Informative Nature and Nonlinearity of Lagged Poincaré Plots Indices in Analysis of Heart Rate Variability

Abstract

Lagged Poincaré plots have been successful in characterizing abnormal cardiac function. However, the current research practices do not favour any specific lag of Poincaré plots, thus complicating the comparison of results of different researchers in their analysis of heart rate of healthy subjects and patients. We researched the informative nature of lagged Poincaré plots in different states of the autonomic nervous system. It was tested in three models: different age groups, groups with different balance of autonomous regulation, and in hypertensive patients. Correlation analysis shows that for lag l = 6, SD1/SD2 has weak (r = 0.33) correlation with linear parameters of heart rate variability (HRV). For l more than 6 it displays even less correlation with linear parameters, but the changes in SD1/SD2 become statistically insignificant. Secondly, surrogate data tests show that the real SD1/SD2 is statistically different from its surrogate value and the conclusion could be made that the heart rhythm has nonlinear properties. Thirdly, the three models showed that for different functional states of the autonomic nervous system (ANS), SD1/SD2 ratio varied only for lags l = 5 and 6. All of this allow to us to give cautious recommendation to use SD1/SD2 with lags 5 and 6 as a nonlinear characteristic of HRV. The received data could be used as the basis for continuing the research in standardisation of nonlinear analytic methods.

Heart Rate Variability in Psychology: A Review of HRV Indices and an Analysis Tutorial

“…SD1/SD2 has been shown to additionally capture complexity in HR patterns (e.g., healthy heart displays a "comet" shaped Poincaré plot while cardiac abnormalities display atypical "fan" or "complex" shapes [71][72][73]). However, SD1/SD2 seems to be sensitive to the time lag used, with some recent research recommending a lag of five or six heartbeats [72,74]. Nevertheless, there is no consensus on the optimal time lag yet, which itself could be subject to inter-individual differences.…”

Unravelling COVID-19 waves in Rio de Janeiro city: Qualitative insights from nonlinear dynamic analysis

“…Fig. 2 illustrates Poincaré plot for the evolution of daily cases for each wave of COVID-19 as time varies from τ = 1 to τ = 5, to capture the temporal nonlinear variation ( Koichubekov et al., 2017 ; Satti et al., 2019 ).

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“…For time series, Poincaré plot is a widely used method to analyze the correlation between time series. Generally, Poincaré plots have been employed to analyze heart rate variability and identify abnormalities in cardiac dynamics ( dos Santos et al., 2013 ; Brennan, Palaniswami, & Kamen, 2002 ; Koichubekov et al., 2017 ; Facioli et al., 2021 ). The construction of a Poincaré map is done on a geometric representation of a data series, in which the consecutive points of the time series are plotted.…”

“…In general, they represent the variation of short and long and term that allows a guided visual inspection of the distribution of points. Is important to mention that these measures are linear statistics and, therefore, do not directly quantify the temporal nonlinear variation, so it is interesting to use different delays in order to capture changes resulting from this variation in the delayed time ( Koichubekov et al., 2017 ; Satti et al., 2019 ).…”

Effects of Missing Data on Heart Rate Variability Metrics

“…Poincaré plots : SD1, SD2, SD1/SD2, ellipse area ( ), mean distance to the ellipse centroid (Md) and standard deviation to the ellipse centroid (Sd) have been computed using the ellipse fitting method [ 37 ]. As S and SD1/SD2 are computed from SD1 and SD2, relative errors are not shown for these metrics.…”