Montserrat Torres: Stability of intracellular calcium in cardiac myocytes

Montserrat Torres successfully defended her Bachelor thesis in Mathematics in 15th May 2019

Stability of intracellular calcium in cardiac myocytes

The relationship between alternations in cardiac contractions, known as alternans, and the dynamics of intracellular calcium has been proven in several studies. In this paper, we will study a simple model two-variable model that sets the conditions for alternans due to refractoriness in calcium release. To perform this study, a theoretical background on dynamical systems will be provided, specially focused on the geometrical point of view and the use of Poincaré maps. A second chapter of theoretical background will focus on bifurcation theory and the main types of local bifurcations will be reviewed. The goal of this is to have enough knowledge to perform a complete study of the model while understanding the biological part of it and, eventually, link period doubling bifurcations to cardiac alternans.