Dynamics And Synchronization In Biological Excitable Media

This thesis investigates the origin of spontaneous activity in the uterus. This organ does not show any activity until shortly before delivery, where very fast and efficient contractions are generated. The aim of this work is to provide insight into the origin of spontaneous oscillations and also on the transition from asynchronous to synchronized activity in the pregnant uterus.One intriguing aspect in the uterus is the absence of any pacemaker cell. The organ is composed of muscular cells, which are excitable, and connective tissue with cells whose behavior is purely passive. None of these cells, taken in isolation, spontaneously oscillates. We develop an hypothesis based on the observed strong increase in the electrical coupling between cells in the last days of pregnancy. The study is based on a mathematical model of (muscular) excitable cells, coupled to each other on a regular lattice, and to a fluctuating number of passive cells, consistent with the known structure of the uterus. The two parameters of the model, the coupling between excitable cells, and between excitable and passive cells, grow during pregnancy.Using both a model based on measured electrophysiological properties, and a generic model of excitable cells, we demonstrate that oscillations can appear spon-taneously when increasing the coupling coefficients, ultimately leading to coherent oscillations over the entire tissue. We study the transition towards a coherent regime, both numerically and semi-analytically, using the simple model of excitable cells. Last, we demonstrate that, the realistic model reproduces irregular action propaga-tion patterns as well as the bursting behavior observed in the in-vitro experiments.