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Granger causality (GC) analysis is based on the comparison between prediction error variances computed over the full and restricted models after identifying the coefficients of appropriate vector regressions. GC markers can be computed via a double regression (DR) approach identifying two separate, independent models and a single regression (SR) strategy optimizing the description of the dynamics of the target over the full model and, then, reusing some parts of it in the restricted model. The present study compares the SR and DR strategies over heart period (HP), systolic arterial pressure (SAP) and respiration (R) beat-to-beat series collected during a graded orthostatic challenge induced by head-up tilt in 17 healthy individuals (age: 21-36 yrs; median: 29 yrs; 9 females and 8 males). We found that the DR approach was more powerful than the SR one in detecting the expected stronger involvement of the baroreflex during the challenge, while the expected weaker cardiorespiratory coupling was identified by both SR and DR strategies. The less powerful ability of the SR approach was the result of the greater variance of GC markers compared to the DR strategy. We conclude that, contrary to the suggestions present in literature, the SR approach is not necessarily associated with a smaller dispersion of GC markers. Moreover, we suggest that additional factors, such as the strategy utilized to build embedding spaces and metric utilized to compare prediction error variances, might play an important role in differentiating SR and DR approaches.

Baroreflex is commonly typified from heart period (HP) and systolic arterial pressure (SAP) spontaneous variations in the frequency domain mainly by estimating its sensitivity. However, an informative parameter linked to the rapidity of the HP response to SAP changes, such as the baroreflex bandwidth, remains unquantified. We propose a model-based parametric approach for estimating the baroreflex bandwidth from the impulse response function (IRF) of the HP-SAP transfer function (TF). The approach accounts explicitly for the action of mechanisms modifying HP regardless of SAP changes. The method was tested during graded baroreceptor unloading induced by head-up tilt (HUT) at 15°, 30°, 45°, 60°, and 75° (T15, T30, T45, T60, and T75) in 17 healthy individuals (age: 21-36 yr; 9 females and 8 males) and during baroreceptor loading obtained via head-down tilt (HDT) at -25° in 13 healthy men (age: 41-71 yr). The bandwidth was estimated as the decay constant of the monoexponential IRF fitting. The method was robust because the monoexponential fitting described adequately the HP dynamics following an impulse of SAP. We observed that 1 ) baroreflex bandwidth is reduced during graded HUT and this narrowing is accompanied by the reduction of the bandwidth of mechanisms that modify HP regardless of SAP changes and 2 ) baroreflex bandwidth is not affected by HDT but that of SAP-unrelated mechanisms becomes wider. This study provides a method for estimating a baroreflex feature that provides different information compared with the more usual baroreflex sensitivity while accounting explicitly for the action of mechanisms changing HP irrespective of SAP.

Quantification of the cardiorespiratory and cerebrovascular couplings is a relevant clinical issue given that their changes are considered signs of pathological status. The inherent nonlinearity of mechanisms underlying cardiorespiratory and cerebrovascular links requires nonlinear tools for their reliable evaluation. In the present study we compare two nonlinear methods for the assessment of coupling strength between two time series, namely cross-sample entropy (CSampEn) and k-nearest-neighbor cross-predictability (KNNCP). CSampEn uses a strategy that fixes the pattern length, while KNNCP optimizes the pattern length to maximize cross-predictability. CSampEn and KNNCP were applied to the beat-to-beat series of heart period (HP) and respiration (R) during a controlled breathing protocol with the aim at assessing cardiorespiratory coupling and to the beat-to-beat series of mean cerebral blood flow (MCBF) and mean arterial pressure (MAP) during an orthostatic stressor with the aim at evaluating cerebrovascular coupling. Although both the methods have the possibility to quantify the degree of HP-R and MCBF-MAP association, they exhibited different statistical power and even diverse trends in response to the considered physiological challenges. CSampEn and KNNCP are not interchangeable and should be utilized in association more than in alternative for the quantification of the HP-R and MCBF-MAP coupling strength. Clinical Relevance - This study proves that cross-entropy and cross-predictability might lead to different conclusions about cardiorespiratory and cerebrovascular couplings.

