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

Characterization of autonomic states by complex sympathetic and parasympathetic dynamics

Assessment of heartbeat dynamics provides a promising framework for non-invasive monitoring of cardiovascular and autonomic states. Nevertheless, the non-specificity of such measurements among clinical populations and healthy conditions associated with different autonomic states severely limits their applicability and exploitation in naturalistic conditions. This limitation arises especially when pathological or postural change-related sympathetic hyperactivity is compared to autonomic changes across age and experimental conditions. In this frame, we investigate the intrinsic irregularity and complexity of cardiac sympathetic and vagal activity series in different populations, which are associated with different cardiac autonomic dynamics. Sample entropy, fuzzy entropy, and distribution entropy are calculated on the recently proposed sympathetic and parasympathetic activity indices (SAI and PAI) series, which are derived from publicly available heartbeat series of congestive heart failure patients, elderly and young subjects watching a movie in the supine position, and healthy subjects undergoing slow postural changes. Results show statistically significant differences between pathological/old subjects and young subjects in the resting state and during slow tilt, with interesting trends in SAI- and PAI-related entropy values. Moreover, while CHF patients and healthy subjects in upright position show the higher cardiac sympathetic activity, elderly and young subjects in resting state showed higher vagal activity. We conclude that quantification of intrinsic cardiac complexity from sympathetic and vagal dynamics may provide new physiology insights and improve on the non-specificity of heartbeat-derived biomarkers.

Heart rate variability and the dawn of complex physiological signal analysis: methodological and clinical perspectives

Spontaneous beat-to-beat variations of heart rate (HR) have intrigued scientists and casual observers for centuries; however, it was not until the 1970s that investigators began to apply engineering tools to the analysis of these variations, fostering the field we now know as heart rate variability or HRV. Since then, the field has exploded to not only include a wide variety of traditional linear time and frequency domain applications for the HR signal, but also more complex linear models that include additional physiological parameters such as respiration, arterial blood pressure, central venous pressure and autonomic nerve signals. Most recently, the field has branched out to address the nonlinear components of many physiological processes, the complexity of the systems being studied and the important issue of specificity for when these tools are applied to individuals. When the impact of all these developments are combined, it seems likely that the field of HRV will soon begin to realize its potential as an important component of the toolbox used for diagnosis and therapy of patients in the clinic. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Functional brain-heart interplay extends to the multifractal domain

The study of functional brain-heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain-heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain-heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain-heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Intrinsic Complexity of Sympathetic and Parasympathetic Dynamics from HRV series: a Preliminary Study on Postural Changes

The analysis of complex heartbeat dynamics has been widely used to characterize heartbeat autonomic control in healthy and pathological conditions. However, underlying physiological correlates of complexity measurements from heart rate variability (HRV) series have not been identified yet. To this extent, we investigated intrinsic irregularity and complexity of cardiac sympathetic and vagal activity time series during postural changes. We exploited our recently proposed HRV-based, time-varying Sympathetic and Parasympathetic Activity Indices (SAI and PAI) and performed Sample Entropy, Fuzzy Entropy, and Distribution Entropy calculations on publicly-available heartbeat series gathered from 10 healthy subjects undergoing resting state and passive slow tilt sessions. Results show significantly higher entropy values during the upright position than resting state in both SAI and PAI series. We conclude that an increase in HRV complexity resulting from postural changes may derive from sympathetic and vagal activities with higher complex dynamics.

