Cardiorespiratory coupling strength in athletes and non-athletes

PURPOSE

Despite the relevant presence of nonlinear components on heart period (HP) likely due to cardiorespiratory coupling (CRC), the HP is frequently analyzed in absence of concomitant recordings of respiratory movements (RESP). This study aims to assess the cardiovascular dynamics and CRC during postural challenge in athletes and non-athletes via joint symbolic analysis (JSA).

METHODS

A cross-sectional study was conducted in 50 men, aged between 20 and 40 yrs, divided into athletes (n = 25) and non-athletes (n = 25) groups. The electrocardiogram, blood pressure and RESP signals were recorded during 15 min in both supine position (REST) and after active postural maneuver (STAND). From the beat-to-beat series of HP, systolic arterial pressure (SAP) and RESP, we computed the time and frequency domain indexes and baroreflex sensitivity. The JSA was based on the definition of symbolic HP and RESP patterns and on the evaluation of the rate of their simultaneous occurrence in both HP and RESP series.

RESULTS

The JSA analysis was able to identify higher CRC strength at REST in athletes. Moreover, the response of CRC to STAND depended on the time scales of the analysis and was much more evident in athletes than in non-athletes, thus indicating a more reactive autonomic control in athletes.

CONCLUSION

Assessing CRC in athletes via JSA provides additional information compared to standard linear time and frequency domain tools likely due to the more relevant presence of nonlinearities in HP-RESP variability relationship.

Comparison of fetal heart rate variability by symbolic dynamics at the third trimester of pregnancy and low-risk parturition

Fetal heart rate variability (fHRV) is an essential source of information to monitor fetal well-being during pregnancy. This study aimed to apply a nonlinear approach, known as symbolic dynamics (SD), for comparing human fHRV in the third trimester of pregnancy during active fetal state (TT) and active labor at term (P). We performed a longitudinal, prospective, descriptive, and comparative study composed of 42 longitudinal recordings of 5-minutes of fetal heartbeat interval series. Recordings were collected from 21 low-risk, healthy, pregnant women attending the Maternal and Child Research Center (CIMIGen), Mexico City. We calculated relevant linear parameters of fHRV between TT and P stages, such as the percentage of differences between adjacent RR intervals >5 ms (PRR5, related to vagal modulations) and other SD parameters such as the percentage of no variations between three successive symbols (%0V, reflects sympathetic modulations) and the probability of low variability with a threshold of 4 ms (POLVAR4, associated with a low variability). We identified statistical differences for PRR5 between TT and P (37.13% [28.47-47.60%] vs. 28.84% [19.36-36.76%], p = 0.03), respectively. Also, for 0V% (65.66% [59.01-71.80%] vs. 71.14% [65.94-75.87%], p = 0.03) and for POLVAR4 values (0.06 [0.04-0.11] vs. 0.15 [0.09-0.24], p = 0.002), respectively. Our results indicate that during parturition, the short-term fetal fHRV is decreased, showing a decreased vagal modulations and higher adrenergic response of the heart. These autonomic modifications may result from the fetal response to the stressful inflammatory challenge of labor. We thus confirmed that the analysis of the SD applied to fHRV time series could be a potential clinical biomarker to differentiate the fetal autonomic cardiac condition at different stages of pregnancy.

Symbolic analysis of heart rate fluctuations identifies cardiac autonomic modifications during LPS-induced endotoxemia

The present study aimed to compare linear and symbolic dynamics (SD) indices for detecting the autonomic cardiac changes produced by endotoxemia in freely-moving rats. In this context, we analyzed ECG-derived R-R time series in freely moving Dark Agouti rats, which received lipopolysaccharide (LPS, n = 9), or vehicle (V, n = 7). Five minutes R-R time series were assessed every hour up to +12 h and + 24 h post-LPS injection. We found that SD indices showed significant differences at +7 h between V vs. LPS groups and at +9 h between basal levels of LPS (-3 h) and post-LPS injection (pre-LPS vs. post-LPS). In general, SD seems more appropriate than linear indices to evaluate the autonomic changes of endotoxemic rats. Overall, the symbolic parameters detected decreased R-R variability and complexity, which indicate a modification of the autonomic regulation during LPS-induced endotoxemia. This modification is probably related to a reduced activity of the cholinergic anti-inflammatory pathway at the long term.

Symbolic time series analysis of electroencephalographic (EEG) epileptic seizure and brain dynamics with eye-open and eye-closed subjects during resting states

Objective

Epilepsy is a neuronal disorder for which the electrical discharge in the brain is synchronized, abnormal and excessive. To detect the epileptic seizures and to analyse brain activities during different mental states, various methods in non-linear dynamics have been proposed. This study is an attempt to quantify the complexity of control and epileptic subject with and without seizure as well as to distinguish eye-open (EO) and eye-closed (EC) conditions using threshold-based symbolic entropy.

