Predictability of normal heart rhythms and deterministic chaos

Skin Conductance-Based Acupoint and Non-Acupoint Recognition Using Machine Learning

Acupoints (APs) prove to have positive effects on disease diagnosis and treatment, while intelligent techniques for the automatic detection of APs are not yet mature, making them more dependent on manual positioning. In this paper, we realize the skin conductance-based APs and non-APs recognition with machine learning, which could assist in APs detection and localization in clinical practice. Firstly, we collect skin conductance of traditional Five-Shu Point and their corresponding non-APs with wearable sensors, establishing a dataset containing over 36000 samples of 12 different AP types. Then, electrical features are extracted from the time domain, frequency domain, and nonlinear perspective respectively, following which typical machine learning algorithms (SVM, RF, KNN, NB, and XGBoost) are demonstrated to recognize APs and non-APs. The results demonstrate XGBoost with the best precision of 66.38%. Moreover, we also quantify the impacts of the differences among AP types and individuals, and propose a pairwise feature generation method to weaken the impacts on recognition precision. By using generated pairwise features, the recognition precision could be improved by 7.17%. The research systematically realizes the automatic recognition of APs and non-APs, and is conducive to pushing forward the intelligent development of APs and Traditional Chinese Medicine theories.

Multifractal foundations of biomarker discovery for heart disease and stroke

Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the same individual to result in the minimum possible false-positive and false-negative rates. The application of standard cut-off points and risk scores across populations hinges upon the assumption of such generalizability. Such generalizability, in turn, hinges upon this condition that the phenomenon investigated by current statistical methods is ergodic, i.e., its statistical measures converge over individuals and time within the finite limit of observations. However, emerging evidence indicates that biological processes abound with nonergodicity, threatening this generalizability. Here, we present a solution for how to make generalizable inferences by deriving ergodic descriptions of nonergodic phenomena. For this aim, we proposed capturing the origin of ergodicity-breaking in many biological processes: cascade dynamics. To assess our hypotheses, we embraced the challenge of identifying reliable biomarkers for heart disease and stroke, which, despite being the leading cause of death worldwide and decades of research, lacks reliable biomarkers and risk stratification tools. We showed that raw R-R interval data and its common descriptors based on mean and variance are nonergodic and non-specific. On the other hand, the cascade-dynamical descriptors, the Hurst exponent encoding linear temporal correlations, and multifractal nonlinearity encoding nonlinear interactions across scales described the nonergodic heart rate variability more ergodically and were specific. This study inaugurates applying the critical concept of ergodicity in discovering and applying digital biomarkers of health and disease.

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor

We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss

We apply nonlinear forecasting to the time series of the flame front instability induced by radiative heat loss to test for the short-term predictability and long-term unpredictability characteristic of deterministic chaos in flame front instability. Our results indicate that the flame front instability represents high-dimensional chaos generated via the period-doubling cascade process reported in our previous study [H. Gotoda, K. Michigami, K. Ikeda, and T. Miyano, Combust Theory Modell. 14, 479 (2010)], while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method [H. Gotoda, H. Nikimoto, T. Miyano, and S. Tachibana, Chaos 20, 013124 (2011); G. Sugihara and R. M. May, Nature 344, 734 (1990)] as well as a generalized radial basis function network as a global nonlinear predictor. The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems.

Multifractality and heart rate variability

In this paper, we participate to the discussion set forth by the editor of Chaos for the controversy, "Is the normal heart rate chaotic?" Our objective was to debate the question, "Is there some more appropriate term to characterize the heart rate variability (HRV) fluctuations?" We focused on the approximately 24 h RR series prepared for this topic and tried to verify with two different techniques, generalized structure functions and wavelet transform modulus maxima, if they might be described as being multifractal. For normal and congestive heart failure subjects, the h(q) exponents showed to be decreasing for increasing q with both methods, as it should be for multifractal signals. We then built 40 surrogate series to further verify such hypothesis. For most of the series (approximately 75%-80% of cases) multifractality stood the test of the surrogate data employed. On the other hand, series coming from patients in atrial fibrillation showed a small, if any, degree of multifractality. The population analyzed is too small for definite conclusions, but the study supports the use of multifractal series to model HRV. Also it suggests that the regulatory action of autonomous nervous system might play a role in the observed multifractality.

