The effect of boundary conditions on epicardial potential distributions

This study presents a comparison of semi-analytical and numerical solution techniques for solving the passive bidomain equation in simple tissue geometries containing a region of subendocardial ischaemia. When the semi-analytical solution is based on Fourier transforms, recovering the solution from the frequency domain via fast Fourier transforms imposes a periodic boundary condition on the solution of the partial differential equation. On the other hand, the numerical solution uses an insulation boundary condition. When these techniques are applied to calculate the epicardial surface potentials, both yield a three well potential distribution which is identical if fibre rotation within the tissue is ignored. However, when fibre rotation is included, the resulting three-well distribution rotates, but through different angles, depending on the solution method. A quantitative comparison between the semi-analytical and numerical solutiontechniques is presented in terms of the effect fibre rotation has on the rotation of the epicardial potential distribution. It turns out that the Fourier transform approach predicts a larger rotation of the epicardial potential distribution than the numerical solution. The conclusion from this study is that it is not always possible to use analytical or semi-analytical solutions to check the accuracy of numerical solution procedures. For the problem considered here, this checking is only possible when it is assumed that there is no fibre rotation through the tissue.