New skip parameter to facilitate recurrence quantification of signals comprised of multiple components

Recurrence analyses are typically performed on discretized time series after applying proper embeddings, delays, and thresholds. In our study of atrial electrograms, we found limitations to this approach when sequential bipolar complexes were defined as the timings of the first two zero crosses following the initiation of each event. The reason for this is that each bipolar component consists of two points in odd-even pairings. Since recurrence analysis starts vectors on each sequential point, incorrect even-odd pairings occur for every other vector. To overcome this limitation, a new parameter SKIP is introduced such that recurrence vectors can skip 1 (or 2) points for signals with defined multiple components. To demonstrate the utility of parameter SKIP, we used the Courtemanche model to simulate the electrical activity in the human atrium on a square, two-dimensional plane with 800 × 800 nodes. Over this plane, a grid of 39 × 39 virtual unipoles was created. Neighboring unipoles formed 39 × 38 bipolar pairs, which were recorded as 1482 continuous and synchronous time series. At each unipolar site, the actual wavefront direction was determined by comparing the relative activation timings of the local intracellular potentials. Parameters were set such that the "tissue" exhibited both spiral waves (organized activity) and wave breakups (chaotic activity). For each bipolar complex in the continuous electrogram, discretized electrogram conformation was defined as the timing delays from the start of the complex to the first two zero-crosses. Long sequences of paired zero-cross timings were subjected to recurrence analysis using SKIP values of 0 (no skipping) and 1 (single skipping). Recurrence variables were computed and correlated with the absolute wavefront directions. The results showed that the introduction of the skipping window improved the correlations of some recurrence variables with absolute wavefront directions. This is critically important because such variables may be better markers for wavefront directions in human recordings when the absolute wavefront directions cannot be calculated directly.