Causality in physiological signals

The contribution of granger causality analysis to our understanding of cardiovascular homeostasis: from cardiovascular and respiratory interactions to central autonomic network control

Homeostatic regulation plays a fundamental role in maintenance of multicellular life. At different scales and in different biological systems, this principle allows a better understanding of biological organization. Consequently, a growing interest in studying cause-effect relations between physiological systems has emerged, such as in the fields of cardiovascular and cardiorespiratory regulations. For this, mathematical approaches such as Granger causality (GC) were applied to the field of cardiovascular physiology in the last 20 years, overcoming the limitations of previous approaches and offering new perspectives in understanding cardiac, vascular and respiratory homeostatic interactions. In clinical practice, continuous recording of clinical data of hospitalized patients or by telemetry has opened new applicability for these approaches with potential early diagnostic and prognostic information. In this review, we describe a theoretical background of approaches based on linear GC in time and frequency domains applied to detect couplings between time series of RR intervals, blood pressure and respiration. Interestingly, these tools help in understanding the contribution of homeostatic negative feedback and the anticipatory feedforward mechanisms in homeostatic cardiovascular and cardiorespiratory controls. We also describe experimental and clinical results based on these mathematical tools, consolidating previous experimental and clinical evidence on the coupling in cardiovascular and cardiorespiratory studies. Finally, we propose perspectives allowing to complete the understanding of these interactions between cardiovascular and cardiorespiratory systems, as well as the interplay between brain and cardiac, and vascular and respiratory systems, offering a high integrative view of cardiovascular and cardiorespiratory homeostatic regulation.

From physiological complexity to data interactions-A case study of recordings from exercise monitoring

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

CVRanalysis: a free software for analyzing cardiac, vascular and respiratory interactions

Introduction: Simultaneous beat-to-beat R-R intervals, blood pressure and respiration signals are routinely analyzed for the evaluation of autonomic cardiovascular and cardiorespiratory regulations for research or clinical purposes. The more recognized analyses are i) heart rate variability and cardiac coherence, which provides an evaluation of autonomic nervous system activity and more particularly parasympathetic and sympathetic autonomic arms; ii) blood pressure variability which is mainly linked to sympathetic modulation and myogenic vascular function; iii) baroreflex sensitivity; iv) time-frequency analyses to identify fast modifications of autonomic activity; and more recently, v) time and frequency domain Granger causality analyses were introduced for assessing bidirectional causal links between each considered signal, thus allowing the scrutiny of many physiological regulatory mechanisms. Methods: These analyses are commonly applied in various populations and conditions, including mortality and morbidity predictions, cardiac and respiratory rehabilitation, training and overtraining, diabetes, autonomic status of newborns, anesthesia, or neurophysiological studies. Results: We developed CVRanalysis, a free software to analyze cardiac, vascular and respiratory interactions, with a friendly graphical interface designed to meet laboratory requirements. The main strength of CVRanalysis resides in its wide scope of applications: recordings can arise from beat-to-beat preprocessed data (R-R, systolic, diastolic and mean blood pressure, respiration) or raw data (ECG, continuous blood pressure and respiratory waveforms). It has several tools for beat detection and correction, as well as setting of specific areas or events. In addition to the wide possibility of analyses cited above, the interface is also designed for easy study of large cohorts, including batch mode signal processing to avoid running repetitive operations. Results are displayed as figures or saved in text files that are easily employable in statistical softwares. Conclusion: CVRanalysis is freely available at this website: anslabtools.univ-st-etienne.fr. It has been developed using MATLAB® and works on Windows 64-bit operating systems. The software is a standalone application avoiding to have programming skills and to install MATLAB. The aims of this paper area are to describe the physiological, research and clinical contexts of CVRanalysis, to introduce the methodological approach of the different techniques used, and to show an overview of the software with the aid of screenshots.

Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices

We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset of indices most suitable for our classification problem in order to build an optimal yet simple model for distinguishing between patients suffering from obstructive sleep apnea and a control group.

