A method to assess linear self-predictability of physiologic processes in the frequency domain: application to beat-to-beat variability of arterial compliance.

The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

Diagnostic Importance of OCT Pachymetry in Keratoconus.

AIMS: To demonstrate changes in distance and near fusional vergence measured with prism bars, while compensating for present heterophoria using current ametropia correction. In addition, to determine the differences in values of the AC/A ratio determined by the heterophoric (calculation) and gradient methods. MATERIAL AND METHODS: The basic sample includes 19 subjects with a mean age of 21.5 ±3.0 years (min. 18, max. 27). We used the Von Graefe technique for examination of distance and near phoria, and prism bars for examination of fusion vergences measured in prism diopters. We divided the basic cohort into six research sets according to the size of distance and near heterophoria. This was a cohort of patients with distance (D OR) and near orthophoria (N OR), a cohort of patients with distance (D EX) and near exophoria (N EX) and a set of patients with distance (D ES) and near esophoria (N ES). RESULTS: In the case of both groups with exophoria (distance, near) we found a statistically significant result only for negative fusion vergence (NFV). There was a statistically significant increase in NFV in the sample with distance and near exophoria (D EX, p = 0.01 and B EX, p = 0.02, respectively). In our study, we also demonstrated a statistically significant difference (p < 0.001) in the values of the AC/A ratio measured by the gradient and heterophoric methods. The values determined by the gradient method are lower (3.0 ±1.1 pD/D versus 5.8 ±0.9 pD/D) than by the heterophoric method. CONCLUSION: By comparing fusion vergence values in patients with exophoria and orthophoria, we demonstrated that in the presence of distance or near exophoria there is an increase in ipsilateral fusion vergence. In the case of an increase in ipsilateral fusion vergence, the finding was statistically significant both distance and near (p = 0.01 and p = 0.02, respectively). By contrast, we were unable to prove this fact in the group of patients with esophoria. In our study, we also demonstrated a statistically significant difference (p < 0.001) in the values of the AC/A ratio measured by the gradient and heterophoric methods. The values determined by the gradient method are lower (3.0 ±1.1 pD/D versus 5.8 ±0.9 pD/D) than by the heterophoric method.

Decomposing the Mutual Information Rate of Heart Period and Respiration Variability Series to Assess Cardiorespiratory Interactions.

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.

Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures.

Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) are widely employed tools for characterizing the complex behavior of cardiovascular dynamics. Usually, HRV and BPV analyses are carried out through short-term (ST) measurements, which exploit ~five-minute-long recordings. Recent research efforts are focused on reducing the time series length, assessing whether and to what extent Ultra-Short-Term (UST) analysis is capable of extracting information about cardiovascular variability from very short recordings. In this work, we compare ST and UST measures computed on electrocardiographic R-R intervals and systolic arterial pressure time series obtained at rest and during both postural and mental stress. Standard time-domain indices are computed, together with entropy-based measures able to assess the regularity and complexity of cardiovascular dynamics, on time series lasting down to 60 samples, employing either a faster linear parametric estimator or a more reliable but time-consuming model-free method based on nearest neighbor estimates. Our results are evidence that shorter time series down to 120 samples still exhibit an acceptable agreement with the ST reference and can also be exploited to discriminate between stress and rest. Moreover, despite neglecting nonlinearities inherent to short-term cardiovascular dynamics, the faster linear estimator is still capable of detecting differences among the conditions, thus resulting in its suitability to be implemented on wearable devices.

Simple Formula for pH/Impedance Probe Positioning in Children-Time to Update Standard Practice?

OBJECTIVE: To develop a novel formula for pH probe placement with adequate accuracy. METHODS: Children (3-18 y) undergoing pH-metry were prospectively evaluated. Their height and corrected pH probe position under X-ray (2 vertebrae above the diaphragm) was recorded and the linear-regression analysis was performed to derive a novel formula. Its accuracy was checked on an additional group of prospectively included children. The success rate of a newly developed formula was estimated and compared to the performance of previously used formulae. The difference in the suggested placement of the probe (cm from nostrils) was calculated. RESULTS: Based on 670 children with pH probe placed under X-ray, the following formula was developed using the linear-regression analysis: L = 0.184x + 4.4 (cm) (L = probe placement depth, x = body height). Its accuracy was confirmed on additional 111 children resulting in almost 85% success rate. The formula showed significant difference in the suggested placement from formulae used previously: +4.9 ± 0.8 cm, +2.4 ± 0.1 cm, +0.7 ± 0.6 cm, +1.1 ± 0.4 cm, +1.8 ± 0.3 cm, +2.2 ± 0.5 cm from the one by the Strobel, Moreau, Wilson, Nowak, Staiano-Clouse formulae, and the GOSH table with the calculated success rates of 1.8%, 43.2%, 65.8%, 77.5%, 65.8% and 54.1%, respectively. A table suggesting placement depth based on the body height was developed. CONCLUSION: The present formula provides 85% success of pH probe placement in children ≥ 3 y suggesting its use in routine practice. More data are needed to confirm that probe adjustment under X-ray is unnecessary.