Introduction to controversial topics in nonlinear science: is the normal heart rate chaotic?

In June 2008, the editors of Chaos decided to institute a new section to appear from time to time that addresses timely and controversial topics related to nonlinear science. The first of these deals with the dynamical characterization of human heart rate variability. We asked authors to respond to the following questions: Is the normal heart rate chaotic? If the normal heart rate is not chaotic, is there some more appropriate term to characterize the fluctuations (e.g., scaling, fractal, multifractal)? How does the analysis of heart rate variability elucidate the underlying mechanisms controlling the heart rate? Do any analyses of heart rate variability provide clinical information that can be useful in medical assessment (e.g., in helping to assess the risk of sudden cardiac death)? If so, please indicate what additional clinical studies would be useful for measures of heart rate variability to be more broadly accepted by the medical community. In addition, as a challenge for analysis methods, PhysioNet [A. L. Goldberger et al., "PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals," Circulation 101, e215-e220 (2000)] provided data sets from 15 patients of whom five were normal, five had heart failure, and five had atrial fibrillation (http://www.physionet.org/challenge/chaos/). This introductory essay summarizes the main issues and introduces the essays that respond to these questions.

Normal heartbeat series are nonchaotic, nonlinear, and multifractal: new evidence from semiparametric and parametric tests

We present new evidence that normal heartbeat series are nonchaotic, nonlinear, and multifractal. In addition to considering the largest Lyapunov exponent and the correlation dimension, the results of the parametric and semiparametric estimation of the long memory parameter (long-range dependence) unambiguously reveal that the underlying process is nonstationary, multifractal, and has strong nonlinearity.

Stratification pattern of static and scale-invariant dynamic measures of heartbeat fluctuations across sleep stages in young and elderly

Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk.

Conceptualizing compensatory responses: implications for treatment and research

Many scientists approach the discovery and application of knowledge of physiological processes from a reductionistic paradigm. A reductionistic approach focuses on treating one or a few key disease-related variables but overlooks the interaction of systems and their dependency on one another to produce homeostasis. The purposes of this article are to examine the current paradigm underlying treatment and its effect on patient outcome and to present an alternative perspective for understanding the body's compensatory responses and their implications for treatment and research. Chaos theory and nonlinear methods are presented as possible ways to conceptualize and explore the complex integration of physiological patterns in response to disease, aging, and treatment.

Long-term invariant parameters obtained from 24-h Holter recordings: a comparison between different analysis techniques

Over the last two decades, a large number of different methods had been used to study the fractal-like behavior of the heart rate variability (HRV). In this paper some of the most used techniques were reviewed. In particular, the focus is set on those methods which characterize the long memory behavior of time series (in particular, periodogram, detrended fluctuation analysis, rescale range analysis, scaled window variance, Higuchi dimension, wavelet-transform modulus maxima, and generalized structure functions). The performances of the different techniques were tested on simulated self-similar noises (fBm and fGn) for values of alpha, the slope of the spectral density for very small frequency, ranging from -1 to 3 with a 0.05 step. The check was performed using the scaling relationships between the various indices. DFA and periodogram showed the smallest mean square error from the expected values in the range of interest for HRV. Building on the results obtained from these tests, the effective ability of the different methods in discriminating different populations of patients from RR series derived from Holter recordings, was assessed. To this extent, the Noltisalis database was used. It consists of a set of 30, 24-h Holter recordings collected from healthy subjects, patients suffering from congestive heart failure, and heart transplanted patients. All the methods, with the exception at most of rescale range analysis, were almost equivalent in distinguish between the three groups of patients. Finally, the scaling relationships, valid for fBm and fGn, when empirically used on HRV series, also approximately held.