Pathological Heart Rate Regulation in Apparently Healthy Individuals

Cardiovascular diseases are the leading cause of morbidity and mortality in adults worldwide. There is one common pathophysiological aspect present in all cardiovascular diseases-dysfunctional heart rhythm regulation. Taking this aspect into consideration for cardiovascular risk predictions opens important research perspectives, allowing for the development of preventive treatment techniques. The aim of this study was to find out whether certain pathologically appearing signs in the heart rate variability (HRV) of an apparently healthy person, even with high HRV, can be defined as biomarkers for a disturbed cardiac regulation and whether this can be treated preventively by a drug-free method. This multi-phase study included 218 healthy subjects of either sex, who consecutively visited the physician at Gesundheit clinic because of arterial hypertension, depression, headache, psycho-emotional stress, extreme weakness, disturbed night sleep, heart palpitations, or chest pain. In study phase A, baseline measurement to identify individuals with cardiovascular risks was done. Therefore, standard HRV, as well as the new cardiorhythmogram (CRG) method, were applied to all subjects. The new CRG analysis used here is based on the recently introduced LF drops and HF counter-regulation. Regarding the mechanisms of why these appear in a steady-state cardiorhythmmogram, they represent non-linear event-based dynamical HRV biomarkers. The next phase of the study, phase B, tested whether the pathologically appearing signs identified via CRG in phase A could be clinically influenced by drug-free treatment. In order to validate the new CRG method, it was supported by non-linear HRV analysis in both phase A and in phase B. Out of 218 subjects, the pathologically appearing signs could be detected in 130 cases (60%), p < 0.01, by the new CRG method, and by the standard HRV analysis in 40 cases (18%), p < 0.05. Thus, the CRG method was able to detect 42% more cases with pathologically appearing cardiac regulation. In addition, the comparative CRG analysis before and after treatment showed that the pathologically appearing signs could be clinically influenced without the use of medication. After treatment, the risk group decreased eight-fold-from 130 people to 16 (p < 0.01). Therefore, progression of the detected pathological signs to structural cardiac pathology or arrhythmia could be prevented in most of the cases. However, in the remaining risk group of 16 apparently healthy subjects, 8 people died due to all-cause mortality. In contrast, no other subject in this study has died so far. The non-linear parameter which is able to quantify the changes in CRGs before versus after treatment is FWRENYI4 (symbolic dynamic feature); it decreased from 2.85 to 2.53 (p < 0.001). In summary, signs of pathological cardiac regulation can be identified by the CRG analysis of apparently healthy subjects in the early stages of development of cardiac pathology. Thus, our method offers a sensitive biomarker for cardiovascular risks. The latter can be influenced by non-drug treatments (acupuncture) to stop the progression into structural cardiac pathologies or arrhythmias in most but not all of the patients. Therefore, this could be a real and easy-to-use supplemental method, contributing to primary prevention in cardiology.

Cardiorespiratory Coordination in Collegiate Rowing: A Network Approach to Cardiorespiratory Exercise Testing

Collegiate rowing performance is often assessed by a cardiopulmonary exercise test (CPET). Rowers' on-water performance involves non-linear dynamic interactions and synergetic reconfigurations of the cardiorespiratory system. Cardiorespiratory coordination (CRC) method measures the co-variation among cardiorespiratory variables. Novice (n = 9) vs. Intermediate (n = 9) rowers' CRC (H0: Novice CRC = Intermediate CRC; HA: Novice CRC < Intermediate CRC) was evaluated through principal components analysis (PCA). A female NCAA Division II team (N = 18) grouped based on their off-water performance on 6000 m time trial. Rowers completed a customized CPET to exhaustion and a variety of cardiorespiratory values were recorded. The number of principal components (PCs) and respective PC eigenvalues per group were computed on SPSS vs28. Intermediate (77%) and Novice (33%) groups showed one PC1. Novice group formed an added PC2 due to the shift of expired fraction of oxygen or, alternatively, heart rate/ventilation, from the PC1 cluster of examined variables. Intermediate rowers presented a higher degree of CRC, possible due to their increased ability to utilize the bicarbonate buffering system during the CPET. CRC may be an alternative measure to assess aerobic fitness providing insights to the complex cardiorespiratory interactions involved in rowing during a CPET.

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems, certain channels may overshadow the patterns of others, resulting in information loss. Here, we introduce the framework of Stratified Entropy to prioritize each channels' dynamics based on their allocation to respective strata, leading to a richer description of the multi-channel time-series. As an implementation of the framework, three algorithmic variations of the Stratified Multivariate Multiscale Dispersion Entropy are introduced. These variations and the original algorithm are applied to synthetic time-series, waveform physiological time-series, and derivative physiological data. Based on the synthetic time-series experiments, the variations successfully prioritize channels following their strata allocation while maintaining the low computation time of the original algorithm. In experiments on waveform physiological time-series and derivative physiological data, increased discrimination capacity was noted for multiple strata allocations in the variations when benchmarked to the original algorithm. This suggests improved physiological state monitoring by the variations. Furthermore, our variations can be modified to utilize a priori knowledge for the stratification of channels. Thus, our research provides a novel approach for the extraction of previously inaccessible information from multi-channel time series acquired from heterogeneous systems.

