Mathematical cardiac physiology
The course covers mathematical and numerical aspects of cardiac physiology. The course is composed by 4 lectures in total. The first lecture will focus on electrophysiology. We will present the bidomain model and its derivation from basic principles, and excitation waves solutions associated to it. We will also cover simplified models such as the monodomain and eikonal models. The second lecture is on the numerical discretization and computational aspects for the bidomain model. The third lecture is devoted to cardiac mechanics and the electro-mechanic and mechano-electric coupling. Finally, the last lecture will focus on applications of clinical interest, including ECG simulation, cardiac resynchronization therapy and atrial fibrillation.
The course will also benefit from 2 guest presentations from Sonia Pozzi, on computational electromechanics and the implementation in MOOSE, and from Ali Gharaviri, on modeling of atrial fibrillation. The guest talks are respectively scheduled on the third and fourth lecture.
10/10: bidomain model
17/10: computational electrophysiology
24/10: cardiac mechanics + S. Pozzi seminar
31/10: clinical applications + A. Gharaviri seminar
- Keener, Syned “Mathematical Physiology”, 2nd ed. 2009
- Hille, “Ion channels of excitable membranes”, 3rd ed. 2001
- Colli Franzone et al, “Mathematical cardiac electrophysiology”, 2014
- Smith et al, “Multiscale computational modelling of the heart”, Acta Numerica 13, 2004