Electrostatic potential on the boundary of cardiac tissue
The goal of this study is to determine the distribution of an electrostatic potential on the boundary of cardiac tissue. The mathematical development, based on the two-scale asymptotic expansion and boundary layer theory, is presented for the case of Neumann boundary conditions. A two-dimensional model of cardiac tissue is used to assess the magnitude and the extent of the boundary layer potential arising under such conditions. Numerical simulation indicates that the effect of the boundary is limited to the membrane immediately under the electrode; however, over 70% of the transmembrane potential across this membrane is due to the boundary layer term. This result is especially important for applications that rely on the effects of a localized electrical field, such as pacing, electroporation, or ablation.
