Analysing complex excitation patterns in cardiac tissue using wave event networks

Figures

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  FIGURE 1. Schematic overview over the algorithm for generating wave event networks. Further details of its implementation can be found in the code Schlemmer (2025).

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  FIGURE 2. This figure shows the binarized wave parts in five exemplary frames of a Fenton-Karma simulation with spontaneous excitations every five frames and with wave pixels (pixels above a certain threshold, 0.4 in this case) being shown in black and non-wave pixels being shown in white.

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  FIGURE 3. This figure shows connected wave parts in different colors for the same simulation as in Figure 2. As waves are tracked throughout the simulation, their colors stay constant over time.

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  FIGURE 4. Here normalized and filtered experimental data is displayed for multiple frames. After these preprocessing steps the data is fed into the wave tracking algorithm.

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  FIGURE 5. This figure shows an excerpt of the same simulation as Figure 3 but instead of single frames it displays the graph with the colored nodes corresponding to the colored waves. The horizontal arrows show continuing waves and the diagonal ones show splits and mergers of waves. One can see, for example, the regular pacings without any interactions with other waves in frames 31 and 36 and the turquoise wave (ID 9) merging into the orange one (ID 13) on frame 51. Additionally, one can see, that due to the evolution of the wave patterns and the threshold used, the violet wave (ID 7) is not recognized as the source of the orange wave (ID 13).

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  FIGURE 6. The graph over 150 frames of the experimental video, binarized at a threshold of 0.2, shows a large number of waves with very short lifetimes. The analysed excerpt was captured at 500 frames per second and downsampled 10 times, hence the 150 frames correspond to 3 s of real time.

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  FIGURE 7. This figure shows an unfiltered excerpt from the experimental graph along with a few example frames from the experimental data. While some of the many waves visible in the frames and at the wave event network may grow into significant waves on the tissue, others are likely artifacts caused by noise or other unwanted effects at the border.

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  FIGURE 8. In contrast to Figure 7, this figure displays the section of experimental data, but with waves filtered to exclude those with a lifetime of only one frame and a maximum size of fewer than 20 pixels. Most small artifacts have been effectively removed, the wave event network now contains essentially only waves showing the relevant dynamics. The violet wave in the top right corner of frame 30 is considered as one wave object due to the used radius parameter of 3 px.

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  FIGURE 9. Both wave sizes and wave lifetimes for the experimental video are displayed at a logarithmic scale. Especially for the wave sizes it is clear, that a large number of very small waves are observed which are in many cases insignificant for the actual dynamics.