New systems--analytical approaches to nonlinear coordination

Nonlinearities of heart rate variability in animal models of impaired cardiac control: contribution of different time scales

Heart rate variability (HRV) has been extensively explored by traditional linear approaches (e.g., spectral analysis); however, several studies have pointed to the presence of nonlinear features in HRV, suggesting that linear tools might fail to account for the complexity of the HRV dynamics. Even though the prevalent notion is that HRV is nonlinear, the actual presence of nonlinear features is rarely verified. In this study, the presence of nonlinear dynamics was checked as a function of time scales in three experimental models of rats with different impairment of the cardiac control: namely, rats with heart failure (HF), spontaneously hypertensive rats (SHRs), and sinoaortic denervated (SAD) rats. Multiscale entropy (MSE) and refined MSE (RMSE) were chosen as the discriminating statistic for the surrogate test utilized to detect nonlinearity. Nonlinear dynamics is less present in HF animals at both short and long time scales compared with controls. A similar finding was found in SHR only at short time scales. SAD increased the presence of nonlinear dynamics exclusively at short time scales. Those findings suggest that a working baroreflex contributes to linearize HRV and to reduce the likelihood to observe nonlinear components of the cardiac control at short time scales. In addition, an increased sympathetic modulation seems to be a source of nonlinear dynamics at long time scales. Testing nonlinear dynamics as a function of the time scales can provide a characterization of the cardiac control complementary to more traditional markers in time, frequency, and information domains.NEW & NOTEWORTHY Although heart rate variability (HRV) dynamics is widely assumed to be nonlinear, nonlinearity tests are rarely used to check this hypothesis. By adopting multiscale entropy (MSE) and refined MSE (RMSE) as the discriminating statistic for the nonlinearity test, we show that nonlinear dynamics varies with time scale and the type of cardiac dysfunction. Moreover, as complexity metrics and nonlinearities provide complementary information, we strongly recommend using the test for nonlinearity as an additional index to characterize HRV.

Comparison of heart rate variability analysis methods in patients with Parkinson's disease

The aim of the present study was to evaluate different analysis methods for revealing heart rate variability (HRV) differences between untreated patients with Parkinson's disease and healthy controls. HRV in standard cardiovascular reflex tests and during a 10 min rest period were measured by time- and frequency-domain and geometrical and non-linear analysis methods. Both frequency- and time-domain measures revealed abnormal HRV in the patients, whereas non-linear and geometrical measures did not. The absolute high-frequency spectral power of HRV was the strongest independent predictor to separate the patients from the controls (p = 0.001), when the main time-domain and absolute frequency-domain measures were compared with each other. When the corresponding normalised spectral units, instead of the absolute units, were used in the comparison, the two best single measures for separating the groups were the 30/15 ratio of the tilting test (p = 0.003) and the max/min ratio during deep breathing (p = 0.024). When the correlations between the different measures were estimated, the time-domain measures, fractal dimension and absolute spectral powers correlated with each other. The frequency- and time-domain analysis techniques of stationary short-term HRV recordings revealed significant differences in cardiovascular regulation between untreated patients with Parkinson's disease and the controls. This confirms cardiovascular regulation failure before treatment in the early stages of Parkinson's disease. The HRV spectral powers, in absolute units, were the most effective single parameters in segregating the two groups, emphasising the role of spectral analysis in the evaluation of HRV in Parkinson's disease.

Coupling patterns between spontaneous rhythms and respiration in cardiovascular variability signals

We performed a quantitative study of coupling patterns between respiration and spontaneous rhythms of heart rate and blood pressure variability signals by using the Recurrence Quantification Analysis (RQA). We applied RQA to both simulated and experimental data obtained in control breathing at three different frequencies (0.25, 0.20, and 0.13 Hz) from ten normal subjects. RQA succeeded in quantifying different degrees of non-linear coupling associated to several interference patterns. We found higher degrees of non-linear coupling when the respiratory frequency was close to the spontaneous Low Frequency (LF) rhythm (0.13 Hz), or almost twice the LF frequency (0.2 Hz), whereas weaker coupling was observed when the respiratory frequency was 0.25 Hz. Clinical applications of our approach should focus on new experimental protocols, featuring the stimulation of one of the two branches of the autonomic nervous system (ANS) or aimed at the analysis of pathologies linked to the ANS.

Short and long term non-linear analysis of RR variability series

The complexity of RR variability is approached in the short and in the long term by means of black-box data analysis. Short term series of a few hundred beats are explored by means of informational entropy and predictability indexes. A correction to biases toward false determinism is performed assuming maximum uncertainty, whenever data do not furnish sufficient recurrences. Non-randomness and non-linearity are tested by means of surrogate data provided by random shuffling and phase randomization respectively. In the long term of the 24-h or of several hours, similar tests based on mutual information are applied and validated by means of surrogate series. In addition the state space reconstruction is carried out by means of state space non-linear filtering addressing directly the reconstructed trajectories. In this condition, parameters characterizing the hypothetical attractor, mainly the maximum Lyapunov exponent, can be reliably identified.

Transient phase locking patterns among respiration, heart rate and blood pressure during cardiorespiratory synchronisation in humans

The interactions between respiration, heart rate and blood pressure variability (HRV, BPV), are considered to be of paramount importance for the study of the functional organisation of the autonomic nervous system (ANS). The aim of the reported study is to detect and classify the intermittent phase locking (PL) phenomena between respiration, HRV and BPV during cardiorespiratory synchronisation experiments, by using the following time-domain techniques: Poincaré maps, recurrence plots, time-space separation plots and frequency tracking locus. The experimental protocol consists of three stages, with normal subjects in paced breathing at 15, 12 and 8 breaths min-1. Transient phenomena of coordination between respiration and the major rhythms of HRV and BPV (low and high frequency, LF and HF) have been detected and classified: no interaction between LF and HF rhythms at 15 breaths min-1; short time intervals of stable 1:2 frequency and phase synchronisation during the 12 breaths min-1 stage; 1:1 PL during the 8 breaths min-1 stage. 1:1 and 1:2 PL phenomena occurred when the respiration frequency was quite close to the LF frequency or when it was about twice the LF frequency, respectively. The complex organisation of the ANS seems to provoke transient rather than permanent PL phenomena between the co-ordinating components of respiration and cardiovascular variability series.