Nonlinear Statistical Analysis of Normal and Pathological Infant Cry Signals in Cepstrum Domain by Multifractal Wavelet Leaders

Multifractal behavior in the cepstrum representation of healthy and unhealthy infant cry signals is examined by means of wavelet leaders and compared using the Student t-test. The empirical results show that both expiration and inspiration signals exhibit clear evidence of multifractal properties under healthy and unhealthy conditions. In addition, expiration and inspiration signals exhibit more complexity under healthy conditions than under unhealthy conditions. Furthermore, distributions of multifractal characteristics are different across healthy and unhealthy conditions. Hence, this study improves the understanding of infant crying by providing a complete description of its intrinsic dynamics to better evaluate its health status.

The Reconstruction of Causal Networks in Physiology

We systematically compare strengths and weaknesses of two methods that can be used to quantify causal links between time series: Granger-causality and Bivariate Phase Rectified Signal Averaging (BPRSA). While a statistical test method for Granger-causality has already been established, we show that BPRSA causality can also be probed with existing statistical tests. Our results indicate that more data or stronger interactions are required for the BPRSA method than for the Granger-causality method to detect an existing link. Furthermore, the Granger-causality method can distinguish direct causal links from indirect links as well as links that arise from a common source, while BPRSA cannot. However, in contrast to Granger-causality, BPRSA is suited for the analysis of non-stationary data. We demonstrate the practicability of the Granger-causality method by applying it to polysomnography data from sleep laboratories. An algorithm is presented, which addresses the stationarity condition of Granger-causality by splitting non-stationary data into shorter segments until they pass a stationarity test. We reconstruct causal networks of heart rate, breathing rate, and EEG amplitude from young healthy subjects, elderly healthy subjects, and subjects with obstructive sleep apnea, a condition that leads to disruption of normal respiration during sleep. These networks exhibit differences not only between different sleep stages, but also between young and elderly healthy subjects on the one hand and subjects with sleep apnea on the other hand. Among these differences are 1) weaker interactions in all groups between heart rate, breathing rate and EEG amplitude during deep sleep, compared to light and REM sleep, 2) a stronger causal link from heart rate to breathing rate but disturbances in respiratory sinus arrhythmia (breathing to heart rate coupling) in subjects with sleep apnea, 3) a stronger causal link from EEG amplitude to breathing rate during REM sleep in subjects with sleep apnea. The Granger-causality method, although initially developed for econometric purposes, can provide a quantitative, testable measure for causality in physiological networks.

Interpersonal Physiological Synchrony for Detecting Moments of Connection in Persons With Dementia: A Pilot Study

Interpersonal physiological synchrony has been successfully used to characterize social interactions and social processes during a variety of interpersonal interactions. There are a handful of measures of interpersonal physiological synchrony, but those that exist have only been validated on able-bodied adults. Here, we present a novel information-theory based measure of interpersonal physiological synchrony-normalized Symbolic Transfer Entropy (NSTE)-and compare its performance with a popular physiological synchrony measure-physiological concordance and single session index (SSI). Using wearable sensors, we measured the electrodermal activity (EDA) of five individuals with dementia and six able-bodied individuals as they participated in a movement activity that aimed to foster connection in persons with dementia. We calculated time-resolved NSTE and SSI measures for case studies of three dyads and compared them against moments of observed interpersonal connection in video recordings of the activity. Our findings suggest that NSTE-based measures of interpersonal physiological synchrony may provide additional advantages over SSI, including resolving moments of ambiguous SSI and providing information about the direction of information flow between participants. This study also investigated the feasibility of using interpersonal synchrony to gain insight into moments of connection experienced by individuals with dementia and further encourages exploration of these measures in other populations with reduced communicative abilities.

Coupling feature extraction method of resting state EEG Signals from amnestic mild cognitive impairment with type 2 diabetes mellitus based on weight permutation conditional mutual information

