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The sleep spindle is a graphoelement of an electroencephalogram (EEG), which can be observed in light and deep sleep. Alterations in spindle activity have been described for a range of psychiatric disorders. Due to their relatively constant properties, sleep spindles may therefore be potential biomarkers in psychiatric diagnostics.This article presents an overview of the state of the science on the characteristics and functions of the sleep spindle as well as known alterations of spindle activity in psychiatric disorders. Various methodological approaches and developments of spindle detection are explained with respect to their potential for application in psychiatric diagnostics.Although alterations in spindle activity in psychiatric disorders are known and have been described in detail, their exact potential for psychiatric diagnostics has yet to be fully determined. In this respect, the acquisition of knowledge in research is currently constrained by manual and automated methods for spindle detection, which require high levels of resources and are error prone. Newer approaches to spindle detection based on deep-learning procedures could overcome the difficulties of previous detection methods, and thus open up new possibilities for the practical application of sleep spindles as biomarkers in the psychiatric practice.HINTERGRUND: Die Schlafspindel ist ein Graphoelement des Elektroenzephalogramms (EEG), das im Leicht- und Tiefschlaf beobachtet werden kann. Veränderungen der Spindelaktivität wurden für verschiedene psychiatrische Erkrankungen beschrieben. Schlafspindeln zeigen aufgrund ihrer relativ konstanten Eigenschaften Potenzial als Biomarker in der psychiatrischen Diagnostik.Dieser Beitrag liefert einen Überblick über den Stand der Wissenschaft zu Eigenschaften und Funktionen der Schlafspindeln sowie über beschriebene Veränderungen der Spindelaktivität bei psychiatrischen Erkrankungen. Verschiedene methodische Ansätze und Ausblicke zur Spindeldetektion werden hinsichtlich deren Anwendungspotenzial in der psychiatrischen Diagnostik erläutert.Während Veränderungen der Spindelaktivität bei psychiatrischen Erkrankungen beschrieben wurden, ist deren exaktes Potenzial für die psychiatrische Diagnostik noch nicht ausreichend erforscht. Diesbezüglicher Erkenntnisgewinn wird in der Forschung gegenwärtig durch ressourcenintensive und fehleranfällige Methoden zur manuellen oder automatisierten Spindeldetektion ausgebremst. Neuere Detektionsansätze, die auf Deep-Learning-Verfahren basieren, könnten die Schwierigkeiten bisheriger Detektionsmethoden überwinden und damit neue Möglichkeiten für die praktische Anwendung von Schlafspindeln als Biomarker in der psychiatrischen Praxis eröffnen.

Cellular plasticity at the structural level and sleep at the behavioural level are both essential for memory formation. The link between the two is not well understood. A functional connection between adult neurogenesis and hippocampus-dependent memory consolidation during NREM sleep has been hypothesized but not experimentally shown. Here, we present evidence that during a three-day learning session in the Morris water maze task a genetic knockout model of adult neurogenesis (Cyclin D2−/−) showed changes in sleep macro- and microstructure. Sleep EEG analyses revealed a lower total sleep time and NREM fraction in Cyclin D2−/− mice as well as an impairment of sleep specific neuronal oscillations that are associated with memory consolidation. Better performance in the memory task was associated with specific sleep parameters in wild-type, but not in Cyclin D2−/− mice. In wild-type animals the number of proliferating cells correlated with the amount of NREM sleep. The lack of adult neurogenesis led to changes in sleep architecture and oscillations that represent the dialog between hippocampus and neocortex during sleep. We suggest that adult neurogenesis—as a key event of hippocampal plasticity—might play an important role for sleep-dependent memory consolidation and modulates learning-induced changes of sleep macro- and microstructure.

