Coexistence of critical phenomena: the concept of manifold multi-spectral criticality.

Prompted by the ubiquity of empirical observations of critical phenomena, often in non-equilibrium macrostates, we developed a modelling approach in which several critical phenomena coexist. Instead of a single critical point, many coexisting critical points in the system are identified, forming a one-dimensional critical manifold. Identified within our game-of-life-like heterogeneous agent-based simulation model, where agents can be created and annihilated in the presence of a catalyst, each critical point belonging to the critical manifold is associated with a multi-spectrum of critical exponents. We find this situation in non-equilibrium mixed percolation-like macrostates obeying continuous phase transitions. These macrostates are quasi-stationary, where some system characteristics are time-independent while others are not. This novel look at universality signals the existance of complexity of critical phenomena richer than described to date.

Dynamic theta/beta ratio of clinical EEG in Alzheimer's disease.

BACKGROUND: EEG of a resting state in Alzheimer disease (AD) patients and healthy controls (HC) are analyzed to identify the characteristics of EEG in AD. NEW METHOD: A dynamic box plot approach to the theta/beta ratio with various window durations is proposed to analyze EEG. RESULTS: Spectral results during a resting state in AD patients demonstrate the effect of relatively greater power in the low-frequency bands (i.e. 'slowing down' of the EEG). A significant difference is observed in the dynamic distribution of the theta/beta ratio in the AD and HC groups, which is related to the effect of 'slowing down'. There is a more obvious visual separation between the theta/beta ratio results for the AD and HC groups with increasing window durations. Variability of the theta/beta ratio can be observed with shorter window durations with a dynamic functional box plot. This provides a better classification accuracy by using the dynamic theta/beta ratio as a sensor to discriminate AD EEG from HC EEG by using the receiver operating characteristics (ROC) curve and the area under curve (AUC) with various window durations. COMPARISON WITH EXISTING METHOD(S): EEG spectral analysis and theta/beta ratio used to evaluate EEG typically rely on long time averaging. CONCLUSIONS: The dynamic box plot approach to the theta/beta ratio with various window durations provides the possibility of observing features of the EEG. The dynamic theta/beta ratio is a better sensor to discriminate AD EEG from HC EEG. Moreover, the reliability and accuracy of results can be increased by combining spectral analysis and the dynamic box plot approach to theta/beta ratio with various window durations.

Towards a Universal Measure of Complexity.

Recently, it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity that is based on Gell-Mann's view of complexity. Our universal measure of complexity is based on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is the optimally mixed state consisting of pure states, i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), suitability to the analysis of system critical behaviour, and suitability to study the dynamic complexity.

C. elegans episodic swimming is driven by multifractal kinetics.

Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.

Multibranch multifractality and the phase transitions in time series of mean interevent times.

Empirical time series of interevent or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the nonmonotonic behavior of the generalized Hurst exponent h(q)-the fundamental exponent in the study of multifractals. The consequence of this behavior is the nonmonotonic behavior of the coarse Hölder exponent α(q) leading to multibranchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multibranched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multibranchedness is tantamount in significance to extending multifractal analysis.

Dynamical Landscape of Heart Rhythm in Long-Term Heart Transplant Recipients: A Way to Discern Erratic Rhythms.

It is commonly believed that higher values of heart rate variability (HRV) indices account for better organization of the network of feedback reflexes driving an organism's response to actual bodily needs. In order to evaluate this organization in heart transplant (HTX) recipients, 58 nocturnal Holter signals of 14 HTX patients were analyzed. Their dynamical properties were evaluated by short-term HRV indices and measures grounded on entropy. Estimates grouped according to the patients' clinical progress: free of complications versus with complications, and arranged in order of the length of time since the HTX, lead us to the conclusion that higher HRV is associated with a worse outcome for HTX patients. Moreover, short-term HRV indices that are constant, rather than increasing over time, serve well in the prognosis of the future state of a HTX patient. These findings suggest that increases observed in HRV indices are related to erratic rhythms resulting from remodeling of the cardiac tissue (including heterogeneous innervation) in long-term HTX patients. Therefore, we hypothesize that dynamical landscape markers (entropy and fragmentation measures together with the short-term HRV indices) can serve as a tool in the exploration of the genesis of (non-respiratory sinus) arrhythmia.

