Mathematical Modeling in Cardiac Electrophysiology
| školitel: | prof. Dr. Ing. Michal Beneš |
| e-mail: | zobrazit e-mail |
| typ práce: | dizertační práce |
| zaměření: | MI_MM |
| klíčová slova: | electrophysiology; excitable media; FitzHugh–Nagumo model; Sobolev spaces; electromechanics |
| odkaz: | http://geraldine.fjfi.cvut.cz/~benes/mb_home.html |
| popis: | Abstract: Treatment of serious cardiovascular diseases requires medicine to collaborate with variety of other scientific areas including mathematics. Mathematical models can help in simulating phenomena accompanying activity of myocardium as well as they can help in designing laboratory experiments with samples of myocardium, or with in vivo experiments made with hearts of animals, devoted to verification of new treatment strategies. Mathematical modelling of the excitable medium of myocardium is based on nonlinear reaction-diffusion partial differential equations describing transfer of electric signal across the medium. They can be linked to electromechanics of myocardium. Within the topic, these processes will be considered in a planar geometry describing planar experiments of the LMS cuts, and in curved 3D geometry describing in vivo experiments, both performed by collaborating laboratories. Mathematical analysis of the underlying system of equations can be performed using the framework of weak solutions in Sobolev spaces provided crucial properties of the Galerkin approximation are shown by the method of invariant regions, apriori estimates and the compactness method. Numerical solution will be obtained by means of the finite-volume and finite-element method in space and the Runge-Kutta method in time. Computational studies will address two-dimensional and three-dimensional behavior of the solution using algorithms prepared by the student. The topic is designed for the Ph.D. degree in Mathematical Engineering. It is motivated by the collaboration with the Department of Physiology of the Faculty of Natural Sciences, and with the Institute of Physiology of the First Faculty of Medicine, Charles University in Prague. It also belongs to the framework of collaboration with the Kanazawa University, the Meiji University, and the Shibaura Institute of Technology in Japan. It is expected to lead to the impacted publications and to contributions in international conferences. |
| literatura: | [1] J. Keener and J. Sneyd, Mathematical Physiology, Springer, New York, 2009. [2] P. Colli Franzone, L.F. Pavarino and S. Scacchi, Mathematical Cardiac Electrophysiology, Springer, Heidelberg, 2014. [3] S.A. Niederer, J. Lumens and N.A. Trayanova, Computational models in cardiology. Nat Rev Cardiol 16, 100–111 (2019). [4] M. Fedele et al., A comprehensive and biophysically detailed computational model of the whole human heart electromechanics, Computer Methods in Applied Mechanics and Engineering, Volume 410, 2023, 115983. [5] J. Kantner, M. Beneš, Mathematical Model of Signal Propagation in Excitable Media, Discrete and Continuous Dynamical Systems S, 2021, 14(3) 935--951. [6] M. Beneš, M. Kolář, J. M. Sischka, A. Voigt, Degenerate area preserving surface Allen-Cahn equation and its sharp interface limit, arXiv:2303.04018, accepted to International Journal of Numerical and Applied Mathematics (2024). |
| naposledy změněno: | 09.12.2024 09:46:46 |
za obsah této stránky zodpovídá:
Ľubomíra Dvořáková | naposledy změněno: 12.9.2011