Fig. 7.

Anchoring of spiral waves in the 10$\times$10 homogenised model. Activation time (AT) maps for the finescale and 10$\times$10 homogenised models in a 6 cm$\times$6 cm slice of tissue. Pictured are an activation before dynamics have stabilised (“early”) and two subsequent activations after stabilisation (“loop 1” and “loop 2”). Light grey sites are those that were not activated in the 210 ms time window, and dark grey sites are those fully occupied by fibrosis. Values of $\Delta t$ indicate the difference in timing between the finescale and homogenised models for the same activation event. The scar region causes a spiral wave that would otherwise break up to instead anchor and persist indefinitely. The homogenised model successfully predicts this anchoring despite losing the detailed structure of the obstructed region, but slightly underpredicts re-entrant frequency (here 5.45 Hz in finescale versus 5.32 Hz in homogenised). Precise paths of tortuous conduction (and conduction block) are lost in the homogenised model, but the resultant patterns of activation are similar after stabilisation (bottom two rows). Before dynamics stabilise, the over-prediction of conduction due to linear boundary conditions can allow activation to traverse the scar region, resulting in premature activation of the opposing side (light blue arrow in top right panel).