Semi-Automated Biomarker Discovery from Pharmacodynamic Effects on EEG in ADHD Rodent Models.

We propose a novel semi-automatic approach to design biomarkers for capturing pharmacodynamic effects induced by pharmacological agents on the spectral power of electroencephalography (EEG) recordings. We apply this methodology to investigate the pharmacodynamic effects of methylphenidate (MPH) and atomoxetine (ATX) on attention deficit/hyperactivity disorder (ADHD), using rodent models. We inject the two agents into the spontaneously hypertensive rat (SHR) model of ADHD, the Wistar-Kyoto rat (WKY), and the Wistar rat (WIS), and record their EEG patterns. To assess individual EEG patterns quantitatively, we use an integrated methodological approach, which consists of calculating the mean, slope and intercept parameters of temporal records of EEG spectral power using a smoothing filter, outlier truncation, and linear regression. We apply Fisher discriminant analysis (FDA) to identify dominant discriminants to be heuristically consolidated into several new composite biomarkers. Results of the analysis of variance (ANOVA) and t-test show benefits in pharmacodynamic parameters, especially the slope parameter. Composite biomarker evaluation confirms their validity for genetic model stratification and the effects of the pharmacological agents used. The methodology proposed is of generic use as an approach to investigating thoroughly the dynamics of the EEG spectral power.

Combining behavior and EEG analysis for exploration of dynamic effects of ADHD treatment in animal models.

BACKGROUND: We analyze the dynamics of rodent EEG amplitude in an experiment accompanied by video recordings. Brain activity of animals is commonly acquired together with a video of behavior, but recordings are rarely combined in analysis. The data acquired is most commonly analyzed separately. To our knowledge, no study has used behavior to improve the analysis of EEG waveforms, specifically for artifact removal - other than through manual editing. COMPARISON WITH EXISTING METHOD(S): We explore two approaches: a traditional approach that relies on data preprocessing and artifact rejection by an expert; and an alternative approach that combines analysis of EEG with behavior extracted from video recordings. NEW METHOD: We use the level of activity extracted from the behavioral video as a measure of confidence in the acquired EEG waveform, and as a weighting factor in averaging and statistical comparisons. RESULTS: We find in analysis of the EEG that the two approaches lead to similar conclusions, but the analysis leveraging behavioral data achieves this while avoiding many subjective choices often required for artifact rejection and data preprocessing. CONCLUSIONS: The methods we describe allow for the inclusion of all recorded data in the analysis, thereby making statistical tests more friendly to interpretation, and making the data processing transparent and reproducible.

Dynamical Pattern Representation of Cardiovascular Couplings Evoked by Head-up Tilt Test.

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties-in particular inter-system coupling-and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop.

Heart Rhythm Insights Into Structural Remodeling in Atrial Tissue: Timed Automata Approach.

The heart rhythm of a person following heart transplantation (HTX) is assumed to display an intrinsic cardiac rhythm because it is significantly less influenced by the autonomic nervous system-the main source of heart rate variability in healthy people. Therefore, such a rhythm provides evidence for arrhythmogenic processes developing, usually silently, in the cardiac tissue. A model is proposed to simulate alterations in the cardiac tissue and to observe the effects of these changes on the resulting heart rhythm. The hybrid automata framework used makes it possible to represent reliably and simulate efficiently both the electrophysiology of a cardiac cell and the tissue organization. The curve fitting method used in the design of the hybrid automaton cycle follows the well-recognized physiological phases of the atrial myocyte membrane excitation. Moreover, knowledge of the complex architecture of the right atrium, the ability of the almost free design of intercellular connections makes the automata approach the only one possible. Two particular aspects are investigated: impairment of the impulse transmission between cells and structural changes in intercellular connections. The first aspect models the observed fatigue of cells due to specific cardiac tissue diseases. The second aspect simulates the increase in collagen deposition with aging. Finally, heart rhythms arising from the model are validated with the sinus heart rhythms recorded in HTX patients. The modulation in the impairment of the impulse transmission between cells reveals qualitatively the abnormally high heart rate variability observed in patients living long after HTX.

