A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode

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Abstract
Numerical simulations of electrical stimulation of cardiac tissue using a unipolar extracellular electrode were performed. The bidomain model with unequal anisotropy ratios represented the tissue, and the Beeler-Reuter model represented the active membrane properties. Four types of excitation were considered: cathode make (CM), anode make (AM), cathode break (CB), and anode break (AB). The mechanisms of excitation were: for CM, tissue under the cathode was depolarized to threshold; for AM, tissue at a virtual cathode was depolarized to threshold; for CB, a long cathodal pulse produced a steady-state depolarization under the cathode and hyperpolarization at a virtual anode. At the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue, resulting in excitation. For AB, a long anodal pulse produced a steady-state hyperpolarization under the anode and depolarization at a virtual cathode. At the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue, resulting in excitation. For AB stimulation, decay of the hyperpolarization faster than that of the depolarization was necessary. The thresholds for rheobase and diastolic CM, AM, CB, and AB stimulation were 0.038, 0.41, 0.49, and 5.3 mA, respectively, for an electrode length of 1 mm and a surface area of 1.5 mm2. Threshold increased as the size of the electrode increased. The strength-duration curves for CM and AM were similar except when the duration was shorter than 0.2 ms, in which case the AM threshold rose more quickly with decreasing duration than did the CM threshold. CM and AM resulted in similar strength-frequency curves. The model agrees qualitatively, but (in some cases) not quantitatively, with experiments.