In heart period (HP) variability (HPV) recordings the percentage of negative HP variations tends to be greater than that of positive ones and this pattern is referred to as HPV asymmetry (HPVA). HPVA has been studied in several experimental conditions in healthy and pathological populations, but its origin is unclear. The baroreflex (BR) exhibits an asymmetric behavior as well given that it reacts more importantly to positive than negative arterial pressure (AP) variations. We tested the hypothesis that the BR asymmetry (BRA) is a HPVA determinant over spontaneous fluctuations of HP and systolic AP (SAP). We studied 100 healthy subjects (age from 21 to 70 yr, 54 men) comprising 20 subjects in each age decade. Electrocardiogram and noninvasive AP were recorded for 15 min at rest in supine position (REST) and during active standing (STAND). The HPVA was evaluated via Porta's index and Guzik's index, while the BRA was assessed as the difference, and normalized difference, between BR sensitivities computed over positive and negative SAP variations via the sequence method applied to HP and SAP variability. HPVA significantly increased during STAND and decreased progressively with age. BRA was not significantly detected both at REST and during STAND. However, we found a significant positive association between BRA and HPVA markers during STAND persisting even within the age groups. This study supports the use of HPVA indexes as descriptors of BRA and identified a challenge soliciting the BR response like STAND to maximize the association between HPVA and BRA markers.

The coupling and latency between heart period (HP) and systolic arterial pressure (SAP) variability can be investigated along the two arms of the HP-SAP closed loop, namely along the baroreflex feedback from SAP to HP, and along the feedforward pathway from HP to SAP. This study investigates the HP-SAP closed loop variability interactions through cross-correlation function (CCF). Coupling strength and delay between HP and SAP variability series were monitored in 13 subjects prone to develop orthostatic syncope (SYNC, 28±9 yrs, 5 males) and in 13 subjects with no history of postural syncope (noSYNC, age: 27±8 yrs, 5 males). Analysis was carried out at rest in supine position (REST) and during head-up tilt (TILT) at 60 degrees. The null hypothesis of HP-SAP uncoupling was tested through a surrogate analysis associating the HP series of a subject with a SAP sequence of a different one. Results showed that during TILT the coupling strength increased along the baroreflex and latency augmented along the mechanical feedforward pathway exclusively in noSYNC subjects. Finally, closed loop HP-SAP interactions were detected in about one third of subjects and the situation of full uncoupling was rarely found. CCF analysis was found to be a straightforward and easily applicable method to investigate HP-SAP control deserving a direct comparison with more sophisticated signal processing tools assessing causality.

Cardiovascular regulation and autonomic function change across sleep stages and compared to wake. Little information is present in literature about cardiac control during sleep especially in relation to new information-theoretic quantities such as synergy and redundancy. In the present work we compute synergy and redundancy of baroreflex and non-baroreflex components of the cardiac control according to two information-theoretic approaches, namely predictive information decomposition (PID) and minimal mutual information (MMI) methods. We applied a bivariate approach to heart period (HP) and systolic arterial pressure (SAP) beat-to-beat variability series during sleep in a healthy subject. PID approach computes the net balance between synergy and redundancy, while MMI calculates the two quantities as separate entities. Results suggested that: i) redundancy was dominant over synergy during NREM phases; ii) redundancy increased during NREM phase; iii) synergy did not change across the sleep stages. We interpret this result as a consequence of the vagal enhancement, slowing and deepening of respiration during NREM phases. These preliminary findings support the potential of assessing redundancy/synergy of baroreflex-related and unrelated regulations during sleep to improve our knowledge about physiological mechanisms.

The study compares a recently proposed shortterm model-based linear multiscale complexity approach to a single-scale application of the same method and to a model-free nonlinear one based on the computation of conditional entropy with the aim at assessing the complementary information. Comparison was carried out over 24 hours Holter recordings of heart period variability during daytime and nighttime in 12 healthy men (age: 34-55 years). Single-scale methods were able to detect the increased complexity of the cardiac control during nighttime. Multiscale complexity analysis showed that this increase was due to an increase of complexity in the low frequency band (from 0.04 to 0.15 Hz), while complexity in the range of frequencies typical of the respiratory rate was unmodified. Regardless of the method (i.e. linear or nonlinear) single-scale complexity indexes were uncorrelated to the multiscale ones. We conclude that short-term model-based linear multiscale complexity approach provides complementary information to single-scale methods in an application devoted to the analysis of cardiac control from 24 hours Holter recordings.

