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Heart rate variability results from the coupled activity of the cardiovascular and cardiorespiratory systems, which have their own internal regulation mechanisms but also interact with each other and with the autonomic nervous system to maintain homeostasis. In this work, the assessment of these physiological mechanisms is carried out decomposing the Mutual Information Rate (MIR), an information-theoretic measure of the interdependence between coupled processes, into terms of entropy rate or conditional mutual information related respectively to complexity and causality measures. These measures are computed using a non-parametric approach based on nearest-neighbors. The proposed framework is first tested on simulated autoregressive processes and then applied to experimental data consisting of heart period and respiratory time series measured in healthy subjects monitored at rest and during head-up tilt. Our results evidence that MIR decomposition is able to highlight the interdependence of short-term physiological mechanisms of cardiorespiratory interactions during postural stress.

Heart Period (H) results from the activity of several coexisting control mechanisms, involving Systolic Arterial Pressure (S) and Respiration (R), which operate across multiple time scales encompassing not only short-term dynamics but also long-range correlations. In this work, multiscale representation of Transfer Entropy (TE) and of its decomposition in the network of these three interacting processes is obtained by extending the multivariate approach based on linear parametric VAR models to the Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This approach allows to dissect the different contributions to cardiac dynamics accounting for the simultaneous presence of short and long term dynamics. The proposed method is first tested on simulations of a benchmark VARFI model and then applied to experimental data consisting of H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress. The results reveal that the proposed method can highlight the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems.

Extensive efforts have been recently devoted to implement fast and reliable algorithms capable of assessing the physiological response of the organism to physiological stress. In this study, we propose the comparison between model-free and linear parametric methods as regards their ability to detect alterations in the dynamics and in the complexity of cardiovascular and respiratory variability evoked by postural and mental stress. Dynamic entropy (DE) and information storage (IS) measures were calculated on three physiological time-series, i.e. heart period, respiratory volume and systolic arterial pressure, on 61 healthy subjects monitored in resting conditions as well as during head-up tilt and while performing a mental arithmetic task. The results of the comparison suggest the feasibility of DE and IS measures computed from different physiological signals to discriminate among resting and stress states. If compared to the model-free algorithm, the faster linear method appears to be capable of detecting the same (or even more) statistically significant variations of DE or IS between resting and stress conditions, being thus in perspective more suitable for the integration within wearable devices. The computation of entropy indices extracted from multiple physiological signals acquired through wearables will allow a real-time stress assessment on people in daily-life situations.

The dynamical interplay between brain and heart is mediated by several feedback mechanisms including the central autonomic network and baroreflex loop at a peripheral level, also for a short-term regulation. State of the art focused on the characterization of each regulatory pathway through a single stressor elicitation. However, no studies targeted the actual quantification of different mediating routes leading to the generation of heartbeat dynamics, particularly in case of combined exogenous stimuli. In this study, we propose a new approach based on computational modeling to quantify the contribution of multiple concurrent stimuli in modulating cardiovascular dynamics. In this preliminary attempt, the model estimates the high-frequency power of heartbeat dynamics, and derives disentangling coefficients quantifying the effect of multiple elicitations. Model evaluation is performed on healthy rate variability (HRV) series from fourteen healthy subjects undergoing physical (tilt-table) and mental stressors (aritmetics), as well as their combined administration. Results indicate that, at a group-wise level, in base of concurrent physical and mental elicitations, the physical stressor contributes for the 85% of the resulting heartbeat dynamics. These findings are in agreement with the current knowledge on heartbeat regulatory systems, providing valuable perspectives on the quantification of underlying generative mechanisms of HRV.