Methods

The threshold-dependent symbolic entropy was applied to distinguish the healthy and epileptic subjects with seizure and seizure-free intervals (i.e. interictal and ictal) as well as to distinguish EO and EC conditions. The original time series data was converted into symbol sequences using quantization level, and word series of symbol sequences was generated using a word length of three or more. Then, normalized corrected Shannon entropy (NCSE) was computed to quantify the complexity. The NCSE values were not following the normal distribution, and the non-parametric Mann–Whitney–Wilcoxon (MWW) test was used to find significant differences among various groups at 0.05 significance level. The values of NCSE were presented in a form of topographic maps to show significant brain regions during EC and EO conditions. The results of the study were compared to those of the multiscale entropy (MSE).

Results

The results indicated that the dynamics of healthy subjects are more complex compared to epileptic subjects (during seizure and seizure-free intervals) in both EO and EC conditions. The comparison of the dynamics of epileptic subjects revealed that seizure-free intervals are more complex than seizure intervals. The dynamics of healthy subjects during EO conditions are more complex compared to those during EC conditions. Further, the results clearly demonstrated that threshold-dependent symbolic entropy outperform MSE in distinguishing different physiological and pathological conditions.

Conclusion

The threshold symbolic entropy has provided improved accuracy in quantifying the dynamics of healthy and epileptic subjects during EC an EO conditions for each electrode compared to the MSE.

Symbolic features and classification via support vector machine for predicting death in patients with Chagas disease

This paper introduces a technique for predicting death in patients with Chagas disease using features extracted from symbolic series and time-frequency indices of heart rate variability (HRV). The study included 150 patients: 15 patients who died and 135 who did not. The HRV series were obtained from 24-h Holter monitoring. Sequences of symbols from 5-min epochs from series of RR intervals were generated using symbolic dynamics and ordinal pattern statistics. Fourteen features were extracted from symbolic series and four derived from clinical aspects of patients. For classification, the 18 features from each epoch were used as inputs in a support vector machine (SVM) with a radial basis function (RBF) kernel. The results showed that it is possible to distinguish between the two classes, patients with Chagas disease who did or did not die, with a 95% accuracy rate. Therefore, we suggest that the use of new features based on symbolic series, coupled with classic time-frequency and clinical indices, proves to be a good predictor of death in patients with Chagas disease.

Topological chaos of the spatial prisoner's dilemma game on regular networks

The spatial version of evolutionary prisoner's dilemma on infinitely large regular lattice with purely deterministic strategies and no memories among players is investigated in this paper. Based on the statistical inferences, it is pertinent to confirm that the frequency of cooperation for characterizing its macroscopic behaviors is very sensitive to the initial conditions, which is the most practically significant property of chaos. Its intrinsic complexity is then justified on firm ground from the theory of symbolic dynamics; that is, this game is topologically mixing and possesses positive topological entropy on its subsystems. It is demonstrated therefore that its frequency of cooperation could not be adopted by simply averaging over several steps after the game reaches the equilibrium state. Furthermore, the chaotically changing spatial patterns via empirical observations can be defined and justified in view of symbolic dynamics. It is worth mentioning that the procedure proposed in this work is also applicable to other deterministic spatial evolutionary games therein.

High atrioventricular phase index on near-field intracardiac electrogram is associated with risk of ventricular arrhythmia

The purposes of this study were to characterize and quantify concordance between consecutive atrial and ventricular activation time points through analysis of phases and to explore its association with outcomes in patients with implantable cardioverter-defibrillator (ICD). Patients with structural heart disease and dual-chamber ICDs underwent 5min baseline right ventricular (V) near-field and atrial (A) electrogram (EGM) recording. The cross-dependencies of phase dynamics of the changes in consecutive A (AA') and V (VV') were quantified and the AV phase dependency index was determined. In Cox regression analysis, a high AV phase index (in the highest quartile, >0.259) was significantly associated with higher risk of ventricular tachyarrhythmias (HR 2.84; 95% CI 1.05-7.67; P=0.04). In conclusion, in ICD patients with structural heart disease, high sinus AV phase dependency index on EGM is associated with the risk of ventricular arrhythmia.

Contextual emergence of mental states

The concept of contextual emergence has been proposed as a non-reductive, yet well-defined relation between different levels of description of physical and other systems. It yields a formally sound and empirically applicable procedure to translate between descriptive levels in an overall consistent fashion. This will be discussed for the contextual emergence of mental states from a neural level of description.

