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Area of Science:

  • Computational Biology
  • Cardiac Electrophysiology
  • Nonlinear Dynamics

Background:

  • Spiral breakup in excitable media is a complex spatiotemporal pattern.
  • This phenomenon underlies ventricular fibrillation, a primary cause of global sudden cardiac deaths.
  • The precise mechanisms driving spiral breakup are not fully understood.

Purpose of the Study:

  • To numerically investigate the instability of periodic planar traveling wave solutions in a two-dimensional excitable medium.
  • To elucidate the mechanisms leading to spiral wave breakup in cardiac models.
  • To analyze the role of alternans in the transition from stable spiral patterns to fibrillation.

Main Methods:

  • Numerical simulations of two-dimensional excitable media models.
  • Analysis of planar traveling wave solutions and their stability.
  • Calculation of spiral pulse widths and identification of bifurcations.

Main Results:

  • Stable spiral patterns emerge in the model, mimicking malfunctioning heart rhythms like ventricular tachycardia.
  • Spiral wave breakup is identified as a consequence of transverse instability in planar traveling waves.
  • Simulations show alternans (oscillation of pulse widths) and a bifurcation to oscillatory wave patterns, with breakup occurring when alternans become pronounced.

Conclusions:

  • Transverse instability of planar traveling waves is a key mechanism driving spiral breakup.
  • Alternans play a significant role in the transition to spiral breakup and fibrillation.
  • Numerical findings provide insights into the dynamics of cardiac arrhythmias and sudden cardiac death.