This study aimed to find a good coupling feature extraction method to effectively analyze resting state EEG signals (rsEEG) of amnestic mild cognitive impairment(aMCI) with type 2 diabetes mellitus(T2DM) and normal control (NC) with T2DM. A method of EEG signal coupling feature extraction based on weight permutation conditional mutual information (WPCMI) was proposed in this research. With the WPCMI method, coupling feature strength of two time series in Alpha1, Alpha2, Beta1, Beta2 and Gamma bands for aMCI with T2DM and NC with T2DM could be extracted respectively. Then selected three frequency bands coupling feature matrix with the help of multi-spectral image transformation method to map it as spectral image characteristics. And finally classified these characteristics through the convolution neural network method(CNN). For aMCI with T2DM and NC with T2DM, the highest classification accuracy of 96%, 95%, 95% could be achieved respectively in the combination of three frequency bands (Alpha1, Alpha2, Gamma), (Beta1, Beta2 and Gamma) and (Alpha2, Beta1, Beta2). This WPCMI method highlighted the coupling dynamic characteristics of EEG signals, and its classification performance was better than all previous methods in aMCI with T2DM diagnosis field. WPCMI method could be used as an effective biomarker to distinguish EEG signals of aMCI with T2DM and NC with T2DM. The coupling feature extraction method used in this paper provided a new perspective for the EEG analysis of aMCI with T2DM.

Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

Transfer entropy (TE) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate TE, but there is no consensus about which one performs best in specific applications. In this study, five methods (linear, k-nearest neighbors, fixed-binning with ranking, kernel density estimation and adaptive partitioning) were compared. The comparison was made on three simulation models (linear, nonlinear and linear + nonlinear dynamics). From the simulations, it was found that the best method to quantify the different interactions was adaptive partitioning. This method was then applied on data from a polysomnography study, specifically on the ECG and the respiratory signals (nasal airflow and respiratory effort around the thorax). The hypothesis that the linear and nonlinear components of cardio-respiratory interactions during light and deep sleep change with the sleep stage, was tested. Significant differences, after performing surrogate analysis, indicate an increased TE during deep sleep. However, these differences were found to be dependent on the type of respiratory signal and sampling frequency. These results highlight the importance of selecting the appropriate signals, estimation method and surrogate analysis for the study of linear and nonlinear cardio-respiratory interactions.

Fast and effective pseudo transfer entropy for bivariate data-driven causal inference

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efficient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard definition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real-world data. In all cases we find that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time-shifted (T-S) surrogates for significance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T-S reduce the computational time by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$82\%$$\end{document}82% with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.

Interlimb Coordination: A New Order Parameter and a Marker of Fatigue During Quasi-Isometric Exercise?

Although exercise-induced fatigue has been mostly studied from a reductionist and component-dominant approach, some authors have started to test the general predictions of theories of self-organized change during exercises performed until exhaustion. However, little is known about the effects of fatigue on interlimb coordination in quasi-isometric actions. The aim of this study was to investigate the effect of exercise-induced fatigue on upper interlimb coordination during a quasi-isometric exercise performed until exhaustion. In order to do this, we hypothesized an order parameter that governs the interlimb coordination as an interlimb correlation measure. In line with general predictions of theory of phase transitions, we expected that the locally averaged values of the order parameter will increase as the fatigue driven system approaches the point of spontaneous task disengagement. Seven participants performed a quasi-isometric task holding an Olympic bar maintaining an initial elbow flexion of 90 degrees until fatigue induced spontaneous task disengagement. The variability of the elbow angle was recorded through electrogoniometry and the obtained time series were divided into three segments for further analysis. Running correlation function (RCF) and adopted bivariate phase rectified signal averaging (BPRSA) were applied to the corresponding initial (30%) and last (30%) segments of the time series. The results of both analyses showed that the interlimb correlation increased between the initial and the final segments of the performed task. Hence, the hypothesis of the research was supported by evidence. The enhancement of the correlation in the last part means a less flexible coordination among limbs. Our results also show that the high magnitude correlation (%RCF > 0.8) and the %Range (END-BEG) may prove to be useful markers to detect the effects of effort accumulation on interlimb coordination. These results may provide information about the loss of adaptability during exercises performed until exhaustion. Finally, we briefly discuss the hypothesis of the inhibitory percolation process being the general explanation of the spontaneous task disengagement phenomenon.

The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges

The field of Network Physiology aims to advance our understanding of how physiological systems and sub-systems interact to generate a variety of behaviors and distinct physiological states, to optimize the organism's functioning, and to maintain health. Within this framework, which considers the human organism as an integrated network, vertices are associated with organs while edges represent time-varying interactions between vertices. Likewise, vertices may represent networks on smaller spatial scales leading to a complex mixture of interacting homogeneous and inhomogeneous networks of networks. Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions-namely strength, direction, and functional form-from time-locked recordings of physiological observables. To this end, a variety of bivariate or, in general, multivariate time-series-analysis techniques, which are derived from diverse mathematical and physical concepts, are employed and the resulting time-dependent networks can then be further characterized with methods from network theory. Despite the many promising new developments, there are still problems that evade from a satisfactory solution. Here we address several important challenges that could aid in finding new perspectives and inspire the development of theoretic and analytical concepts to deal with these challenges and in studying the complex interactions between physiological systems.

