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.

Aging affects the phase coherence between spontaneous oscillations in brain oxygenation and neural activity.

The risk of neurodegenerative disorders increases with age, due to reduced vascular nutrition and impaired neural function. However, the interactions between cardiovascular dynamics and neural activity, and how these interactions evolve in healthy aging, are not well understood. Here, the interactions are studied by assessment of the phase coherence between spontaneous oscillations in cerebral oxygenation measured by fNIRS, the electrical activity of the brain measured by EEG, and cardiovascular functions extracted from ECG and respiration effort, all simultaneously recorded. Signals measured at rest in 21 younger participants (31.1 ± 6.9 years) and 24 older participants (64.9 ± 6.9 years) were analysed by wavelet transform, wavelet phase coherence and ridge extraction for frequencies between 0.007 and 4 Hz. Coherence between the neural and oxygenation oscillations at ∼ 0.1 Hz is significantly reduced in the older adults in 46/176 fNIRS-EEG probe combinations. This reduction in coherence cannot be accounted for in terms of reduced power, thus indicating that neurovascular interactions change with age. The approach presented promises a noninvasive means of evaluating the efficiency of the neurovascular unit in aging and disease.

Multiscale Time-resolved Analysis Reveals Remaining Behavioral Rhythms in Mice Without Canonical Circadian Clocks.

Circadian rhythms are internal processes repeating approximately every 24 hours in living organisms. The dominant circadian pacemaker is synchronized to the environmental light-dark cycle. Other circadian pacemakers, which can have noncanonical circadian mechanisms, are revealed by arousing stimuli, such as scheduled feeding, palatable meals and running wheel access, or methamphetamine administration. Organisms also have ultradian rhythms, which have periods shorter than circadian rhythms. However, the biological mechanism, origin, and functional significance of ultradian rhythms are not well-elucidated. The dominant circadian rhythm often masks ultradian rhythms; therefore, we disabled the canonical circadian clock of mice by knocking out Per1/2/3 genes, where Per1 and Per2 are essential components of the mammalian light-sensitive circadian mechanism. Furthermore, we recorded wheel-running activity every minute under constant darkness for 272 days. We then investigated rhythmic components in the absence of external influences, applying unique multiscale time-resolved methods to analyze the oscillatory dynamics with time-varying frequencies. We found four rhythmic components with periods of ∼17 h, ∼8 h, ∼4 h, and ∼20 min. When the ∼17-h rhythm was prominent, the ∼8-h rhythm was of low amplitude. This phenomenon occurred periodically approximately every 2-3 weeks. We found that the ∼4-h and ∼20-min rhythms were harmonics of the ∼8-h rhythm. Coupling analysis of the ridge-extracted instantaneous frequencies revealed strong and stable phase coupling from the slower oscillations (∼17, ∼8, and ∼4 h) to the faster oscillations (∼20 min), and weak and less stable phase coupling in the reverse direction and between the slower oscillations. Together, this study elucidated the relationship between the oscillators in the absence of the canonical circadian clock, which is critical for understanding their functional significance. These studies are essential as disruption of circadian rhythms contributes to diseases, such as cancer and obesity, as well as mood disorders.

Beyond the Baroreflex: A New Measure of Autonomic Regulation Based on the Time-Frequency Assessment of Variability, Phase Coherence and Couplings.

For decades the role of autonomic regulation and the baroreflex in the generation of the respiratory sinus arrhythmia (RSA) - modulation of heart rate by the frequency of breathing - has been under dispute. We hypothesized that by using autonomic blockers we can reveal which oscillations and their interactions are suppressed, elucidating their involvement in RSA as well as in cardiovascular regulation more generally. R-R intervals, end tidal CO2, finger arterial pressure, and muscle sympathetic nerve activity (MSNA) were measured simultaneously in 7 subjects during saline, atropine and propranolol infusion. The measurements were repeated during spontaneous and fixed-frequency breathing, and apnea. The power spectra, phase coherence and couplings were calculated to characterise the variability and interactions within the cardiovascular system. Atropine reduced R-R interval variability (p < 0.05) in all three breathing conditions, reduced MSNA power during apnea and removed much of the significant coherence and couplings. Propranolol had smaller effect on the power of oscillations and did not change the number of significant interactions. Most notably, atropine reduced R-R interval power in the 0.145-0.6 Hz interval during apnea, which supports the hypothesis that the RSA is modulated by a mechanism other than the baroreflex. Atropine also reduced or made negative the phase shift between the systolic and diastolic pressure, indicating the cessation of baroreflex-dependent blood pressure variability. This result suggests that coherent respiratory oscillations in the blood pressure can be used for the non-invasive assessment of autonomic regulation.

