cross-frequency power-power coupling (PPC) as a post-processing of independent component (IC) analysis (ICA) to distinguish brain components from muscle and environmental artifact sources. We conclude that post-ICA PPC analysis could serve as a new data-driven EEG classifier in M/EEG studies. For the reader's convenience, we offer a brief literature overview on the disparate use of PPC. The proposed cross-frequency power-power coupling analysis toolbox (PowPowCAT) is a free, open-source toolbox, which works as an EEGLAB extension.

Detecting Brain Tumor using Machines Learning Techniques Based on Different Features Extracting Strategies

BACKGROUND

Brain tumor is the leading cause of death worldwide. It is obvious that the chances of survival can be increased if the tumor is identified and properly classified at an initial stage. MRI (Magnetic Resonance Imaging) is one source of brain tumors detection tool and is extensively used in the diagnosis of brain to detect blood clots. In the past, many researchers developed Computer-Aided Diagnosis (CAD) systems that help the radiologist to detect the abnormalities in an efficient manner.

OBJECTIVE

The aim of this research is to improve the brain tumor detection performance by proposing a multimodal feature extracting strategy and employing machine learning techniques.

METHODS

In this study, we extracted multimodal features such as texture, morphological, entropybased, Scale Invariant Feature Transform (SIFT), and Elliptic Fourier Descriptors (EFDs) from brain tumor imaging database. The tumor was detected using robust machine learning techniques such as Support Vector Machine (SVM) with kernels: polynomial, Radial Base Function (RBF), Gaussian; Decision Tree (DT), and Naïve Bayes. Most commonly used Jack-knife 10-fold Cross- Validation (CV) was used for testing and validation of dataset.

RESULTS

The performance was evaluated in terms of specificity, sensitivity, Positive Predictive Value (PPV), Negative Predictive Value (NPV), False Positive Rate (FPR), Total Accuracy (TA), Area under the receiver operating Curve (AUC), and P-value. The highest performance of 100% in terms of Specificity, Sensitivity, PPV, NPV, TA, AUC using Naïve Bayes classifiers based on entropy, morphological, SIFT and texture features followed by Decision Tree classifier with texture features (TA=97.81%, AUC=1.0) and SVM polynomial kernel with texture features (TA=94.63%). The highest significant p-value was obtained using SVM polynomial with texture features (P-value 2.65e-104) followed by SVM RB with texture features (P-value 1.96e-98).

CONCLUSION

The results reveal that Naïve Bayes followed by Decision Tree gives highest detection accuracy based on entropy, morphological, SIFT and texture features.

EEG state-trajectory instability and speed reveal global rules of intrinsic spatiotemporal neural dynamics

Spatiotemporal dynamics of EEG/MEG (electro-/magneto-encephalogram) have typically been investigated by applying time-frequency decomposition and examining amplitude-amplitude, phase-phase, or phase-amplitude associations between combinations of frequency bands and scalp sites, primarily to identify neural correlates of behaviors and traits. Instead, we directly extracted global EEG spatiotemporal dynamics as trajectories of k-dimensional state vectors (k = the number of estimated current sources) to investigate potential global rules governing neural dynamics. We chose timescale-dependent measures of trajectory instability (approximately the 2^nd temporal derivative) and speed (approximately the 1^st temporal derivative) as state variables, that succinctly characterized trajectory forms. We compared trajectories across posterior, central, anterior, and lateral scalp regions as the current sources under those regions may serve distinct functions. We recorded EEG while participants rested with their eyes closed (likely engaged in spontaneous thoughts) to investigate intrinsic neural dynamics. Some potential global rules emerged. Time-averaged trajectory instability from all five regions tightly converged (with their variability minimized) at the level of generating nearly unconstrained but slightly conservative turns (~100° on average) on the timescale of ~25 ms, suggesting that spectral-amplitude profiles are globally adjusted to maintain this convergence. Further, within-frequency and cross-frequency phase relations appear to be independently coordinated to reduce average trajectory speed and increase the variability in trajectory speed and instability in a relatively timescale-invariant manner, and to make trajectories less oscillatory. Future research may investigate the functional relevance of these intrinsic global-dynamics rules by examining how they adjust to various sensory environments and task demands or remain invariant. The current results also provide macroscopic constraints for quantitative modeling of neural dynamics as the timescale dependencies of trajectory instability and speed are relatable to oscillatory dynamics.