Assessing Autonomic Function from Electrodermal Activity and Heart Rate Variability During Cold-Pressor Test and Emotional Challenge

Standard functional assessment of autonomic nervous system (ANS) activity on cardiovascular control relies on spectral analysis of heart rate variability (HRV) series. However, difficulties in obtaining a reliable measure of sympathetic activity from HRV spectra limits the exploitation of sympatho-vagal metrics. On the other hand, measures of electrodermal activity (EDA) have been demonstrated to provide a reliable quantifier of sympathetic dynamics. In this study we propose novel indices of phasic autonomic regulation mechanisms by combining HRV and EDA correlates and thoroughly investigating their time-varying dynamics. HRV and EDA series were gathered from 26 healthy subjects during a cold-pressor test and emotional stimuli. Instantaneous linear and nonlinear (bispectral) estimates of vagal dynamics were obtained from HRV through inhomogeneous point-process models, and combined with a sensitive maker of sympathetic tone from EDA spectral power. A wavelet decomposition analysis was applied to estimate phasic components of the proposed sympatho-vagal indices. Results show significant statistical differences for the proposed indices between the cold-pressor elicitation and previous resting state. Furthermore, an accuracy of 73.08% was achieved for the automatic emotional valence recognition. The proposed nonlinear processing of phasic ANS markers brings novel insights on autonomic functioning that can be exploited in the field of affective computing and psychophysiology.

Uncovering complex central autonomic networks at rest: a functional magnetic resonance imaging study on complex cardiovascular oscillations

This study aims to uncover brain areas that are functionally linked to complex cardiovascular oscillations in resting-state conditions. Multi-session functional magnetic resonance imaging (fMRI) and cardiovascular data were gathered from 34 healthy volunteers recruited within the human connectome project (the '100-unrelated subjects' release). Group-wise multi-level fMRI analyses in conjunction with complex instantaneous heartbeat correlates (entropy and Lyapunov exponent) revealed the existence of a specialized brain network, i.e. a complex central autonomic network (CCAN), reflecting what we refer to as complex autonomic control of the heart. Our results reveal CCAN areas comprised the paracingulate and cingulate gyri, temporal gyrus, frontal orbital cortex, planum temporale, temporal fusiform, superior and middle frontal gyri, lateral occipital cortex, angular gyrus, precuneous cortex, frontal pole, intracalcarine and supracalcarine cortices, parahippocampal gyrus and left hippocampus. The CCAN visible at rest does not include the insular cortex, thalamus, putamen, amygdala and right caudate, which are classical CAN regions peculiar to sympatho-vagal control. Our results also suggest that the CCAN is mainly involved in complex vagal control mechanisms, with possible links with emotional processing networks.

Heartbeat Dynamics Analysis under Cold-Pressure Test using Wavelet p-Leader Non-Gaussian Multiscale Expansions

Multiscale and multifractal (MF) analyses have been proven an effective tool for the characterisation of heartbeat dynamics in physiological and pathological conditions. However, pre-processing methods for the unevenly sampled heartbeat interval series are known to affect the estimation of MF properties. In this study, we employ a recently proposed method based on wavelet p-leaders MF spectra to estimate MF properties from cardiovascular variability series, which are also pre-processed through an inhomogeneous point-process modelling. Particularly, we exploit a non-Gaussian multiscale expansion to study changes in heartbeat dynamics as a response to a sympathetic elicitation given by the cold-pressor test. By comparing MF estimates from raw heartbeat series and the point-process model, results suggest that the proposed modelling provides features statistically discerning between stress and resting condition at different time scales. These findings contribute to a comprehensive characterization of autonomic nervous system activity on cardiovascular control during cold-pressor elicitation.

Lateralization of directional brain-heart information transfer during visual emotional elicitation