The EEG Signal Analysis for Spatial Cognitive Ability Evaluation Based on Multivariate Permutation Conditional Mutual Information-Multi-Spectral Image

This study aims to find an effective method to evaluate the efficacy of cognitive training of spatial memory under a virtual reality environment, by classifying the EEG signals of subjects in the early and late stages of spatial cognitive training. This study proposes a new EEG signal analysis method based on Multivariate Permutation Conditional Mutual Information-Multi-Spectral Image (MPCMIMSI). This method mainly considers the relationship between the coupled features of EEG signals in different channel pairs and transforms the multivariate permutation conditional mutual information features into multi-spectral images. Then, a convolutional neural networks (CNN) model classifies the resultant image data into different stages of cognitive training to objectively assess the efficacy of the training. Compared to the multi-spectral image transformation method based on Granger causality analysis (GCA) and permutation conditional mutual information (PCMI), the MPCMIMSI led to better classification performance, which can be as high as 95% accuracy. More specifically, the Theta-Beta2-Gamma-band combination has the best accuracy. The proposed MPCMIMSI method outperforms the multi-spectral image transformation methods based on GCA and PCMI in terms of classification performance. The MPCMIMSI feature in the Theta-Beta2-Gamma band is an effective biomarker for assessing the efficacy of spatial memory training. The proposed EEG feature-extraction method based on MPCMIMSI offers a new window to characterize spatial information of the noninvasive EEG recordings and might apply to assessing other brain functions.

Dynamic Neuromagnetic Network Changes of Seizure Termination in Absence Epilepsy: A Magnetoencephalography Study

Objective: With increasing efforts devoted to investigating the generation and propagation mechanisms of spontaneous spike and wave discharges (SWDs), little attention has been paid to network mechanisms associated with termination patterns of SWDs to date. In the current study, we aimed to identify the frequency-dependent neural network dynamics during the offset of absence seizures.

Methods: Fifteen drug-naïve patients with childhood absence epilepsy (CAE) were assessed with a 275-Channel Magnetoencephalography (MEG) system. MEG data were recorded during and between seizures at a sampling rate of 6,000 Hz and analyzed in seven frequency bands. Source localization was performed with accumulated source imaging. Granger causality analysis was used to evaluate effective connectivity networks of the entire brain at the source level.

Results: At the low-frequency (1–80 Hz) bands, activities were predominantly distributed in the frontal cortical and parieto–occipito–temporal junction at the offset transition periods. The high-frequency oscillations (HFOs, 80–500 Hz) analysis indicated significant source localization in the medial frontal cortex and deep brain areas (mainly thalamus) during both the termination transition and interictal periods. Furthermore, an enhanced positive cortico–thalamic effective connectivity was observed around the discharge offset at all of the seven analyzed bands, the direction of which was primarily from various cortical regions to the thalamus.

Conclusions: Seizure termination is a gradual process that involves both the cortices and the thalamus in CAE. Cortico–thalamic coupling is observed at the termination transition periods, and the cerebral cortex acts as the driving force.

Time-Frequency Analysis of Cardiovascular and Cardiorespiratory Interactions During Orthostatic Stress by Extended Partial Directed Coherence

In this study, the linear method of extended partial directed coherence (ePDC) was applied to establish the temporal dynamic behavior of cardiovascular and cardiorespiratory interactions during orthostatic stress at a 70° head-up tilt (HUT) test on young age-matched healthy subjects and patients with orthostatic intolerance (OI), both male and female. Twenty 5-min windows were used to analyze the minute-wise progression of interactions from 5 min in a supine position (baseline, BL) until 18 min of the orthostatic phase (OP) without including pre-syncopal phases. Gender differences in controls were present in cardiorespiratory interactions during OP without compromised autonomic regulation. However in patients, analysis by ePDC revealed considerable dynamic alterations within cardiovascular and cardiorespiratory interactions over the temporal course during the HUT test. Considering the young female patients with OI, the information flow from heart rate to systolic blood pressure (mechanical modulation) was already increased before the tilt-up, the information flow from systolic blood pressure to heart rate (neural baroreflex) increased during OP, while the information flow from respiration to heart rate (respiratory sinus arrhythmia) decreased during the complete HUT test. Findings revealed impaired cardiovascular interactions in patients with orthostatic intolerance and confirmed the usefulness of ePDC for causality analysis.

