Study of electrical conduction processes in blood vessels using cable theory

Traditionally, the electrical conduction processes in blood vessels are explained using cable theory where locally generated signals (membrane potential ) passively spread along the arteriolar wall. As a rule, decomposition is quantified, with a constant of length derived from cable theory. Using cable theory on blood vessels depends on assumptions that may not be necessarily performed for small arteries and arterioles. It is known that arterioles are composed of at least two layers of cells: endothelial cells (EC) and one or more layers of smooth muscle cells (SMC), which are connected by myoendothelial gap junctions (MEGJ). In this study, arterioles composed of two cell layers are studied, focusing on changes in membrane potential within both EC and SMC layers. A suitable stationary problem is formulated and solved analytically using the method of separation of variables. Additionally, numerical modelling of membrane potential propagation is conducted using MATLAB software. Isopotential contours of the membrane, as well as two-dimensional and three-dimensional graphs depicting the numerical results, are presented in the study. Mathematics Subject Classification. 35Q92, 35J05, 74B99, 35F15