Using the ADI-FDTD method to compute currents induced in the human body by HEMI devices at low frequencies

Abstract

The traditional explicit Finite-Difference Time-Domain (FDTD) is a condition- ally stable method where the time step must adhere to the Courant-Friedrichs-Lewy (CFL) limit. In problems such as those encountered in the bioelectromagnetics and VLSI circuits, the spatial resolution is dictated by the geometric detail rather than the resolution of the smallest wavelength. Thus, severe limitations are often imposed on the time step, leading to long time-domain simulations. This is particularly true for the low-frequency problems, which would require prohibitively large number of time steps with the explicit method. The Alternating-Direction Implicit Finite Difference Time Domain (ADI-FDTD) is a theoretically unconditionally stable method, which allows the use of an arbitrarily large time step for the simulations. Research presented in this thesis aims to compute the induced electric field and current densities in the human body due to the contact electrodes of a Human Electro-Muscular Incapacitation (HEMI) device at frequencies below 200 KHz using the ADI-FDTD method in a D-H formulation. In order to reduce the memory and simulation time requirements, logarithmic expanding grid technique has been used for modeling the human body. Computational model resolution of 1 mm has been used for most of the human body model, including regions proximal to the current contact points, while a progressively coarser resolution up to 5 mm is utilized according to an expanding grid scheme for body regions distant from the source, such as the lower extremities. Discrete Fourier Transform (DFT) of the electric field has been computed at the dominant frequencies present in the source signal to find out the electric field distribution in the model due to the application of the HEMI pulse. Using quasi-static assumptions, computation of the DFT values have been done for time durations much shorter than the time periods of the different frequencies. The field values induced in the human body were then obtained as the ratios of the DFT magnitudes with respect to the source, which can be scaled depending on the magnitude of the electric field at source. This study suggests that the ADI-FDTD method can be effectively used for the solution of low frequency bioelectromagnetic problems. When paired with quasi-static assumptions and Fourier series decomposition for the considered problem, this can lead to simulations that are four orders of magnitude faster than the computational time required with the use of a traditional FDTD method.