Mathematical models for excitable systems in biology and medicine

The excitable systems play a very important role in Biology and Medicine. Phenomena such as the transmission of impulses between neurons, the cardiac arrhythmia, the aggregation of amoebas, the appearance of organized structures in the cortex of egg cells, all derive from the activity of excitable media. In the first part of this work a general definition of excitable system is given; we then analyze some cases of excitability, distinguishing between electrical and chemical excitability and comparing experimental observations with simulations carried out by appropriate mathematical models. Such models are almost always formulated by partial differential equations of "reaction-diffusion" type and they have the characteristic to describe propagations of electrical waves (neurons, pacemaker cardiac cells, pancreatic b-cells) or chemical and mechanical waves (propagation of Ca++ waves or mechanical waves in the endoplasmic reticulum). The aim is to put in evidence that the biological systems can show not only excitability of electrical type, but also excitability of chemical nature, which can be observed in the first steps of development of egg cells or, for example, in the formation of pigments in vertebrate skin or in clam shells.