Previous studies have characterized the physiological interactions between central nervous system (brain) and peripheral cardiovascular system (heart) during affective elicitation in healthy subjects; however, questions related to the directionality of this functional interplay have been gaining less attention from the scientific community. Here, we explore brain-heart interactions during visual emotional elicitation in healthy subjects using measures of Granger causality (GC), a widely used descriptor of causal influences between two dynamical systems. The proposed approach inferences causality between instantaneous cardiovagal dynamics estimated from inhomogeneous point-process models of the heartbeat and high-density electroencephalogram (EEG) dynamics in 22 healthy subjects who underwent pleasant/unpleasant affective elicitation by watching pictures from the International Affective Picture System database. Particularly, we calculated the GC indexes between the EEG spectrogram in the canonical θ-, α-, β-, and γ-bands and both the instantaneous mean heart rate and its continuous parasympathetic modulations (i.e., the instantaneous HF power). Thus we looked for significant statistical differences among GC values estimated during the resting state, neutral elicitation, and pleasant/unpleasant arousing elicitation. As compared with resting state, coupling strength increases significantly in the left hemisphere during positive stimuli and in the right hemisphere during negative stimuli. Our results further reveal a correlation between emotional valence and lateralization of the dynamical information transfer going from brain-to-heart, mainly localized in the prefrontal, somatosensory, and posterior cortexes, and of the information transfer from heart-to-brain, mainly reflected into the fronto-parietal cortex oscillations in the γ-band (30 −45 Hz).

Central modulation of parasympathetic outflow is impaired in de novo Parkinson's disease patients

Task- and stimulus-based neuroimaging studies have begun to unveil the central autonomic network which modulates autonomic nervous system activity. In the present study, we aimed to evaluate the central autonomic network without the bias constituted by the use of a task. Additionally, we assessed whether this circuitry presents signs of dysregulation in the early stages of Parkinson’s disease (PD), a condition which may be associated with dysautonomia. We combined heart-rate-variability based methods for time-varying assessments of the autonomic nervous system outflow with resting-state fMRI in 14 healthy controls and 14 de novo PD patients, evaluating the correlations between fMRI time-series and the instantaneous high-frequency component of the heart-rate-variability power spectrum, a marker of parasympathetic outflow. In control subjects, the high-frequency component of the heart-rate-variability power spectrum was significantly anti-correlated with fMRI time-series in several cortical, subcortical and brainstem regions. This complex central network was not detectable in PD patients. In between-group analysis, we found that in healthy controls the brain activation related to the high-frequency component of the heart-rate-variability power spectrum was significantly less than in PD patients in the mid and anterior cingulum, sensorimotor cortex and supplementary motor area, insula and temporal lobe, prefrontal cortex, hippocampus and in a region encompassing posterior cingulum, precuneus and parieto-occipital cortex. Our results indicate that the complex central network which modulates parasympathetic outflow in the resting state is impaired in the early clinical stages of PD.

Resting-state brain correlates of cardiovascular complexity

While estimates of complex heartbeat dynamics have provided effective prognostic and diagnostic markers for a wide range of pathologies, brain correlates of complex cardiac measures in general and of complex sympatho-vagal dynamics in particular are still unknown. In this study we combine resting state functional Magnetic Resonance Imaging (fMRI) and physiological signal acquisition from 34 healthy subjects selected from the Human Connectome Project (HCP) repository with inhomogeneous point-process approximate and sample heartbeat entropy measures (ipApEn and ipSampEn) to investigate brain areas involved in complex cardiovascular control. Our results show that activity in the Temporal Gyrus, Frontal Orbital Cortex, Temporal Fusiform and Opercular cortices, Planum Temporale, and Paracingulate cortex are negatively correlated with ipApEn dynamics. Activity in the same cortical areas as well as in the Temporal Fusiform cortex are negatively correlated with ipSampEn dynamics. No significant positive correlations were found. These pioneering results suggest that cardiovascular complexity at rest is linked to a few specific cortical brain structures, including crucial areas connected with parasympathetic outflow. This corroborates the hypothesis of a multidimensional central network which controls nonlinear cardiac dynamics under a predominantly vagally-driven tone.