Race-specific differences in the phase coherence between blood flow and oxygenation: A simultaneous NIRS, white light spectroscopy and LDF study.

Race-specific differences in the level of glycated hemoglobin are well known. However, these differences were detected by invasive measurement of mean oxygenation, and their understanding remains far from complete. Given that oxygen is delivered to the cells by hemoglobin through the cardiovascular system, a possible approach is to investigate the phase coherence between blood flow and oxygen transportation. Here we introduce a noninvasive optical method based on simultaneous recordings using NIRS, white light spectroscopy and LDF, combined with wavelet-based phase coherence analysis. Signals were recorded simultaneously for individuals in two groups of healthy subjects, 16 from Sub-Saharan Africa (BA group) and 16 Europeans (CA group). It was found that the power of myogenic oscillations in oxygenated and de-oxygenated hemoglobin is higher in the BA group, but that the phase coherence between blood flow and oxygen saturation, or blood flow and hemoglobin concentrations is higher in the CA group.

Relationship between cardiorespiratory phase coherence during hypoxia and genetic polymorphism in humans.

KEY POINTS: High altitude-induced hypoxia in humans evokes a pattern of breathing known as periodic breathing (PB), in which the regular oscillations corresponding to rhythmic expiration and inspiration are modulated by slow periodic oscillations. The phase coherence between instantaneous heart rate and respiration is shown to increase significantly at the frequency of periodic breathing during acute and sustained normobaric and hypobaric hypoxia. It is also shown that polymorphism in specific genes, NOTCH4 and CAT, is significantly correlated with this coherence, and thus with the incidence of PB. Differences in phase shifts between blood flow signals and respiratory and PB oscillations clearly demonstrate contrasting origins of the mechanisms underlying normal respiration and PB. These novel findings provide a better understanding of both the genetic and the physiological mechanisms responsible for respiratory control during hypoxia at altitude, by linking genetic factors with cardiovascular dynamics, as evaluated by phase coherence. ABSTRACT: Periodic breathing (PB) occurs in most humans at high altitudes and is characterised by low-frequency periodic alternation between hyperventilation and apnoea. In hypoxia-induced PB the dynamics and coherence between heart rate and respiration and their relationship to underlying genetic factors is still poorly understood. The aim of this study was to investigate, through novel usage of time-frequency analysis methods, the dynamics of hypoxia-induced PB in healthy individuals genotyped for a selection of antioxidative and neurodevelopmental genes. Breathing, ECG and microvascular blood flow were simultaneously monitored for 30 min in 22 healthy males. The same measurements were repeated under normoxic and hypoxic (normobaric (NH) and hypobaric (HH)) conditions, at real and simulated altitudes of up to 3800 m. Wavelet phase coherence and phase difference around the frequency of breathing (approximately 0.3 Hz) and around the frequency of PB (approximately 0.06 Hz) were evaluated. Subjects were genotyped for common functional polymorphisms in antioxidative and neurodevelopmental genes. During hypoxia, PB resulted in increased cardiorespiratory coherence at the PB frequency. This coherence was significantly higher in subjects with NOTCH4 polymorphism, and significantly lower in those with CAT polymorphism (HH only). Study of the phase shifts clearly indicates that the physiological mechanism of PB is different from that of the normal respiratory cycle. The results illustrate the power of time-evolving oscillatory analysis content in obtaining important insight into high altitude physiology. In particular, it provides further evidence for a genetic predisposition to PB and may partly explain the heterogeneity in the hypoxic response.

Modeling Cell Energy Metabolism as Weighted Networks of Non-autonomous Oscillators.

Networks of oscillating processes are a common occurrence in living systems. This is as true as anywhere in the energy metabolism of individual cells. Exchanges of molecules and common regulation operate throughout the metabolic processes of glycolysis and oxidative phosphorylation, making the consideration of each of these as a network a natural step. Oscillations are similarly ubiquitous within these processes, and the frequencies of these oscillations are never truly constant. These features make this system an ideal example with which to discuss an alternative approach to modeling living systems, which focuses on their thermodynamically open, oscillating, non-linear and non-autonomous nature. We implement this approach in developing a model of non-autonomous Kuramoto oscillators in two all-to-all weighted networks coupled to one another, and themselves driven by non-autonomous oscillators. Each component represents a metabolic process, the networks acting as the glycolytic and oxidative phosphorylative processes, and the drivers as glucose and oxygen supply. We analyse the effect of these features on the synchronization dynamics within the model, and present a comparison between this model, experimental data on the glycolysis of HeLa cells, and a comparatively mainstream model of this experiment. In the former, we find that the introduction of oscillator networks significantly increases the proportion of the model's parameter space that features some form of synchronization, indicating a greater ability of the processes to resist external perturbations, a crucial behavior in biological settings. For the latter, we analyse the oscillations of the experiment, finding a characteristic frequency of 0.01-0.02 Hz. We further demonstrate that an output of the model comparable to the measurements of the experiment oscillates in a manner similar to the measured data, achieving this with fewer parameters and greater flexibility than the comparable model.

