Cardiac behaviors and chaotic arrhythmias in the Hindmarsh–Rose model

Abstract

The Hindmarsh–Rose is one of the best-known models of computational neuroscience. Despite its popularity as a neuron model, we demonstrate that it is also a complete cardiac model. We employ a method based on bifurcations of the interspike interval to redraw its phase diagram and reveal a cardiac region. This diagram bears great resemblance to that of the map-based model for neurons and cardiac cells, the KTz model. Both phase diagrams are compared, showing a very similar placement of behaviors in the parameter space. Adjusting the Hindmarsh–Rose parameters allows us to obtain behaviors similar to atrial, ventricular and pacemaker cells. We also report the neuronal behavior of sustained subthreshold oscillations in the diagram, also unknown in the model. We demonstrate the existence of periodic and chaotic early afterdepolarizations, a behavior linked to life-threatening arrhythmias. In a second phase diagram, we find a chaotic region with early afterdepolarizations and self-organized periodic structures known as shrimps. We also propose a new and simple method to calculate the electrocardiogram using the membrane potential of a point cell and demonstrate its use for the study of QT syndromes using the Hindmarsh–Rose model. Given the smaller number of equations and parameters than detailed conductance models and richer dynamics than other general models, this work presents the Hindmarsh–Rose as a promising alternative for computational cardiology studies.