Investigating Dynamic High-Order Interactions in Physiological Networks through Predictive Information Decomposition.

We present an approach to assess redundant and synergistic interactions in network systems via the information-theoretic analysis of multivariate physiological processes. The approach sets up a strategy to decompose the information shared between the present states of a group of random processes and their own past states into unique contributions arising from the past of subgroups of processes and redundant and synergistic contributions arising from the dynamic interaction among the subgroups. The method is illustrated in a theoretical example of linearly interacting Gaussian processes, showing that redundancy and synergy are related mostly to unidirectional coupling and to bidirectional coupling with internal dynamics. It is then applied to the network of short-term heart period, arterial pressure and respiratory variability probed in healthy subjects, showing that redundancy and synergy prevail respectively in cardiorespiratory interactions and in cardiovascular interactions in the resting state, and that postural stress increases the predictive information and the redundancy of physiological interactions.

Exploring the Short-Term Memory of Heart Rate Variability through Model-Free Information Measures.

In this work, we perform a comparative analysis of discrete- and continuous-time estimators of information-theoretic measures quantifying the concept of memory utilization in short-term heart rate variability (HRV). Specifically, considering heartbeat intervals in discrete time we compute the measure of information storage (IS) and decompose it into immediate memory utilization (IMU) and longer memory utilization (MU) terms; considering the timings of heartbeats in continuous time we compute the measure of MU rate (MUR). All measures are computed through model-free approaches based on nearest neighbor entropy estimators applied to the HRV series of a group of 15 healthy subjects measured at rest and during postural stress. We find, moving from rest to stress, statistically significant increases of the IS and the IMU, as well as of the MUR. Our results suggest that both discrete-time and continuous-time approaches can detect the higher predictive capacity of HRV occurring with postural stress, and that such increased memory utilization is due to fast mechanisms likely related to sympathetic activation.

Statistical Approaches to Identify Pairwise and High-Order Brain Functional Connectivity Signatures on a Single-Subject Basis.

Keeping up with the shift towards personalized neuroscience essentially requires the derivation of meaningful insights from individual brain signal recordings by analyzing the descriptive indexes of physio-pathological states through statistical methods that prioritize subject-specific differences under varying experimental conditions. Within this framework, the current study presents a methodology for assessing the value of the single-subject fingerprints of brain functional connectivity, assessed both by standard pairwise and novel high-order measures. Functional connectivity networks, which investigate the inter-relationships between pairs of brain regions, have long been a valuable tool for modeling the brain as a complex system. However, their usefulness is limited by their inability to detect high-order dependencies beyond pairwise correlations. In this study, by leveraging multivariate information theory, we confirm recent evidence suggesting that the brain contains a plethora of high-order, synergistic subsystems that would go unnoticed using a pairwise graph structure. The significance and variations across different conditions of functional pairwise and high-order interactions (HOIs) between groups of brain signals are statistically verified on an individual level through the utilization of surrogate and bootstrap data analyses. The approach is illustrated on the single-subject recordings of resting-state functional magnetic resonance imaging (rest-fMRI) signals acquired using a pediatric patient with hepatic encephalopathy associated with a portosystemic shunt and undergoing liver vascular shunt correction. Our results show that (i) the proposed single-subject analysis may have remarkable clinical relevance for subject-specific investigations and treatment planning, and (ii) the possibility of investigating brain connectivity and its post-treatment functional developments at a high-order level may be essential to fully capture the complexity and modalities of the recovery.

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls.

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing orthostatic syncope in response to prolonged postural stress, and in healthy controls. The spectral measures of total, causal and instantaneous coupling between HP and SAP, and between MAP and CBFV, are averaged in the low-frequency band of the spectrum to focus on specific rhythms, and over all frequencies to get time-domain measures. The analysis of cardiovascular interactions indicates that postural stress induces baroreflex involvement, and its prolongation induces baroreflex dysregulation in syncope subjects. The analysis of cerebrovascular interactions indicates that the postural stress enhances the total coupling between MAP and CBFV, and challenges cerebral autoregulation in syncope subjects, while the strong sympathetic activation elicited by prolonged postural stress in healthy controls may determine an increased coupling from CBFV to MAP during late tilt. These results document that the combination of time-domain and spectral measures allows us to obtain an integrated view of cardiovascular and cerebrovascular regulation in healthy and diseased subjects.

Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic.

