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Exact analytical 2D model of the human head surrounded by a dielectric pad

Sufficiently large values of the magnetic field B1 are necessary to obtain high-quality MRI images and one approach to increase the B1 field is to use high permittivity dielectric pads [1-3]. In order to understand how the presence of a dielectric pad affects the distribution of the electromagnetic field, we consider a 2D model of the human head, so that an exact analytical solution can be obtained. Since one challenge is to obtain large values of the magnetic field close to the center of the human head, we focus our attention on the evaluation of the magnetic field along the axis of symmetry of the 2D model. Our analytical model is based on the assumption that the human head is modeled as a lossy dielectric cylinder, with circular cross section, which is surrounded by a high-permittivity dielectric coating with uniform thickness. The incident electromagnetic field is due to an electric line source, oriented parallel to the axis of symmetry of the cylinder, thus resulting in a 2D problem because of the symmetry in any plane perpendicular to the axis of the structure. There are three different regions in this problem and, within each one of them, the electromagnetic field is expanded as a series of products of an expansion coefficient, Bessel and trigonometric functions. This is a boundary value problem that can be solved exactly, thus leading to an analytical closed form expression of the electromagnetic field in each region. Due to a property of the Bessel functions, it turns out that the series representing the electromagnetic field along the axis reduces to just one term, thus leading to a very simple formula to compute the magnetic field. Then, we consider the superposition of many line sources. Under the condition that they have the same intensity, they are placed at the same radial distance and equally spaced, one obtains that the magnetic field along the axis of the structure is circularly polarized and proportional to the number of lines. Finally, we present numerical result to show how the strength of the magnetic field along the axis of the structure is affected by the thickness of the dielectric padding and its relative permittivity.