High Entropy Identifies Regions of Repetitive Wave Cross-Propagation: Insights from Computational Simulations

D Dharmaprani, P Kuklik, A McGavigan, A Ganesan

Research output: Contribution to conferenceAbstractpeer-review


Background: High entropy (En) of bipolar electrograms correlates with the pivot of rotating waves in atrial fibrillation. We hypothesised high En could also co-localise with regions of direct wave collision and repetitive cross-propagation, and study the behavior of approximate, sample, and Shannon entropy (ApEn/SampEn/ShEn), and dominant frequency (DF) in computational simulations. Methods: Multiple atrial fibrillation scenarios demonstrating regions of complex wave–wave interaction (cross-propagation regions), as well as simulations of direct colliding waves were developed using two-dimensional, isotropic, square grids in a custom C++ environment and the Tusscher–Panfilov phenomenological model. Extracellular bipolar electrograms were constructed. ApEn/SampEn/ShEn/DF of each scenario was computed, and En and DF maps constructed to visualise peak ApEn/SampEn/ShEn/DF regions. Results: In simulations depicting the head-on collision of waves, low ShEn/ApEn/SampEn were associated with collision zone. Contrastingly, DF was uniform across entire mapped region. Repetitive wave break was analysed in 10 scenarios, including (1) stable rotational wave surrounded by spiral break-up; and (2) multi-wavelet re-entry. Peak En at the cross propagation zone was compared with surrounding planar propagation. The difference between repetitive wave break and planar zones was (ApEn:1.75 bits ± 0.9, p < 0.01; ShEn:0.75 bits ± 0.3, p < 0.01; SampEn:2.5 bits ± 0.3, p < 0.01). Qualitatively, high ShEn/ApEn/SampEn regions were associated with interaction zones in which waves repeatedly arrive from different directions, whereas high DF regions did not show association to such behaviour. Conclusion: This analysis, for the first time, demonstrates that repetitive wave cross-propagation regions are associated with high En, whereas direct wave collision creates lower En. Contrastingly, high DF regions were not associated with either case.


Conference66th Cardiac Society of Australia and New Zealand Annual Scientific Meeting, the International Society for Heart Research Australasian Section Annual Scientific Meeting and the 12th Annual Australia and New Zealand Endovascular Therapies Meeting
Abbreviated titleCSANZ2018 ANZET18


  • bipolar electrograms
  • atrial fibrillation
  • computational modelling


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