Measures of sympathetic and parasympathetic autonomic outflow from heartbeat dynamics

Reliable and effective noninvasive measures of sympathetic and parasympathetic peripheral outflow are of crucial importance in cardiovascular physiology. Although many techniques have been proposed to take up this long-lasting challenge, none has proposed a satisfying discrimination of the dynamics of the two separate branches. Spectral analysis of heart rate variability is the most currently used technique for such assessment. Despite its widespread use, it has been demonstrated that the subdivision in the low-frequency (LF) and high-frequency (HF) bands does not fully reflect separate influences of the sympathetic and parasympathetic branches, respectively, mainly due to their simultaneous action in the LF. Two novel heartbeat-derived autonomic measures, the sympathetic activity index (SAI) and parasympathetic activity index (PAI), are proposed to separately assess the time-varying autonomic nervous system synergic functions. Their efficacy is validated in landmark autonomic maneuvers generally employed in clinical settings. The novel measures move beyond the classical frequency domain paradigm through identification of a set of coefficients associated with a proper combination of Laguerre base functions. The resulting measures were compared with the traditional LF and HF power. A total of 236 ECG recordings were analyzed for validation, including autonomic outflow changes elicited by procedures of different nature and temporal variation, such as postural changes, lower body negative pressure, and handgrip tests. The proposed SAI-PAI measures consistently outperform traditional frequency-domain indexes in tracking expected instantaneous autonomic variations, both vagal and sympathetic, and may aid clinical decision making, showing reduced intersubject variability and physiologically plausible dynamics. NEW & NOTEWORTHY While it is possible to obtain reliable estimates of parasympathetic activity from the ECG, a satisfying method to disentangle the sympathetic component from HRV has not been proposed yet. To overcome this long-lasting limitation, we propose two novel HRV-based indexes, the sympathetic and parasympathetic activity indexes.

Mortality Prediction in Severe Congestive Heart Failure Patients with Multifractal Point-Process Modeling of Heartbeat Dynamics

Multifractal analysis of human heartbeat dynamics has been demonstrated to provide promising markers of Congestive Heart Failure (CHF). Yet, it crucially builds on the interpolation of RR intervals series, which has been generically performed with limited links to CHF pathophysiology. We devise a novel methodology estimating multifractal autonomic dynamics from heartbeat-derived series defined in the continuous time. We hypothesize that markers estimated from our novel framework are also effective for mortality prediction in severe CHF. We merge multifractal analysis within a methodological framework based on inhomogeneous point process models of heartbeat dynamics. Specifically, wavelet coefficients and wavelet leaders are computed over measures extracted from instantaneous statistics of probability density functions characterizing and predicting the time until the next heartbeat event occurs. The proposed approach is tested on data from 94 CHF patients, aiming at predicting survivor and non-survivor individuals as determined after a 4 years follow up. Instantaneous markers of vagal and sympatho-vagal dynamics display power-law scaling for a large range of scales, from s to s. Using standard SVM algorithms, the proposed inhomogeneous point-process representation based multifractal analysis achieved the best CHF mortality prediction accuracy of 79.11 % (sensitivity 90.48%, specificity 67.74%). Our results suggest that heartbeat scaling and multifractal properties in CHF patients are not generated at the sinus-node level, but rather by the intrinsic action of vagal short-term control and of sympatho-vagal fluctuations associated with circadian cardiovascular control, especially within the VLF band. These markers might provide critical information in devising a clinical tool for individualized prediction of survivor and non-survivor CHF patients.

Validation of instantaneous bispectral high-frequency power of heartbeat dynamics as a marker of cardiac vagal activity

Nonlinear analysis has been advocated as a very powerful methodological framework to study physiological signals, particularly when applied to heartbeat dynamics. To this extent, estimation of high-frequency (0.15-0.40 Hz) power from bispectra of cardiovascular variability series has been engaged as a marker of nonlinear vagal activity. Nevertheless, a proper validation of this specific measure has not been yet performed. In this study, we estimate instantaneous, nonlinear bispectral indices during postural changes under sympathetic and parasympathetic nervous system blockade. The analysis was performed on data from 14 healthy subjects undergoing a control supine-to-upright routine where they were selectively administered either atropine or propanolol. Instantaneous bispectra were obtained through Laguerre-transformed, linear and nonlinear kernels of a Wiener-Volterra model applied to heartbeat dynamics, embedded into a recently proposed inhomogeneous point-process framework. Results demonstrate that the integration of bispectra accounting for nonlinear cardiovascular control dynamics within the high-frequency band provides potentially reliable markers of vagal activity.

