The Poincaré plot is a popular two-dimensional, time series analysis tool because of its intuitive display of dynamic system behavior. Poincaré plots have been used to visualize heart rate and respiratory pattern variabilities. However, conventional quantitative analysis relies primarily on statistical measurements of the cumulative distribution of points, making it difficult to interpret irregular or complex plots. Moreover, the plots are constructed to reflect highly correlated regions of the time series, reducing the amount of nonlinear information that is presented and thereby hiding potentially relevant features. We propose temporal Poincaré variability (TPV), a novel analysis methodology that uses standard techniques to quantify the temporal distribution of points and to detect nonlinear sources responsible for physiological variability. In addition, the analysis is applied across multiple time delays, yielding a richer insight into system dynamics than the traditional circle return plot. The method is applied to data sets of R-R intervals and to synthetic point process data extracted from the Lorenz time series. The results demonstrate that TPV complements the traditional analysis and can be applied more generally, including Poincaré plots with multiple clusters, and more consistently than the conventional measures and can address questions regarding potential structure underlying the variability of a data set.

Physiological rhythms, including respiration, exhibit endogenous variability associated with health, and deviations from this are associated with disease. Specific changes in the linear and nonlinear sources of breathing variability have not been investigated. In this study, we used information theory-based techniques, combined with surrogate data testing, to quantify and characterize the vagal-dependent nonlinear pattern variability in urethane-anesthetized, spontaneously breathing adult rats. Surrogate data sets preserved the amplitude distribution and linear correlations of the original data set, but nonlinear correlation structure in the data was removed. Differences in mutual information and sample entropy between original and surrogate data sets indicated the presence of deterministic nonlinear or stochastic non-Gaussian variability. With vagi intact (n = 11), the respiratory cycle exhibited significant nonlinear behavior in templates of points separated by time delays ranging from one sample to one cycle length. After vagotomy (n = 6), even though nonlinear variability was reduced significantly, nonlinear properties were still evident at various time delays. Nonlinear deterministic variability did not change further after subsequent bilateral microinjection of MK-801, an N-methyl-D-aspartate receptor antagonist, in the Kölliker-Fuse nuclei. Reversing the sequence (n = 5), blocking N-methyl-D-aspartate receptors bilaterally in the dorsolateral pons significantly decreased nonlinear variability in the respiratory pattern, even with the vagi intact, and subsequent vagotomy did not change nonlinear variability. Thus both vagal and dorsolateral pontine influences contribute to nonlinear respiratory pattern variability. Furthermore, breathing dynamics of the intact system are mutually dependent on vagal and pontine sources of nonlinear complexity. Understanding the structure and modulation of variability provides insight into disease effects on respiratory patterning.

In this work, cardio-ventilatory coupling (CVC) refers to the statistical relationship between the onset of either inspiration (I) or expiration (E) and the timing of heartbeats (R-waves) before and after these respiratory events. CVC was assessed in healthy, young (<45 yr), resting, supine subjects (n = 19). Four intervals were analyzed: time from I-onset to both the prior R-wave (R-to-I) and the following R-wave (I-to-R), as well as time from E-onset to both the prior R-wave (R-to-E) and following R-wave (E-to-R). The degree of coupling was quantified in terms of transformed relative Shannon entropy (tRSE), and χ(2) tests based on histograms of interval times from 200 breaths. Subjects were studied twice, from 5 to 27 days apart, and the test-retest reliability of CVC measures was computed. Several factors pointed to the relative importance of the R-to-I interval compared with other intervals. Coupling was significantly stronger for the R-to-I interval, coupling reliability was largest for the R-to-I interval, and only tRSE for the R-to-I interval was correlated with height, weight, and body surface area. The high test-retest reliability for CVC in the R-to-I interval provides support for the hypothesis that CVC strength is a subject trait. Across subjects, a peak ~138 ms prior to I-onset was characteristic of CVC in the R-to-I interval, although individual subjects also had earlier peaks (longer R-to-I intervals). CVC for the R-to-I interval was unrelated to two separate measures of respiratory sinus arrhythmia (RSA), suggesting that these two forms of coupling (CVC and RSA) are independent.

We hypothesize that isoflurane and ketamine impact ventilatory pattern variability (VPV) differently. Adult Sprague-Dawley rats were recorded in a whole-body plethysmograph before, during and after deep anesthesia. VPV was quantified from 60-s epochs using a complementary set of analytic techniques that included constructing surrogate data sets that preserved the linear structure but disrupted nonlinear deterministic properties of the original data. Even though isoflurane decreased and ketamine increased respiratory rate, VPV as quantified by the coefficient of variation decreased for both anesthetics. Further, mutual information increased and sample entropy decreased and the nonlinear complexity index (NLCI) increased during anesthesia despite qualitative differences in the shape and period of the waveform. Surprisingly mutual information and sample entropy did not change in the surrogate sets constructed from isoflurane data, but in those constructed from ketamine data, mutual information increased and sample entropy decreased significantly in the surrogate segments constructed from anesthetized relative to unanesthetized epochs. These data suggest that separate mechanisms modulate linear and nonlinear variability of breathing.

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