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Complexity analysis of short-term cardiovascular control is traditionally performed using entropy-based approaches including corrective terms or strategies to cope with the loss of reliability of conditional distributions with pattern length. This study proposes a new approach aiming at the estimation of conditional entropy (CE) from short data segments (about 250 samples) based on the k-nearest-neighbor technique. The main advantages are: (i) the control of the loss of reliability of the conditional distributions with the pattern length without introducing a priori information; (ii) the assessment of complexity indexes without fixing the pattern length to an arbitrary low value. The approach, referred to as k-nearest-neighbor conditional entropy (KNNCE), was contrasted with corrected approximate entropy (CApEn), sample entropy (SampEn) and corrected CE (CCE), being the most frequently exploited approaches for entropy-based complexity analysis of short cardiovascular series. Complexity indexes were evaluated during the selective pharmacological blockade of the vagal and/or sympathetic branches of the autonomic nervous system. We found that KNNCE was more powerful than CCE in detecting the decrease of complexity of heart period variability imposed by double autonomic blockade. In addition, KNNCE provides indexes indistinguishable from those derived from CApEn and SampEn. Since this result was obtained without using strategies to correct the CE estimate and without fixing the embedding dimension to an arbitrary low value, KNNCE is potentially more valuable than CCE, CApEn and SampEn when the number of past samples most useful to reduce the uncertainty of future behaviors is high and/or variable among conditions and/or groups. [ABSTRACT FROM AUTHOR]

Objective. The percentages of cardiac and sympathetic baroreflex patterns detected via baroreflex sequence (SEQ) technique from spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) and of muscle nerve sympathetic activity (MSNA) burst rate and diastolic arterial pressure (DAP) are utilized to assess the level of the baroreflex engagement. The cardiac baroreflex patterns can be distinguished in those featuring both HP and SAP increases (cSEQ++) and decreases (cSEQ--), while the sympathetic baroreflex patterns in those featuring a MSNA burst rate decrease and a DAP increase (sSEQ+-) and vice versa (sSEQ-+). The present study aims to assess the modifications of the involvement of the cardiac and sympathetic arms of the baroreflex with age and postural stimulus intensity. Approach. We monitored the percentages of cSEQ++ (%cSEQ++) and cSEQ-- (%cSEQ--) in 100 healthy subjects (age: 21-70 years, 54 males, 46 females), divided into five sex-balanced groups consisting of 20 subjects in each decade at rest in supine position and during active standing (STAND). We evaluated %cSEQ++, %cSEQ--, and the percentages of sSEQ+- (%sSEQ+-) and sSEQ-+ (%sSEQ-+) in 12 young healthy subjects (age 23 ± 2 years, 3 females, 9 males) undergoing incremental head-up tilt. Main results. We found that: (i) %cSEQ++ and %cSEQ-- decreased with age and increased with STAND and postural stimulus intensity; (ii) %sSEQ+- and %sSEQ-+ augmented with postural challenge magnitude; (iii) the level of cardiac and sympathetic baroreflex engagement did not depend on either the absolute value of arterial pressure or the direction of its changes. Significance. This study stresses the limited ability of the cardiac and sympathetic arms of the baroreflex in controlling absolute arterial pressure values and the equivalent ability of both positive and negative arterial pressure changes in soliciting them., (Creative Commons Attribution license.)

Objective. Aortic valve stenosis (AVS) induces left ventricular function adaptations and surgical aortic valve replacement (SAVR) restores blood flow profile across aortic valve. Modifications of cardiac hemodynamics induced by AVS and SAVR might alter cardiovascular (CV) and cerebrovascular (CBV) controls. The study aims at characterizing CV and CBV regulations one day before SAVR (PRE), within one week after SAVR (POST), and after a three-month follow-up (POST3) in 73 AVS patients (age: 63.9 ± 12.9 yrs; 48 males, 25 females) from spontaneous fluctuations of heart period (HP), systolic arterial pressure, mean arterial pressure and mean cerebral blood velocity. Approach. CV and CBV regulations were typified via a bivariate autoregressive approach computing traditional frequency domain markers and causal squared coherence ( CK 2 We found that: (i) CV regulation is impaired in AVS patients; (ii) CV regulation worsens in POST; (iii) CV regulation recovers in POST3 and CV response to active standing is even better than in PRE; (iv) CBV regulation is preserved in AVS patients; (v) SAVR does not affect CBV control; (vi) parameters of the CBV control in POST3 and PRE are similar. Main results. We found that: (i) CV regulation is impaired in AVS patients; (ii) CV regulation worsens in POST; (iii) CV regulation recovers in POST3 and CV response to active standing is even better than in PRE; (iv) CBV regulation is preserved in AVS patients; (v) SAVR does not affect CBV control; (vi) parameters of the CBV control in POST3 and PRE are similar. Significance. CK 2 is particularly useful to characterize CV and CBV controls in AVS patients and to monitor of patient's evolution after SAVR., (Creative Commons Attribution license.)

