A stochastic nonlinear autoregressive algorithm reflects nonlinear dynamics of heart-rate fluctuations

Characterization of Physiological Noise in Complex Cardiovascular Variability Series

The cardiovascular system can be analyzed using spectral, nonlinear, and complexity metrics. Nevertheless, dynamical noise may significantly impact these quantifiers. To our knowledge, there has been no attempt to quantify the intrinsic cardiovascular system noise driving heartbeat dynamics. To this end, this study presents a novel, model-free framework to define and quantify physiological noise using nonlinear Approximate Entropy profile. The framework was tested using analytical noisy series and then applied to real Heart Rate Variability (HRV) series gathered from a publicly-available dataset of recordings from 19 young and 19 elderly subjects watching the movie "Fantasia". Results suggest that physiological noise may account for over 15% of cardiovascular dynamics and is influenced by aging, with decreased cardiac noise in the elderly compared to the young subjects. Our findings indicate that physiological noise is a crucial factor in characterizing cardiovascular dynamics, and current spectral, nonlinear, and complexity assessments should take into account underlying dynamical noise estimates.

Automated Method for Discrimination of Arrhythmias Using Time, Frequency, and Nonlinear Features of Electrocardiogram Signals

We developed an automated approach to differentiate between different types of arrhythmic episodes in electrocardiogram (ECG) signals, because, in real-life scenarios, a software application does not know in advance the type of arrhythmia a patient experiences. Our approach has four main stages: (1) Classification of ventricular fibrillation (VF) versus non-VF segments—including atrial fibrillation (AF), ventricular tachycardia (VT), normal sinus rhythm (NSR), and sinus arrhythmias, such as bigeminy, trigeminy, quadrigeminy, couplet, triplet—using four image-based phase plot features, one frequency domain feature, and the Shannon entropy index. (2) Classification of AF versus non-AF segments. (3) Premature ventricular contraction (PVC) detection on every non-AF segment, using a time domain feature, a frequency domain feature, and two features that characterize the nonlinearity of the data. (4) Determination of the PVC patterns, if present, to categorize distinct types of sinus arrhythmias and NSR. We used the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database, Creighton University’s VT arrhythmia database, the MIT-BIH atrial fibrillation database, and the MIT-BIH malignant ventricular arrhythmia database to test our algorithm. Binary decision tree (BDT) and support vector machine (SVM) classifiers were used in both stage 1 and stage 3. We also compared our proposed algorithm’s performance to other published algorithms. Our VF detection algorithm was accurate, as in balanced datasets (and unbalanced, in parentheses) it provided an accuracy of 95.1% (97.1%), sensitivity of 94.5% (91.1%), and specificity of 94.2% (98.2%). The AF detection was accurate, as the sensitivity and specificity in balanced datasets (and unbalanced, in parentheses) were found to be 97.8% (98.6%) and 97.21% (97.1%), respectively. Our PVC detection algorithm was also robust, as the accuracy, sensitivity, and specificity were found to be 99% (98.1%), 98.0% (96.2%), and 98.4% (99.4%), respectively, for balanced and (unbalanced) datasets.

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardiorespiratory Nonstationary Dynamics

OBJECTIVE

Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions.

METHODS

We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance.

RESULTS AND CONCLUSION

Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling.

SIGNIFICANCE

This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).

Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson's Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.

Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics

KEY POINTS

Beat-to-beat alternation (alternans) of the cardiac action potential duration is known to precipitate life-threatening arrhythmias and can be driven by the kinetics of voltage-gated membrane currents or by instabilities in intracellular calcium fluxes. To prevent alternans and associated arrhythmias, suitable markers must be developed to quantify the susceptibility to alternans; previous theoretical studies showed that the eigenvalue of the alternating eigenmode represents an ideal marker of alternans. Using rabbit ventricular myocytes, we show that this eigenvalue can be estimated in practice by pacing these cells at intervals varying stochastically. We also show that stochastic pacing permits the estimation of further markers distinguishing between voltage-driven and calcium-driven alternans. Our study opens the perspective to use stochastic pacing during clinical investigations and in patients with implanted pacing devices to determine the susceptibility to, and the type of alternans, which are both important to guide preventive or therapeutic measures.