Objective Bipolar disorder is a severe mental disorder for which currently no reliable biomarkers exist. It has been shown that patients with schizophrenia but not with unipolar depression have a reduced density of fast sleep spindles during N2 sleep. The aim of this study was to assess fast sleep spindle density in euthymic patients with bipolar disorder. Methods Patients with bipolar disorder (n = 24) and healthy control subjects (n = 25) were assessed using all-night polysomnography. Sleep spindles within stage N2 sleep were identified by visual inspection and subdivided into fast (>13 Hz) and slow (≤13 Hz) spindles. All spindles were subsequently characterised by density, frequency, amplitude, duration and coherence. Results Euthymic patients with bipolar disorder were found to have a reduced density and a lower mean frequency of fast spindles. Slow spindle density and frequency did not differ between groups. There were no differences regarding amplitude, duration or coherence. Conclusions A reduction in fast spindle density during N2 sleep points towards thalamic dysfunction as a potential neurobiological mechanism of relevance in bipolar disorder. In addition, a reduced sleep spindle density could be interpreted as a common endophenotype shared with schizophrenia but not unipolar depression and may - if replicated - be of utility in early recognition and risk stratification.

Inhibitory circuits of relaxation oscillators are often-used models for dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three generic oscillators (of a Fitzhugh-Nagumo type) as its nodes coupled reciprocally. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmicity of up to five simultaneously stable rhythms. With methods of bifurcation analysis and phase reduction, we investigate qualitative changes in stability of these circuit rhythms for a wide range of parameters. Furthermore, we quantify robustness of the rhythms maintained under random perturbations by monitoring phase diffusion in the circuit. Our findings allow us to describe how circuit dynamics relate to dynamics of individual nodes. We also find that quantitative and qualitative stability properties of polyrhythmicity do not always align.

Maintaining temporal coordination across physiological systems is crucial at the wake-sleep transition. As shown in recent studies, the degree of coordination between brain and autonomic arousal influences attention, which highlights a previously unrecognised point of potential failure in the attention system. To investigate how cortical and autonomic dynamics are linked to the attentive process we analysed electroencephalogram, electrocardiogram and skin conductance data of 39 healthy adults recorded during a 2-h resting-state oddball experiment. We related cross-correlations to fluctuation periods of cortical and autonomic signals and correlated obtained measures to event-related potentials N1 and P2, reflecting excitatory and inhibitory processes. Increasing alignment of cortical and autonomic signals and longer periods of vigilance fluctuations corresponded to a larger and earlier P2; no such relations were found for N1. We compared two groups, with (I) and without measurable (II) delay in cortico-autonomic correlations. Individuals in Group II had more stable vigilance fluctuations, larger and earlier P2 and fell asleep more frequently than individuals in Group I. Our results support the hypothesis of a link between cortico-autonomic coupling and dynamics and central inhibition. Quantifying this link could help refine classification in psychiatric disorders with attention and sleep-related symptoms, particularly in ADHD, depression, and insomnia.

Appearances of alpha waves in the sleep electrencephalogram indicate physiological, brief states of awakening that lie in between wakefulness and sleep. These microstates may also cause the loss in sleep quality experienced by individuals suffering from insomnia. To distinguish such pathological awakenings from physiological ones, differences in alpha-wave characteristics between transient awakening and wakefulness observed before the onset of sleep were studied. In polysomnographic datasets of sleep-healthy participants (n = 18) and patients with insomnia (n = 10), alpha waves were extracted from the relaxed, wake state before sleep onset, wake after sleep-onset periods and arousals of sleep. In these, alpha frequency and variability were determined as the median and standard deviation of inverse peak-to-peak intervals. Before sleep onset, patients with insomnia showed a decreased alpha variability compared with healthy participants (P

We present a method that facilitates a phase description of collective, irregular-oscillatory dynamics from unreliable multichannel recordings. The collective oscillations may be represented in each channel with fluctuating amplitude, phase offsets, and substantial amounts of measurement noise. Our method performs well under such realistic conditions, as we exemplify with collective brain rhythms in multichannel electroencephalogram recordings.