Objective. Closed loop cardiovascular (CV) and cerebrovascular (CBV) variability interactions are assessed via transfer entropy (TE) from systolic arterial pressure (SAP) to heart period (HP) and vice versa and from mean arterial pressure (MAP) to mean cerebral blood velocity (MCBv) and vice versa. This analysis is exploited to assess the efficiency of baroreflex and cerebral autoregulation. This study aims at characterizing CV and CBV controls in postural orthostatic tachycardiac syndrome (POTS) subjects experiencing exaggerated sympathetic response during orthostatic challenge via unconditional TE and TE conditioned on respiratory activity ( R ). Approach. In 18 healthy controls (age: 28 ± 13 yrs; 5 males, 13 females) and 15 POTS individuals (age: 29 ± 11 yrs; 3 males, 12 females) we acquired beat-to-beat variability of HP, SAP, MAP and MCBv and two R signals, namely respiratory chest movement (RCM) and capnogram (CAP). Recordings were made at sitting rest and during active standing (STAND). TE was computed via vector autoregressive approach. Main results. We found that: (i) when assessing CV interactions, the increase of the TE from SAP to HP during STAND, indicating baroreflex activation, is detected solely when conditioning on RCM; (ii) when assessing CBV interactions, the impact of R on the TE computation is negligible; (iii) POTS shows baroreflex impairment during STAND; (iv) POTS exhibits a normal CBV response to STAND. Significance. TE is useful for detecting the impairment of specific regulatory mechanisms in POTS. Moreover, using different R signals highlights the sensitivity of CV and CBV controls to specific R aspects., (Creative Commons Attribution license.)

Objective . Cardiovascular control mechanisms are commonly studied during baroreceptor unloading induced by head-up tilt. Conversely, the effect of a baroreceptor loading induced by head-down tilt (HDT) is less studied especially when the stimulus is of moderate intensity and using model-based spectral causality markers. Thus, this study computes model-based causality markers in the frequency domain derived via causal squared coherence and Geweke spectral causality approach from heart period (HP) and systolic arterial pressure (SAP) variability series. Approach . We recorded HP and SAP variability series in 12 healthy men (age: from 41 to 71 yrs, median: 57 yrs) during HDT at -25°. The approaches are compared by considering two different bivariate model structures, namely the autoregressive and dynamic adjustment models. Markers are computed in traditional frequency bands utilized in cardiovascular control analysis, namely the low frequency (LF, from 0.04 to 0.15 Hz) and high frequency (HF, from 0.15 to 0.4 Hz) bands. Main results . We found that: (i) the two spectral causality metrics are deterministically related but spectral causality markers exhibit different discriminative ability; (ii) HDT reduces the involvement of the baroreflex in regulating HP-SAP variability interactions in the LF band, while leaving unmodified the action of mechanical feedforward mechanisms in both LF and HF bands; (iii) this conclusion does not depend on the model structure. Significance . We conclude that HDT can be utilized to reduce the impact of baroreflex and to study the contribution of regulatory mechanisms different from baroreflex to the complexity of cardiovascular control in humans., (Creative Commons Attribution license.)