Cardiac baroreflex (cBR) is activated by both arterial pressure (AP) increases and decreases. Sequence method, a widely utilized tool assessing cBR sensitivity (cBRS) from spontaneous heart period (HP) and systolic AP (SAP) variations, allows the separated computation of cBRS from positive and negative SAP variations. The recently proposed phase-rectified signal averaging (PRSA) method has the same feature but it has been applied so far solely to positive SAP variations. We adapted the PRSA method to compute cBRS over negative SAP variations and we compared the results with those derived from sequence method over two protocols: (i) graded head-up tilt (HUT) at 15, 30, 45, 60, and 75° in 19 healthy subjects and (ii) general anesthesia induction in 118 patients undergoing coronary artery bypass graft surgery. Regardless of the sign of SAP changes and method, cBRS moved toward 0 during HUT. Only sequence method detected the cBRS decrease after general anesthesia induction. In both protocols, the correlation between the PRSA-based cBRSs derived from positive and negative SAP changes was higher than that obtained from analogous sequence-based cBRSs and correlation between equivalent cBRSs derived from different methods might be absent. We conclude that the two methods are not interchangeable in assessing cBRS. Graphical abstract Graphical representation of the baroreflex sensitivity (BRS) estimation procedures carried out using sequence (SEQ) and phase-rectified signal averaging (PRSA) techniques over spontaneous fluctuations of heart period (HP) and systolic arterial pressure (SAP). BRS SEQ and BRS PRSA was separately computed over positive (+) and negative (-) SAP variations.

This study checks whether autonomic markers derived from spontaneous fluctuations of heart period (HP) and systolic arterial pressure (SAP) and from their interactions with spontaneous or mechanical respiration (R) are associated with mortality in patients admitted to intensive care unit (ICU). Three-hundred consecutive HP, SAP and R values were recorded during the first day in ICU in 123 patients. Population was divided into survivors (SURVs, n = 83) and non-survivors (NonSURVs, n = 40) according to the outcome. SURVs and NonSURVs were aged- and gender-matched. All subjects underwent modified head-up tilt (MHUT) by tilting the bed back rest segment to 60°. Autonomic control indexes were computed using time-domain, spectral, cross-spectral, complexity, symbolic and causality techniques via univariate, bivariate and conditional approaches. SAP indexes derived from time-domain, model-free complexity and symbolic approaches were associated with the endpoint, while none of HP variability markers was. The association was more powerful during MHUT. Linear cross-spectral and causality indexes were useless to separate SURVs from NonSURVs, while nonlinear bivariate symbolic markers were successful. When indexes were combined with clinical scores, only SAP variance provided complementary information. Cardiovascular control variability indexes, especially when derived after an autonomic challenge such as MHUT, can improve mortality risk stratification in ICU.

Objective: We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals., Methods: An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs., Results: The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones., Conclusion: The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation., Significance: The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.

Cardioventilatory phase synchronization was studied in ten critically ill patients admitted in intensive care unit (ICU) for acute respiratory failure under two mechanical ventilatory modes: (i) pressure controlled ventilation (PCV); (ii) pressure support ventilation (PSV). The two modalities were administered to the same patient in different times in a random order. Cardioventilatory phase interactions were typified by plotting the relative position of a heartbeat, detected from the electrocardiogram and collected in n groups, within m ventilatory cycles as a function of the progressive cardiac beat number via the synchrogram. n:m phase synchronized patterns were detected by computing the variability of each phase group. The percent duration of the recording featuring phase synchronization was assessed as a measure of the strength of phase synchrony and tested against situations of full phase desynchronization between cardiac and ventilatory rhythms. Indexes quantifying the variability of the cardiac and ventilatory activities were computed as well. Findings proved that: (i) a significant presence of n:m phase synchronized patterns was detected in PCV; (ii) the strength of n:m phase synchronization was stronger during PCV than PSV; (iii) different strengths of cardioventilatory phase synchronization detected during PCV and PSV were found in presence of similar heart and ventilatory rates and alike variability. We conclude that mechanical ventilation can induce a significant presence of cardioventilatory phase synchronized patterns and this amount depends on the mode of mechanical ventilation. Future studies should test the eventual link of the level of phase coordination between heart and mechanical ventilation to a clinical outcome to understand whether featuring a certain degree of cardioventilatory phase synchronization is beneficial for the critical patient in ICU.

