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Arterial compliance (C) is a complex parameter influencing ventricular-arterial coupling depending on structural (arterial wall remodeling) and functional (blood pressure, smooth muscles tone) changes. Based on Windkessel model, C can be calculated as the ratio of a time constant Tau characterizing diastolic blood pressure decay and total peripheral resistance (TPR). The aim of this study was to assess changes of C in the context of systolic arterial pressure (SAP) perturbations during four physiological states (supine rest, head-up tilt, supine recovery, mental arithmetic). In order to compare pressure independent changes of C a new index of C120 was proposed predicting C value at 120 mm Hg of SAP. Eighty-one healthy young subjects (48 f, average age 18.6 years) were examined. Hemodynamic parameters were measured beat-to-beat using volume-clamp photoplethysmographic method and impedance cardiography. We observed that C was strongly related to SAP values on the beat-to-beat time scale. Interestingly, C120 decreased significantly during stress phases. In conclusion, potential changes of SAP should be considered when measuring C. Arterial compliance changes in the opposite direction to TPR pointing towards influence of vascular tone changes on its value.

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'.

Baroreflex response consists of cardiac chronotropic (effect on heart rate), cardiac inotropic (on contractility), venous (on venous return) and vascular (on vascular resistance) arms. Because of its measurement simplicity, cardiac chronotropic arm is most often analysed. The aim was to introduce a method to assess vascular baroreflex arm, and to characterize its changes during stress. We evaluated the effect of orthostasis and mental arithmetics (MA) in 39 (22 female, median age: 18.7 yrs.) and 36 (21 female, 19.2 yrs.) healthy volunteers, respectively. We recorded systolic and mean blood pressure (SBP and MBP) by volume-clamp method and R-R interval (RR) by ECG. Cardiac output (CO) was recorded using impedance cardiography. From MBP and CO, peripheral vascular resistance (PVR) was calculated. The directional spectral coupling and gain of cardiac chronotropic (SBP to RR) and vascular arms (SBP to PVR) were quantified. The strength of the causal coupling from SBP to PVR was significantly higher than SBP to RR coupling during whole protocol (P < 0.001). Along both arms, the coupling was higher during orthostasis compared to supine (P < 0.001 and P = 0.006), no MA effect was observed. No significant changes in the spectral gain (ratio of RR or PVR change to a unit SBP change) across all phases were found (0.111 ≤ P ≤ 0.907). We conclude that changes in PVR are tightly coupled with SBP oscillations via the baroreflex providing an approach for the baroreflex vascular arm analysis with a potential to reveal new aspects of blood pressure dysregulation.

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.

Heart rate variability (HRV, variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer T RESP , SBP &rarr, RR is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration ( U SBP &rarr, RR ), nonbaroreflex ( U RESP &rarr, RR ) and baroreflex-mediated ( R RESP , SBP &rarr, RR ) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences ( S RESP , SBP &rarr, RR ), respectively. We find that fast (short time scale) HRV oscillations&mdash, respiratory sinus arrhythmia&mdash, originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Heart rate variability (HRV) analysis represents an important tool for the characterization of complex cardiovascular control. HRV indexes are usually calculated from electrocardiographic (ECG) recordings after measuring the time duration between consecutive R peaks, and this is considered the gold standard. An alternative method consists of assessing the pulse rate variability (PRV) from signals acquired through photoplethysmography, a technique also employed for the continuous noninvasive monitoring of blood pressure. In this work, we carry out a thorough analysis and comparison of short-term variability indexes computed from HRV time series obtained from the ECG and from PRV time series obtained from continuous blood pressure (CBP) signals, in order to evaluate the reliability of using CBP-based recordings in place of standard ECG tracks. The analysis has been carried out on short time series (300 beats) of HRV and PRV in 76 subjects studied in different conditions: resting in the supine position, postural stress during 45° head-up tilt, and mental stress during computation of arithmetic test. Nine different indexes have been taken into account, computed in the time domain (mean, variance, root mean square of the successive differences), frequency domain (low-to-high frequency power ratio LF/HF, HF spectral power, and central frequency), and information domain (entropy, conditional entropy, self entropy). Thorough validation has been performed using comparison of the HRV and PRV distributions, robust linear regression, and Bland–Altman plots. Results demonstrate the feasibility of extracting HRV indexes from CBP-based data, showing an overall relatively good agreement of time-, frequency-, and information-domain measures. The agreement decreased during postural and mental arithmetic stress, especially with regard to band-power ratio, conditional, and self-entropy. This finding suggests to use caution in adopting PRV as a surrogate of HRV during stress conditions.

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.

Cardiovascular complexity is a feature of healthy physiological regulation, which stems from the simultaneous activity of several cardiovascular reflexes and other non-reflex physiological mechanisms. It is manifested in the rich dynamics characterizing the spontaneous heart rate and blood pressure variability (HRV and BPV). The present study faces the challenge of disclosing the origin of short-term HRV and BPV from the statistical perspective offered by information theory. To dissect the physiological mechanisms giving rise to cardiovascular complexity in different conditions, measures of predictive information, information storage, information transfer and information modification were applied to the beat-to-beat variability of heart period (HP), systolic arterial pressure (SAP) and respiratory volume signal recorded non-invasively in 61 healthy young subjects at supine rest and during head-up tilt (HUT) and mental arithmetics (MA). Information decomposition enabled to assess simultaneously several expected and newly inferred physiological phenomena, including: (i) the decreased complexity of HP during HUT and the increased complexity of SAP during MA; (ii) the suppressed cardiorespiratory information transfer, related to weakened respiratory sinus arrhythmia, under both challenges; (iii) the altered balance of the information transferred along the two arms of the cardiovascular loop during HUT, with larger baroreflex involvement and smaller feedforward mechanical effects; and (iv) an increased importance of direct respiratory effects on SAP during HUT, and on both HP and SAP during MA. We demonstrate that a decomposition of the information contained in cardiovascular oscillations can reveal subtle changes in system dynamics and improve our understanding of the complexity changes during physiological challenges.

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 study of short-term cardiovascular interactions is classically performed through the bivariate analysis of the interactions between the beat-to-beat variability of heart period (RR interval from the ECG) and systolic blood pressure (SBP). Recent progress in the development of multivariate time series analysis methods is making it possible to explore how directed interactions between two signals change in the context of networks including other coupled signals. Exploiting these advances, the present study aims at assessing directional cardiovascular interactions among the basic variability signals of RR, SBP and diastolic blood pressure (DBP), using an approach which allows direct comparison between bivariate and multivariate coupling measures. To this end, we compute information-theoretic measures of the strength and delay of causal interactions between RR, SBP and DBP using both bivariate and trivariate (conditioned) formulations in a group of healthy subjects in a resting state and during stress conditions induced by head-up tilt (HUT) and mental arithmetics (MA). We find that bivariate measures better quantify the overall (direct + indirect) information transferred between variables, while trivariate measures better reflect the existence and delay of directed interactions. The main physiological results are: (i) the detection during supine rest of strong interactions along the pathway RR → DBP → SBP, reflecting marked Windkessel and/or Frank-Starling effects; (ii) the finding of relatively weak baroreflex effects SBP → RR at rest; (iii) the invariance of cardiovascular interactions during MA, and the emergence of stronger and faster SBP → RR interactions, as well as of weaker RR → DBP interactions, during HUT. These findings support the importance of investigating cardiovascular interactions from a network perspective, and suggest the usefulness of directed information measures to assess physiological mechanisms and track their changes across different physiological states.

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.