Background: Patients undergoing coronary artery bypass graft (CABG) surgery might experience postoperative complications and some of them, such as acute kidney dysfunction (AKD), are the likely consequence of hypoperfusion. We hypothesized that an impaired cerebrovascular control is a hallmark of a vascular damage that might favor AKD after CABG., Objective: Our aim is to characterize cerebrovascular control in CABG patients through the assessment of the relationship between mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV) and to check whether markers describing MCBFV-MAP dynamical interactions could identify subjects at risk to develop postoperative AKD., Approach: MAP and MCBFV beat-to-beat series were extracted from invasive arterial pressure and transcranial Doppler recordings acquired simultaneously in 23 patients just before CABG after the induction of propofol general anesthesia. Subjects were divided into AKD group (n  =  9, age: 68  ±  9, 8 males) and noAKD group (n  =  14, age: 65  ±  8, 12 males) according to whether they developed postoperative AKD or not after CABG. We computed MAP and MCBFV time-domain and spectral markers as well as MCBFV-MAP cross-spectral indexes in very-low-frequency (VLF, 0.02-0.07 Hz), low-frequency (LF, 0.07-0.15 Hz) and high-frequency (HF, 0.15-0.30 Hz) bands. We also calculated model-based transfer entropy (TE) to quantify the degree of MCBFV dependence on MAP and vice versa. The null hypothesis of MCBFV-MAP uncoupling was tested via a surrogate approach associating MAP and MCBFV in different patients., Main Results: Time, spectral and cross-spectral markers had a limited power in separating AKD from noAKD individuals. Conversely, TE from MAP to MCBFV was significantly above the level set by surrogates only in AKD groups and significantly larger than that computed in noAKD., Significance: The reduced cerebrovascular autoregulation in AKD patients suggest a vascular impairment likely making them more at risk of hypoperfusion during CABG and AKD after CABG.

Background: Low cardiac output syndrome (LCOS) is a myocardial dysfunction leading to systemic hypoperfusion, favored by particular conditions of the autonomic nervous system. LCOS is one of the adverse events that might occur after cardiac surgery., Objective: The aim is to test the hypothesis that short-term multiscale complexity (MSC) analysis of heart period (HP) and systolic arterial pressure (SAP) variability series in the frequency bands typical of cardiovascular control could be fruitfully exploited in identifying subjects at risk of developing LCOS after coronary artery bypass graft (CABG)., Approach: HP and SAP beat-to-beat series were derived from electrocardiogram (ECG) and invasive arterial pressure (AP) signal acquired in 128 patients scheduled for CABG before (PRE) and after (POST) the induction of general anesthesia with propofol and remifentanil. Subjects were labeled as LCOS (n  =  14) and noLCOS (n  =  114) according to the LCOS development. MSC markers were calculated as the complement to 1 of the modulus of the average position of the poles dropping in the low-frequency (LF, 0.04-0.15 Hz) and high-frequency (HF, 0.15-0.5 Hz) bands as derived from the autoregressive model of HP and SAP series. Traditional time and frequency domain indexes were also calculated., Main Results: Traditional parameters were able to assess the depression of the cardiovascular regulation induced by general anesthesia, but showed weak performances in differentiating LCOS and noLCOS groups. Conversely, HP complexity in LF band and SAP complexity in HF band assessed during POST remained associated with LCOS even after entering a multivariate logistic regression model adjusted for clinical and demographic factors., Significance: The MSC approach can be fruitfully applied to improve risk stratification for LCOS after CABG likely because MSC markers describe the dysfunction of the sympathetic control and the impairment of the mechanical properties of the heart in the LCOS group.

Background: The sympathetic baroreflex (sBR) adjusts muscle sympathetic nerve activity (MSNA) in response to arterial pressure changes but the relevance of assessing sBR control complexity is unclear., Objective: We propose a method for the evaluation of sBR control complexity., Approach: The approach comprises the quantification of complexity of the sBR latency regulation and the assessment of complexity of the relationship linking MSNA burst to R-wave peak regardless of the variability of the sBR latency. The Shannon entropy (SE) of the sBR latency distribution is taken as an estimate of complexity of the sBR latency regulation. The conditional entropy (CE) of the beat-to-beat binary series obtained by coding the presence/absence of the MSNA burst after an R-wave peak is taken as an estimate of complexity of the sBR control regardless of the sBR latency variability. Surrogate analysis was utilized to set the level of inactive or impaired sBR. The approach was applied to 10 young healthy subjects undergoing head-up tilt (HUT) followed by lower body negative pressure to evoke presyncope (preSYNC) before and after 21 d head-down bed rest (HDBR), and to five amyotrophic lateral sclerosis (ALS) patients undergoing HUT., Main Results: In healthy subjects the surrogate analysis suggested that HUT and preSYNC significantly activated the sBR control but its response was weakened after 21 d HDBR. During preSYNC sBR latency increased significantly only after 21 d HDBR. In ALS patients the complexity of the sBR latency regulation was close to the level set by surrogate analysis and HUT did not trigger any sBR control response., Significance: The proposed method for sBR control complexity quantification was useful in detecting the impairment of the sBR control after 21 d HDBR in healthy subjects and the dysfunction of the sBR regulation in ALS patients.

