Evaluating heart rate coupling with Multi-dimensional Recurrence Quantification Analysis (MdRQA) and Cross-Correlation (CC): Analytical decisions and implications

Figures

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  Fig 1. An illustration representing the 3 steps for generating the synthetic coupled RR intervals and BPM time series. SubFig A shows the time series with 1/f noise adjusted to usual RR interval scale. Then each data point is duplicated into a vector the length of its value (B); as a reference, the length of B equals to the sum of A. A moving average is applied on the stretched time series which is then rounded resulting in RR intervals (C), while under the ‘coupled’ conditions a different window size is used for ts2 to generate coupled yet not equal time series pair. To compute BPM, we applied non overlapping windows of 512ms.

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  Fig 2. Exemplary BPM time series of the 2 conditions – two BPM-series that are coupled, and two series that are uncoupled.

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  Fig 3. An illustration representing the extraction of %REC and %LAM through unembedded MdRQA. SubFig A shows two time series. Based on them, the distance matrix is computed with Euclidean distance between each pair of data points (B). The distance matrix is then discretized according to a certain threshold (r) yielding the recurrence plot (C) in which each blue square represents a recurrent point – for this toy example the threshold was chosen so it provides a high enough number of recurrent points. Among the recurrent points, only the ones with a vertical or horizontal neighboring recurrent points were painted in orange (D) to represent the Laminarity.