Background Simultaneous downregulation of the autonomic and central nervous system activity enables the gradual physiological state change from wakefulness to sleep onset. Dysregulation of central or autonomic arousal has been found in neurological ( Silvani et al., 2016 ) and psychiatric disorders ( Hegerl and Hensch, 2014 , Hegerl et al., 2012 , Schulz et al., 2016 , Schwabedal et al., 2016 ), often associated with dysregulated sleep-wake patterns. Aim We investigated the hypothesis that brain-autonomic co-regulation affects the attentive process in the transition from wakefulness to sleep onset. We propose that the degree to which autonomic and brain dynamics are correlated predicts the level of cortical excitability or inhibition and sleep onset behavior in this transition. To test our hypothesis, we explored electroencephalogram (EEG), electrocardiogram (ECG) and skin conductance data recorded during a 2-h resting state oddball experiment. Methods 39 healthy study participants underwent a 2-h resting EEG with eyes closed including ECG-derived heart rate (HR) and measurement of skin conductance level (SCL). The Vigilance Algorithm Leipzig (VIGALL 2.1) was used to assess brain arousal regulation based on automatic EEG-vigilance stage classification of 1-s EEG segments. These vigilance stages (=vigilance; V) were scored and cross-correlated with HR and SCL over a range of ±100 s, and a mean period of vigilance fluctuations was estimated from the frequency of maxima after low-pass filtering. Mean amplitudes of event-related potentials N100 and P200 to standard and deviant stimuli at Cz were calculated as indices of cortical excitability (N100) and cortical inhibition (P200) ( Cortoos et al., 2014 ). Results In all subjects, higher max cross-correlation coefficients (V-HR mean: r = 0.362, range: −0.069 to 0.762; SD = 0.192; V-SCL mean: r = 0.277, range: −0.299 to 0.629; SD = 0.211) were associated with longer mean periods of cortico-autonomic signals (V-HR: r = 0.462, p = .003; V-SCL: r = 0.516, p = .001). The cross-correlation of V with either HR and SCL partitioned the subjects into two groups (group no lag: n0 = 20, τ = 0; group lag: n1 = 19, τ (range) = −98 to −87) dependent on the time lag of maximal correlation. Subjects in n0, who fell asleep more often (indexed by the frequency of falling asleep: t37 = 2.49, p = .018) during the 2-h EEG compared to subjects in n1, had higher max cross-correlation coefficients (V-HR: t37 = 4.24, p = 1.43E−4; V-SCL: t37 = 5.02, p = 1.35E−5) and displayed an increased standard (t30.235 = 3.19, p = .003) and deviant P200 amplitude (t37 = 3.63, p = .001) compared to subjects in n1. No significant group differences were found for N100 amplitudes and KSS score either before or after the recording. Conclusion Healthy individuals with no time lag between cortical and autonomic signals showed a stronger brain-autonomic coupling and increased P200 amplitudes (indicating a higher level of cortical inhibition) compared to individuals with a temporal misalignment. This may explain differences in sleep-onset behavior between groups. Present results indicate possible diagnostic value in the assessment of brain-autonomic regulation, for example in disorders with sleep-related symptoms such as insomnia, dementia or depression.

Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincar\'e return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.

We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The approach allows to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill-defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine the isophases for experimentally observed irregular oscillations, providing a basis for a refined phase description of observed oscillatory dynamics., Comment: 4 pages

We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled of the amplitude dynamics, and provides a proper description of phase resetting of chaotic oscillations. The method is illustrated with the R\"ossler and Lorenz systems., Comment: 10 Pages, 14 Figures

An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations., This paper has been withdrawn by the author due to errors in Fig. 3 and faulty conclusions drawn from Fig. 4

Parametric phase diffusion analysis (ΦDA), a method to determine variability of irregular oscillations, is presented. ΦDA is formulated as an analysis technique for sequences of Poincare return times found in numerous applications. The method is unbiased by the arbitrary choice of Poincare section, i.e. isophase, which causes a spurious component in the Poincare return times. Other return-time variability measures can be biased drastically by these spurious return times, as shown for the Fano factor of chaotic oscillations in the Rossler system. The empirical use of ΦDA is demonstrated in an application to heart rate data from the Fantasia Database, for which ΦDA parameters successfully classify heart rate variability into groups of age and gender.

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.