Transition dynamics of EEG-based network microstates during mental arithmetic and resting wakefulness reflects task-related modulations and developmental changes

We studied how maturation influences the organization of functional brain networks engaged during mental calculations and in resting state. Surface EEG measurements from 20 children (8-12 years) and 25 students (21-26 years) were analyzed. Interregional synchronization of brain activity was quantified by means of Phase Lag Index and for various frequency bands. Based on these pairwise estimates of functional connectivity, we formed graphs which were then characterized in terms of local structure [local efficiency (LE)] and overall integration (global efficiency). The overall data analytic scheme was applied twice, in a static and time-varying mode. Our results showed a characteristic trend: functional segregation dominates the network organization of younger brains. Moreover, in childhood, the overall functional network possesses more prominent small-world network characteristics than in early acorrect in xmldulthood in accordance with the Neural Efficiency Hypothesis. The above trends were intensified by the time-varying approach and identified for the whole set of tested frequency bands (from δ to low γ). By mapping the time-indexed connectivity patterns to multivariate timeseries of nodal LE measurements, we carried out an elaborate study of the functional segregation dynamics and demonstrated that the underlying network undergoes transitions between a restricted number of stable states, that can be thought of as "network-level microstates". The rate of these transitions provided a robust marker of developmental and task-induced alterations, that was found to be insensitive to reference montage and independent component analysis denoising.

Symbolic patterns of heart rate dynamics reflect cardiac autonomic changes during childhood and adolescence

Symbolic dynamics derived from heart rate variability (HRV) is able to reflect changes of cardiac autonomic modulations in healthy subjects. It has been shown that linear measures of HRV in children and adolescents monotonically increase or decrease (depending on the measure) with age whereas non-linear measures show a local extreme value at the age of 7 to 9 years. In this study, the age-related variations of dynamical features of the R-R interval series during childhood and adolescence were addressed. In particular, the binary symbolic dynamics reflecting the sequence of acceleration (='1') and deceleration (='0') of heart rate was examined. The R-R interval series of 409 healthy children and adolescents (age range: 1 to 22 years, 220 females) was analyzed with respect to the regularity of binary patterns of length 8 using Approximate Entropy (ApEn). Binary patterns were grouped to patterns sets according to the level of their regularity as assessed by ApEn. Pattern sets containing regular binary patterns occurred more often with increasing age whereas irregular binary patterns occurred less often. Specific regular binary patterns show an unexpected behavior. They occurred fewest in the group 7 to 9 years. Furthermore, regular binary patterns occur more often during daytime whereas irregular binary patterns occur more often during nighttime. In conclusion, the analysis of binary symbolic dynamics is able to reflect age-related changes during childhood and adolescence in spite of the considerable reduction of information involved. As many binary patterns are linked to sympathetic or parasympathetic modulations of the autonomic nervous system e.g. spectral analysis of HRV may be complemented by this kind of analysis.

Visualization for understanding of neurodynamical systems

Complex neurodynamical systems are quite difficult to analyze and understand. New type of plots are introduced to help in visualization of high-dimensional trajectories and show global picture of the phase space, including relations between basins of attractors. Color recurrence plots (RPs) display distances from each point on the trajectory to all other points in a two-dimensional matrix. Fuzzy Symbolic Dynamics (FSD) plots enhance this information mapping the whole trajectory to two or three dimensions. Each coordinate is defined by the value of a fuzzy localized membership function, optimized to visualize interesting features of the dynamics, showing to which degree a point on the trajectory belongs to some neighborhood. The variance of the trajectory within the attraction basin plotted against the variance of the synaptic noise provides information about sizes and shapes of these basins. Plots that use color to show the distance between each trajectory point and a larger number of selected reference points (for example centers of attractor basins) are also introduced. Activity of 140 neurons in the semantic layer of dyslexia model implemented in the Emergent neural simulator is analyzed in details showing different aspects of neurodynamics that may be understood in this way. Influence of connectivity and various neural properties on network dynamics is illustrated using visualization techniques. A number of interesting conclusions about cognitive neurodynamics of lexical concept activations are drawn. Changing neural accommodation parameters has very strong influence on the dwell time of the trajectories. This may be linked to attention deficits disorders observed in autism in case of strong enslavement, and to ADHD-like behavior in case of weak enslavement.

A novel symbolization scheme for multichannel recordings with emphasis on phase information and its application to differentiate EEG activity from different mental tasks

Symbolic dynamics is a powerful tool for studying complex dynamical systems. So far many techniques of this kind have been proposed as a means to analyze brain dynamics, but most of them are restricted to single-sensor measurements. Analyzing the dynamics in a channel-wise fashion is an invalid approach for multisite encephalographic recordings, since it ignores any pattern of coordinated activity that might emerge from the coherent activation of distinct brain areas. We suggest, here, the use of neural-gas algorithm (Martinez et al. in IEEE Trans Neural Netw 4:558-569, 1993) for encoding brain activity spatiotemporal dynamics in the form of a symbolic timeseries. A codebook of k prototypes, best representing the instantaneous multichannel data, is first designed. Each pattern of activity is then assigned to the most similar code vector. The symbolic timeseries derived in this way is mapped to a network, the topology of which encapsulates the most important phase transitions of the underlying dynamical system. Finally, global efficiency is used to characterize the obtained topology. We demonstrate the approach by applying it to EEG-data recorded from subjects while performing mental calculations. By working in a contrastive-fashion, and focusing in the phase aspects of the signals, we show that the underlying dynamics differ significantly in their symbolic representations.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11571-011-9186-5) contains supplementary material, which is available to authorized users.