The course proposes an introduction to the mathematical modelling and simulation of physiological systems (cellular electrophysiology, reaction-diffusion systems, bioelectric cardiac processes) providing the main analytical and numerical methods, for investigating the mathematical models and for the interpretation of the simulated results.

Lectures

Oral examination with discussion and interpretation of the dimulations developed at the computer.

The courses of the "laurea triennale"

1) Models of cellular physiology: biochemical reactions, enzyme kinetics and quasi-steady approximation, cooperative and inhibition phenomena.
Introduction to reaction-diffusion systems: balance laws, diffusion equation, reactive terms, initial and boundary conditions; travelling wave solutions; numerical approximation of non-linear parabolic equations.
Cellular electrophysiology: Transmembrane potential, dynimics of the ionic currents, Hodgkin-Huxley formalism; excitability e refractoriness. FitzHugh-Nagumo, Morris-Lecar models.
Introduction to propagation in excitable media: excitable cable model,, homogeneization of an arrangement of cells, bidomain model, propagation of the excitation wavefront .
Mathematical models in electrocardiology: Anisotropic bidomain model, macroscopic structure of bioelectric cardiac sources, extracellular potential and electrograms.

F. Britton Essential Mathematical Biology, Springer Verlag, Heidelberg, 2000.
J.P. Keneer, J. Sneyd : Mathematical Physiology. I: Cellular Physiology, II: System Physiology,Springer-Verlag, New York, 2009.
J. D. Murray, Mathematical Biology I : An Introduction, Springer-Verlag, New York, 2002.