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'.

On the suitability of laser-Doppler flowmetry for capturing microvascular blood flow dynamics from darkly pigmented skin.

OBJECTIVE: To assess the performance of laser Doppler flowmetry (LDF) in measuring blood perfusion from darkly-pigmented skin, i.e. skin with high melanin concentration. LDF provides for the noninvasive monitoring of microvascular blood flow dynamics. It has been used extensively on light-skinned subjects, i.e. on skin with low melanin concentration, in both the healthy and pathological states. Because the optical properties of human skin might affect the reliability of optically-based diagnostic equipment, the effectiveness of LDF needs to be checked and evaluated on dark skin, too, if this method is to be useful in global healthcare. APPROACH: Thirteen dark-skinned subjects and ten light-skinned subjects were included in the study. Microvascular blood flow dynamics was measured on both the right and left ankles using LDF with a laser diode of wavelength 780 nm. The characteristics of time-varying blood flow oscillations were investigated by wavelet analysis, nonlinear mode decomposition and wavelet phase coherence. An electrocardiogram (ECG), skin temperature, and respiratory effort were measured simultaneously with the LDF for each subject. MAIN RESULTS: No significant differences were observed between the groups in the mean blood perfusion (p  > 0.1), or wavelet power (p  > 0.6). The instantaneous heart rate (IHR), extracted from the LDF at each of the recording sites, and from the ECG, did not differ significantly between the groups (p  > 0.8). Nor did the wavelet power of the IHR differ (p  > 0.8) between the groups. The only significant difference found between the groups lay in left/right ankle blood flow coherence near the cardiac frequency, attributable to known ethnic physiological differences. SIGNIFICANCE: These results indicate that high melanin concentrations in skin exert no significant influence on the ability of LDF to monitor microvascular blood flow dynamics when using a laser diode of wavelength 780 nm. Hence LDF can help in the diagnosis and exploration of the pathogenesis of diseases such as diabetes, hypertension, or malaria in darkly pigmented patients across sub-Saharan Africa.

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.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation.

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Human subarachnoid space width oscillations in the resting state.

Abnormal cerebrospinal fluid (CSF) pulsatility has been implicated in patients suffering from various diseases, including multiple sclerosis and hypertension. CSF pulsatility results in subarachnoid space (SAS) width changes, which can be measured with near-infrared transillumination backscattering sounding (NIR-T/BSS). The aim of this study was to combine NIR-T/BSS and wavelet analysis methods to characterise the dynamics of the SAS width within a wide range of frequencies from 0.005 to 2 Hz, with low frequencies studied in detail for the first time. From recordings in the resting state, we also demonstrate the relationships between SAS width in both hemispheres of the brain, and investigate how the SAS width dynamics is related to the blood pressure (BP). These investigations also revealed influences of age and SAS correlation on the dynamics of SAS width and its similarity with the BP. Combination of NIR-T/BSS and time-frequency analysis may open up new frontiers in the understanding and diagnosis of various neurodegenerative and ageing related diseases to improve diagnostic procedures and patient prognosis.

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.

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.

Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states.

Altered cellular energy metabolism is a hallmark of many diseases, one notable example being cancer. Here, we focus on the identification of the transition from healthy to abnormal metabolic states. To do this, we study the dynamics of energy production in a cell. Due to the thermodynamic openness of a living cell, the inability to instantaneously match fluctuating supply and demand in energy metabolism results in nonautonomous time-varying oscillatory dynamics. However, such oscillatory dynamics is often neglected and treated as stochastic. Based on experimental evidence of metabolic oscillations, we show that changes in metabolic state can be described robustly by alterations in the chronotaxicity of the corresponding metabolic oscillations, i.e. the ability of an oscillator to resist external perturbations. We also present a method for the identification of chronotaxicity, applicable to general oscillatory signals and, importantly, apply this to real experimental data. Evidence of chronotaxicity was found in glycolytic oscillations in real yeast cells, verifying that chronotaxicity could be used to study transitions between metabolic states.

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

The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general.

Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.

The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.