Cardiorespiratory Temporal Causal Links and the Differences by Sport or Lack Thereof

Fitness level, fatigue and adaptation are important factors for determining the optimal training schedule and predicting future performance. We think that adding analysis of the mutual relationships between cardiac and respiratory activity enables better athlete profiling and feedback for improving training. Therefore, the main objectives were (1) to apply several methods for temporal causality analysis to cardiorespiratory data; (2) to establish causal links between the signals; and (3) to determine how parameterized connections differed across various subgroups. One hundred elite athletes (31 female) and a control group of 20 healthy students (6 female) took part in the study. All were asked to follow a protocol comprising two 5-min sessions of free breathing - once supine, once standing. The data were collected using Pneumonitor 2. Respiratory-related curves were obtained through impedance pneumography, along with a single-lead ECG. Several signals (e.g., tidal volume, instantaneous respiratory rate, and instantaneous heart rate) were derived and stored as: (1) raw data down-sampled to 25Hz; (2) further down-sampled to 2.5Hz; and (3) beat-by-beat sequences. Granger causality frameworks (pairwise-conditional, spectral or extended), along with Time Series Models with Independent Noise (TiMINo), were studied. The connections enabling the best distinctions were found using recursive feature elimination with a random forest kernel. Temporal causal links are the most evident between tidal volume and instantaneous heart rate signals. Predictions of the “effect” variable were improved by adding preceding “cause” samples, by medians of 20.3% for supine and 14.2% for standing body positions. Parameterized causal link structures and directions distinguish athletes from non-athletes with 83.3% accuracy on average. They may also be used to supplement standard analysis and enable classification into groups exhibiting different static and dynamic components during performance. Physiological markers of training may be extended to include cardiorespiratory data, and causality analysis may improve the resolution of training profiling and the precision of outcome prediction.

Heart Rhythm Insights Into Structural Remodeling in Atrial Tissue: Timed Automata Approach

The heart rhythm of a person following heart transplantation (HTX) is assumed to display an intrinsic cardiac rhythm because it is significantly less influenced by the autonomic nervous system-the main source of heart rate variability in healthy people. Therefore, such a rhythm provides evidence for arrhythmogenic processes developing, usually silently, in the cardiac tissue. A model is proposed to simulate alterations in the cardiac tissue and to observe the effects of these changes on the resulting heart rhythm. The hybrid automata framework used makes it possible to represent reliably and simulate efficiently both the electrophysiology of a cardiac cell and the tissue organization. The curve fitting method used in the design of the hybrid automaton cycle follows the well-recognized physiological phases of the atrial myocyte membrane excitation. Moreover, knowledge of the complex architecture of the right atrium, the ability of the almost free design of intercellular connections makes the automata approach the only one possible. Two particular aspects are investigated: impairment of the impulse transmission between cells and structural changes in intercellular connections. The first aspect models the observed fatigue of cells due to specific cardiac tissue diseases. The second aspect simulates the increase in collagen deposition with aging. Finally, heart rhythms arising from the model are validated with the sinus heart rhythms recorded in HTX patients. The modulation in the impairment of the impulse transmission between cells reveals qualitatively the abnormally high heart rate variability observed in patients living long after HTX.

Estimating coupling strength between multivariate neural series with multivariate permutation conditional mutual information

Recently, coupling between groups of neurons or different brain regions has been widely studied to provide insights into underlying mechanisms of brain functions. To comprehensively understand the effect of such coupling, it is necessary to accurately extract the coupling strength information among multivariate neural signals from the whole brain. This study proposed a new method named multivariate permutation conditional mutual information (MPCMI) to quantitatively estimate the coupling strength of multivariate neural signals (MNS). The performance of the MPCMI method was validated on the simulated MNS generated by multi-channel neural mass model (MNMM). The coupling strength feature of simulated MNS extracted by MPCMI showed better performance compared with standard methods, such as permutation conditional mutual information (PCMI), multivariate Granger causality (MVGC), and Granger causality analysis (GCA). Furthermore, the MPCMI was applied to estimate the coupling strengths of two-channel resting-state electroencephalographic (rsEEG) signals from different brain regions of 19 patients with amnestic mild cognitive impairment (aMCI) with type 2 diabetes mellitus (T2DM) and 20 normal control (NC) with T2DM in Alpha1 and Alpha2 frequency bands. Empirical results showed that the MPCMI could effectively extract the coupling strength features that were significantly different between the aMCI and the NC. Hence, the proposed MPCMI method could be an effective estimate of coupling strengths of MNS, and might be a viable biomarker for clinical applications.