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).

Causal brain-heart information transfer during visual emotional elicitation in healthy subjects: Preliminary evaluations and future perspectives

Complex heartbeat dynamics is known to reflect subject's emotional state, thanks to numerous links to brain cortical and subcortical regions. Likewise, specific brain regions are deeply involved in vagally-mediated emotional processing and regulation. Nevertheless, although the brain-heart interplay has been studied during visual emotion elicitation, directional interactions have not been investigated so far. To fill this gap, in this study we investigate brain-heart dynamics during emotional elicitation in healthy subjects through measures of Granger causality (GC) between the two physiological systems. Data were gathered from 22 healthy volunteers who underwent pleasant/ unpleasant affective elicitation using pictures from the International Affective Picture System. Neutral emotional stimuli were elicited as well. High density electroencephalogram (EEG) signals were processed to obtain time-varying maps of cortical activation, whereas the associated instantaneous cardiovascular dynamics was estimated through inhomogeneous point-process models. Concerning the information transfer brain-to-heart, GE highlighted significant valence-dependent lateralization with respect to resting states. Furthermore, as a proof of concept, the study of heart-to-brain dynamics considering EEG oscillations in the γ band (30-45 Hz) highlighted differential information transfer between neutral and positive elicitations directed to the prefrontal cortex.

Disentanglement of sympathetic and parasympathetic activity by instantaneous analysis of human heartbeat dynamics

Spectral analysis of heart rate variability (HRV) is one of the most effective techniques for the assessment of the influence of the autonomic nervous system (ANS) on the heartbeat. Despite its widespread use, it has been demonstrated that HRV subdivision in the low frequency (LF) and high frequency (HF) bands does not accurately reflect separate sympathetic and parasympathetic influences, respectively, mainly due to overlap of the two branches in the low frequencies. Here we propose two novel indices, namely the instantaneous sympathetic autonomic index (SAI) and parasympathetic autonomic index (PAI), that are able to separately assess the time-varying ANS synergic functions. The application of the paradigm is presented here by associating proper combinations of orthonormal Laguerre functions defined within the heartbeat point-process continuous model. Preliminary results from ten subjects recorded during a tilt-table protocol show that the proposed methodology, differently than the traditional spectral parameters, is able to separately track the independent changes associated with the two ANS branches.

Brain-heart linear and nonlinear dynamics during visual emotional elicitation in healthy subjects

This study investigates brain-heart dynamics during visual emotional elicitation in healthy subjects through linear and nonlinear coupling measures of EEG spectrogram and instantaneous heart rate estimates. To this extent, affective pictures including different combinations of arousal and valence levels, gathered from the International Affective Picture System, were administered to twenty-two healthy subjects. Time-varying maps of cortical activation were obtained through EEG spectral analysis, whereas the associated instantaneous heartbeat dynamics was estimated using inhomogeneous point-process linear models. Brain-Heart linear and nonlinear coupling was estimated through the Maximal Information Coefficient (MIC), considering EEG time-varying spectra and point-process estimates defined in the time and frequency domains. As a proof of concept, we here show preliminary results considering EEG oscillations in the θ band (4-8 Hz). This band, indeed, is known in the literature to be involved in emotional processes. MIC highlighted significant arousal-dependent changes, mediated by the prefrontal cortex interplay especially occurring at intermediate arousing levels. Furthermore, lower and higher arousing elicitations were associated to not significant brain-heart coupling changes in response to pleasant/unpleasant elicitations.

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.

