Complexity Of Heart Period Variability Research Articles

On the validity of the state space correspondence strategy based on k-nearest neighbor cross-predictability in assessing directionality in stochastic systems: Application to cardiorespiratory coupling estimation.

We tested the validity of the state space correspondence (SSC) strategy based on k-nearest neighbor cross-predictability (KNNCP) to assess the directionality of coupling in stochastic nonlinear bivariate autoregressive (NBAR) processes. The approach was applied to assess closed-loop cardiorespiratory interactions between heart period (HP) variability and respiration (R) during a controlled respiration (CR) protocol in 19 healthy humans (aged from 27 to 35 yrs, 11 females) and during active standing (STAND) in 25 athletes (aged from 20 to 40 yrs, all men) and 25 non-athletes (aged from 20 to 40 yrs, all men). Over simulated NBAR processes, we found that (i) the SSC approach can detect the correct causal relationship as the direction leads to better KNNCP from the past of the driver to the future state of the target and (ii) simulations suggest that the ability of the method is preserved in any condition of complexity of the interacting series. Over CR and STAND protocols, we found that (a) slowing the breathing rate increases the strength of the causal relationship in both temporal directions in a balanced modality; (b) STAND is more powerful in modulating the coupling strength on the pathway from HP to R; (c) regardless of protocol and experimental condition, the strength of the link from HP to R is stronger than that from R to HP; (d) significant causal relationships in both temporal directions are found regardless of the level of complexity of HP variability and R. The SSC strategy is useful to disentangle closed-loop cardiorespiratory interactions.

Effect of variations of the complexity of the target variable on the assessment of Wiener–Granger causality in cardiovascular control studies

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.

Multiscale Complexity Analysis of the Cardiac Control Identifies Asymptomatic and Symptomatic Patients in Long QT Syndrome Type 1

The study assesses complexity of the cardiac control directed to the sinus node and to ventricles in long QT syndrome type 1 (LQT1) patients with KCNQ1-A341V mutation. Complexity was assessed via refined multiscale entropy (RMSE) computed over the beat-to-beat variability series of heart period (HP) and QT interval. HP and QT interval were approximated respectively as the temporal distance between two consecutive R-wave peaks and between the R-wave apex and T-wave end. Both measures were automatically taken from 24-hour electrocardiographic Holter traces recorded during daily activities in non mutation carriers (NMCs, n = 14) and mutation carriers (MCs, n = 34) belonging to a South African LQT1 founder population. The MC group was divided into asymptomatic (ASYMP, n = 11) and symptomatic (SYMP, n = 23) patients according to the symptom severity. Analyses were carried out during daytime (DAY, from 2PM to 6PM) and nighttime (NIGHT, from 12PM to 4AM) off and on beta-adrenergic blockade (BBoff and BBon). We found that the complexity of the HP variability at short time scale was under vagal control, being significantly increased during NIGHT and BBon both in ASYMP and SYMP groups, while the complexity of both HP and QT variability at long time scales was under sympathetic control, being smaller during NIGHT and BBon in SYMP subjects. Complexity indexes at long time scales in ASYMP individuals were smaller than those in SYMP ones regardless of therapy (i.e. BBoff or BBon), thus suggesting that a reduced complexity of the sympathetic regulation is protective in ASYMP individuals. RMSE analysis of HP and QT interval variability derived from routine 24-hour electrocardiographic Holter recordings might provide additional insights into the physiology of the cardiac control and might be fruitfully exploited to improve risk stratification in LQT1 population.

K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control

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.

Progressive decrease of heart period variability entropy-based complexity during graded head-up tilt

Complexity (or its opposite, regularity) of heart period variability has been related to age and disease but never linked to a progressive shift of the sympathovagal balance. We compare several well established estimates of complexity of heart period variability based on entropy rates [i.e., approximate entropy (ApEn), sample entropy (SampEn), and correct conditional entropy (CCE)] during an experimental protocol known to produce a gradual shift of the sympathovagal balance toward sympathetic activation and vagal withdrawal (i.e., the graded head-up tilt test). Complexity analysis was carried out in 17 healthy subjects over short heart period variability series ( approximately 250 cardiac beats) derived from ECG recordings during head-up tilt with table inclination randomly chosen inside the set {0, 15, 30, 45, 60, 75, 90}. We found that 1) ApEn does not change significantly during the protocol; 2) all indices measuring complexity based on entropy rates, including ad hoc corrections of the bias arising from their evaluation over short data sequences (i.e., corrected ApEn, SampEn, CCE), evidence a progressive decrease of complexity as a function of the tilt table inclination, thus indicating that complexity is under control of the autonomic nervous system; 3) corrected ApEn, SampEn, and CCE provide global indices that can be helpful to monitor sympathovagal balance.

Effects of sympathetic activation and regular periodic breathing on complexity of heart period variability

Background. Heart rate exhibits different levels of complexity which are probably related to the neural autonomic modulation. Aim of the study. The aim is to analyze the effect of the sympathetic activation and of a regular periodical external input on the complexity of heart period. Methods. Fifteen healthy young subjects were recorded at rest during spontaneous breathing, during head-up tilt, and at rest during controlled breathing at different rates (10, 15, and 20 breaths/min). The minimum of corrected conditional entropy (CCE) was used to measure complexity (the higher the minimum, the larger the complexity). Spectral indexes in low and high frequency (LF and HF) bands were calculated as well. Results. CCE minimum was significantly lower during tilt and controlled respiration at 10 breaths/min compared to rest during spontaneous breathing, while LF/HF ratio was larger during tilt but smaller during controlled respiration at 10 breaths/min. During faster respiratory rates CCE minimum and the LF/HF were unchanged. No significant correlation was detected between the CCE minimum and the mean or variance of the heart period. CCE minimum was correlated with LF/HF ratio only at rest and during tilt. Conclusions. These results indicate that complexity of heart period is not related to its mean or variance, does not depend only on regularity of respiration, and is affected by interventions capable of entraining different regulatory mechanisms and reducing the number of temporal scales involved on heart period regulation.