Shrimp hubs in the Hindmarsh-Rose model.

Abstract

In a previous work, we reported cardiac behaviors and, most notably, chaotic arrhythmias of the early afterdepolarization type in the Hindmarsh-Rose model. This behavior appeared to be associated with shrimp-shaped structures in the phase diagram. In this work, we investigate the shrimp region in more detail. We show that shrimps are in fact organized in a spiral pattern known as a hub. Such structures have previously been hypothesized to exist in the Hindmarsh-Rose model but have never been found. Using bifurcation and phase diagrams based on the interspike interval, together with the Lyapunov exponents, we characterize the region of interest. We further clarify the biological behaviors present there and their placement. We use the arrhythmic cardiac behaviors to calculate the corresponding electrocardiogram and interpret its meaning in a clinical setting. We also investigate the movement of the shrimp hub in the parameter space as we change a key parameter of the model. We find evidence that the hub disappears as we decrease the parameter in the direction of one of the most commonly used Hindmarsh-Rose phase diagrams.