The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy.

Due to the fact that respiratory breath-to-breath and cardiac intervals between two successive R peaks (BBI and RRI, respectively) are not temporally concurrent, in a previous paper, we proposed a method to calculate both the integer and non-integer parts of the pulse respiration quotient (PRQ = BBI/RRI = PRQ int + b1 + b2), b1 and b2 being parts of the border RRIs for each BBI. In this work, we study the correlations between BBI and PRQ, as well as those between BBI and mean RRI within each BBI (mRRI), on a group of twenty subjects in four conditions: in supine and standing positions, in combination with spontaneous and slow breathing. Results show that the BBI vs. PRQ correlations are positive; whereas the breathing regime had little or no effect on the linear regression slopes, body posture did. Two types of scatter plots were obtained with the BBI vs. mRRI correlations: one showed points aggregated around the concurrent PRQ int lines, while the other showed randomly distributed points. Five out of six of the proposed aggregation measures confirmed the existence of these two cardio-respiratory coupling regimes. We also used b1 to study the positions of R pulses relative to the respiration onsets and showed that they were more synchronous with sympathetic activation. Overall, this method should be used in different pathological states.

In this work we applied generalized Poincaré plots (gPp) analysis of interbeat intervals in patients with heart failure. More, we compared gPp with its nearest analogy methods based on existing extended Poincaré plots techniques. Obtained results showed advantages of gPp method over usually used distanced (lagged) Poincaré plots analysis. Only gPp has the potential of three-dimensional visualization of results with quantification of new multiscaling parameters. It is comparable with other methods only in two-dimensional planes where all methods showed a strong negative correlation between patterns of Pearson correlation coefficients and patterns of the SD1/SD2 ratio over the whole range of Pp orders (lags). These results could be used as the basis for further research in new standardization of multiscaling methods in heart rhythm analysis where it is important to follow the pattern of regulatory mechanisms dynamics which is related to the duration of RR intervals.

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.