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.

Multiscale partial information decomposition of dynamic processes with short and long-range correlations: theory and application to cardiovascular control.

Objective.In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations.Approach.We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress.Main Results.We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors.Significance.The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.

Feasibility of Linear Parametric Estimation of Dynamic Information Measures to assess Physiological Stress from Short-Term Cardiovascular Variability.

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.

Assessing Transfer Entropy in cardiovascular and respiratory time series under long-range correlations.

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.

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'.

Blood Pressure Variability and Baroreflex Sensitivity in Premature Newborns-An Effect of Postconceptional and Gestational Age.

Introduction: Cardiovascular system is the vitally important system in the dynamical adaptation process of the newborns to the extrauterine environment. To reliably detect immaturity in the given organ system, it is crucial to study the development of the organ functions in relation to maturation process. Objectives: The objective was to determine the changes in the spontaneous short-term blood pressure variability (BPV) and baroreflex sensitivity (BRS) reflecting various aspects of cardiovascular control during the process of maturation in preterm babies and to separate effects of gestational age and postnatal age. Methods: Thirty-three prematurely born infants without any signs of cardio-respiratory disorders (gestational age: 31.8, range: 27-36 weeks; birth weight: 1,704, range: 820-2,730 grams) were enrolled. Continuous peripheral blood pressure signal was obtained by non-invasive volume-clamp photoplethysmography method during supine rest. The recordings of 250 continuous beat-to-beat blood pressure values were processed by spectral analysis of BPV (assessed measures: total power, low frequency and high frequency powers of systolic BPV) and BRS calculation. For each infant we also assessed systolic, diastolic and mean blood pressures, heart rate and respiratory rate. Results: With the postconceptional age, BPV measures decreased (for total power: Spearman correlation coefficient rs = -0.345, P = 0.049; for low frequency power: rs = -0.365, P = 0.037; for high frequency power rs = -0.349; P = 0.046); and BRS increased significantly (rs = 0.448, P = 0.009). The further analysis demonstrated that these effects were more attributable to gestational age than to postnatal age. BRS correlated negatively with BPV magnitude (rs = -0.479 to -0.592, P = 0.001-0.005). Mean blood pressure and diastolic blood pressure increased during maturation (rs = 0.517 and 0.537, P = 0.002 and 0.001, respectively) while heart rate and respiratory rate decreased (rs = -0.366 and -0.516, P = 0.036 and 0.002, respectively). Conclusion: We conclude that maturation process is accompanied by an increased involvement of baroreflex buffering of spontaneous short-term blood pressure oscillations. Gestational age plays a dominant role not only in BPV changes but also in BRS, mean blood pressure, diastolic blood pressure and heart rate changes.

Quantifying multidimensional control mechanisms of cardiovascular dynamics during multiple concurrent stressors.

Heartbeat regulation is achieved through different routes originating from central autonomic network sources, as well as peripheral control mechanisms. While previous studies successfully characterized cardiovascular regulatory mechanisms during a single stressor, to the best of our knowledge, a combination of multiple concurrent elicitations leading to the activation of different autonomic regulatory routes has not been investigated yet. Therefore, in this study, we propose a novel modeling framework for the quantification of heartbeat regulatory mechanisms driven by different neural routes. The framework is evaluated using two heartbeat datasets gathered from healthy subjects undergoing physical and mental stressors, as well as their concurrent administration. Experimental results indicate that more than 70% of the heartbeat regulatory dynamics is driven by the physical stressor when combining physical and cognitive/emotional stressors. The proposed framework provides quantitative insights and novel perspectives for neural activity on cardiac control dynamics, likely highlighting new biomarkers in the psychophysiology and physiopathology fields. A Matlab implementation of the proposed tool is available online.

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.

Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series.

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

Respiratory Sinus Arrhythmia Mechanisms in Young Obese Subjects.

