Abstract
A differential model of a cardiac pacemaker cell with only ten state variables is proposed. It is intended for 0D or 3D simulation of the heart under the vagal control of the autonomous nervous system. Three variables are used to describe the membrane (membrane potential and two gate variables of ionic channels), taking into account the dynamics of the main ionic currents (inward sodium, L-type calcium and outward potassium), Na+/Ca2+ exchangers and Na+/K+ pumps. The remaining seven variables are associated with the fluid compartment model that includes Ca2+ binding by myoplasmic proteins, and the intracellular concentrations of free Calcium, Sodium and Potassium. Despite its moderate number of state variables, this model includes the main processes thought to be important in pacemaking on the cell scale and predicts the experimentally observed ionic concentration of calcium, sodium and potassium, action potential and membrane currents. The control by the calcium of the pacemaking activity is also considered.
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