96783 - BIOMEDICAL MATHEMATICAL MODELS

Course Unit Page

Academic Year 2021/2022

Learning outcomes

At the end of the course, the student has knowledge of analytic approach to biomedical and biomechanical problems. The student is able to express these problems with instruments of geometrical analysis and differential equations.

Course contents

1) visual perception problems and models of the primary visual cortex.

Classical models as minima of functionals: Perona Malik and total variation functionals. Differential calculus in Banach spaces, steepest descent method, Palais Smale condition

Riemannian and subriemannian manifolds, exponential map. subriemannian distance, subriemannian models of cortext

2) Evolution of an electrical signal along nerve fibers: the Hodgkin-Huxley model and the FitzHug-Nagumo system. Models for the propagation of electrical impulses in heart cells.

Readings/Bibliography

Citti Sarti, Neuromathematics of vision, Springer

Corrado Mascia, Eugenio Montefusco, "Un invito alla biomatematica", Edizioni LaDotta

Office hours

See the website of Giovanna Citti

See the website of Maria Carla Tesi