Autonomic nervous system (ANS) activity and imbalance between its sympathetic and parasympathetic components are important factors contributing to the initiation and progression of many cardiovascular disorders related to obesity. The results on respiratory sinus arrhythmia (RSA) magnitude changes as a parasympathetic index were not straightforward in previous studies on young obese subjects. Considering the potentially unbalanced ANS regulation with impaired parasympathetic control in obese patients, the aim of this study was to compare the relative contribution of baroreflex and non-baroreflex (central) mechanisms to the origin of RSA in obese vs. control subjects. To this end, we applied a recently proposed information-theoretic methodology - partial information decomposition (PID) - to the time series of heart rate variability (HRV, computed from RR intervals in the ECG), systolic blood pressure (SBP) variability, and respiration (RESP) pattern measured in 29 obese and 29 age- and gender-matched non-obese adolescents and young adults monitored in the resting supine position and during postural and cognitive stress evoked by head-up tilt and mental arithmetic. PID was used to quantify the so-called unique information transferred from RESP to HRV and from SBP to HRV, reflecting, respectively, non-baroreflex and RESP-unrelated baroreflex HRV mechanisms, and the redundant information transferred from (RESP, SBP) to HRV, reflecting RESP-related baroreflex RSA mechanisms. Our results suggest that obesity is associated: (i) with blunted involvement of non-baroreflex RSA mechanisms, documented by the lower unique information transferred from RESP to HRV at rest; and (ii) with a reduced response to postural stress (but not to mental stress), documented by the lack of changes in the unique information transferred from RESP and SBP to HRV in obese subjects moving from supine to upright, and by a decreased redundant information transfer in obese compared to controls in the upright position. These findings were observed in the presence of an unchanged RSA magnitude measured as the high frequency (HF) power of HRV, thus suggesting that the changes in ANS imbalance related to obesity in adolescents and young adults are subtle and can be revealed by dissecting RSA mechanisms into its components during various challenges.

Repolarization variability independent of heart rate during sympathetic activation elicited by head-up tilt.

The fraction of repolarization variability independent of RR interval variability is of clinical interest. It has been linked to direct autonomic nervous system (ANS) regulation of the ventricles in healthy subjects and seems to reflect the instability of the ventricular repolarization process in heart disease. In this study, we sought to identify repolarization measures that best reflect the sympathetic influences on the ventricles independent of the RR interval. ECG was recorded in 46 young subjects during supine and then following 45 degrees head-up tilt. RR intervals and five repolarization features (QTend, QTpeak, RTend, RTpeak, and TpTe) were extracted from the ECG recordings. Repolarization variability was separated into RR-dependent and RR-independent variability using parametric spectral analysis. Results show that LF power of TpTe is independent of RR in both supine and tilt, while the LF power of QTend and RTend independent of RR and respiration increases following tilt. We conclude that TpTe is independent of RR and is highly affected by respiration. QTend and RTend LF power might reflect the sympathetic influences on the ventricles elicited by tilt. Graphical abstract.

Arterial Stiffness and Endothelial Function in Young Obese Patients - Vascular Resistance Matters.

AIM: Motivated by the paradoxical and differing results of the early atherosclerosis related indices - Cardio-Ankle Vascular Index (CAVI) reflecting arterial stiffness and Reactive Hyperemia Index (RHI) evaluating endothelium dependent flow-induced vasodilation - in obesity, we aimed to assess CAVI and RHI in obese adolescents and young adults in the context of differences in systemic vascular resistance (SVR). METHODS: We examined 29 obese (14f, 15.4 [12.3-18.5] y; BMI: 33.2±4.4 kg.m-2) and 29 non-obese gender and age matched adolescents and young adults (BMI: 21.02±2.3 kg.m-2). CAVI and RHI were measured using VaSera VS-1500 (Fukuda Denshi, Japan) and Endo-PAT 2000 (Itamar Medical, Israel), respectively. Hemodynamic measures were recorded using volume-clamp plethysmography (Finometer Pro, FMS, Netherlands) and impedance cardiography (CardioScreen 2000, Medis GmbH, Germany). SVR and sympathetic activity related indices - Velocity Index (VI) and Heather Index (HI), and LFSAP (spectral power in low frequency band of systolic blood pressure oscillations) were determined. RESULTS: In obese group, CAVI (4.59±0.88 vs. 5.18±0.63, p=0.002) and its refined version CAVI0 (6.46±1.39 vs.7.33±0.99, p=0.002) were significantly lower. No significant difference in RHI was found. SVR and sympathetic activity indices were all significantly lower in the obese group than in the non-obese group. RHI correlated positively with SVR (r=0.390, p=0.044) in obese subjects. CONCLUSION: Our results indicate that both indices used for the detection of early atherosclerotic changes are influenced by vascular tone. Vascular resistance could influence CAVI and RHI results impairing their interpretation.

Multiscale information storage of linear long-range correlated stochastic processes.

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then its complexity is evaluated in terms of conditional entropy. Within this framework, our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive analytical expressions for the information storage computed at multiple timescales. Specifically, we exploit state space models to provide the representation of lowpass filtered and downsampled ARFI processes, from which information storage is computed at any given timescale relating the process variance to the prediction error variance. This enhances the practical usability of multiscale information storage, as it enables a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short timescales, and that reliable estimation of complexity can be achieved at longer timescales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

Comparison of short-term heart rate variability indexes evaluated through electrocardiographic and continuous blood pressure monitoring.

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.