Fractal rigidity by enhanced sympatho-vagal antagonism in heartbeat interval dynamics elicited by central application of corticotropin-releasing factor in mice

The dynamics of heartbeat interval fluctuations were studied in awake unrestrained mice following intracerebroventricular application of the neuropeptide corticotropin-releasing factor (CRF). The cardiac time series derived from telemetric ECG monitoring were analyzed by non-parametric techniques of nonlinear signal processing: delay-vector variance (DVV) analysis, higher-order variability (HOV) analysis, empirical mode decomposition (EMD), multiscale embedding-space decomposition (MESD), multiexponent multifractal (MEMF) analysis. The analyses support the conjecture that cardiac dynamics of normal control mice has both deterministic and stochastic elements, is nonstationary, nonlinear, and exerts multifractal properties. Central application of CRF results in bradycardia and increased variability of the beat-to-beat fluctuations. The altered dynamical properties elicited by CRF reflect a significant loss of intrinsic structural complexity of cardiac control which is due to central neuroautonomic hyperexcitation, i.e., enhanced sympatho-vagal antagonism. The change in dynamical complexity is characterized by an effect referred to as fractal rigidity, leading to a significant impairment of adaptability to extrinsic challenges in a fluctuating environment. The impact of dynamical neurocardiopathy as a major precipiting factor for the propensity of cardiac arrhythmias or sudden cardiac death by unchecked central CRF release in significant acute life events in man is critically discussed.

Poincaré plot indexes of heart rate variability capture dynamic adaptations after haemodialysis in chronic renal failure patients

The hypothesis that the Poincaré plot indexes of heart rate variability (HRV) detect dynamic changes after haemodialysis (HD) over the HRV in haemodynamically stable chronic renal failure (CRF) patients was examined. Minor axis (SD1), major axis (SD2) and the SD1/SD2 ratio were compared against standard HRV indexes in time and frequency domain, in a group of healthy subjects and in a group of CRF patients before and after HD. These indexes were estimated from Poincaré plots reconstructed with lags of one, two and four heartbeats. The surrogate data analysis technique was applied in order to discern if only random components or linear features of HRV contribute to its dynamics. None of the standard linear HRV indexes changed after HD. The Poincaré plot indexes measured from CRF patients were smaller than the ones measured from healthy subjects. In CRF patients the SD1/SD2 ratio decreased after HD, when a lag of four heartbeats was used (0.68 +/- 0.19 before HD versus 0.55 +/- 0.12 after HD, P<0.05). The presence of deterministic components in HRV were confirmed for all measures of the SD1/SD2 ratio. Moreover, a loss of non-linear components after HD was detected by the surrogate analysis over the SD1/SD2 ratio with a lag of four heartbeats. In conclusion, the SD1/SD2 ratio measured at lag of 4 heartbeats capture dynamic changes after HD upon the HRV of CRF patients that are not solely related to linear autocorrelations of HRV. This suggests that the SD1/SD2 ratio reflects non-linear information of HRV.

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.

Effect of prolonged head-down bed rest on complex cardiovascular dynamics

We postulated that a change in complex dynamics of the cardiovascular system could be involved in the orthostatic intolerance observed after simulated weightlessness. Supine recordings of 1024 consecutive pulse intervals and systolic blood pressures were obtained on 7 subjects adapted to a 42 day head-down bed rest (day 22 and 42) but also before and 6 days after head-down bed rest (-6 degrees). Coarse graining spectral analysis was used to extract the non-harmonic (fractal) component from each time series. The power spectral densities of this fractal component are inversely proportional to their frequency (1/f beta). We fitted an inverse power law estimate to the fractal component to determine the spectral exponent beta. The complex dynamics of blood pressure and heart rate variability were also analyzed by correlation dimension and non-linear prediction. Bed rest induced orthostatic intolerance in 4 subjects. There was a significant increase in the spectral exponent beta of RR-interval variability during and after head-down bed rest (before: 1.039 +/- 0.090; during: 1.552 +/- 0.080 and 1.547 +/- 0.100; after: 1.428 +/- 0.040). Analysis of the blood pressure dynamics indicated lower correlation dimensions during head-down bed rest and higher coefficients of predictability after head-down bed rest. Complexity alterations of RR-interval and blood pressure variability were not linked with one another during head-down bed rest. These alterations seemed to be correlated with the orthostatic intolerance observed after bed rest. These results suggest a change of the integration level of cardiovascular autonomic regulation.

Multifractality in human heartbeat dynamics

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis

The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D(2) or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D(2) and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics. (c) 1998 American Institute of Physics.

