SIE method of analysing microwave fields of a 3D heart model

Abstract

The Singular Integral Equations Method (SIE) used in this article allowed us to solve Maxwell's Equations for a Three-Dimensional (3D) asymmetric heart model when a microwave catheter (MC) was placed inside the model and radiated microwaves. Here we explain the main idea of our SIE method. We first separated the solution of equations from satisfying the boundary conditions. For this purpose, we found the solution of the differential equations having a point source. This fundamental solution is used in our integral representation of a problem. The integral representation automatically satisfied the differential equations but has an unknown density function which must be found from the boundary conditions. The solution of the differential equations, obtained by our SIE method, was rigorous, that is it satisfied the differential equations and all boundary conditions. The false roots did not occur when applying our SIE method. All surfaces of the heart model were defined as a triangular mesh covering the 3D heart surfaces. The heart model consisted of cardiac muscle and the right and left atriums with ventricles which were filled with blood. In this article we presented our calculations of the microwave electric field inside of a heart model. We have seen that our SIE method enabled one to optimal the size and shape of a MC when used to remove abnormal tissue in a heart model.