Effect of Eccentricity on Electric Field Profiles in Ellipsoids Rafael R. Canales 1 , Luis F. Fonseca, Fredy R. Zypman University of Puerto Rico 1 R_Canales@cuhac.upr.clu.edu Abstract We study the effect of shape on the electric field profiles in ellipsoids, by means of the T- Matrix method. We considered two non- concentric ellipsoidal objects; one completely embedded inside the other. By varying the semi-axes of the smaller ellipsoid, we mimic various tumor eccentricities (maintaining a constant volume) in the brain. The results are of interest as a diagnostics tools for clinical techniques such as magnetic resonant imaging (MRI), since it is well known that the morphology of the tumor determines its degree of malignance [1]. 1. Introduction Since its inception by P.C. Waterman as a technique to calculate electromagnetic scattered fields, T-Matrix [2,3], also called “Extended Boundary Condition” method, has been applied in different kinds of electromagnetic problems [4]. Later on, Peterson and Ström contributed to the method by providing the capability to handle multilayers and an arbitrary number of scatterers [5,6]. The algorithm that we used in this paper, to calculate the electromagnetic fields, is based on those results. T-Matrix expresses the incident, scattered, and internal fields as corresponding multipolar vector expansions. Each order of expansion is given in terms of spherical Bessel, and Hankel functions. The expansion coefficients and the boundary conditions are used to construct the matrices that relate known field with unknowns ones. The elements of those matrices are surface integrals on the various boundaries, of expressions containing the multipolar functions. The convergence of this method is strongly dependent on the system geometry, frequency, and electromagnetic properties of the scatterers [7]. As the values of the parameters vary, T-Matrix may include higher multipolar orders. For example, we find that as the frequency increases, so does the number of multipoles necessary to maintain a constant accuracy. On the other hand, the dimensions of the matrices increase as a quadratic function of the order [7,8]. Thus, it would seem as if one needed a supercomputer to pursue our project. However, it turned out that we obtained results of excellent accuracy on a Pentium I, 90 MHz, 64 Mbytes RAM in 10 hours for a multipolar order of 10. The time was significantly reduced to 1 hour when a Z {Axis of revolution} (cm) Figure I -7.5 -5.0 -2.5 0.0 2.5 5.0 X (cm) -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 Boundary of First Layer Boundary of Second Layer