[Simulation of the distribution of electronic potential in two- dimensional anisotropic resistive-capacitive medium]

The work was centered on theoretical investigation of the spread of electrotonic potential in the cardiac tissue during the delivery of long-term rectangular pre-threshold current impulses to the tissue. A mathematical model of two-dimensional anisotropic medium, with a circumference-shaped current source, has been developed. In accordance with the superposition principle well-known in electrostatics, the source of current was approximated by point sources placed on the perimeter of the current source in two ways: 1) by regular division of the perimeter of the current source in metric coordinate system, 2) by regular division of the perimeter of current source in the normalized coordinate system. Computerized programs have been developed for the computation of the distribution of electrotonic potential in the two-dimensional anisotropic medium. Families of curves were established evaluating the dependence of half-time (time during which electrotonic potential reaches half the stationary amplitude) on the size of the current source, anisotropy, the distance between the center of the current source and the point of registration (calculation) of electrotonic potential. Near the current source the dependence of half-time on the distance declines from linear.