Effect of Gaussian gradient in the medium's action potential morphology on spiral waves

Disorders in the heart's conduction system can lead to the formation of rotating spiral waves, and terminating the re-entrant seeds is crucial to restore cardiac function. Myocyte action potential (AP) morphology is spatially dependent within the myocardium, forming an intrinsic gradient. This study investigates the impact of gradients in AP morphology on the behavior of spiral seeds and their traveling wavefronts, explicitly focusing on spatial variations in action potential duration (APD) and resting level. By employing a memristive FitzHugh-Nagumo grid, a gradient of Gaussian distribution is introduced in distinct parametric planes capable of altering AP morphology. The steepness of the AP gradient is controlled via the variance of the Gaussian formulation. It is found that when APD is shortened along a gradient, the spiral tip tends to drift towards more excitable regions. In contrast, when the APD is prolonged, the spiral seed is stationary, and the wavelength of the spiral wave increases. The gradient in the resting levels induces instability, possibly eliminating the spiral seed and leading to disturbed patterns. The distribution variance is not a determining factor in the scenarios seen in the APD gradient. However, changing the variance in the resting levels gradient tends to affect the wave pattern's homogeneity.