Dynamic network interactions among distinct brain rhythms as a hallmark of physiologic state and function

Brain rhythms are associated with a range of physiologic states, and thus, studies have traditionally focused on neuronal origin, temporal dynamics and fundamental role of individual brain rhythms, and more recently on specific pair-wise interactions. Here, we aim to understand integrated physiologic function as an emergent phenomenon of dynamic network interactions among brain rhythms. We hypothesize that brain rhythms continuously coordinate their activations to facilitate physiologic states and functions. We analyze healthy subjects during sleep, and we demonstrate the presence of stable interaction patterns among brain rhythms. Probing transient modulations in brain wave activation, we discover three classes of interaction patterns that form an ensemble representative for each sleep stage, indicating an association of each state with a specific network of brain-rhythm communications. The observations are universal across subjects and identify networks of brain-rhythm interactions as a hallmark of physiologic state and function, providing new insights on neurophysiological regulation with broad clinical implications.

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.

Inferring the dynamics of rising radical right-wing party support using Gaussian processes

The use of classical regression techniques in social science can prevent the discovery of complex, nonlinear mechanisms and often relies too heavily on both the expertise and prior expectations of the data analyst. In this paper, we present a regression methodology that combines the interpretability of traditional, well used, statistical methods with the full predictability and flexibility of Bayesian statistics techniques. Our modelling approach allows us to find and explain the mechanisms behind the rise of Radical Right-wing Populist parties (RRPs) that we would have been unable to find using traditional methods. Using Swedish municipality-level data (2002-2018), we find no evidence that the proportion of foreign-born residents is predictive of increases in RRP support. Instead, education levels and population density are the significant variables that impact the change in support for the RRP, in addition to spatial and temporal control variables. We argue that our methodology, which produces models with considerably better fit of the complexity and nonlinearities often found in social systems, provides a better tool for hypothesis testing and exploration of theories about RRPs and other social movements. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

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'.

Multiscale entropy analysis to quantify the dynamics of motor movement signals with fist or feet movement using topographic maps

BACKGROUND

Brain neural activity is measured using electroencephalography (EEG) recording from the scalp. The EEG motor/imagery tasks help disabled people to communicate with the external environment.

OBJECTIVE

In this paper, robust multiscale sample entropy (MSE) and wavelet entropy measures are employed using topographic maps' analysis and tabulated form to quantify the dynamics of EEG motor movements tasks with actual and imagery opening and closing of fist or feet movements.

METHODS

To distinguish these conditions, we used the topographic maps which visually show the significance level of the brain regions and probes for dominant activities. The paired t-test and Posthoc Tukey test are used to find the significance levels.

RESULTS

The topographic maps results obtained using MSE reveal that maximum electrodes show the significance in frontpolar, frontal, and few frontal and parietal brain regions at temporal scales 3, 4, 6 and 7. Moreover, it was also observed that the distribution of significance is from frontoparietal brain regions. Using wavelet entropy, the significant results are obtained at frontpolar, frontal, and few electrodes in right hemisphere. The highest significance is obtained at frontpolar electrodes followed by frontal and few central and parietal electrodes.