This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns of EF intensity of varying conditions of human mobility, including regular teaching and exam activity within the campus, as well as limitations to mobility related to the COVID-19 pandemic. Time series analysis was performed using both simple statistics (mean and variance) and combining the information-theoretic measure of information storage (IS) with the method of surrogate data to quantify the regularity of EF dynamic patterns and detect the presence of nonlinear dynamics. Moreover, to assess the possible coexistence of dynamic behaviors across multiple temporal scales, IS analysis was performed over consecutive observation windows lasting one day, week, month, and year, respectively coarse grained at time scales of 6 min, 30 min, 2 h, and 1 day. Our results document that the EF intensity patterns of variability are modulated by the movement of people at daily, weekly, and monthly scales, and are blunted during periods of restricted mobility related to the COVID-19 pandemic. Mobility restrictions also affected significantly the regularity of the EF intensity time series, resulting in lower values of IS observed simultaneously with a loss of nonlinear dynamics. Thus, our analysis can be useful to investigate changes in the global patterns of human mobility both during pandemics or other types of events, and from this perspective may serve to implement strategies for safety assessment and for optimizing the design of networks of EF sensors.

A new Framework for the Spectral Information Decomposition of Multivariate Gaussian Processes.

Different information-theoretic measures are available in the literature for the study of pairwise and higher-order interactions in multivariate dynamical systems. While these measures operate in the time domain, several physiological and non-physiological systems exhibit a rich oscillatory content that is typically analyzed in the frequency domain through spectral and cross-spectral approaches. For Gaussian systems, the relation between information and spectral measures has been established considering coupling and causality measures, but not for higher-order interactions. To fill this gap, in this work we introduce an information-theoretic framework in the frequency domain to quantify the information shared between a target process and two sources, even multivariate, and to highlight the presence of redundancy and synergy in the analyzed dynamical system. Firstly, we simulate different linear interacting processes by showing the capability of the proposed framework to retrieve amounts of information shared by the processes in specific frequency bands which are not detectable by the related time-domain measures. Then, the framework is applied on EEG time series representative of the brain activity during a motor execution task in a group of healthy subjects.

Measuring the Rate of Information Transfer in Point-Process Data: Application to Cardiovascular Interactions.

We present the implementation to cardiovascular variability of a method for the information-theoretic estimation of the directed interactions between event-based data. The method allows to compute the transfer entropy rate (TER) from a source to a target point process in continuous time, thus overcoming the severe limitations associated with time discretization of event-based processes. In this work, the method is evaluated on coupled cardiovascular point processes representing the heartbeat dynamics and the related peripheral pulsation, first using a physiologically-based simulation model and then studying real point-process data from healthy subjects monitored at rest and during postural stress. Our results document the ability of TER to detect direction and strength of the interactions between cardiovascular processes, also highlighting physiologically plausible interaction mechanisms.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations.

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Assessment of Cardiorespiratory Interactions during Apneic Events in Sleep via Fuzzy Kernel Measures of Information Dynamics.

Apnea and other breathing-related disorders have been linked to the development of hypertension or impairments of the cardiovascular, cognitive or metabolic systems. The combined assessment of multiple physiological signals acquired during sleep is of fundamental importance for providing additional insights about breathing disorder events and the associated impairments. In this work, we apply information-theoretic measures to describe the joint dynamics of cardiorespiratory physiological processes in a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERAs). We analyze the heart period as the target process and the airflow amplitude as the driver, computing the predictive information, the information storage, the information transfer, the internal information and the cross information, using a fuzzy kernel entropy estimator. The analyses were performed comparing the information measures among segments during, immediately before and after the respiratory event and with control segments. Results highlight a general tendency to decrease of predictive information and information storage of heart period, as well as of cross information and information transfer from respiration to heart period, during the breathing disordered events. The information-theoretic measures also vary according to the breathing disorder, and significant changes of information transfer can be detected during RERAs, suggesting that the latter could represent a risk factor for developing cardiovascular diseases. These findings reflect the impact of different sleep breathing disorders on respiratory sinus arrhythmia, suggesting overall higher complexity of the cardiac dynamics and weaker cardiorespiratory interactions which may have physiological and clinical relevance.

An Information-Theoretic Framework to Measure the Dynamic Interaction Between Neural Spike Trains.

OBJECTIVE: While understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience, existing methods either do not consider the inherent point-process nature of spike trains or are based on parametric assumptions. This work presents an information-theoretic framework for the model-free, continuous-time estimation of both undirected (symmetric) and directed (Granger-causal) interactions between spike trains. METHODS: The framework computes the mutual information rate (MIR) and the transfer entropy rate (TER) for two point processes X and Y, showing that the MIR between X and Y can be decomposed as the sum of the TER along the directions X → Y and Y → X. We present theoretical expressions and introduce strategies to estimate efficiently the two measures through nearest neighbor statistics. RESULTS: Using simulations of independent and coupled point processes, we show the accuracy of MIR and TER to assess interactions even for weakly coupled and short realizations, and demonstrate the superiority of continuous-time estimation over the standard discrete-time approach. We also apply the MIR and TER to real-world data, specifically, recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons. Using this dataset, we demonstrate the ability of MIR and TER to describe how the functional networks between recording units emerge over the course of the maturation of the neuronal cultures. CONCLUSION AND SIGNIFICANCE: the proposed framework provides principled measures to assess undirected and directed spike train interactions with more efficiency and flexibility than previous discrete-time or parametric approaches, opening new perspectives for the analysis of point-process data in neuroscience and many other fields.

