Finite-Difference Time-Domain Methods for Electromagnetic Problems Involving Biological Bodies

Abstract

As more applications of wireless devices in the personal space are emerging, the analysis of interactions between electromagnetic energy and the human body will become increasingly important. Due to the risk of adverse health effects caused by the use of wireless devices adjacent to or implanted into the human body, it is important to minimize their electromagnetic interaction with biological objects.

Efficient numerical methods may play an integral role in the design and analysis of wireless telemetry in implanted biomedical devices, as well as computation and minimization of the specific absorption rate (SAR) associated with wireless devices as an alternative to repetitive design prototyping and measurements. Research presented in this dissertation addresses the need to develop efficient numerical methods for the solution of such bio-electromagnetic problems. Bio-electromagnetic problems involving inhomogeneous dispersive media are traditionally solved using the Finite-Difference Time-Domain (FDTD) method. In this class of problems, the spatial discretization is often dominated by very fine geometric details rather than the smallest wavelength of interest. For an explicit FDTD scheme, these fine details dictate a small time-step due to the Courant-Friedrichs-Lewy (CFL) stability bound, which in turn leads to a large number of computational steps.

In this dissertation, numerical methods are considered that overcome the CFL stability bound for particular bio-electromagnetic problems. One such method is to incorporate a thin wire sub-cell model into the explicit FDTD method for the computation of inductive coupling. The sub-cell model allows the use of larger FDTD cells, hence relaxing the CFL stability bound. A novel stability bound for the method is derived. Furthermore, an extension to the Thin-Strut FDTD method is proposed for the modeling of thin wire elements in lossy dielectric materials. Numerical results obtained by the Thin-Strut FTDT method were compared with measurements.

Furthermore, the Partial Inductance Method (PIM) was implemented using arbitrarily oriented cylindrical wire elements to obtain an analytical approximation of inductive coupling and to verify the Thin-Strut FDTD method. The PIM method was also shown to be a very efficient tool for the approximation of free-space or low frequency inductive coupling problems for biomedical applications.

The Alternating-Direction-Implicit (ADI) FDTD method is another method considered in this dissertation. Due to its unconditional stability, the ADI FDTD method alleviates the CFL stability bound. The objective is to apply the ADI method to the simulation of bio-electromagnetic problems and the computation of the SAR. For large time-steps, the ADI method has larger dispersion and phase errors than the explicit FDTD method, but it is still useful for the computation of SAR where those errors are tolerable.

An improved anisotropic-material Perfectly-Matched-Layer (PML) Absorbing-Boundary-Condition(ABC) is presented for the ADI FDTD method. The material independent D-H-field formulation of the PML ABC leads to an efficient and simple implementation and allows the truncation of dispersive material models. Furthermore, this formulation is easily extended to n[superscript th]-order dispersive materials. Numerical results for reflection errors associated with the PML and their dependence on parameters like PML conductivity and time-step size are investigated.

Furthermore, uniform and expanding grid implementations of the ADI FDTD method are used to compute the Specific Absorption Rate (SAR) distribution inside spherical objects representative of bio-electromagnetic problem. Different grid implementation sizes are considered, and errors associated with the ADI FDTD method are investigated by comparing numerical results to those obtained using the explicit FDTD method.