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

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.

Advantage of four-electrode over two-electrode defibrillators

“…This effect is called "anode break excitation" (ABE) [25]. Although this effect has been observed in experiments [26][27][28] on canine, rat and guinea pig ventricular myocytes, it is not captured by the equations of the standard BR model.…”

The topology of defibrillation

“…The depolarization creates a region with elevated potential, which, even if it is unrecovered and so cannot propagate outward, can electrotonically excite the neighboring region in which recovery has been promoted by hyperpolarization. Thus, a front can be created in a region which is initially unrecovered if there is adequate nearby hyperpolarization (Roth 1995;Wikswo et al 1995). A reentrant wave on a 1D ring is created if the depolarization/hyperpolarization is not symmetric, so that one of the transitions is converted to a front while the second transition remains a back.…”

Modeling Defibrillation

“…APD can be either extended (by positive VEP) or shortened (by negative VEP) to a degree that depends on VEP magnitude and shock timing, with strong negative VEP completely abolishing (de-exciting) the action potential thus creating post-shock excitable gaps. As demonstrated in bidomain modeling studies (Ashihara et al, 2008;Roth, 1995), the post-shock VEP pattern is also the major determinant of the origin of post-shock activations. In those regions where shock-induced virtual anodes and virtual cathodes are in close proximity, a "break" excitation at shock-end (i.e, the "break" of the shock) can be elicited.…”