The study evaluates the k-nearest-neighbor (KNN) strategy for the assessment of complexity of the cardiac neural control from spontaneous fluctuations of heart period (HP). Two different procedures were assessed: i) the KNN estimation of the conditional entropy (CE) proposed by Porta et al; ii) the KNN estimation of mutual information proposed by Kozachenko-Leonenko, refined by Kraskov-Stögbauer-Grassberger and here adapted for the CE estimation. The two procedures were compared over HP variability recordings obtained at rest in supine position and during head-up tilt (HUT) in amyotrophic lateral sclerosis patients and healthy subjects. We found that the indexes derived from the two procedures were significantly correlated and both methods were able to detect the effect of HUT on HP complexity within the same group and distinguish the two populations within the same experimental condition. We recommend the use of the KNN strategy to quantify the dynamical complexity of cardiac neural control in addition to more traditional approaches.

The study demonstrates the ability of an information-theoretic measure, such as the transfer entropy (TE), in detecting the depression of the cardiac baroreflex control and circulatory-cardio mechanical feedforward link during propofol-induced general anesthesia. TE was computed from spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) in patients undergoing coronary artery bypass graft (CABG). TE from SAP to HP and from HP to SAP were evaluated by accounting for the confounding effect of respiration (R) affecting both HP and SAP (i.e. TESAP→HP|R and TEHP→SAP|R respectively). Both TESAP→HP|R and TEHP→SAP|R decreased during general anesthesia, thus suggesting that the strength of the causal relation diminished over both arms of the closed loop HP-SAP control. The squared coherence function between HP and SAP confirmed the decreased HP-SAP coupling during general anesthesia, even though it could not distinguish directionality.

Self-entropy (SE) and transfer entropy (TE) are widely utilized in biomedical signal processing to assess the information stored into a system and transferred from a source to a destination respectively. The study proposes a more specific definition of the SE, namely the conditional SE (CSE), and a more flexible definition of the TE based on joint TE (JTE), namely the conditional JTE (CJTE), for the analysis of information dynamics in multivariate time series. In a protocol evoking a gradual sympathetic activation and vagal withdrawal proportional to the magnitude of the orthostatic stimulus, such as the graded head-up tilt, we extracted the beat-to-beat spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiratory activity (R) in 19 healthy subjects and we computed SE of HP, CSE of HP given SAP and R, JTE from SAP and R to HP, CJTE from SAP and R to HP given SAP and CJTE from SAP and R to HP given R. CSE of HP given SAP and R was significantly smaller than SE of HP and increased progressively with the amplitude of the stimulus, thus suggesting that dynamics internal to HP and unrelated to SAP and R, possibly linked to sympathetic activation evoked by head-up tilt, might play a role during the orthostatic challenge. While JTE from SAP and R to HP was independent of tilt table angle, CJTE from SAP and R to HP given R and from SAP and R to HP given SAP showed opposite trends with tilt table inclination, thus suggesting that the importance of the cardiac baroreflex increases and the relevance of the cardiopulmonary pathway decreases during head-up tilt. The study demonstrates the high specificity of CSE and the high flexibility of CJTE over real data and proves that they are particularly helpful in disentangling physiological mechanisms and in assessing their different contributions to the overall cardiovascular regulation.