Self-organized segmentation of time series: separating growth hormone secretion in acromegaly from normal controls

The pulsatile pattern of growth hormone (GH) secretion was assessed by sampling blood every 10 min over 24 h in healthy subjects (n = 10) under normal food intake and under fasting conditions (n = 6) and in patients with a GH-producing tumor (acromegaly, n = 6), before and after treatment with the somatostatin analog octreotide. Using autocorrelation, we found no consistent separation in the temporal dynamics of GH secretion in healthy controls and acromegalic patients. Time series prediction based on a single neural network has recently been demonstrated to separate the secretory dynamics of parathyroid hormone in healthy controls from osteoporotic patients. To better distinguish the differences in GH dynamics in healthy subjects and patients, we tested time series predictions based on a single neural network and a more refined system of multiple neural networks acting in parallel (adaptive mixtures of local experts). Both approaches significantly separated GH dynamics under the various conditions. By performing a self-organized segmentation of the alternating phases of secretory bursts and quiescence of GH, we significantly improved the performance of the multiple network system over that of the single network. It thus may represent a potential tool for characterizing alterations of the dynamic regulation associated with diseased states.

Left-insular cortex lesions perturb cardiac autonomic tone in humans

The insular cortex is involved in cardiac regulation. The left insula is predominantly responsible for parasympathetic cardiovascular effects. Damage to this area could shift cardiovascular balance towards increased basal sympathetic tone (a pro-arrhythmic condition) and contribute to the excess cardiac mortality following stroke. Acute left insular stroke increased basal cardiac sympathetic tone and was associated with a decrease in randomness of heart rate variability. In addition, phase relationships between heart rate and blood pressure were disturbed, implying a disruption of oscillators involved in cardiovascular control. The insula appears to be involved in human heart rate regulation and damage to it may encourage a pro-arrhythmic state.

Nonlinear control of heart rate variability in human infants

Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation greater than or equal to 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation > or = to 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A.L., Rigney, D.R. & West, B.J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.

Nonlinear noise reduction for electrocardiograms

The electrical activity of the heart usually shows dynamical behavior which is neither periodic nor deterministically chaotic: The interbeat intervals seem to contain a random component. Although long term predictions are thus impossible, good predictions can be made for times smaller than one heart cycle. This fact is used in order to suppress measurement errors by a local geometric projection method which was originally developed for chaotic signals. The result constitutes evidence that techniques of time series analysis based on chaos theory can be useful despite the fact that very few natural phenomena have been actually established to be deterministically chaotic. (c) 1996 American Institute of Physics.

Nonlinear analysis of epicardial atrial electrograms of electrically induced atrial fibrillation in man

INTRODUCTION

We applied methods from the theory of nonlinear dynamics to characterize unipolar epicardial right atrial electrograms of electrically induced atrial fibrillation (AF) in man.

METHODS AND RESULTS

Electrograms were selected from a high-density mapping study, which confirmed the existence of at least 3 different types of induced AF (types I, II, and III) in patients undergoing open chest surgery. We analyzed sets of 5 electrograms (4 sec, sampling frequency 1 kHz, resolution 8 bits) in 9 patients (AF type I, n = 3; type II, n = 3; type III, n = 3). The Grassberger-Procaccia method was applied to estimate the correlation dimension and correlation entropy from the electrograms. In 2 patients (AF type I) some electrograms (2 of 5 and 3 of 5, respectively) showed scaling at normalized distances ranging from 0.2 to 0.5 in phase space. Correlation dimension D ranged from 1.8 to 3.2 and correlation entropy K from 2.2 to 3.8 nats/sec. The patients were ranked according to increasing coarse-grained correlation dimension Dcg (range 3.7 to 7.9) and coarse-grained correlation entropy Kcg (range 5.6 to 18.6 nats/sec). The method of surrogate data was applied to detect nonlinearity in the electrograms. Using the correlation integral as test statistic, it could be excluded that electrograms of type I AF have been generated by linear stochastic dynamics. Episodes of sinus rhythm (D ranging from 1.0 to 5.1 and K from 2.0 to 8.6 nats/sec) and induced atrial flutter (D ranging from 2.7 to 4.2 and K from 2.2 to 4.2 nats/sec) in 2 different patients showed features of low-dimensional chaos.

CONCLUSION

Nonlinear analysis discriminated between electrograms during electrically induced AF in humans. The results are consistent with a classification of AF into 3 types based on the spatiotemporal complexity of right atrial activation patterns.