Altered Causal Coupling Pathways within the Central-Autonomic-Network in Patients Suffering from Schizophrenia

The multivariate analysis of coupling pathways within physiological (sub)systems focusing on identifying healthy and diseased conditions. In this study, we investigated a part of the central-autonomic-network (CAN) in 17 patients suffering from schizophrenia (SZO) compared to 17 age–gender matched healthy controls (CON) applying linear and nonlinear causal coupling approaches (normalized short time partial directed coherence, multivariate transfer entropy). Therefore, from all subjects continuous heart rate (successive beat-to-beat intervals, BBI), synchronized maximum successive systolic blood pressure amplitudes (SYS), synchronized calibrated respiratory inductive plethysmography signal (respiratory frequency, RESP), and the power P_EEG of frontal EEG activity were investigated for 15 min under resting conditions. The CAN revealed a bidirectional coupling structure, with central driving towards blood pressure (SYS), and respiratory driving towards P_EEG. The central-cardiac, central-vascular, and central-respiratory couplings are more dominated by linear regulatory mechanisms than nonlinear ones. The CAN showed significantly weaker nonlinear central-cardiovascular and central-cardiorespiratory coupling pathways, and significantly stronger linear central influence on the vascular system, and on the other hand significantly stronger linear respiratory and cardiac influences on central activity in SZO compared to CON, and thus, providing better understanding of the interrelationship of central and autonomic regulatory mechanisms in schizophrenia might be useful as a biomarker of this disease.

Alterations in Maternal-Fetal Heart Rate Coupling Strength and Directions in Abnormal Fetuses

Because fetal gas exchange takes place via the maternal placenta, there has been growing interests in investigating the patterns and directions of maternal-fetal cardiac coupling to better understand the mechanisms of placental gas transfer. We recently reported the evidence of short-term maternal–fetal cardiac couplings in normal fetuses by using Normalized Short Time Partial Directed Coherence (NSTPDC) technique. Our results have shown weakening of coupling from fetal heart rate to maternal heart rate as the fetal development progresses while the influence from maternal to fetal heart rate coupling behaves oppositely as it shows increasing coupling strength that reaches its maximum at mid gestation. The aim of this study is to test if maternal-fetal coupling patterns change in various types of abnormal cases of pregnancies. We applied NSTPDC on simultaneously recorded fetal and maternal beat-by-beat heart rates collected from fetal and maternal ECG signals of 66 normal and 19 abnormal pregnancies. NSTPDC fetal-to-maternal coupling analyses revealed significant differences between the normal and abnormal cases (normal: normalized factor (NF) = −0.21 ± 0.85, fetus-to-mother coupling area (A_fBBI→ mBBI) = 0.44 ± 0.13, mother-to-fetus coupling area (A_mBBI→ fBBI) = 0.46 ± 0.12; abnormal: NF = −1.66 ± 0.77, A_fBBI→ mBBI = 0.08 ± 0.12, A_mBBI→ fBBI = 0.66 ± 0.24; p < 0.01). In conclusion, maternal-fetal cardiac coupling strength and direction and their associations with regulatory mechanisms (patterns) of developing autonomic nervous system function could be novel clinical markers of healthy prenatal development and its deviation. However, further research is required on larger samples of abnormal cases.

Dynamic causal modelling of fluctuating connectivity in resting-state EEG

Functional and effective connectivity are known to change systematically over time. These changes might be explained by several factors, including intrinsic fluctuations in activity-dependent neuronal coupling and contextual factors, like experimental condition and time. Furthermore, contextual effects may be subject-specific or conserved over subjects. To characterize fluctuations in effective connectivity, we used dynamic causal modelling (DCM) of cross spectral responses over 1- min of electroencephalogram (EEG) recordings during rest, divided into 1-sec windows. We focused on two intrinsic networks: the default mode and the saliency network. DCM was applied to estimate connectivity in each time-window for both networks. Fluctuations in DCM connectivity parameters were assessed using hierarchical parametric empirical Bayes (PEB). Within-subject, between-window effects were modelled with a second-level linear model with temporal basis functions as regressors. This procedure was conducted for every subject separately. Bayesian model reduction was then used to assess which (combination of) temporal basis functions best explain dynamic connectivity over windows. A third (between-subject) level model was used to infer which dynamic connectivity parameters are conserved over subjects. Our results indicate that connectivity fluctuations in the default mode network and to a lesser extent the saliency network comprised both subject-specific components and a common component. For both networks, connections to higher order regions appear to monotonically increase during the 1- min period. These results not only establish the predictive validity of dynamic connectivity estimates - in virtue of detecting systematic changes over subjects - they also suggest a network-specific dissociation in the relative contribution of fluctuations in connectivity that depend upon experimental context. We envisage these procedures could be useful for characterizing brain state transitions that may be explained by their cognitive or neuropathological underpinnings.

