Locally Implicit Discontinuous Galerkin Time Domain Method for Electromagnetic Wave Propagation in Dispersive Media Applied to Numerical Dosimetry in Biological Tissues

• Published in: SIAM journal on scientific computing 2016-01, Vol.38 (5), p.A2611-A2633
• Main Authors: Descombes, Stéphane, Lanteri, Stéphane, Moya, Ludovic
• Format: Article
• Language: English
• Subjects: Analysis of PDEs; Computer Science; Mathematics; Numerical Analysis
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/15M1010282

We are concerned here with the numerical simulation of electromagnetic wave propagation in biological media. Because of their water content, these media are dispersive i.e. their electromagnetic material characteristics depend of the frequency. In the time-domain, this translates in a time dependency of these parameters that can be taken into account through and additional (auxiliary) differential equation for, e.g, the electric polarization, which is coupled to the system of Maxwell's equations. From the application point of view, the problems at hand most often involve irregularly shaped structures corresponding to biological tissues. Modeling realistically the interfaces between tissues is particularly important if one is interested in evaluating accurately the impact of field discontinuities at these interfaces. In this paper, we propose and study a locally implicit discon-tinuous Galerkin time-domain method formulated on an unstructured tetrahedral mesh for solving the resulting system of differential equations in the case of Debye-type media. Three-dimensional numerical simulations are presented concerning the exposure of head tissues to a localized source radiation. 1. Introduction. This article is concerned with the numerical simulation of electromagnetic wave propagation in dispersive media. These are materials in which either or both of the electromagnetic material parameters ε and µ are functions of frequency. Note that the conductivity σ may also be a function of frequency, but its effect can be rolled into the complex permittivity. In reality, all materials have frequency-dependent ε and µ, but many materials can be approximated as frequency-independent over a frequency band of interest, simplifying their analysis and simulation. Here, we will focus on the much more common case of frequency-dependent permittivity. A lot of practical electromagnetic wave propagation problems involve such propagation media, such as those involving the interaction of an electromagnetic wave with biological tissues. The numerical modeling of the propagation of electromagnetic waves through human tissues is at the heart of many biomedical applications such as the microwave imaging of cancer tumors or the treatment of the latter by hy-perthermia. For example, microwave imaging for breast cancer detection is expected to be safe for the patient and has the potential to detect very small cancerous tumors in the breast [3, 14, 24]. Beside, the definition of microwave-ba