Representation of the Cardiomyocytes of the Heart Muscle in the Form of an Electrical Circuit Element
DOI:
https://doi.org/10.18372/1990-5548.67.15613Keywords:
cardiomyocyte, algorithm, ferroelectric, modeling, differential equationsAbstract
The article considers the simulation approach to describe the electrical functioning of the main heart muscle cell - cardiomyocyte, when instead of describing elements of different nature, whether electronic devices or biological objects, at the microphysical level of model ideas about the structure of matter, they are all considered from a single point of view in the sense that the nature of the application of these devices and objects is determined by the functions implemented at the available external inputs, while the degree of complexity of their internal structure has no significance for the operation of the system they belong to and whose operation is determined. A ferroelectric capacitor was chosen as a meaningful model for studying the mechanism of formation of electrical signals of the cardiomyocyte, because the mathematical description of its operation allows to model both nonlinearity and feedback of electrical processes occurring in the heart muscle. This model was mathematically formalized using the charge transfer equation in a nonlinear inertial system in the form of the balance equation, a delayed differential equation.
References
V. G. Eliseev, Yu. I. Afanasyev, and N. А. Yurina, Histology, Мoscow, Medicina, 1983, 592 p. [in Russian]
Mathematical models of the heart. Available at: http://lischouk.ru/?page_id=153. [in Russian]
A. A. Ezhov and V. V. Nechetky, “Neural networks in medicine,” Open systems, no. 4, pp. 34–37, 1997, https://doi.org/10.1145/2493432.2493449
S. A. Regirer, Lectures on biological mechanics, P. 1., Moscow, Publishing house of Moscow University, 1980, 144 p.
L. D. Landau and E. M. Lifshitz, Hydrodynamics, Mosow, Nauka, 1988, 587 p. [in Russian]
M. V. Abakumov, I. V. Ashmetkov and others, “Methods of mathematical modeling of the cardiovascular system,” Matematicheskoe modelirovanie. vol. 12, no. 2, 2000. https://doi.org/10.1145/2348543.2348580
A. A. Bokrinskaya, “Generalized models of the state,” International Conference on Nonlinear Oscillations: Abstracts, Sofia, Publishing House of the Bulgarian Academy of Sciences, 1984, 129 p. [in Russian]
E. G. Aznakaev and D. E. Melnikov, “Modeling of electrical signals of the heart muscle,” Collection of IESU, no. 7, pp. 59–63, 2008. [in Russian]
E. G. Aznakaev and D. E Melnikov, “Investigation of nonlinear models of biological systems,” Collection of IESU, no.7, pp. 45–50, 2007. [in Russian]
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).