Electrical wave propagation in memristive cardiac tissue under electric field

Inspired by the physical property of charge-controlled memristor, equivalent memristive current and charge variable are used to describe the wave stability in cardiac tissue under an electric field. The memristive current generated in a single myocardial cell results from the changes in the static distribution of intracellular ions and external forced electric field. A reaction-diffusion equation is used to estimate the propagation of electrical signals in the cardiac tissue as traveling waves, and the variations in memristive currents and charge levels reflect the effect of the electric field on the cardiac electrical behaviors, which are illustrated by the wave propagation and patterns' stability in the excitable media. An external stimulus is applied to control the wave propagation, and the self-sustained wave property is explored. An external electric field is applied to control the charge pumping and the wave stability is controlled. The improved memristive cardiac model considering the effect of electric fields is converted into an equivalent neural network for finding a numerical solution, and the statistical synchronization factor and energy function are defined for the theoretical analysis. This theoretical memristive cardiac model is effective to discover the wave characteristic, and then, an appropriate control scheme can be applied to prevent wave instability (breakup of spiral waves). As a result, heartbeat is maintained by generating and propagating continuous wavefronts in the cardiac tissue, and then, blood is pumped in and out of the heart exposed to an external electric field.