A model of slow conduction in bullfrog atrial trabeculae

The success or failure of the propagation of electrical activity in cardiac tissue is dependent on both cellular membrane characteristics and intercellular coupling properties. This paper considers a linear arrangement of individual bullfrog atrial cells that are resistively coupled end to end to form a cylindrical strand. The strand, in turn, is encased by an endothelial sheath that provides a restricted extracellular space and an ion diffusion barrier to the outer bathing medium. This encased strand serves as an idealized model of an atrial trabeculum. Excitable membrane characteristics of the atrial cell are specified in terms of a Hodgkin-Huxley type of model that is quantitatively based on single-microelectrode voltage clamp data from bullfrog atrial myocytes. This membrane model can simulate the behavior of normal cells as well as of ischemic cells that exhibit depressed electrophysiological behavior (e.g., decreased resting potential, upstroke velocity, peak height, and action potential duration). Depressed activity can be easily simulated with variation of a single model parameter, the gain of the Na+/K+ pump current (INaK). Intercellular coupling properties are specified in terms of a lumped resistive T-type network between adjacent cells. The atrial strand model provides a means for studying the theoretical aspects of slow conduction in a "hybrid" strand that consists of a central region of cells having abnormal membrane or coupling properties, flanked on either side by normal atrial cells. Both uniform and discontinuous conduction are simulated by means of appropriate changes in the coupling resistance between cells. In addition, by varying either the degree of depressed electrical activity or the intercalated disc resistance in the central zone of the strand, slow conduction or complete conduction block in that region is demonstrated. Since the cellular model used in this study is based on experimental data and closely mimics both the atrial action potential and the underlying membrane currents, it has the potential to (1) accurately represent the current and voltage wave-forms occurring in the region of intercalated discs and (2) provide detailed information regarding the mechanisms in intercellular current spread in the region of slow conduction.