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

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.

Plantar pressure alterations associated with increased BMI in young adults

BACKGROUND

Despite evidence suggesting that excess weight is linked to gait alterations and foot disorders, its effect on peak plantar pressure (PPP) variability and complexity during walking remains poorly understood.

RESEARCH QUESTION

This study aimed to examine the influence of overweight (BMI ≥ 25) on the dynamic PPP distribution during gait using traditional and nonlinear dynamic measures in young college students.

METHODS

Fifty-two overweight (BMI >25, average 29.3 ± 4.02) and sixty-four control college students (BMI<25, 21.7 ± 1.76) aged 18-25 years, walked across a Tekscan gait assessment system at their preferred speed. A t-test or a Mann Whitney U test was used for analysis, subject to data normality. Kinematic, kinetic, spatiotemporal, and GaitEn (sample entropy of 2D spatial PPP maps) for window lengths (m=2) at various filtering levels (r) were used to explore the impact of BMI on PPP alterations.

RESULTS AND SIGNIFICANCE

The overweight group exhibited significantly higher mean PPP. The PPP under the forefoot region was also significantly higher for the overweight group as compared to the heel. The mean GaitEn values of overweight and control groups were found significantly different at r = (0.7-0.8) x STD, where GaitEn of the control group was relatively higher, which indicates better gait performance as compared to the overweight group in alignment with previous studies. A significant correlation of GaitEn with STD of PPP was revealed for the overweight group only, suggesting that overweight could significantly change the regularity or the complexity of the PPP series. Although no spatiotemporal parameters (stride length, step length, step width) were significantly affected by the increased BMI, GaitEn dynamic measure, along with spatiotemporal (decrease in gait velocity and cadence with increased BMI), and kinetic measures (increased maximum forces and plantar pressure with increased BMI), were significantly affected by overweight, indicating the feasibility of assessing the impact of increased BMI using pressure platforms in clinical settings.

PIC micro-controller based synchronization of two fractional order jerk systems

The paper studies a 3D Chaotic Jerk oscillator with fractional derivatives. An approach is proposed to implement it on a PIC16F877A microcontroller in order to reduce the requirements for multiple analogue electronic components such as resistors, capacitors, coils, multipliers, operational amplifiers, which are very bulky and consume a lot of power. The behaviours of the underlying system are analysed analytically, numerically and experimentally. It comes from this analysis that the fractional model exhibits chaotic dynamics when for parameters for which the equivalent integer derivative system exhibits limit-cycles. The synchronization under two closed initial conditions is also studied, highlighting one of the most common applications of the chaos concept.

Periodic recurrent waves of Covid-19 epidemics and vaccination campaign

While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enforcing mitigation and vaccination strategy. The spreading rate is measured by the ratio between the reproductive number R_t(t) and the doubling time T_d(t) called RIC-index and the daily fatalities number. The dynamics of the Covid-19 epidemics have been studied by wavelet analysis and represented by a non-linear helicoid vortex in a 3D space where both RIC-index and fatalities change with time. The onset of periodic recurrent waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of recurrent waves of 120 days and the elongation of this period after the vaccination campaign.

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'.

Quantitative assessment of the relationship between behavioral and autonomic dynamics during propofol-induced unconsciousness

During general anesthesia, both behavioral and autonomic changes are caused by the administration of anesthetics such as propofol. Propofol produces unconsciousness by creating highly structured oscillations in brain circuits. The anesthetic also has autonomic effects due to its actions as a vasodilator and myocardial depressant. Understanding how autonomic dynamics change in relation to propofol-induced unconsciousness is an important scientific and clinical question since anesthesiologists often infer changes in level of unconsciousness from changes in autonomic dynamics. Therefore, we present a framework combining physiology-based statistical models that have been developed specifically for heart rate variability and electrodermal activity with a robust statistical tool to compare behavioral and multimodal autonomic changes before, during, and after propofol-induced unconsciousness. We tested this framework on physiological data recorded from nine healthy volunteers during computer-controlled administration of propofol. We studied how autonomic dynamics related to behavioral markers of unconsciousness: 1) overall, 2) during the transitions of loss and recovery of consciousness, and 3) before and after anesthesia as a whole. Our results show a strong relationship between behavioral state of consciousness and autonomic dynamics. All of our prediction models showed areas under the curve greater than 0.75 despite the presence of non-monotonic relationships among the variables during the transition periods. Our analysis highlighted the specific roles played by fast versus slow changes, parasympathetic vs sympathetic activity, heart rate variability vs electrodermal activity, and even pulse rate vs pulse amplitude information within electrodermal activity. Further advancement upon this work can quantify the complex and subject-specific relationship between behavioral changes and autonomic dynamics before, during, and after anesthesia. However, this work demonstrates the potential of a multimodal, physiologically-informed, statistical approach to characterize autonomic dynamics.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.

Toward a Taxonomy for Analyzing the Heart Rate as a Physiological Indicator of Posttraumatic Stress Disorder: Systematic Review and Development of a Framework

BACKGROUND

Posttraumatic stress disorder (PTSD) is a prevalent psychiatric condition that is associated with symptoms such as hyperarousal and overreactions. Treatments for PTSD are limited to medications and in-session therapies. Assessing the way the heart responds to PTSD has shown promise in detecting and understanding the onset of symptoms.

