From cardiac cells to genetic regulatory networks
A fundamental question in the treatment of cardiac disorders, such as tachycardia and fibrillation, is under what circumstances does such a disorder arise? To answer to this question, we develop a multiaffine hybrid automaton (MHA) cardiac-cell model, and restate the original question as one of identification of the parameter ranges under which the MHA model accurately reproduces the disorder. The MHA model is obtained from the minimal cardiac model of one of the authors (Fenton) by first bringing it into the form of a canonical, genetic regulatory network, and then linearizing its sigmoidal switches, in an optimal way. By leveraging the Rovergene tool for genetic regulatory networks, we are then able to successfully identify the parameter ranges of interest.
In this article, we study a piecewise smooth dynamical system inspired by a previous reduced system modeling compartimentalized brain metabolism. The piecewise system allows the introduction of an autoregulation induced by a feedback of the extracellular or capillary Lactate concentrations on the Capillary Blood Flow. New dynamical phenomena are uncovered and we discuss existence and nature of two equilibrium points, attractive segment, boundary equilibrium and periodic orbits depending of the Capillary Blood Flow.