ПРИБЛИЖЕННОЕ АНАЛИТИЧЕСКОЕ РЕШЕНИЕ ПРЯМОЙ ЗАДАЧИ ЭЛЕКТРОИМПЕДАНСНОЙ ТОМОГРАФИИ В НЕОДНОРОДНОМ КРУГЕ С УЧЕТОМ СОПРОТИВЛЕНИЯ ЭЛЕКТРОДОВ

Abstract

An approximate analytical solution of the potential distribution in a two-dimensional circle with a radially inhomogeneous conductivity is obtained for the boundary conditions of the full electrode model, which takes into account the contact resistance of the electrodes at a given current strength. The solution is obtained by separating variables and using Fourier series, for the coefficients of which it is necessary to solve a system of linear equations. The obtained solution was compared with an approximate analytical solution of a similar problem for a homogeneous disk and with the Neumann-Robin boundary conditions. A good agreement was obtained, the quality of which improved with an increase in the number of terms taken into account in the series.