A method for analyzing temporal patterns of variability of a time series from Poincaré plots

Abstract

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.

Increased cardio-respiratory coupling evoked by slow deep breathing can persist in normal humans

“…4). But the delay (τ) defined by the number of cycles separating the cycle compared to the current cycles should not be limited to 1 (as in n+1 versus n) (Fishman et al, 2012). Poincaré plots with (n+(>1) vs n) can reveal the relationship between repetitive events at that occur a multiples of cycles, such as RSA.…”

“…We have developed analytical tools for quantifying Poincaré plots, specifically to analyze the temporal patterns of variability in Poincaré plots (Fishman et al, 2012). We applied temporal Poincaré variability (TPV) to quantify the temporal-dependence of the distribution of points in the Poincaré plot and to detect nonlinear sources underlying the variability.…”

Semi-automated assessment of transdiaphragmatic pressure variability across motor behaviors

“…However, there was minimal evidence of complex temporal structure or dynamic clustering. Differences in normalized Pdi amplitude for successive inspiratory events during eupnea and hypoxia-hypercapnia was evaluated comprehensively using methodology developed by Dick and colleagues for analyses of temporal patterns of variability (Fishman et al, 2012). There was no difference in the variance in Pdi amplitude between eupnea and exposure to hypoxia-hypercapnia in anesthetized mice, when examined either as the extent of variability (CV), the standard deviation of successive differences in normalized Pdi amplitudes (SD1) or the standard deviation in the variance of all normalized Pdi amplitudes (SD2).…”

“…Accordingly, comparisons across animals were facilitated by normalizing Pdi amplitude in eupnea and hypoxia-hypercapnia to the average amplitude of spontaneous sighs measured during these ventilatory behaviors. Variance in normalized Pdi amplitude was analyzed by constructing standard Poincaré plots (Brennan et al, 2001, 2002) and using the methods developed by Dick and colleagues (Fishman et al, 2012) for evaluation of variability in long time series of physiological events. The publically-available, executable analytical program developed in MATLAB by these authors was used in such analyses.…”

“…Specifically, the standard deviation of successive differences in normalized Pdi amplitudes (SD1) and the standard deviation in the variance of all normalized Pdi amplitudes (SD2) were calculated. In addition, temporal pattern variability was analyzed using time-delayed temporal Poincaré variability (TVP TD ) and long-term temporal Poincaré variability (TVP A ), as previously described (Fishman et al, 2012). TVP TD was analyzed with a time delay of up to 10 inspiratory events.…”