In this work, we present the feasibility to use a simpler methodological approach for the assessment of the short-term complexity of Heart Rate Variability (HRV). Specifically, we propose to exploit Pulse Rate Variability (PRV) recorded through photoplethysmography in place of HRV measured from the ECG, and to compute complexity via a linear Gaussian approximation in place of the standard model-free methods (e.g., nearest neighbor entropy estimates) usually applied to HRV. Linear PRV-based and model-free HRV-based complexity measures were compared via statistical tests, correlation analysis and Bland-Altman plots, demonstrating an overall good agreement. These results support the applicability of the simpler proposed approach, which is faster and easier-to-implement, making our approach eligible for portable/wearable devices and thus broadening the out-of-lab accessibility of autonomic indexes.

We present a new method to quantify in the frequency domain the strength of directed interactions between linear stochastic processes. This issue is traditionally addressed by the directed coherence (DC), a popular causality measure derived from the spectral representation of vector autoregressive (AR) processes. Here, to overcome intrinsic limitations of the DC when it needs to be objectively quantified within specific frequency bands, we propose an approach based on spectral decomposition, which allows to isolate oscillatory components related to the pole representation of the vector AR process in the Z-domain. Relating the causal and non-causal power content of these components we obtain a new spectral causality measure, denoted as pole-specific spectral causality (PSSC). In this study, PSSC is compared with DC in the context of cardiovascular variability analysis, where evaluation of the spectral causality from arterial pressure to heart period variability is of interest to assess baroreflex modulation in the low frequency band (0.04-0-15 Hz). Using both a theoretical example in which baroreflex interactions are simulated, and real cardiovascular variability series measured from a group of healthy subjects during a postural challenge, we show that - compared with DC- PSSC leads to a frequency-specific evaluation of spectral causality which is more objective and more focused on the frequency band of interest.

The gold standard method to monitor heart rate variability (HRV) comprises measuring the time series of interbeat interval durations from electrocardiographic (ECG) recordings. However, due to the widespread use, simplicity and usability of photoplethysmographic (PPG) techniques, monitoring pulse rate variability (PRV) from pulse wave recordings has become a viable alternative to standard HRV analysis. The present study investigates the accuracy of PRV, measured as a surrogate of HRV, for the quantification of descriptive indexes computed in the time domain (mean, variance), frequency domain (low-to-high frequency power ratio LF/HF, HF band central frequency) and information domain (entropy, conditional entropy). We analyze short time series (300 intervals) of HRV measured from the ECG and of PRV acquired from Finometer device in 76 subjects monitored in the resting supine position (SU) and in the upright position during head-up tilt (HUT). Time, frequency and information domain indexes are computed for each HRV and PRV series and, for each index, the comparison between the two approaches is performed through statistical comparison of the distributions across subjects, robust linear regression, and Bland-Altman plots. Results of the comparison indicate an overall good agreement between PRV-based and HRV-based indexes, with an accuracy that is slightly lower during HUT than during SU, and for the band-power ratio and conditional entropy. These results suggest the feasibility of PRV-based assessment of HRV descriptive indexes, and suggest to further investigate the agreement in conditions of physiological stress.

To fully elucidate the complex physiological mechanisms underlying the short-term autonomic regulation of heart period (H), systolic and diastolic arterial pressure (S, D) and respiratory (R) variability, the joint dynamics of these variables need to be explored using multivariate time series analysis. This study proposes the utilization of information-theoretic measures to measure causal interactions between nodes of the cardiovascular/cardiorespiratory network and to assess the nature (synergistic or redundant) of these directed interactions. Indexes of information transfer and information modification are extracted from the H, S, D and R series measured from healthy subjects in a resting state and during postural stress. Computations are performed in the framework of multivariate linear regression, using bootstrap techniques to assess on a single-subject basis the statistical significance of each measure and of its transitions across conditions. We find patterns of information transfer and modification which are related to specific cardiovascular and cardiorespiratory mechanisms in resting conditions and to their modification induced by the orthostatic stress.

