Differentiation of Heart Failure Patients by the Ratio of the Scaling Exponents of Cardiac Interbeat Intervals

Heart Rate Asymmetry in Healthy Children

Heart rate asymmetry (HRA) is a physiological phenomenon characterized by an unequal contribution of heart rate decelerations and accelerations to different heart rate variability (HRV) features. While HRA has been demonstrated in adults' ECGs of different duration, a similar investigation in healthy children has not been conducted. This study investigated the variance- and number-based HRA features in 96 healthy children (50 girls and 46 boys, aged 3-18 years) using 24-h ECGs. Additionally, we studied sex differences in HRA. To quantify HRA, variance-based and relative contributions of heart rate decelerations to short-term (C1d), long-term (C2d), and total (CTd) HRV, and the number of all heartbeats (Nd) were computed. Heart rate decelerations contributed more to C1d, but less to C2d and CTd, and were less frequent than heart rate accelerations. Short-term HRA was better expressed in boys. The majority of children (93.7%) had short-term HRA, 88.5% had long-term HRA, 88.5% had total HRA, and 99.0% had more accelerations than decelerations. No sex differences were observed for the rate of various HRA features. Heart rate asymmetry is a common phenomenon in healthy children, as observed in 24-h ECGs. Our findings can be used as reference data for future clinical studies on HRA in children.

Effects of Cardiac Resynchronization Therapy on Cardio-Respiratory Coupling

In this study, the effect of cardiac resynchronization therapy (CRT) on the relationship between the cardiovascular and respiratory systems in heart failure subjects was examined for the first time. We hypothesized that alterations in cardio-respiratory interactions, after CRT implantation, quantified by signal complexity, could be a marker of a favorable CRT response. Sample entropy and scaling exponents were calculated from synchronously recorded cardiac and respiratory signals 20 min in duration, collected in 47 heart failure patients at rest, before and 9 months after CRT implantation. Further, cross-sample entropy between these signals was calculated. After CRT, all patients had lower heart rate and CRT responders had reduced breathing frequency. Results revealed that higher cardiac rhythm complexity in CRT non-responders was associated with weak correlations of cardiac rhythm at baseline measurement over long scales and over short scales at follow-up recording. Unlike CRT responders, in non-responders, a significant difference in respiratory rhythm complexity between measurements could be consequence of divergent changes in correlation properties of the respiratory signal over short and long scales. Asynchrony between cardiac and respiratory rhythm increased significantly in CRT non-responders during follow-up. Quantification of complexity and synchrony between cardiac and respiratory signals shows significant associations between CRT success and stability of cardio-respiratory coupling.

Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives

Despite significant effort on understanding complex biological systems, we lack a unified theory for modeling, inference, analysis, and efficient control of their dynamics in uncertain environments. These problems are made even more challenging when considering that only limited and noisy information is accessible for modeling, which can prove insufficient for explaining, and predicting the behavior of complex systems. For instance, missing information hampers the capabilities of analytical tools to uncover the true degrees of freedom and infer the model structure and parameters of complex biological systems. Toward this end, in this paper, we discuss several important mathematical challenges that could open new theoretical avenues in studying complex systems: (1) By understanding the universal laws characterizing the asymmetric statistics of magnitude increments and the complex space-time interdependency within one process and across many processes, we can develop a class of compact yet accurate mathematical models capable to potentially providing higher degree of predictability, and more efficient control strategies. (2) In order to better predict the onset of disease and their root cause, as well as potentially discover more efficient quality-of-life (QoL)-control strategies, we need to develop mathematical strategies that not only are capable to discover causal interactions and their corresponding mathematical expressions for space and time operators acting on biological processes, but also mathematical and algorithmic techniques to identify the number of unknown unknowns (UUs) and their interdependency with the observed variables. (3) Lastly, to improve the QoL of control strategies when facing intra- and inter-patient variability, the focus should not only be on specific values and ranges for biological processes, but also on optimizing/controlling knob variables that enforce a specific spatiotemporal multifractal behavior that corresponds to an initial healthy (patient specific) behavior. All in all, the modeling, analysis and control of complex biological collective systems requires a deeper understanding of the multifractal properties of high dimensional heterogeneous and noisy data streams and new algorithmic tools that exploit geometric, statistical physics, and information theoretic concepts to deal with these data challenges.