Mechanisms of repolarization and conduction in a mathematical model of electrophysiological responses in the human atrium

We have developed a mathematical model of the human atrial myocyte, based on averaged voltage-clamp data recorded from isolated single myocytes. This formulation can reconstruct action potential data which are representative of recordings from a majority of human atrial cells in our laboratory, and therefore provides a biophysically based account of the underlying ionic currents. This work is based in part on a model of the rabbit atrial myocyte, and was motivated by differences in some of the repolarizing currents between human and rabbit atrium. We have therefore given particular attention to the sustained outward $K\sp+$ current, $I\sb{sus}$, which putatively has a prominent role in determining the duration of the human atrial action potential. Our results demonstrate that the action potential shape during the peak and plateau phases is determined primarily by $I\sb{t}$, $I\sb{sus}$, and $I\sb{Ca,L}$, and that the role of $I\sb{sus}$ in the human atrial action potential can be modulated by the baseline sizes of $I\sb{Ca,L}$, $I\sb{sus}$, and $I\sb{K,r}.$ As a result, our simulations suggest that the functional role of $I\sb{sus}$ can depend on the physiological/disease state of the cell. We have furthermore used our single-cell model to formulate a multicellular model of one-dimensional propagation in an idealized human atrial strand. Three different formulations for this model was explored: the classical cable equations with fixed ion concentrations, an "electrodiffusion" formulation which accounts for variable ion concentrations due to axial and radial transport, and an intermediate cable equation formulation which accounts for variable ion concentrations due to radial transport only. Comparative simulations show that the variable-concentration cable equation formulation can accurately simulate ion concentration dynamics during propagation, and therefore provides a less computationally demanding alternative to the electrodiffusion formulation. Simulations using the multicellular model predict that conduction velocity in the human atrium has a similar dependence on extracellular $\lbrack K\sp+\rbrack$ as in ventricular cells, including a region of "supernormal conduction" at moderate $\lbrack K\sp+\rbrack\sb{o}$-elevations, but that this response spans a smaller range of conduction velocities in the atrium. Our results suggest that this difference can he explained in terms of the smaller $I\sb{K1}$, and higher input resistance, of atrial cells