The aim of this study is to characterize cardiovascular and respiratory signals during orthostatic and mental stress as reflected in indices of entropy and complexity, providing a comparison between the performance of different estimators. To this end, the heart rate variability, systolic blood pressure, diastolic blood pressure and respiration time series were extracted from the recordings of 61 healthy volunteers undergoing a protocol consisting of supine rest, head-up tilt test and mental arithmetic task. The analysis was performed in the information domain using measures of entropy and conditional entropy, estimated through model-based (linear) and model-free (binning, nearest neighbor) approaches. Our results show that different types of stress elicited different responses in the employed indices. On one hand, entropy mainly reflected known changes in the variance of physiological time series. On the other hand, the information conveyed by conditional entropy allowed to characterize the complexity of the four time series during the two stress tasks: we found that cardiac and vascular dynamics underwent a reduction in complexity as a consequence of postural stress, while vascular and respiratory complexity increased as a result of mental stress. As for the performance of different estimators, we did not find substantial differences between model-based and model-free approaches, possibly indicating that significant non-linear dynamics did not appear in the studied conditions.

Obesity during adulthood has been associated with cardiovascular disease, but its adverse effects during adolescence are less well established. The aim of this study was to probe cardiovascular control in obese adolescence by studying causal coherence between cardiovascular variables. Sixty minutes of resting ECG and finger blood pressure were recorded in 19 obese and 19 non-obese subjects in the supine position to measure pair-wise spectral coherence in the low frequency band between heart rate, systolic and diastolic blood pressure, pulse pressure, total peripheral resistance and left ventricular ejection time. We observed that causal coherences in {systolic blood pressure → total peripheral resistance} and {left ventricular ejection time → systolic blood pressure} directions were significantly decreased in obese preadolescents and adolescents when compared to the healthy control group, despite the lack of difference in the magnitude of oscillations of cardiovascular variables. In conclusion, causal coherence analysis of cardiovascular variables may give new insight into cardiovascular dysregulation in young obese subjects.

Coarse graining of physiological time series such as the cardiac interbeat interval series by means of a symbolic transformation retains information about dynamical properties of the underlying system and complements standard measures of heart rate variability. The transformations of the original time series to the coarse grained symbolic series usually lead to a non-uniform occurrence of the different symbols, i.e. some symbols appear more often than others influencing the results of the subsequent symbolic series analysis. Here, we defined a transformation procedure to assure that each symbol appears with equal probability using a short alphabet {0,1,2,3} and a long alphabet {0,1,2,3,4,5}. The procedure was applied to the cardiac interbeat interval series RRi of 17 healthy subjects obtained during graded head-up tilt testing. The symbolic dynamics is analyzed by means of the occurrence of short sequences (`words') of length 3. The occurrence of words is grouped according to words without variations of the symbols (0V%), one variation (1V%), two like variations (2LV%) and two unlike variations (2UV%). Linear regression analysis with respect to tilt angle showed that for the short alphabet 0V% increased with increasing tilt angle whereas 1V%, 2LV% and 2UV% decreased. For the long alphabet 0V%, and 1V% increased with increasing tilt angle whereas 2LV% and 2UV% decreased. These results were slightly better compared to the results from non-uniform symbolic transformations reflecting the deviation from the mean. In conclusion, the symbolic transformation assuring the appearance of symbols with equal probability is capable of reflecting changes of the cardiac autonomic nervous system during graded head-up tilt. Furthermore, the transformation is independent of the time series' distribution.

Heart rate fluctuates beat by beat in a complex manner. The aim of this study was to develop a framework for entropy assessment of heart rate fluctuations on multiple time scales. We employed the Lempel-Ziv algorithm for lossless data compression to investigate the compressibility of RR interval time series on different time scales, using a coarse-graining procedure. We estimated the entropy of RR interval time series of 20 young and 20 old subjects and also investigated the compressibility of randomly shuffled surrogate RR time series. The original RR time series displayed significantly smaller compression entropy values than randomized RR interval data. The RR interval time series of older subjects showed significantly different entropy characteristics over multiple time scales than those of younger subjects. In conclusion, data compression may be useful approach for multiscale entropy assessment of heart rate variability.