Discovery of Causal Paths in Cardiorespiratory Parameters: A Time-Independent Approach in Elite Athletes

Training of elite athletes requires regular physiological and medical monitoring to plan the schedule, intensity and volume of training, and subsequent recovery. In sports medicine, ECG-based analyses are well-established. However, they rarely consider the correspondence of respiratory and cardiac activity. Given such mutual influence, we hypothesize that athlete monitoring might be developed with causal inference and that detailed, time-related techniques should be preceded by a more general, time-independent approach that considers the whole group of participants and parameters describing whole signals. The aim of this study was to discover general causal paths among cardiac and respiratory variables in elite athletes in two body positions (supine and standing), at rest. ECG and impedance pneumography signals were obtained from 100 elite athletes. The mean heart rate, the root-mean-square difference of successive RR intervals (RMSSD), its natural logarithm (lnRMSSD), the mean respiratory rate (RR), the breathing activity coefficients, and the resulting breathing regularity (BR) were estimated. Several causal discovery frameworks were applied, comprising Generalized Correlations (GC), Causal Additive Modeling (CAM), Fast Greedy Equivalence Search (FGES), Greedy Fast Causal Inference (GFCI), and two score-based Bayesian network learning algorithms: Hill-Climbing (HC) and Tabu Search. The discovery of cardiorespiratory paths appears ambiguous. The main, still mild, rules best supported by data are: for supine - tidal volume causes heart activity variation, which causes average heart activity, which causes respiratory timing; and for standing - normalized respiratory activity variation causes average heart activity. The presented approach allows data-driven and time-independent analysis of elite athletes as a particular population, without considering prior knowledge. However, the results seem to be consistent with the medical background. Causality inference is an interesting mathematical approach to the analysis of biological responses, which are complex. One can use it to profile athletes and plan appropriate training. In the next step, we plan to expand the study using time-related causality analyses.

Analysis of diagonals in cross recurrence plots between heart rate and systolic blood pressure during supine position and active standing in healthy adults

The inter beat interval (IBI) duration and systolic blood pressure (SBP) are cardiovascular variables related through several feedback mechanisms. We propose the analysis of diagonal lines in cross recurrence plots (CRPs) from IBI and SBP embedded within the same phase space to identify events where trajectories of both variables concur. The aim of the study was to describe the relationship between IBI and SBP of healthy subjects using CRP and diagonal analysis during baseline condition-supine position (SP)-and how the relationship changes during the physiological stress of active standing (AS). IBI and SBP time series were obtained from continuous blood pressure recordings during SP and AS (15 min each) in 19 young healthy subjects. IBI and SBP time series were embedded within a five-dimensional phase space using an embedding delay estimated from cross correlation between IBI and SBP. During SP, mean CRP showed high determinism (≥85%) and also brief but repeated events where both variables stay within a reduced space. Most quantitative recurrences analysis indexes of CRP increased significantly (p < 0.05) during AS. CRP analysis showed short diagonals indicating a very strong deterministic relationship between IBI and SBP with intermittent unlocking periods. The strength of IBI and SBP relationship increased during the physiological stress of AS. The CRP method allowed a rigorous quantitative description of the deterministic association between these two variables. Diagonal lines were intermittent and not always parallel, showing that there is not a defined and unique rhythm. This suggests the activation of different influences at different times and with different precedence between the heart rate and blood pressure in response to AS.

Dynamical Pattern Representation of Cardiovascular Couplings Evoked by Head-up Tilt Test

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties—in particular inter-system coupling—and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop.

Time, frequency, and time-varying Granger-causality measures in neuroscience

This article proposes a systematic methodological review and an objective criticism of existing methods enabling the derivation of time, frequency, and time-varying Granger-causality statistics in neuroscience. The capacity to describe the causal links between signals recorded at different brain locations during a neuroscience experiment is indeed of primary interest for neuroscientists, who often have very precise prior hypotheses about the relationships between recorded brain signals. The increasing interest and the huge number of publications related to this topic calls for this systematic review, which describes the very complex methodological aspects underlying the derivation of these statistics. In this article, we first present a general framework that allows us to review and compare Granger-causality statistics in the time domain, and the link with transfer entropy. Then, the spectral and the time-varying extensions are exposed and discussed together with their estimation and distributional properties. Although not the focus of this article, partial and conditional Granger causality, dynamical causal modelling, directed transfer function, directed coherence, partial directed coherence, and their variant are also mentioned.

