N. F. Otani, Deep entry of defibrillating effects into homogeneous cardiac tissue, IEEE Transactions on Biomedical Engineering 51, 401-407 (2004).
A simple, idealized mathematical model of cardiac tissue is used to show that electrical fields applied with the intent of defibrillating the heart can be effective deep within (that is, many space constants into) cardiac tissue, even in cases when the tissue is assumed to have completely homogeneous electrical properties. This conclusion is drawn from the analysis of the two eigenmodes present in the model, which have fundamentally different characteristics. One mode decays very rapidly with space, implying that the associated membrane potential is only present with appreciable amplitude within a few space constants of the tissue surface. The other mode, however, is not directly dependent on the value of the space constant, and allows deep penetration of the membrane potential and, by implication, its associated defibrillating effects. For deep membrane potentials to be generated by this mechanism, the intracellular and extracellular resistivity anisotropy ratios must be unequal, as is typically the case in cardiac tissue. The model also predicts that this mechanism is most effective for a given applied field strength when the electrode size and separation, or spatial features of the externally applied field at the heart surface, are characterized by scalelengths that are commensurate with approximately two times the heart wall thickness.