Background: Probabilistic causality (PC) is a framework for checking that the occurrence of a cause raises the probability of the effect by comparing the probability of the effect conditioned and unconditioned to the cause. Even though it is less frequently utilized with respect to the more traditional model-based Wiener-Granger causality (WGC) that is based on the predictability improvement of an effect resulting from the inclusion of the presumed cause in the multivariate linear regression model, PC has the advantage of being model-free., Objective: The aim of the study is to apply the PC framework to assess the evolution of cardiac baroreflex control with age from spontaneous fluctuations of heart period (HP) and systolic arterial pressure (SAP) and to compare it to the more common WGC approach., Approach: We studied 100 healthy humans (54 males, age: 21-70 years, 20 subjects for each 10 years bin). HP and SAP were extracted on a beat-to-beat basis from 5 min recordings of electrocardiogram and plethysmographic arterial pressure at rest in supine position (REST) and during active standing (STAND) under spontaneous breathing. The WGC ratio (WGCR) was computed as the log ratio of the prediction error variance of the autoregressive model on HP to that on HP with exogenous SAP. The PC ratio (PCR) was computed as the probability of observing an HP ramp given an associated parallel SAP variation divided by the probability of observing an HP ramp., Main Results: The WGCR and PCR suggested the gradual impairment of cardiac baroreflex with age, especially during STAND. Moreover, they were significantly associated both at REST and during STAND but the degree of the PCR-WGCR association was weak., Significance: PC can be effectively exploited to assess modification of the cardiovascular control during senescence even though a limited agreement was observed with WGC.

Objective: A network physiology approach to evaluate the strength of the directed interactions among cardiac controls at sinoatrial and ventricular levels and respiration (R) is proposed., Approach: The network is composed of three nodes (i.e. sinoatrial and ventricular cardiac controls and R) and their activity is exemplified by the variability of heart period (HP), the variability of the duration of the electrical activity of the heart approximated as the temporal distance between Q-wave onset and T-wave end or apex (i.e. QTe or QTa) and thoracic movements respectively. Model-based transfer entropy provided the estimate of the strength of the causal link from the source to the destination conditioned on the remaining node activity. The interactions were monitored in 15 healthy subjects aged from 24 to 54 years (9 males). Increasing levels of sympathetic activity were induced by graded head-up tilt with table inclination of 0, 15, 30, 45, 60, 75°., Main Results: We found that: (i) the strength of the causal link from HP to QTe gradually decreases with tilt table angle, while that in the reverse direction is weak, even though significant, and constant; (ii) the action of R on HP is stronger than that from R to QTe; (iii) the strength of the relation from R to HP is weakly related to tilt table inclination, while that from R to QTe does not depend on it; (iv) while QTe cannot affect R, a weak causal dependence of R on HP is detected; (v) the network computed over QTa is qualitatively similar to that over QTe, even though the strength of the causal relations might be different., Significance: The proposed network physiology approach provides a comprehensive picture of the directed links among relevant cardiac regulatory mechanisms and their evolution with sympathetic tone usable to identify pathological conditions.

Objective: We exploited a model-based Wiener-Granger causality method in the information domain for the evaluation of the transfer entropy (TE) and interaction TE (ITE), the latter taken as a measure of the net balance between redundancy and synergy, to describe the interactions between the spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) and the effect of respiration (R) on both variables., Approach: Cardiac control was typified via the genuine TE from SAP to HP, that from R to HP, and the ITE from SAP and R to HP, while vascular control was characterized via the genuine TE from HP to SAP, that from R to SAP, and the ITE from HP and R to SAP. The approach was applied to study age-related modifications of cardiac and vascular controls in a cohort of 100 healthy humans (age from 21 to 70 years, 54 males) recorded at supine rest (REST) and during active standing (STAND). A surrogate approach was exploited to test the significance of the computed quantities., Main Results: Trends of the genuine information transfer with age, already present in literature, were here confirmed. We originally found that: (i) at REST redundancy was predominant over synergy in both vascular and cardiac controls; (ii) the predominance of redundancy of the cardiac control was not affected by postural challenge, while STAND reduced redundancy of vascular control; (iii) the net redundancy of the cardiac control at REST gradually decreased with age, while that of vascular control remained stable; (iv) during STAND net redundancy of both cardiac and vascular controls was stable with age., Significance: The study confirms the relevance of computing genuine information transfer in cardiovascular control analysis and stresses the importance of evaluating the ITE to quantify the degree of redundancy of physiological mechanisms operating to maintain cardiovascular homeostasis.

