PIERS ONLINE, VOL. 5, NO. 4, 2009 389 Analysis of the Pulse-Modulated Microwave Propagation into 3D Anisotropic Heart Model by SIE Method L. Nickelson 1 , S. Asmontas 1 , R. Martavicius 2 , and V. Engelson 3 1 Semiconductor Physics Institute, A. Gostauto 11, Vilnius, Lithuania 2 Electronic System Department, Gediminas Technical University, Vilnius, Lithuania 3 Linkoping University, SE-58183, Linkoping, Sweden Abstract— Here we present the electrodynamical analyses of microwave pulses propagation in a 3D anisotropic heart model for the first time. The electrodynamical rigorous solution of Maxwell’s equations related to the microwave pulse propagation in the 3D heart model with anisotropic and isotropic media is presented here. The myocardium tissue media is an anisotropic lossy media and blood is an isotropic lossy media. The boundary problem was solved by using the singular integral equations’ (SIE) method. Our solution, obtained by the SIE method, is electrodynamically rigorous. The false roots do not appear and the boundary conditions have to be satisfied only on the surfaces dividing different materials. The frequency of the carrier microwave is 2.45 GHz. The modulating signals are triangular video pulses with the on-off time ratio equal to 5 and 100. The pulse durations were always equal to 20 μs. Microwave electric field distributions were analysed at three longitudinal cross-sections of the heart model. The distributions of electric field for the anisotropic and isotropic heart models are compared here. 1. INTRODUCTION A human heart may be under influence of the microwave radiation for the medical examination of patients [1] or because of hazardous environment [2]. The tissue of a heart, in the normal state possesses anisotropic properties; however, the anisotropy of heart tissue grows with some illnesses [3,4]. Desiring to diagnose diseases of heart with the help of the microwave equipment it is necessary to investigate the process of microwave interaction with the anisotropic heart tissue. Research data of the anisotropic properties of heart tissue along and across of myocardium muscle fibers are given in [3]. An electrodynamical analysis of the diffraction problem relating to scattering of the pulse- modulated microwave on the anisotropic heart model is given in this article. We solve this problem, using the SIE method [5]. In our case the model of heart contains both isotropic and anisotropic area. The model that contains simultaneously anisotropic and isotropic media we will call an anisotropic model. The model that contains only isotropic media we will call an isotropic model. 2. THE FORMULATION OF THE ELECTRODYNAMICAL PROBLEM The 3D heart model, which has the anisotropic layer of myocardium, is located in the homogeneous dielectric medium, with permittivity and permeability ε 3 , µ 3 (Fig. 1). These magnitudes are ε 3 = µ 3 = 1. The point source, which radiates pulse-modulated microwaves, is placed in the point with coordinates y = 0, x = 0, z = 9 (cm). Anisotropic layer of the myocardium muscle is located between the surfaces S 3 − S 1 , S 3 − S 2 and S 2 − S 1 (Fig. 1). We assume that the volumes limited by surfaces S 1 and S 2 , are filled with the isotropic substance, which according to the electrophysical properties corresponds to the blood, which is located in two atriums and ventricles with the complex permittivity ε 2 . The heart model has an intricate shape and it limited by a non-coordinate shape surfaces. The surfaces of the 3D heart model were created in the 3D Studio MAX. This tool exports the surfaces as a set of triangles with a normal vector on certain surface points. The solution of electrodynamical problem let us to analyze the distribution of the microwave electric field inside of the anisotropic heart model. 3. EXPRESSION OF THE MICROWAVE ELECTRIC FIELD IN THE ISOTROPIC MEDIA The components of electromagnetic field are determined from the solution of differential equation ( ∇ 2 + k 2 ) G(r, r 0 )= −δ/ |r − r 0 |. The Fourier transformation makes it possible to express the