On mathematical model of cardiac cells exitation

V. S. Novoselov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 58-65

Résumé

Cardiac muscle cells perform three functions. Some of them automatically oscillate, others get excited and propagate active potential, the rest muscle fibers get excited and under electrical potential action contract therebly enabling pumping of blood. Each cell has specialized contacts with its heighloreng cells. Active heart potential is generated in the first type cells (pacemaker synchrony) in the sinoatrial node (SA), in the atrioventricular node (AV) and even in Purkinje fibers. Then with the help of the second type cells this potential propagates through the cardiac conduction system and activates atria and ventricular muscle fibers (the third type of cardiac cells). In the article the third type of cardiac cells are mainly examined. Mathematical models of the first and second types of cells are constructed in preceding works [7, 8]. The third type cardiac cells (myocardial cells) have a substantially more prolonged active potential as compared with axon spike. These cells are cable-like. The mechanical adhesion of myocardial cells is provided by adhering junction of an intercalated disk. The electrical joining of cells is provided by fissure openings in a junction. Such junctions make it possible for miocardiac cells to reach threshold excitation (cut-off) at the same time. The simplest mathematical model of miocardiac cell excitation with regard to traveling pulse structure and kinetic differential equations of cardiac cell contraction is constructed. Bibliogr. 11. Il. 1.

Détail

Keywords: myocardial cells, structure of a traveling pulse, kinetic differential equations.