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

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

Instantaneous Assessment of Hedonic Olfactory Perception using Heartbeat Nonlinear Dynamics: A Preliminary Study

Emotional perception to hedonic olfactory stimuli is un- der direct control of the limbic system, whose dynam- ics is known to affect autonomic nervous system activity on cardiovascular control. Mainly due to methodologi- cal limitations, previous investigations failed to uncover specific trends in heartbeat dynamics between ultra short- time (i.e., lasting < 10s), pleasant and unpleasant olfac- tory stimuli. To this extent, in this study we computed in- stantaneous estimates from heartbeat series gathered from 32 healthy subjects (age: 26±2; 16M) undergoing hedo- nic olfactory elicitation. Each subject exhibited a simi- lar olfactory perception threshold, and scored five 5s stim- uli in terms of arousal and valence level using the self- assessment manikin test. We analyzed the heartbeat series using our recently proposed inhomogeneous point-process nonlinear framework, obtaining instantaneous estimates defined in the time (mean and standard deviation), fre- quency (power in the LF and HF bands, as well as LF/HF ratio), and nonlinear/complexity (bispectra, sample and approximate entropy, and Lyapunov exponent) domains. A feature set comprising average estimates within the 5s win- dows was taken as an input of a K-Nearest Neighborhood classification algorithm, whose cross-validation relied on a leave-one-subject-out procedure. Results demonstrate that our framework allows to finely characterize affective olfactory elicitation with an average recognition accuracy of 71.88%. Feature selection highlighted that the most dis- criminating power was contributed by instantaneous LF power, instantaneous Lyapunov exponents, and instanta- neous approximate entropy

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

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

Revealing Real-Time Emotional Responses: a Personalized Assessment based on Heartbeat Dynamics

Emotion recognition through computational modeling and analysis of physiological signals has been widely investigated in the last decade. Most of the proposed emotion recognition systems require relatively long-time series of multivariate records and do not provide accurate real-time characterizations using short-time series. To overcome these limitations, we propose a novel personalized probabilistic framework able to characterize the emotional state of a subject through the analysis of heartbeat dynamics exclusively. The study includes thirty subjects presented with a set of standardized images gathered from the international affective picture system, alternating levels of arousal and valence. Due to the intrinsic nonlinearity and nonstationarity of the RR interval series, a specific point-process model was devised for instantaneous identification considering autoregressive nonlinearities up to the third-order according to the Wiener-Volterra representation, thus tracking very fast stimulus-response changes. Features from the instantaneous spectrum and bispectrum, as well as the dominant Lyapunov exponent, were extracted and considered as input features to a support vector machine for classification. Results, estimating emotions each 10 seconds, achieve an overall accuracy in recognizing four emotional states based on the circumplex model of affect of 79.29%, with 79.15% on the valence axis, and 83.55% on the arousal axis

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

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

Autonomic Nervous System Dynamics for Mood and Emotional-State Recognition: Wearable Systems, Modeling, and Advanced Biosignal Processing

This thesis aims at investigating how electrophysiological signals related to the autonomic nervous system (ANS) dynamics could be source of reliable and effective markers for mood state recognition and assessment of emotional responses. In-depth methodological and applicative studies of biosignals such as electrocardiogram, electrodermal response, and respiration activity along with information coming from the eyes (gaze points and pupil size variation) were performed. Supported by the current literature, I found that nonlinear signal processing techniques play a crucial role in understanding the underlying ANS physiology and provide important quantifiers of cardiovascular control dynamics with prognostic value in both healthy subjects and patients. Two main applicative scenarios were identified: the former includes a group of healthy subjects who was presented with sets of images gathered from the International Affective Picture System hav- ing five levels of arousal and five levels of valence, including both a neutral reference level. The latter was constituted by bipolar patients who were followed for a period of 90 days during which psychophysical evaluations were performed. In both datasets, standard signal processing techniques as well as nonlinear measures have been taken into account to automatically and accurately recognize the elicited levels of arousal and valence and mood states, respectively. A novel probabilistic approach based on the point-process theory was also successfully applied in order to model and characterize the instantaneous ANS nonlinear dynamics in both healthy subjects and bipolar patients. According to the reported evidences on ANS complex behavior, experimental results demonstrate that an accurate characterization of the elicited affective levels and mood states is viable only when non- linear information are retained. Moreover, I demonstrate that the instantaneous ANS assessment is effective in both healthy subjects and patients. Besides mathematics and signal processing, this thesis also contributes to pragmatic issues such as emotional and mood state mod- eling, elicitation, and noninvasive ANS monitoring. Throughout the dissertation, a critical review on the current state-of-the-art is reported leading to the description of dedicated experimental protocols, reliable mood models, and novel wearable systems able to perform ANS monitoring in a naturalistic environment