Complexity of cardiovascular rhythms during head-up tilt test by entropy of patterns.

OBJECTIVE: The head-up tilt (HUT) test, which provokes transient dynamical alterations in the regulation of cardiovascular system, provides insights into complex organization of this system. Based on signals with heart period intervals (RR-intervals) and/or systolic blood pressure (SBP), differences in the cardiovascular regulation between vasovagal patients (VVS) and the healthy people group (CG) are investigated. APPROACH: Short-term relations among signal data represented symbolically by three-beat patterns allow to qualify and quantify the complexity of the cardiovascular regulation by Shannon entropy. Four types of patterns: permutation, ordinal, deterministic and dynamical, are used, and different resolutions of signal values in the the symbolization are applied in order to verify how entropy of patterns depends on a way in which values of signals are preprocessed. MAIN RESULTS: At rest, in the physiologically important signal resolution ranges, independently of the type of patterns used in estimates, the complexity of SBP signals in VVS is different from the complexity found in CG. Entropy of VVS is higher than CG what could be interpreted as substantial presence of noisy ingredients in SBP of VVS. After tilting this relation switches. Entropy of CG occurs significantly higher than VVS for SBP signals. In the case of RR-intervals and large resolutions, the complexity after the tilt becomes reduced when compared to the complexity of RR-intervals at rest for both groups. However, in the case of VVS patients this reduction is significantly stronger than in CG. SIGNIFICANCE: Our observations about opposite switches in entropy between CG and VVS might support a hypothesis that baroreflex in VVS affects stronger the heart rate because of the inefficient regulation (possibly impaired local vascular tone alternations) of the blood pressure.

Multistructure index characterization of heart rate and systolic blood pressure reveals precursory signs of syncope.

Recurrent syncope - abrupt loss of consciousness - can have a serious impact on patients' quality of life, comparable with chronic illnesses. Vasovagal syncope (VVS) is a specific reflex syncope, in which an inappropriate reaction of the autonomic nervous system (ANS) plays a key role in the pathophysiology. In syncope diagnosis, an ideal diagnostic method should positively identify vasovagal sensitive patients, without the need to perform a specialised head-up tilt table (HUTT) test. We apply a novel methodology of multistructure index (MI) statistics for seamlessly evaluating the size spectrum of the asymmetry properties of magnitudes of neural reflexes responsible for maintaining the homeostatic dynamics of autonomic control. Simultaneous evaluation using the MI of the effects on heart rate and blood pressure involved in achieving homeostasis of contrasting properties of the dynamics of slow and fast neural regulation reveals a clear distinction between vasovagal patients and healthy subjects, who are/are not susceptible to spontaneous fainting. Remarkably, a healthy cardiovascular response to the HUTT test is indeed evident prior to the test, making the MI a robust novel indicator, clearly distinguishing the cardiovascular autonomic regulation of healthy people from that of vasovagal patients without the need to perform an actual HUTT test.

Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization.

Beat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3) vector plots of gradients of the matrices A and T. Two indices are considered which summarize properties of A and T: the approximate deceleration capacity and the entropy rate. The method, applied to time series of nocturnal RR-intervals recorded from healthy subjects of different ages, reveals important aspect of changes in the autonomic activity caused by biological aging. Independent of the subject's age, following accelerations, a pendulum-like dynamics appears. With decelerations, this dynamics develops in line with the subject's age. This aging transition can be graphically visualized by vectors connecting the maxima of the transition probabilities of T, which, metaphorically, resemble a chronometer or the hands of a clock.

EEG epileptic seizures separation with multivariate empirical mode decomposition for diagnostic purposes.

We present a successful application of a soft computing approach based on the multivariate empirical mode decomposition (MEMD) method to EEG epileptic seizures separation. The results of the automatic multivatiate intrinsic mode functions (IMF) clustering allowed us to separate the seizure related spikes and sharp waves. The results of the proposed method have been compared with classical blind separation approach based on ICA, which failed to identify the non-linear and non-stationary signals related to the brain seizures. The proposed method supports epileptic seizure diagnostic methods.

