Karma model. 2D spiral breakup

M nb ε dt dx

it delay fps
On 2D plane E values are displayed by the red color. n values are displayed by the green color. This script uses simple explicit algorithm and uses 512×512 float32 textures with the CLAMP_TO_EDGE boundary conditions. It makes 2 it time steps per frame. 1024×1024 model.

After relaxation transient this spiral is stable for M = 1. Set M = 3 to watch influence of exitation wave alternation. For M = 5 this instability leads to the spiral breakup [1].

"Spiral breakup is found to occur when the minimum period below which a periodically stimulated tissue exhibits alternans in action potential duration, exceeds by a finite amount the spiral rotation period. At this point, oscillations in action potential duration are of sufficiently large amplitude to cause a spontaneous conduction block to form along the wavefront." [1]

[1] Alain Karma Electrical alternans and spiral wave breakup in cardiac tissue
CHAOS 4, 461 (1994)

Heart rhythms     updated 3 Jan 2012