Separation between virtual sources modifies the response of cardiac tissue to field stimulation

Introduction: While it is now understood that the tissue geometry and the electric field distribution are important in generating virtual electrodes, the effects of interaction between a collection of electrodes have not been examined. To develop a basis for understanding such interactions, we have studied a single pair of oppositely polarized virtual sources. Although such oppositely polarized pairs of virtual electrodes can be generated by a variety of field distributions and tissue geometries, we examine one simple system that incorporates the salient features of source interaction. Methods and Results: Our model system is a homogeneous tissue strip stimulated by a uniform extracellular field. To clarify virtual source interaction, we show that field stimulated tissue can be equivalently polarized by a set of intracellular current sources with magnitude and distribution defined by the generalized activating function. In our model system, an intracellular current source is produced at one edge of the tissue and an intracellular current sink at the other. Therefore, the tissue length acts to modulate the overlap, or interaction, between the polarizations arising from each source. To quantify the effects of source interaction, the chronaxie and rheobase values of the strength-duration relation were determined for source separations varying between 1.0 cm and 100 μm (active membrane dynamics were modeled with the Luo-Rudy phase I formulation). At all separations > 3.0 mm, the chronaxie was constant at 3.09 msec and the rheobase was 0.38 V/cm. Under 0.2 mm, the chronaxie decreased to 0.55 msec while the rheobase increased linearly with the inverse of source separation. The dependence of these parameters on separation primarily reflects passive electrotonic interactions between the two virtual electrodes. However, the exact values are strongly dependent upon active tissue properties - largely the inward rectifier potassium channel and activation of the sodium current. Conclusion: Tissue excitation in response to field stimulation is strongly modulated by the proximity of, and therefore the interaction between, oppositely polarized virtual electrode sources.