The lack of long-range negative correlations in glucose dynamics is associated with worse glucose control in patients with diabetes mellitus.

Glucose dynamics measured in ambulatory settings are fluid in nature and exhibit substantial complexity. We recently showed that a long-range negative correlation of glucose dynamics, which is considered to reflect blood glucose controllability over a substantial period, is absent in patients with diabetes mellitus. This was demonstrated using detrended fluctuation analysis (DFA), a modified random-walk analysis method for the detection of long-range correlations. In the present study, we further assessed the relationships between the established clinical indices of glycemic or insulinogenic control of hemoglobin A(1c) (HbA(1c)), glycated albumin (GA), 1,5-anhydroglucitol, and urine C-peptide immunoreactivity and the recently proposed DFA-based indices obtained from continuous glucose monitoring in 104 Japanese diabetic patients. Significant correlations between the following parameters were observed: (1) HbA(1c) and the long-range scaling exponent α(2) (r = 0.236, P < .05), (2) GA and α(2) (r = 0.254, P < .05), (3) GA and the short-range scaling exponent α(1) (r = 0.233, P < .05), and (4) urine C-peptide immunoreactivity and the mean glucose fluctuations (r = -0.294, P < .01). Therefore, we concluded that increases in the long-range DFA scaling exponent, which are indicative of the lack of a long-range negative correlation in glucose dynamics, reflected abnormalities in average glycemic control as clinically determined using HbA(1c) and GA parameters.

Sleep-stage dynamics in patients with chronic fatigue syndrome with or without fibromyalgia.

STUDY OBJECTIVES: Chronic fatigue syndrome (CFS) and fibromyalgia (FM) are medically unexplained conditions that often have overlapping symptoms, including sleep-related complaints. However, differences between the 2 conditions have been reported, and we hypothesized that dynamic aspects of sleep would be different in the 2 groups of patients. PARTICIPANTS: Subjects were 26 healthy control subjects, 14 patients with CFS but without FM (CFS alone), and 12 patients with CFS and FM (CFS+FM)-all women. MEASUREMENTS AND RESULTS: We studied transition probabilities and rates between sleep stages (waking, rapid eye movement [REM] sleep, stage 1 [S1], stage 2 [S2], and slow-wave sleep [SWS]) and duration distributions of each sleep stage. We found that the probability of transition from REM sleep to waking was significantly greater in subjects with CFS alone than in control subjects, which may be the specific sleep problem for people with CFS alone. Probabilities of (a) transitions from waking, REM sleep, and S1 to S2 and (b) those from SWS to waking and S1 were significantly greater in subjects with CFS+FM than in control subjects; in addition, rates of these transitions were also significantly increased in subjects with CFS+FM. Result (a) might indicate increased sleep pressure in subjects with CFS+FM whereas result (b) may be the specific sleep problem of subjects with CFS+FM. We also found that shorter durations of S2 sleep are specific to patients with CFS+FM, not to CFS alone. CONCLUSIONS: These results suggest that CFS and FM may be different illnesses associated with different problems of sleep regulation.

NREM sleep stage transitions control ultradian REM sleep rhythm.

STUDY OBJECTIVES: The cyclic sequence of NREM and REM sleep, the so-called ultradian rhythm, is a highly characteristic feature of sleep. However, the mechanisms responsible for the ultradian REM sleep rhythm, particularly in humans, have not to date been fully elucidated. We hypothesize that a stage transition mechanism is involved in the determination of the ultradian REM sleep rhythm. PARTICIPANTS: Ten healthy young male volunteers (AGE: 22 ± 4 years, range 19-31 years) spent 3 nights in a sleep laboratory. The first was the adaptation night, and the second was the baseline night. On the third night, the subjects received risperidone (1 mg tablet), a central serotonergic and dopaminergic antagonist, 30 min before the polysomnography recording. MEASUREMENTS AND RESULTS: We measured and investigated transition probabilities between waking, REM, and NREM sleep stages (N1, N2, and N3) within the REM-onset intervals, defined as the intervals between the onset of one REM period and the beginning of the next, altered by risperidone. We also calculated the transition intensity (i.e., instantaneous transition rate) and examined the temporal pattern of transitions within the altered REM-onset intervals. We found that when the REM-onset interval was prolonged by risperidone, the probability of transitions from N2 to N3 was significantly increased within the same prolonged interval, with a significant delay and/or recurrences of the peak intensity of transitions from N2 to N3. CONCLUSIONS: These results suggest that the mechanism governing NREM sleep stage transitions (from light to deep sleep) plays an important role in determining ultradian REM sleep rhythms.

