Inhomogeneous point-process entropy: an instantaneous measure of complexity in discrete systems

Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties

Inhomogeneous Point-Processes to Instantaneously Assess Affective Haptic Perception through Heartbeat Dynamics Information

This study proposes the application of a comprehensive signal processing framework, based on inhomogeneous point-process models of heartbeat dynamics, to instantaneously assess affective haptic perception using electrocardiogram-derived information exclusively. The framework relies on inverse-Gaussian point-processes with Laguerre expansion of the nonlinear Wiener-Volterra kernels, accounting for the long-term information given by the past heartbeat events. Up to cubic-order nonlinearities allow for an instantaneous estimation of the dynamic spectrum and bispectrum of the considered cardiovascular dynamics, as well as for instantaneous measures of complexity, through Lyapunov exponents and entropy. Short-term caress-like stimuli were administered for 4.3?25?seconds on the forearms of 32 healthy volunteers (16 females) through a wearable haptic device, by selectively superimposing two levels of force, 2?N and 6?N, and two levels of velocity, 9.4?mm/s and 65?mm/s. Results demonstrated that our instantaneous linear and nonlinear features were able to finely characterize the affective haptic perception, with a recognition accuracy of 69.79% along the force dimension, and 81.25% along the velocity dimension

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

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health

Assessment of spontaneous cardiovascular oscillations in Parkinson's disease

Parkinson's disease (PD) has been reported to involve postganglionic sympathetic failure and a wide spectrum of autonomic dysfunctions including cardiovascular, sexual, bladder, gastrointestinal and sudo-motor abnormalities. While these symptoms may have a significant impact on daily activities, as well as quality of life, the evaluation of autonomic nervous system (ANS) dysfunctions relies on a large and expensive battery of autonomic tests only accessible in highly specialized laboratories. In this paper we aim to devise a comprehensive computational assessment of disease-related heartbeat dynamics based on instantaneous, time-varying estimates of spontaneous (resting state) cardiovascular oscillations in PD. To this end, we combine standard ANS-related heart rate variability (HRV) metrics with measures of instantaneous complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra). Such measures are computed over 600-s recordings acquired at rest in 29 healthy subjects and 30 PD patients. The only significant group-wise differences were found in the variability of the dominant Lyapunov exponent. Also, the best PD vs. healthy controls classification performance (balanced accuracy: 73.47%) was achieved only when retaining the time-varying, non-stationary structure of the dynamical features, whereas classification performance dropped significantly (balanced accuracy: 61.91%) when excluding variability-related features. Additionally, both linear and nonlinear model features correlated with both clinical and neuropsychological assessments of the considered patient population. Our results demonstrate the added value and potential of instantaneous measures of heartbeat dynamics and its variability in characterizing PD-related disabilities in motor and cognitive domains

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 H�non map and R�ssler 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

Instantaneous monitoring of heart beat dynamics during anesthesia and sedation

Anesthesia-induced altered arousal depends on drugs having their effect in specific brain regions. These effects are also reflected in autonomic nervous system (ANS) outflow dynamics. To this extent, instantaneous monitoring of ANS outflow, based on neurophysiological and computational modeling, may provide a more accurate assessment of the action of anesthetic agents on the cardiovascular system. This will aid anesthesia care providers in maintaining homeostatic equilibrium and help to minimize drug administration while maintaining antinociceptive effects. In previous studies, we established a point process paradigm for analyzing heartbeat dynamics and have successfully applied these methods to a wide range of cardiovascular data and protocols. We recently devised a novel instantaneous nonlinear assessment of ANS outflow, also suitable and effective for real-time monitoring of the fast hemodynamic and autonomic effects during induction and emergence from anesthesia. Our goal is to demonstrate that our framework is suitable for instantaneous monitoring of the ANS response during administration of a broad range of anesthetic drugs. Specifically, we compare the hemodynamic and autonomic effects in study participants undergoing propofol (PROP) and dexmedetomidine (DMED) administration. Our methods provide an instantaneous characterization of autonomic state at different stages of sedation and anesthesia by tracking autonomic dynamics at very high time-resolution. Our results suggest that refined methods for analyzing linear and nonlinear heartbeat dynamics during administration of specific anesthetic drugs are able to overcome nonstationary limitations as well as reducing inter-subject variability, thus providing a potential real-time monitoring approach for patients receiving anesthesia

A Unified Point Process Probabilistic Framework to Assess Heartbeat Dynamics and Autonomic Cardiovascular Control

In recent years, time-varying inhomogeneous point process models have been introduced for assessment of instantaneous heartbeat dynamics as well as specific cardiovascular control mechanisms and hemodynamics. Assessment of the model’s statistics is established through the Wiener-Volterra theory and a multivariate autoregressive (AR) structure. A variety of instantaneous cardiovascular metrics, such as heart rate (HR), heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreceptor-cardiac reflex (baroreflex) sensitivity (BRS), are derived within a parametric framework and instantaneously updated with adaptive and local maximum likelihood estimation algorithms. Inclusion of second-order non-linearities, with subsequent bispectral quantification in the frequency domain, further allows for definition of instantaneous metrics of non-linearity. We here present a comprehensive review of the devised methods as applied to experimental recordings from healthy subjects during propofol anesthesia. Collective results reveal interesting dynamic trends across the different pharmacological interventions operated within each anesthesia session, confirming the ability of the algorithm to track important changes in cardiorespiratory elicited interactions, and pointing at our mathematical approach as a promising monitoring tool for an accurate, non-invasive assessment in clinical practice. We also discuss the limitations and other alternative modeling strategies of our point process approach