Detecting abnormality in heart dynamics from multifractal analysis of ECG signals

The characterization of heart dynamics with a view to distinguish abnormal from normal behavior is an interesting topic in clinical sciences. Here we present an analysis of the Electro-cardiogram (ECG) signals from several healthy and unhealthy subjects using the framework of dynamical systems approach to multifractal analysis. Our analysis differs from the conventional nonlinear analysis in that the information contained in the amplitude variations of the signal is being extracted and quantified. The results thus obtained reveal that the attractor underlying the dynamics of the heart has multifractal structure and the variations in the resultant multifractal spectra can clearly separate healthy subjects from unhealthy ones. We use supervised machine learning approach to build a model that predicts the group label of a new subject with very high accuracy on the basis of the multifractal parameters. By comparing the computed indices in the multifractal spectra with that of beat replicated data from the same ECG, we show how each ECG can be checked for variations within itself. The increased variability observed in the measures for the unhealthy cases can be a clinically meaningful index for detecting the abnormal dynamics of the heart.

Quantify neuromagnetic network changes from pre-ictal to ictal activities in absence seizures

OBJECTIVE

The cortico-thalamo-cortical network plays a key role in childhood absence epilepsy (CAE). However, the exact interaction between the cortex and the thalamus remains incompletely understood. This study aimed to investigate the dynamic changes of frequency-dependent neural networks during the initialization of absence seizures.

METHODS

Magnetoencephalography data from 14 patients with CAE were recorded during and between seizures at a sampling rate of 6000Hz and analyzed in seven frequency bands. Neuromagnetic sources were volumetrically scanned with accumulated source imaging. Effective connectivity networks of the entire brain, including the cortico-thalamo-cortical network, were evaluated at the source level through Granger causality analysis.

RESULTS

The low-frequency (1-80Hz) activities showed significant frontal cortical and parieto-occipito-temporal junction source localization around seizures. The high-frequency (80-250Hz) oscillations showed predominant activities consistently localized in deep brain areas and medial frontal cortex. The increased cortico-thalamic effective connectivity was observed around seizures in both low- and high-frequency ranges. The direction was predominantly from the cortex to the thalamus at the early time, although the cortex that drove connectivity varied among subjects.

CONCLUSIONS

The cerebral cortex plays a key role in driving the cortico-thalamic connections at the early portion of the initialization of absence seizures. The oscillatory activities in the thalamus could be triggered by networks from various regions in the cortex.

SIGNIFICANCE

The dynamic changes of neural network provide evidences that absence seizures are probably resulted from cortical initialized cortico-thalamic network.

Altered Effective Connectivity Network in Childhood Absence Epilepsy: A Multi-frequency MEG Study

Using multi-frequency magnetoencephalography (MEG) data, we investigated whether the effective connectivity (EC) network of patients with childhood absence epilepsy (CAE) is altered during the inter-ictal period in comparison with healthy controls. MEG data from 13 untreated CAE patients and 10 healthy controls were recorded. Correlation analysis and Granger causality analysis were used to construct an EC network at the source level in eight frequency bands. Alterations in the spatial pattern and topology of the network in CAE were investigated by comparing the patients with the controls. The network pattern was altered mainly in 1-4 Hz, showing strong connections within the frontal cortex and weak connections in the anterior-posterior pathways. The EC involving the precuneus/posterior cingulate cortex (PC/PCC) significantly decreased in low-frequency bands. In addition, the parameters of graph theory were significantly altered in several low- and high-frequency bands. CAE patients display frequency-specific abnormalities in the network pattern even during the inter-ictal period, and the frontal cortex and PC/PCC might play crucial roles in the pathophysiology of CAE. The EC network of CAE patients was over-connective and random during the inter-ictal period. This study is the first to reveal the frequency-specific alteration in the EC network during the inter-ictal period in CAE patients. Multiple-frequency MEG data are useful in investigating the pathophysiology of CAE, which can serve as new biomarkers of this disorder.

Uncoupling of cardiac and respiratory rhythm in atrial fibrillation

Rearranged origin of heart rhythm in patients with atrial fibrillation (AF) influences the regulation of the heart and consequently the respiratory rhythm, and the bidirectional interaction of these rhythms not documented. Hence, we examined coupling of the RR interval and the respiration (Resp) signal by coherence, Granger causality and the cross-sample entropy method of time series analysis in patients with AF and a healthy control group. In healthy subjects, the influence of respiration on cardiac rhythm was found as increased coherence at the breathing frequency (BF) range, significantly stronger interaction and synchrony from Resp to RR than from RR to Resp. On the contrary, in patients with AF, coherence at BF diminished, there were no causal interactions between signals in both directions, which resulted in equally great asynchrony between them. In AF, the absence of full functionality of the sinoatrial node, as an integrator of neural cardiac control, resulted in diminished vagal modulation of heart periods and consequently impaired bidirectional cardio-respiratory interaction.