Predicting Bradycardia in Preterm Infants Using Point Process Analysis of Heart Rate

OBJECTIVE

Episodes of bradycardia are common and recur sporadically in preterm infants, posing a threat to the developing brain and other vital organs. We hypothesize that bradycardias are a result of transient temporal destabilization of the cardiac autonomic control system and that fluctuations in the heart rate signal might contain information that precedes bradycardia. We investigate infant heart rate fluctuations with a novel application of point process theory.

METHODS

In ten preterm infants, we estimate instantaneous linear measures of the heart rate signal, use these measures to extract statistical features of bradycardia, and propose a simplistic framework for prediction of bradycardia.

RESULTS

We present the performance of a prediction algorithm using instantaneous linear measures (mean area under the curve = 0.79 ± 0.018) for over 440 bradycardia events. The algorithm achieves an average forecast time of 116 s prior to bradycardia onset (FPR = 0.15). Our analysis reveals that increased variance in the heart rate signal is a precursor of severe bradycardia. This increase in variance is associated with an increase in power from low content dynamics in the LF band (0.04-0.2 Hz) and lower multiscale entropy values prior to bradycardia.

CONCLUSION

Point process analysis of the heartbeat time series reveals instantaneous measures that can be used to predict infant bradycardia prior to onset.

SIGNIFICANCE

Our findings are relevant to risk stratification, predictive monitoring, and implementation of preventative strategies for reducing morbidity and mortality associated with bradycardia in neonatal intensive care units.

Instantaneous transfer entropy for the study of cardio-respiratory dynamics

Measures of transfer entropy have been proposed to quantify the directional coupling and strength between two complex physiological variables. Particular attention has been given to nonlinear interactions within cardiovascular and respiratory dynamics as influenced by the autonomic nervous system. However, standard transfer entropy estimates have shown major limitations in dealing with issues concerning stochastic system modeling, limited observations in time, and the assumption of stationarity of the considered physiological variables. Moreover, standard estimates are unable to track time-varying changes in nonlinear coupling with high resolution in time. Here, we propose a novel definition of transfer entropy linked to inhomogeneous point-process theory. Heartbeat and respiratory dynamics are characterized through discrete time series, and modeled through probability density functions (PDFs) which characterize and predict the time until the occurrence of the next physiological event as a function of the past history. As the derived measures of entropy are instantaneously defined through continuos PDFs, a novel index (the Instantaneous point-process Transfer Entropy, ipT ransfEn) is able to provide instantaneous tracking of the information transfer. The new measure is tested on experimental data gathered from 16 healthy subjects undergoing postural changes, showing fast tracking of the tilting events and low variability during the standing phase.

Predicting seizures in untreated temporal lobe epilepsy using point-process nonlinear models of heartbeat dynamics

Symptoms of temporal lobe epilepsy (TLE) are frequently associated with autonomic dysregulation, whose underlying biological processes are thought to strongly contribute to sudden unexpected death in epilepsy (SUDEP). While abnormal cardiovascular patterns commonly occur during ictal events, putative patterns of autonomic cardiac effects during pre-ictal (PRE) periods (i.e. periods preceding seizures) are still unknown. In this study, we investigated TLE-related heart rate variability (HRV) through instantaneous, nonlinear estimates of cardiovascular oscillations during inter-ictal (INT) and PRE periods. ECG recordings from 12 patients with TLE were processed to extract standard HRV indices, as well as indices of instantaneous HRV complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra) obtained through definition of inhomogeneous point-process nonlinear models, employing Volterra-Laguerre expansions of linear, quadratic, and cubic kernels. Experimental results demonstrate that the best INT vs. PRE classification performance (balanced accuracy: 73.91%) was achieved only when retaining the time-varying, nonlinear, and non-stationary structure of heartbeat dynamical features. The proposed approach opens novel important avenues in predicting ictal events using information gathered from cardiovascular signals exclusively.

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.

