Fig. 4.

Prediction by homogenised models of conduction speeds in different types of obstructed tissue. Top Row: Representative sections of the 5 cm $\times$ 0.5 cm tissue slices showing the patterns of obstruction considered (obstacles in red). Pictured examples are the case of 25% obstacles. Waves of excitation move from left to right. Bottom Rows: Performance of the different types of boundary conditions on the three types of obstruction, for different choices of averaging volume size and boundary conditions for closure subproblems (9). Where a dot does not appear for a given level of obstruction, this corresponds to a failure to propagate the length of the tissue. Both boundary condition selection and averaging volume size have an important effect on homogenisation performance, with periodic conditions most accurate for smaller averaging volumes $(\Delta x\le \text{100}\text{µm})$ and linear conditions most accurate for the larger ($\Delta x=\text{250}\text{µm}$). Homogenised models with $\Delta x=\text{500}\text{µm}$ are universally poor for the more challenging, highly obstructed problems. Best overall performance is obtained by using linear boundary conditions and a 25$\times$25 averaging volume (10 µm up to 250 µm). Particularly notable is the case of “perpendicular” obstructions, where homogenised models using boundary conditions other than linear are prone to over-predicting conduction block.