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.

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.

We propose a sympathetic baroreflex (sBR) sequence method for characterizing sBR from spontaneous beat-to-beat fluctuations of muscle sympathetic nerve activity (MSNA) and diastolic arterial pressure (DAP). The method exploits a previously defined MSNA variability quantifying the fluctuations of MSNA burst rate. The method is based on the detection of MSNA and DAP sequences characterized by the contemporaneous DAP increase and MSNA decrease or vice versa. The percentage of sBR sequences (SEQ%sBR) was taken as an indication of the degree of sBR solicitation and the average slope of the regression lines in the (DAP,MSNA) plane was taken as sBR sensitivity (sBRSSEQ) and expressed in bursts.s-1.mmHg-1. sBRSSEQ was compared to a more traditional estimate based on the baroreflex threshold analysis (sBRSBTA). An incremental head-up tilt protocol, carried out in 12 young healthy subjects (age: 20-36 yr, median = 22.5 yr, 9 females) sequentially tilted at 0°, 20°, 30°, 40°, 60° table inclinations, was utilized to set the sBR sequence method parameters. Traditional sequence analysis was exploited to estimate cardiac baroreflex (cBR) sensitivity (cBRSSEQ) and percentage of cBR sequences (SEQ%cBR). The head-up tilt induced the progressive increase of SEQ%sBR and SEQ%cBR and gradual decrease of both sBRSSEQ and cBRSSEQ, thus suggesting the gradual rise of the sBR and cBR solicitations and the progressive reduction of their effectiveness with the stimulus. sBRSSEQ was significantly associated with sBRSBTA. sBRSSEQ and cBRSSEQ were significantly correlated as well as SEQ%sBR and SEQ%cBR, even though the correlation was not strong, thus suggesting a certain degree of independence between the baroreflex arms. The proposed sBR sequence approach provides a dynamical characterization of the sBR alternative to more traditional static pharmacological and nonpharmacological methods and fully homogenous with the cBR sequence technique.

Muscle sympathetic nerve activity (MSNA) variability is traditionally computed through a low-pass filtering procedure that requires normalization. We proposed a new beat-to-beat MSNA variability computation that preserves dimensionality typical of an integrated neural discharge (i.e., bursts per unit of time). The calibrated MSNA (cMSNA) variability technique is contrasted with the traditional uncalibrated MSNA (ucMSNA) version. The powers of cMSNA and ucMSNA variabilities in the low-frequency (LF, from 0.04 to 0.15 Hz) band were computed with those of the heart period (HP) of systolic and diastolic arterial pressure (SAP and DAP, respectively) in seven healthy subjects (age, 20–28 years; median, 22 years; 5 women) during a graded head-up tilt. Subjects were sequentially tilted at 0°, 20°, 30°, 40°, and 60° table inclinations. The LF powers of ucMSNA and HP variabilities were expressed in normalized units (LFnu), whereas all remaining spectral markers were expressed in absolute units. We found that 1) the LF power of cMSNA variability was positively correlated with tilt angle, whereas the LFnu power of the ucMSNA series was uncorrelated; 2) the LF power of cMSNA variability was correlated with LF powers of SAP and DAP, LFnu power of HP and noradrenaline concentration, whereas the relationship of the LFnu power of ucMSNA variability to LF powers of SAP and DAP was weaker and that to LFnu power of HP was absent; and 3) the stronger relationship of cMSNA variability to SAP and DAP spectral markers compared with the ucMSNA series was confirmed individually. The cMSNA variability appears to be more suitable in describing sympathetic control in humans than traditional ucMSNA variability.

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.

Cardiovascular and cerebrovascular regulatory systems are vital control mechanisms responsible for guaranteeing homeostasis and are affected by respiration. This work proposes the investigation of cardiovascular and cerebrovascular control systems and the nonlinear influences of respiration on both regulations through joint symbolic analysis (JSA), conditioned or unconditioned on respiration. Interactions between cardiovascular and cerebrovascular regulatory systems were evaluated as well by performing correlation analysis between JSA indexes describing the two control systems. Heart period, systolic and mean arterial pressure, mean cerebral blood flow velocity and respiration were acquired on a beat-to-beat basis in 13 subjects experiencing recurrent syncope episodes (SYNC) and 13 healthy individuals (non-SYNC) in supine resting condition and during head-up tilt test at 60° (TILT). Results showed that JSA distinguished conditions and groups, whereas time domain parameters detected only the effect of TILT. Respiration affected cardiovascular and cerebrovascular regulatory systems in a nonlinear way and was able to modulate the interactions between the two control systems with different outcome in non-SYNC and SYNC groups, thus suggesting that the analysis of the impact of respiration on cardiovascular and cerebrovascular regulatory systems might improve our understanding of the mechanisms underpinning the development of postural-related syncope.