ABSTRACT

Alternans of the cardiac action potential (AP) duration (APD) is a well-known arrhythmogenic mechanism. APD depends on several preceding diastolic intervals (DIs) and APDs, which complicates the prediction of alternans. Previous theoretical studies pinpointed a marker called λalt that directly quantifies how an alternating perturbation persists over successive APs. When the propensity to alternans increases, λalt decreases from 0 to -1. Our aim was to quantify λalt experimentally using stochastic pacing and to examine whether stochastic pacing allows discriminating between voltage-driven and Ca(2+) -driven alternans. APs were recorded in rabbit ventricular myocytes paced at cycle lengths (CLs) decreasing progressively and incorporating stochastic variations. Fitting APD with a function of two previous APDs and CLs permitted us to estimate λalt along with additional markers characterizing whether the dependence of APD on previous DIs or CLs is strong (typical for voltage-driven alternans) or weak (Ca(2+) -driven alternans). During the recordings, λalt gradually decreased from around 0 towards -1. Intermittent alternans appeared when λalt reached -0.8 and was followed by sustained alternans. The additional markers detected that alternans was Ca(2+) driven in control experiments and voltage driven in the presence of ryanodine. This distinction could be made even before alternans was manifest (specificity/sensitivity >80% for -0.4 > λalt  > -0.5). These observations were confirmed in a mathematical model of a rabbit ventricular myocyte. In conclusion, stochastic pacing allows the practical estimation of λalt to reveal the onset of alternans and distinguishes between voltage-driven and Ca(2+) -driven mechanisms, which is important since these two mechanisms may precipitate arrhythmias in different manners.

Estimation of instantaneous complex dynamics through Lyapunov exponents: a study on heartbeat dynamics

Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations.

Monitoring heartbeat nonlinear dynamics during general anesthesia by using the instantaneous dominant Lyapunov exponent

We present a novel methodology for instantaneous estimation of quantitative correlates of depth of Anesthesia from noninvasive electrocardiographic recordings. The analysis is based on a point process model of heartbeat dynamics that allows for continuous tracking of linear and nonlinear HRV indices, including a novel instantaneous assessment of the Lyapunov Spectrum by using a cubic autoregressive formulation. The effective estimation of the model parameters is ensured by the Laguerre expansion of the Wiener-Volterra kernels along with the maximum local log-likelihood procedure. We apply the proposed assessment to experimental recordings from healthy subjects during propofol anesthesia. The new assessment reveals novel time-varying complex heartbeat dynamics that underlie the quasi-periodic heartbeat fluctuations elicited by the sympatho-vagal balance. Results suggest that such quantification provides important information which is independent from the standard autonomic assessment and significantly correlated with loss of consciousness. Further investigation will focus on evolving our mathematical approach towards a promising monitoring tool for an accurate, noninvasive assessment of general anesthesia.

Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models

We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

Instantaneous estimation of high-order nonlinear heartbeat dynamics by Lyapunov exponents

This paper introduces a novel methodology able to provide time varying estimates of the Lyapunov Spectrum within a point process framework. The algorithm is applied to ECG-derived data to characterize heartbeat nonlinear dynamics by using a cubic autoregressive point process model. Estimation of the model parameters is ensured by the Laguerre expansion of the Wiener-Volterra kernels along with a maximum local log-likelihood procedure. In addition to the instantaneous Lyapunov exponents, as well as indices related to higher order dynamic polyspectra, our method is also able to provide all the instantaneous time domain and frequency domain measures of instantaneous heart rate (HR) and heart rate variability (HRV) previously considered. Experimental results show that our method is able to track complex cardiovascular control dynamics during fast transitional gravitational changes.

Characterizing nonlinear heartbeat dynamics within a point process framework

Human heartbeat intervals are known to have nonlinear and nonstationary dynamics. In this paper, we propose a model of R-R interval dynamics based on a nonlinear Volterra-Wiener expansion within a point process framework. Inclusion of second-order nonlinearities into the heartbeat model allows us to estimate instantaneous heart rate (HR) and heart rate variability (HRV) indexes, as well as the dynamic bispectrum characterizing higher order statistics of the nonstationary non-gaussian time series. The proposed point process probability heartbeat interval model was tested with synthetic simulations and two experimental heartbeat interval datasets. Results show that our model is useful in characterizing and tracking the inherent nonlinearity of heartbeat dynamics. As a feature, the fine temporal resolution allows us to compute instantaneous nonlinearity indexes, thus sidestepping the uneven spacing problem. In comparison to other nonlinear modeling approaches, the point process probability model is useful in revealing nonlinear heartbeat dynamics at a fine timescale and with only short duration recordings.

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.

Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input

The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.