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.

Using Bayesian dynamical systems, model averaging and neural networks to determine interactions between socio-economic indicators

Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the 'best' explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the 'best' model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.

Functional integration across oscillation frequencies by cross-frequency phase synchronization

Neuronal oscillations and their inter-areal synchronization may be instrumental in regulating neuronal communication in distributed networks. Several lines of research have, however, shown that cognitive tasks engage neuronal oscillations simultaneously in multiple frequency bands that have distinct functional roles in cognitive processing. Gamma oscillations (30-120 Hz) are associated with bottom-up processing, while slower oscillations in delta (1-4 Hz), theta (4-7 Hz), alpha (8-14 Hz) and beta (14-30 Hz) frequency bands may have roles in executive or top-down controlling functions, although also other distinctions have been made. Identification of the mechanisms that integrate such spectrally distributed processing and govern neuronal communication among these networks is crucial for understanding how cognitive functions are achieved in neuronal circuits. Cross-frequency interactions among oscillations have been recognized as a likely candidate mechanism for such integration. We advance here the hypothesis that phase-phase synchronization of neuronal oscillations in two different frequency bands, cross-frequency phase synchrony (CFS), could serve to integrate, coordinate and regulate neuronal processing distributed into neuronal assemblies concurrently in multiple frequency bands. A trail of studies over the past decade has revealed the presence of CFS among cortical oscillations and linked CFS with roles in cognitive integration. We propose that CFS could connect fast and slow oscillatory networks and thereby integrate distributed cognitive functions such as representation of sensory information with attentional and executive functions.

Coherence and Coupling Functions Reveal Microvascular Impairment in Treated Hypertension

The complex interactions that give rise to heart rate variability (HRV) involve coupled physiological oscillators operating over a wide range of different frequencies and length-scales. Based on the premise that interactions are key to the functioning of complex systems, the time-dependent deterministic coupling parameters underlying cardiac, respiratory and vascular regulation have been investigated at both the central and microvascular levels. Hypertension was considered as an example of a globally altered state of the complex dynamics of the cardiovascular system. Its effects were established through analysis of simultaneous recordings of the electrocardiogram (ECG), respiratory effort, and microvascular blood flow [by laser Doppler flowmetry (LDF)]. The signals were analyzed by methods developed to capture time-dependent dynamics, including the wavelet transform, wavelet-based phase coherence, non-linear mode decomposition, and dynamical Bayesian inference, all of which can encompass the inherent frequency and coupling variability of living systems. Phases of oscillatory modes corresponding to the cardiac (around 1.0 Hz), respiratory (around 0.25 Hz), and vascular myogenic activities (around 0.1 Hz) were extracted and combined into two coupled networks describing the central and peripheral systems, respectively. The corresponding spectral powers and coupling functions were computed. The same measurements and analyses were performed for three groups of subjects: healthy young (Y group, 24.4 ± 3.4 y), healthy aged (A group, 71.1 ± 6.6 y), and aged treated hypertensive patients (ATH group, 70.3 ± 6.7 y). It was established that the degree of coherence between low-frequency oscillations near 0.1 Hz in blood flow and in HRV time series differs markedly between the groups, declining with age and nearly disappearing in treated hypertension. Comparing the two healthy groups it was found that the couplings to the cardiac rhythm from both respiration and vascular myogenic activity decrease significantly in aging. Comparing the data from A and ATH groups it was found that the coupling from the vascular myogenic activity is significantly weaker in treated hypertension subjects, implying that the mechanisms of microcirculation are not completely restored by current anti-hypertension medications.