Combining electroencephalographic activity and instantaneous heart rate for assessing brain-heart dynamics during visual emotional elicitation in healthy subjects

Emotion perception, occurring in brain areas such as the prefrontal cortex and amygdala, involves autonomic responses affecting cardiovascular dynamics. However, how such brain-heart dynamics is further modulated by emotional valence (pleasantness/unpleasantness), also considering different arousing levels (the intensity of the emotional stimuli), is still unknown. To this extent, we combined electroencephalographic (EEG) dynamics and instantaneous heart rate estimates to study emotional processing in healthy subjects. Twenty-two healthy volunteers were elicited through affective pictures gathered from the International Affective Picture System. The experimental protocol foresaw 110 pictures, each of which lasted 10 s, associated to 25 different combinations of arousal and valence levels, including neutral elicitations. EEG data were processed using short-time Fourier transforms to obtain time-varying maps of cortical activation, whereas the associated instantaneous cardiovascular dynamics was estimated in the time and frequency domains through inhomogeneous point-process models. Brain-heart linear and nonlinear coupling was estimated through the maximal information coefficient (MIC). Considering EEG oscillations in theθband (4-8 Hz), MIC highlighted significant arousal-dependent changes between positive and negative stimuli, especially occurring at intermediate arousing levels through the prefrontal cortex interplay. Moreover, high arousing elicitations seem to mitigate changes in brain-heart dynamics in response to pleasant/unpleasant visual elicitation.

Globally conditioned Granger causality in brain-brain and brain-heart interactions: a combined heart rate variability/ultra-high-field (7 T) functional magnetic resonance imaging study

The causal, directed interactions between brain regions at rest (brain-brain networks) and between resting-state brain activity and autonomic nervous system (ANS) outflow (brain-heart links) have not been completely elucidated. We collected 7 T resting-state functional magnetic resonance imaging (fMRI) data with simultaneous respiration and heartbeat recordings in nine healthy volunteers to investigate (i) the causal interactions between cortical and subcortical brain regions at rest and (ii) the causal interactions between resting-state brain activity and the ANS as quantified through a probabilistic, point-process-based heartbeat model which generates dynamical estimates for sympathetic and parasympathetic activity as well as sympathovagal balance. Given the high amount of information shared between brain-derived signals, we compared the results of traditional bivariate Granger causality (GC) with a globally conditioned approach which evaluated the additional influence of each brain region on the causal target while factoring out effects concomitantly mediated by other brain regions. The bivariate approach resulted in a large number of possibly spurious causal brain-brain links, while, using the globally conditioned approach, we demonstrated the existence of significant selective causal links between cortical/subcortical brain regions and sympathetic and parasympathetic modulation as well as sympathovagal balance. In particular, we demonstrated a causal role of the amygdala, hypothalamus, brainstem and, among others, medial, middle and superior frontal gyri, superior temporal pole, paracentral lobule and cerebellar regions in modulating the so-called central autonomic network (CAN). In summary, we show that, provided proper conditioning is employed to eliminate spurious causalities, ultra-high-field functional imaging coupled with physiological signal acquisition and GC analysis is able to quantify directed brain-brain and brain-heart interactions reflecting central modulation of ANS outflow.

Electroencephalographic spectral correlates of caress-like affective haptic stimuli

This paper describes how brain dynamics, as estimated through spectral analysis of electroencephalographic (EEG) oscillatory rhythms, is modified by quantifiable, affective haptic stimuli. Specifically, 32 healthy subjects (16 females) interacted with a haptic device able to convey caress-like stimuli while varying force and velocity of the device itself. More specifically, 2 values of force (i.e., "strength of the caress") and 3 velocity levels (i.e. "velocity of the caress") were combined to control the device during the experiment. Subjects were also asked to self-assess the haptic stimuli in terms of arousal (activation/ deactivation) and valence (pleasure/displeasure) scores. Results, shown in terms of p-values topographic maps, revealed a suppression of the oscillations over the controlateral somatosensory cortex, during caresses performed with the lowest force (2N) and the highest velocity (65 mm/s). This occurred in all of the frequency bands considered, α, β, and γ. Lower velocities (9.4 mm/s and 37 mm/s) did not significantly modify EEG reactivity in such bands. Concerning caresses administered at high force (6N), there was a significant decrease of EEG oscillatory activity focused on mid-frontal electrodes, in all of the considered frequency bands, when the velocity of the caresses was the lowest one. Significant sparse decrease of EEG power spectra, in all of the considered frequency bands, occurred at higher strength and velocity of the caress.

