Geodesic
On mathematical model of cardiac cells exitation
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 58-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: myocardial cells, structure of a traveling pulse, kinetic differential equations. 
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V. S. Novoselov. On mathematical model of cardiac cells exitation. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 58-65. http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a6/

[1] O. G. Gazenko, I. A. Agadzhanjanc, O. S. Andrianov, A. A. Bashkirov i dr., Glossary of Terms physiological, Nauka, M., 1987, 448 pp.

[2] M. S. Gilyarov, A. A. Baev, G. G. Winberg, G. A. Zavarzin e. a., Encyclopedic Dictionary of Biology, Sov. jenciklopedija, M., 1989, 864 pp.

[3] Borzjak Je. I., Bocharov V. Ja., Volkova L. I. e. a., Human anatomy, v. 2, ed. M. R. Sapin, Medicina, M., 1986, 480 pp.

[4] Keener J., Sneyd J., “Mathematical physiology”, Interdisciplinary Applied Mathematic, 8 (1998), 727 | MR

[5] Novoselov V. S., Statistical models nejrodinamics, Preprint f-ta prikl. matematiki-processov upravlenija S.-Peterb. gos. un-ta, S.-Peterburg, 2004, 64 pp. | MR

[6] Novoselov V. S., Statistical dynamics, studies allowance, Izd-vo S.-Peterb. un-ta, S.-Petersburg, 2009, 393 pp.

[7] Novoselov V. S., “Simulation of nerve Pulse”, Vestn. S.-Peterb. un-ta, ser. 10: prikladnaja matematika, informatika, processy upravlenija, 2011, no. 4, 73–83

[8] Novoselov V. S., “A mathematical model of pacemaker”, Vestn. S.-Peterb. un-ta, ser. 10: prikladnaja matematika, informatika, processy upravlenija, 2012, no. 4, 59–64

[9] Krinskij V. I., Medvinskij A. B., Panfilov A. V., The evolution of self-wave vortices, Ser. Matematika, kibernetika, 8, Znanie, M., 1986, 48 pp.

[10] Berkinblit M. B., Zherdjaev A. V., Tarasova O. G., Tasks the biology of humans and animals, expert. textbook allowance, MIROS, M., 1995, 176 pp.

[11] Begun P. I., Afonin P. N., Modeling in biomechanics, textbook allowances, Vysshaja shkola, M., 2004, 390 pp.