Fig. 5.

Performance of homogenisation for propagation through obstructed tissue when separated from numerical effects. Displayed conduction velocities are those predicted by homogenised models (6) with different choices of boundary conditions (BCs) and averaging volume size, but solved on the original finescale grid to remove the effects of changing the numerical discretisation. All homogenised models perform well, with best performance obtained using the largest averaging volumes to maximise the difference in length scales between finescale features and the homogenised model. Periodic BCs perform best overall, as the medium is of consistent property and hence admits a representative volume element. When obstacles are aligned perpendicular to the direction of propagation, periodic and confined BCs pre-emptively predict conduction block for high proportions of obstruction. Linear BCs instead predict conduction even in the case where the finescale simulation blocks.