Increased non-gaussianity of heart rate variability predicts cardiac mortality after an acute myocardial infarction.

Non-Gaussianity index (λ) is a new index of heart rate variability (HRV) that characterizes increased probability of the large heart rate deviations from its trend. A previous study has reported that increased λ is an independent mortality predictor among patients with chronic heart failure. The present study examined predictive value of λ in patients after acute myocardial infarction (AMI). Among 670 post-AMI patients, we performed 24-h Holter monitoring to assess λ and other HRV predictors, including SD of normal-to-normal interval, very-low frequency power, scaling exponent α(1) of detrended fluctuation analysis, deceleration capacity, and heart rate turbulence (HRT). At baseline, λ was not correlated substantially with other HRV indices (|r| < 0.4 with either indices) and was decreased in patients taking ß-blockers (P = 0.04). During a median follow-up period of 25 months, 45 (6.7%) patients died (32 cardiac and 13 non-cardiac) and 39 recurrent non-fatal AMI occurred among survivors. While all of these HRV indices but λ were significant predictors of both cardiac and non-cardiac deaths, increased λ predicted exclusively cardiac death (RR [95% CI], 1.6 [1.3-2.0] per 1 SD increment, P < 0.0001). The predictive power of increased λ was significant even after adjustments for clinical risk factors, such as age, diabetes, left ventricular function, renal function, prior AMI, heart failure, and stroke, Killip class, and treatment ([95% CI], 1.4 [1.1-2.0] per 1 SD increment, P = 0.01). The prognostic power of increased λfor cardiac death was also independent of all other HRV indices and the combination of increased λ and abnormal HRT provided the best predictive model for cardiac death. Neither λ nor other HRV indices was an independent predictor of AMI recurrence. Among post-AMI patients, increased λ is associated exclusively with increased cardiac mortality risk and its predictive power is independent of clinical risk factors and of other HRV predictors.

Asymmetric intermittency observed in human heart rate dynamics.

To gain a deeper understanding of intermittent fluctuations observed in complex, real-world systems, we propose positive- or negative-directional non-Gaussian statistics. As a numerical example of asymmetric intermittent fluctuations, we heuristically introduce a random cascade-type model. Using our method, it is demonstrated that the asymmetric properties of heart rate variability depend on aging. This provides new insight into the physiological mechanism controlling heart rate dynamics in health and in autonomic disorder.

Sleep stage transitions in chronic fatigue syndrome patients with or without fibromyalgia.

Chronic fatigue syndrome (CFS) and fibromyalgia (FM) are medically unexplained conditions that share considerable overlapping symptoms, including sleep-related complaints. However, differences between the two conditions have been reported, and we hypothesized that dynamic aspects of sleep, recently attracting scientific interests, would be different in the two groups of patients. We thus study transition probabilities between sleep stages of CFS patients with or without FM. Subjects were 26 healthy controls, 14 CFS patients without FM (CFS alone) and 12 CFS patients with FM (CFS+FM) - all women. We studied transition probabilities between sleep stages (waking, REM sleep and Stage I, Stage II and slow-wave sleep (Stage III+IV)). We found that probabilities of transition from REM sleep to waking were significantly greater in CFS alone than in controls; we have reported previously this sleep disruption as the specific sleep problem for CFS alone [Kishi et al., 2008]. Probabilities of transitions from waking, REM sleep and Stage I to Stage II, and those from slow-wave sleep to Stage I, were significantly greater in CFS+FM than in controls; the former might indicate increased sleep pressure in CFS+FM and the latter may be the specific sleep problem of CFS+FM. These results suggest that CFS and FM are different illnesses associated with different problems of sleep regulation.