Objective: A model-based conditional transfer entropy approach was exploited to quantify the information transfer in cerebrovascular (CBV) and cardiovascular (CV) systems in subjects prone to develop postural syncope., Approach: Spontaneous beat-to-beat variations of mean cerebral blood flow velocity (MCBFV) derived from a transcranial Doppler device, heart period (HP) derived from surface electrocardiogram, mean arterial pressure (MAP) and systolic arterial pressure (SAP) derived from finger plethysmographic arterial pressure device were monitored at rest in supine position (REST) and during 60° head-up tilt (TILT) in 13 individuals (age mean  ±  standard deviation: 28  ±  9 years, min-max range: 18-44 years, 5 males) with a history of recurrent episodes of syncope (SYNC) and in 13 age- and gender-matched controls (NonSYNC). Respiration (R) obtained from a thoracic belt was acquired as well and considered as a conditioning signal in transfer entropy assessment. Synchronous sequences of 250 consecutive MCBFV, HP, MAP, SAP and R values were utilized to estimate the information genuinely transferred from MAP to MCBFV (i.e. disambiguated from R influences) and vice versa. Analogous indexes were computed from SAP to HP and vice versa. Traditional time and frequency domain analyses were carried out as well., Main Results: SYNC subjects showed an increased genuine information transfer from MAP to MCBFV during TILT, while they did not exhibit the expected rise of the genuine information transfer from SAP to HP., Significance: We conclude that SYNC individuals featured an impaired cerebral autoregulation visible during TILT and were unable to activate cardiac baroreflex to cope with the postural challenge. Traditional frequency domain markers based on transfer function modulus, phase and coherence functions were less powerful or less specific in typifying the CBV and CV controls of SYNC individuals. Conditional transfer entropy approach can identify the impairment of CBV and CV controls and provide specific clues to identify subjects prone to develop postural syncope.

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.

We hypothesized that Wiener-Granger causality (WGC) indexes might have different abilities in coping with modifications of the complexity of the target variable in the context of the assessment of the cardiovascular control from spontaneous fluctuations of heart period (HP), systolic arterial pressure (SAP) and respiratory activity (R). After having defined the universe of knowledge as the set Ω = {HP, SAP, R} and the unpredictability decrement (UPD) as the difference between the prediction error variances of the target signal computed in Ω after excluding the presumed cause (i.e. the restricted Ω) and in Ω, we computed the following frequently utilized WGC indexes: (i) the plain UPD; (ii) the fractional UPD (FUPD) by dividing UPD by the prediction error variance in the restricted Ω; (iii) the normalized UPD (NUPD) by dividing UPD by the prediction error variance in Ω; (iv) the log-unpredictability decrement (LUPD) by applying the logarithm transformation to the prediction error variances before computing the UPD. The hypothesis was tested over two experimental protocols known to produce modifications of the complexity of HP variability: graded head-up tilt (HUT) inducing a gradual decrease of the HP complexity with tilt table inclination and head-down tilt (HDT) inducing the opposite trend. We demonstrated that: (1) when the strength of the causal relations from SAP to HP during HUT and from R to HP during HDT is assessed in Ω, WGC indexes reach different conclusions; (2) UPD is biased by modifications of the complexity of HP dynamics; (3) FUPD, NUPD and LUPD are less sensitive to changes of the complexity of the target dynamic, even though they have slightly different statistical power, being the NUPD the weakest one and FUPD and LUPD the strongest ones. We conclude that UPD should be avoided when assessing WGC and FUPD and LUPD should be privileged over NUPD.

