Marcotte & Grigoriev 2017

Key: marcotte2017dynamical

Smoothed version of the Karma model as published by Marcotte & Grigoriev in 2017. In it, a single spiral wave breaks up into spiral wave chaos due to amplification of the alternans instability. It can be used as a model of the transition from tachycardia to fibrillation.

References

  1. https://doi.org/10.1063/1.5003259

  2. https://doi.org/10.1063/1.4915143

  3. https://doi.org/10.1103/PhysRevLett.71.1103

  4. https://doi.org/10.1063/1.166024

Figure

Figure illustrating the Marcotte & Grigoriev 2017 model.

Variables

  1. u = 0.0

  2. v = 0.0

Parameters

  • diffusivity_u = 1.0

  • diffusivity_v = 0.05

  • beta = 1.389

  • eps = 0.01

  • ustar = 1.5415

Source code

OpenCL kernel
const Real e = exp(2. * (1.2571 * (u - 1.)));
const Real V = eps * (beta * ((1. + (e - 1.) / (e + 1.)) / 2.) + (1. + (exp(2. * (1.2571 * (v - 1.))) - 1.) / (exp(2. * (1.2571 * (v - 1.))) + 1.)) / 2. * (v - 1.) - v);
const Real U = (ustar - v * v * v * v) * (1. - (exp(2. * (u - 3.)) - 1.) / (exp(2. * (u - 3.)) + 1.)) * u * u / 2. - u;
*_new_u = u + dt * (U + _diffuse_u);
*_new_v = v + dt * (V + _diffuse_v);

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- phenomenological
example discretisation:
  dt: 0.037
  dx: 0.92
  stimulus: 1.11
units:
  t: 1
  x: 1
  u: 1