OBJECTIVE

This study aimed to extract statistical and mathematical approaches that researchers can use to analyze heart rate (HR) data to understand PTSD.

METHODS

A scoping literature review was conducted to extract HR models. A total of 5 databases including Medical Literature Analysis and Retrieval System Online (Medline) OVID, Medline EBSCO, Cumulative Index to Nursing and Allied Health Literature (CINAHL) EBSCO, Excerpta Medica Database (Embase) Ovid, and Google Scholar were searched. Non-English language studies, as well as studies that did not analyze human data, were excluded. A total of 54 studies that met the inclusion criteria were included in this review.

RESULTS

We identified 4 categories of models: descriptive time-independent output, descriptive and time-dependent output, predictive and time-independent output, and predictive and time-dependent output. Descriptive and time-independent output models include analysis of variance and first-order exponential; the descriptive time-dependent output model includes a classical time series analysis and mixed regression. Predictive time-independent output models include machine learning methods and analysis of the HR-based fluctuation-dissipation method. Finally, predictive time-dependent output models include the time-variant method and nonlinear dynamic modeling.

CONCLUSIONS

All of the identified modeling categories have relevance in PTSD, although the modeling selection is dependent on the specific goals of the study. Descriptive models are well-founded for the inference of PTSD. However, there is a need for additional studies in this area that explore a broader set of predictive models and other factors (eg, activity level) that have not been analyzed with descriptive models.

Autonomic function in amnestic and non-amnestic mild cognitive impairment: spectral heart rate variability analysis provides evidence for a brain-heart axis

Mild cognitive impairment (MCI) is a heterogeneous syndrome with two main clinical subtypes, amnestic (aMCI) and non-amnestic (naMCI). The analysis of heart rate variability (HRV) is a tool to assess autonomic function. Cognitive and autonomic processes are linked via the central autonomic network. Autonomic dysfunction entails several adverse outcomes. However, very few studies have investigated autonomic function in MCI and none have considered MCI subtypes or the relationship of HRV indices with different cognitive domains and structural brain damage. We assessed autonomic function during an active orthostatic challenge in 253 oupatients aged ≥ 65, [n = 82 aMCI, n = 93 naMCI, n = 78 cognitively normal (CN), neuropsychologically tested] with power spectral analysis of HRV. We used visual rating scales to grade cerebrovascular burden and hippocampal/insular atrophy (HA/IA) on neuroimaging. Only aMCI showed a blunted response to orthostasis. Postural changes in normalised low frequency (LF) power and in the LF to high frequency ratio correlated with a memory test (positively) and HA/IA (negatively) in aMCI, and with attention/executive function tests (negatively) and cerebrovascular burden (positively) in naMCI. These results substantiate the view that the ANS is differentially impaired in aMCI and naMCI, consistently with the neuroanatomic substrate of Alzheimer's and small-vessel subcortical ischaemic disease.

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.

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).

Resting-state brain correlates of instantaneous autonomic outflow

A prominent pathway of brain-heart interaction is represented by autonomic nervous system (ANS) heartbeat modulation. While within-brain resting state networks have been the object of intense functional Magnetic Resonance Imaging (fMRI) research, technological and methodological limitations have hampered research on the central correlates of cardiovascular control dynamics. Here we combine the high temporal and spatial resolution as well as data volume afforded by the Human Connectome Project with a probabilistic model of heartbeat dynamics to characterize central correlates of sympathetic and parasympathetic ANS activity at rest. We demonstrate an involvement of a number of brain regions such as the Insular cortex, Frontal Gyrus, Lateral Occipital Cortex, Paracingulate and Cingulate Gyrus and Precuneous Cortex, as well as subcortical structures (Thalamus, Putamen, Pallidum, Brain-Stem, Hippocampus, Amygdala, and Right Caudate) in the modulation of ANS-mediated cardiovascular control, possibly indicating a broader definition of the central autonomic network (CAN). Our findings provide a basis for an informed neurobiological interpretation of the numerous studies which employ HRV-related measures as standalone biomarkers in health and disease.

A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

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.

Multiscale properties of instantaneous parasympathetic activity in severe congestive heart failure: A survivor vs non-survivor study

Multifractal analysis of cardiovascular variability series is an effective tool for the characterization of pathological states associated with congestive heart failure (CHF). Consequently, variations of heartbeat scaling properties have been associated with the dynamical balancing of nonlinear sympathetic/vagal activity. Nevertheless, whether vagal dynamics has multifractal properties yet alone is currently unknown. In this study, we answer this question by conducting multifractal analysis through wavelet leader-based multiscale representations of instantaneous series of vagal activity as estimated from inhomogeneous point process models. Experimental tests were performed on data gathered from 57 CHF patients, aiming to investigate the automatic recognition accuracy in predicting survivor and non-survivor patients after a 4 years follow up. Results clearly indicate that, on both CHF groups, the instantaneous vagal activity displays power-law scaling for a large range of scales, from ≃ 0.5s to ≃ 100s. Using standard SVM algorithms, this information also allows for a prediction of mortality at a single-subject level with an accuracy of 72.72%.

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.

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.