A Measure of Concurrent Neural Firing Activity Based on Mutual Information.

Multiple methods have been developed in an attempt to quantify stimulus-induced neural coordination and to understand internal coordination of neuronal responses by examining the synchronization phenomena in neural discharge patterns. In this work we propose a novel approach to estimate the degree of concomitant firing between two neural units, based on a modified form of mutual information (MI) applied to a two-state representation of the firing activity. The binary profile of each single unit unfolds its discharge activity in time by decomposition into the state of neural quiescence/low activity and state of moderate firing/bursting. Then, the MI computed between the two binary streams is normalized by their minimum entropy and is taken as positive or negative depending on the prevalence of identical or opposite concomitant states. The resulting measure, denoted as Concurrent Firing Index based on MI (CFIMI), relies on a single input parameter and is otherwise assumption-free and symmetric. Exhaustive validation was carried out through controlled experiments in three simulation scenarios, showing that CFIMI is independent on firing rate and recording duration, and is sensitive to correlated and anti-correlated firing patterns. Its ability to detect non-correlated activity was assessed using ad-hoc surrogate data. Moreover, the evaluation of CFIMI on experimental recordings of spiking activity in retinal ganglion cells brought insights into the changes of neural synchrony over time. The proposed measure offers a novel perspective on the estimation of neural synchrony, providing information on the co-occurrence of firing states in the two analyzed trains over longer temporal scales compared to existing measures.

Measuring the Rate of Information Exchange in Point-Process Data With Application to Cardiovascular Variability.

The amount of information exchanged per unit of time between two dynamic processes is an important concept for the analysis of complex systems. Theoretical formulations and data-efficient estimators have been recently introduced for this quantity, known as the mutual information rate (MIR), allowing its continuous-time computation for event-based data sets measured as realizations of coupled point processes. This work presents the implementation of MIR for point process applications in Network Physiology and cardiovascular variability, which typically feature short and noisy experimental time series. We assess the bias of MIR estimated for uncoupled point processes in the frame of surrogate data, and we compensate it by introducing a corrected MIR (cMIR) measure designed to return zero values when the two processes do not exchange information. The method is first tested extensively in synthetic point processes including a physiologically-based model of the heartbeat dynamics and the blood pressure propagation times, where we show the ability of cMIR to compensate the negative bias of MIR and return statistically significant values even for weakly coupled processes. The method is then assessed in real point-process data measured from healthy subjects during different physiological conditions, showing that cMIR between heartbeat and pressure propagation times increases significantly during postural stress, though not during mental stress. These results document that cMIR reflects physiological mechanisms of cardiovascular variability related to the joint neural autonomic modulation of heart rate and arterial compliance.

A novel approach to probabilistic characterisation of neural firing patterns.

BACKGROUND: The advances in extracellular neural recording techniques result in big data volumes that necessitate fast, reliable, and automatic identification of statistically similar units. This study proposes a single framework yielding a compact set of probabilistic descriptors that characterise the firing patterns of a single unit. NEW METHOD: Probabilistic features are estimated from an inter-spike-interval time series, without assumptions about the firing distribution or the stationarity. The first level of proposed firing patterns decomposition divides the inter-spike intervals into bursting, moderate and idle firing modes, yielding a coarse feature set. The second level identifies the successive bursting spikes, or the spiking acceleration/deceleration in the moderate firing mode, yielding a refined feature set. The features are estimated from simulated data and from experimental recordings from the lateral prefrontal cortex in awake, behaving rhesus monkeys. RESULTS: An efficient and stable partitioning of neural units is provided by the ensemble evidence accumulation clustering. The possibility of selecting the number of clusters and choosing among coarse and refined feature sets provides an opportunity to explore and compare different data partitions. CONCLUSIONS: The estimation of features, if applied to a single unit, can serve as a tool for the firing analysis, observing either overall spiking activity or the periods of interest in trial-to-trial recordings. If applied to massively parallel recordings, it additionally serves as an input to the clustering procedure, with the potential to compare the functional properties of various brain structures and to link the types of neural cells to the particular behavioural states.

Time-frequency characterization of local field potential in a decision making task.

This study seeks to characterize the neuronal mechanisms underlying voluntary decisions to check/verify. In order to describe and potentially decode decisions from brain signals we analyzed intracortical recordings from monkey prefrontal regions obtained during a cognitive task requiring self-initiated as well as cue-instructed decisions. Using local field potentials (LFP) and single units, we analyzed power spectral density, oscillatory modes, power profiles in time, single unit firing rate, and spike-phase relationships in the ß band. Our results point toward specific but variable activation patterns of oscillations in ß band from separate recordings, with task-dependent frequency preference and amplitude modulation of power. The results suggest relationships between particular LFP oscillations and functions engaged at specific time in the task.