Optimal Synchronization of Excitable Media

Patterns and Simulations

Print
When spiral waves are present in a 2-dimensional model of excitable media, we find that the state of each cell stays reasonably close to a one-dimensional manifold. Using isostable reduction and Hamilton-Jacobi-Bellman techniques, we develop a novel energy-optimal methodology to synchronize the activity of the cells. This methodology has potential applications to cardiac arrhythmia. Specifically, it represents a significant first step in the development of energy-optimal defibrillation strategies. Animation and figures are taken from: D. Wilson, and J. Moehlis. "An Energy-Optimal Methodology for Synchronization of Excitable Media." SIAM Journal on Applied Dynamical Systems 13.2 (2014): 944-957.
Author Institutional AffiliationUniversity of California, Santa Barbara
Author Email
Keywordsexcitable media, synchronization, Hamilton–Jacobi–Bellman, optimal control, isostables

Documents to download

  • Transient Attractor in an Excitable Medium(.jpg, 30.83 KB) - 3154 download(s) When spiral waves are present in the medium, each cell stays reasonably close to the transient attractor.
  • Isostables for the Excitable System(.jpg, 34.76 KB) - 3145 download(s) An isostable field for the excitable system. In the absence of any external stimulus, each cells on the same isostable will approach the fixed point together, in a well-defined sense.
  • Optimal Synchronization(.jpg, 34.06 KB) - 3144 download(s) The common optimal stimulus drives each cell on the transient attractor to a region of phase space where the isostables are diffuse. This causes the cells to approach the fixed point together.
  • Optimal Synchronization - Animation(.gif, 1.58 MB) - 3159 download(s) The common optimal stimulus drives each cell along the transient attractor to a region of phase space where the isostables are diffuse. This causes the cells to approach the fixed point together.

Please login or register to post comments.

Name:
Email:
Subject:
Message:
x