This study was designed to characterize in time, frequency and information domains heart period (HP) and QT interval variabilities in asymptomatic (ASYMP) long QT syndrome type 2 (LQT2) subjects. HP, approximated as the temporal distance between two consecutive R-wave peaks, and QT, approximated as the temporal distance between the R-wave peak and the T-wave offset, were automatically derived from 24h Holter recordings in 10 ASYMP LQT2 patients and 13 healthy non mutation carriers (NMC) subjects. All analyses were carried out during DAY (from 2 to 6 PM) and NIGHT (from 12 to 4 AM). Mean, variance, spectral power and complexity indices at short, medium and long time scales were assessed over HP and QT beat-to-beat series. Circadian rhythmicity was evident in both NMC and ASYMP LQT2 but ASYMP LQT2 subjects were characterized by higher HP, QT interval and HP variability during both DAY and NIGHT. In addition, multiscale complexity analysis was able to differentiate the groups by showing a higher HP complexity and a lower QT complexity at long time scales in ASYMP LQT2 during DAY. ASYMP LQT2 exhibited a different autonomic control compared to NMC and such a differentiation could be protective and assure them a lower risk profile.

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

This study assesses complexity of cardiovascular control in patients affected by type-1 variant of long QT (LQT1) syndrome. Complexity was assessed by refined multiscale entropy of heart period (HP) and QT interval variabilities. HP was taken as the time distance between two consecutive R peaks (RR) and QT interval was approximated as the time distance between the R-peak and T-wave apex (RTa) and between R-peak and T-wave end (RTe). RR, RTa and RTe intervals were automatically extracted from 24h Holter recordings and the daytime period was analyzed (from 02:00 to 06:00 PM). Non mutation carrier (NMC) individuals (n=11), utilized as a control group, were taken from the same family line of the mutation carrier (MC) subjects (n=26). We found that, while NMC and MC groups were indistinguishable based on time domain and complexity analyses of RR dynamics, complexity analysis of RTa and RTe variabilities clearly separates the two populations and suggests an impairment in the cardiac control mechanisms acting on the ventricles.

We propose a multivariate dynamical adjustment (MDA) modeling approach to assess the strength of baroreflex and cardiopulmonary couplings from spontaneous cardiovascular variabilities. Open loop MDA (OLMDA) and closed loop MDA (CLMDA) models were compared. The coupling strength was assessed during progressive sympathetic activation induced by graded head-up tilt. Both OLMDA and CLMDA models suggested that baroreflex coupling progressively increased with tilt table inclination. Only CLMDA model indicated that cardiopulmonary coupling due to the direct link from respiration to heart period gradually decreased with tilt table angles, while that due to the indirect link mediated by systolic arterial pressure progressively increased., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

A linear model-based (MB) approach for the evaluation of Granger causality is compared to a nonlinear model-free (MF) one. The MB method is based on the identification of the coefficients of a multivariate linear regression via least-squares procedure. The MF technique is grounded on the concept of local prediction and exploits the k-nearest-neighbors approach. Both the methods optimize the multivariate embedding dimension but MF technique is more parsimonious since the number of components taken from each signal can be different. Both methods were applied to the variability series of heart period (HP), systolic arterial pressure (SAP) and respiration (R) recorded during spontaneous and controlled respiration at 15 breaths/minute (SR and RC15) in 19 healthy humans. Both MB and MF methods revealed the increase of HP predictability during RC15 and the unmodified causality from SAP to HP and from R to HP during RC15, thus suggesting that nonlinear methods are not superior to the linear ones in assessing predictability and causality in healthy humans.

We test the hypothesis that the degree of correlation between ventricular repolarization duration (VRD) and heart period (HP) carries information on cardiac autonomic regulation. The degree of correlation was assessed in the frequency domain using squared coherence function during an experimental protocol known to gradually induce a shift of sympathovagal balance toward sympathetic predominance (ie, graded head-up tilt). We observed a progressive decrease of squared coherence with tilt table inclination, thus confirming the working hypothesis. The VRD-HP uncoupling occurs in the high-frequency band, centered on the respiratory rate, thus suggesting that vagal withdrawal is responsible for the VRD-HP uncoupling., (Copyright © 2011 Elsevier Inc. All rights reserved.)