The study compares permutation-based and coarse-grained entropy approaches for the assessment of complexity of short heart period (HP) variability recordings. Shannon permutation entropy (SPE) and conditional permutation entropy (CPE) are computed as examples of permutation-based entropies, while the k-nearest neighbor conditional entropy (KNNCE) is calculated as an example of coarse-grained conditional entropy. SPE, CPE and KNNCE were applied to ad-hoc simulated autoregressive processes corrupted by increasing amounts of broad band noise and to real HP variability series recorded after complete vagal blockade obtained via administration of a high dose of atropine (AT) in nine healthy volunteers and during orthostatic challenge induced by 90° head-up tilt (T90) in 15 healthy individuals. Over the simulated series the performances of SPE and CPE degraded more rapidly with the amplitude of the superimposed broad band noise than those of KNNCE. Over real data KNNCE identified the expected decrease of the HP variability complexity both after AT and during T90. Conversely SPE and CPE detected the decrease of HP variability complexity solely during T90 as a likely result of the more favorable signal-to-noise ratio during T90 than after AT. Results derived from both simulations and real data indicated that permutation-based entropies had a larger susceptibility to broad band noise than KNNCE. We recommend caution in applying permutation-based entropies in presence of short HP variability series characterized by a low signal-to-noise ratio.

We tested the hypothesis that causality analysis, applied to the spontaneous beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP), can identify the improvement of autonomic control linked to plantar mechanical stimulation in patients with Parkinson's disease (PD). A causality index, measuring the strength of the association from SAP to HP variability, and derived according to the Granger paradigm (i.e. SAP causes HP if the inclusion of SAP into the set of signals utilized to describe cardiovascular interactions improves the prediction of HP series), was calculated using both linear model-based (MB) and nonlinear model-free (MF) approaches. Univariate HP and SAP variability indices in time and frequency domains, and bivariate descriptors of the HP-SAP variability interactions were computed as well. We studied ten PD patients (age range: 57-78 years; Hoehn-Yahr scale: 2-3; six males, four females) without orthostatic hypotension or symptoms of orthostatic intolerance and 'on-time' according to their habitual pharmacological treatment. PD patients underwent recordings at rest in a supine position and during a head-up tilt before, and 24 h after, mechanical stimulation was applied to the plantar surface of both feet. The MF causality analysis indicated a greater involvement of baroreflex in regulating HP-SAP variability interactions after mechanical stimulation. Remarkably, MB causality and more traditional univariate or bivariate techniques could not detect changes in cardiovascular regulation after mechanical stimulation, thus stressing the importance of accounting for nonlinear dynamics in PD patients. Due to the higher statistical power of MF causality we suggest its exploitation to monitor the baroreflex control improvement in PD patients, and we encourage the clinical application of the Granger causality approach to evaluate the modification of the autonomic control in relation to the application of a pharmacological treatment, a rehabilitation procedure or external intervention.

The autonomic regulation is non-invasively estimated from heart rate variability (HRV). Many methods utilized to assess autonomic regulation require stationarity of HRV recordings. However, non-stationarities are frequently present even during well-controlled experiments, thus potentially biasing HRV indices. The aim of our study is to quantify the potential bias of spectral, symbolic and entropy HRV indices due to non-stationarities. We analyzed HRV series recorded in healthy subjects during uncontrolled daily life activities typical of 24 h Holter recordings and during predetermined levels of robotic-assisted treadmill-based physical exercise. A stationarity test checking the stability of the mean and variance over short HRV series (about 300 cardiac beats) was utilized to distinguish stationary periods from non-stationary ones. Spectral, symbolic and entropy indices evaluated solely over stationary periods were contrasted with those derived from all the HRV segments. When indices were calculated solely over stationary series, we found that (i) during both uncontrolled daily life activities and controlled physical exercise, the entropy-based complexity indices were significantly larger; (ii) during uncontrolled daily life activities, the spectral and symbolic indices linked to sympathetic modulation were significantly smaller and those associated with vagal modulation were significantly larger; (iii) while during uncontrolled daily life activities, the variance of spectral, symbolic and entropy rate indices was significantly larger, during controlled physical exercise, it was smaller. The study suggests that non-stationarities increase the likelihood to overestimate the contribution of sympathetic control and affect the power of statistical tests utilized to discriminate conditions and/or groups.