Point-process high-resolution representations of heartbeat dynamics for multiscale analysis: A CHF survivor prediction study

Multiscale analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that multiscale analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.

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.

Tracking instantaneous entropy in heartbeat dynamics through inhomogeneous point-process nonlinear models

Measures of entropy have been proved as powerful quantifiers of complex nonlinear systems, particularly when applied to stochastic series of heartbeat dynamics. Despite the remarkable achievements obtained through standard definitions of approximate and sample entropy, a time-varying definition of entropy characterizing the physiological dynamics at each moment in time is still missing. To this extent, we propose two novel measures of entropy based on the inho-mogeneous point-process theory. The RR interval series is modeled through probability density functions (pdfs) 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 such probability functions, the proposed indices are able to provide instantaneous tracking of autonomic nervous system complexity. Of note, the distance between the time-varying phase-space vectors is calculated through the Kolmogorov-Smirnov distance of two pdfs. Experimental results, obtained from the analysis of RR interval series extracted from ten healthy subjects during stand-up tasks, suggest that the proposed entropy indices provide instantaneous tracking of the heartbeat complexity, also allowing for the definition of complexity variability indices.

Temporal trends of neuro-autonomic complexity during severe episodes of bipolar disorders

Bipolar disorder is a chronic psychiatric condition during which patients experience mood swings among depression, hypomania or mania, mixed state (depression-hypomania) and euthymia, i.e., good affective balance. Nowadays, an objective characterization of the temporal trends of the disease as a response to the pharmacological treatment through physiological signatures, especially during severe episodes, is still missing. In this study we show interesting findings relating neuro-autonomic complexity to severe pathological mood states. More specifically, we studied Sample Entropy (SampEn) measures on Heart Rate Variability series gathered from four bipolar patients recruited within the frame of the European project PSYCHE. Patients were monitored through long term ECG recordings from the first hospital admission until clinical remission, i.e., the euthymic state. We observed that a mood transition from mixed-state to euthymia passing through depression can be characterized by increased SampEn values, i.e. as the patient is going to recover, SampEn increases. These results are in agreement with the current literature reporting on the complexity dynamics of the cardiovascular system and can provide a promising and viable clinical decision support to objectify the diagnosis and improve the management of psychiatric disorders.

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.

Maximal-radius multiscale entropy of cardiovascular variability: a promising biomarker of pathological mood states in bipolar disorders

Complexity measures from Multiscale Entropy (MSE) analysis of cardiovascular variability may provide potential biomarkers of pathological mental states such as major depression. To this extent, in this study we investigate whether complexity of Heart Rate Variability (HRV) is also affected in mental disorders such as bipolar disorders (BD). As part of the European project PSYCHE, eight BD patients experiencing multiple pathological mood states among depression, hypomania, and euthymia (i.e., good affective balance) underwent long-term night recordings through a comfortable sensing t-shirt with integrated fabric electrodes and sensors. Standard radius, i.e., 20% of the HRV standard deviation, and a maximal-radius choice for the sample entropy estimation were compared along with a further multiscale Renyi Entropy analysis. We found that, despite the inter-subject variability, the maximal-radius MSE analysis is able to discern the considered pathological mental states of BD. As the current clinical practice in diagnosing BD is only based on verbal interviews and scores from specific questionnaires, these findings provide evidence on the possibility of using heartbeat complexity as the basis of novel clinical biomarkers of mental disorders.