Computation of recruitment volumes in the human body due to external electric or magnetic stimulation using ADI-FDTD method

Abstract

The Alternating-Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) method is a computational electromagnetic method which, unlike the traditional explicit FDTD method, is unconditionally stable and allows arbitrarily large time steps. The decrease in the simulation time is achieved at the cost of accuracy. However, in computational problems where the results are averaging based, the effects of such local errors are largely minimized. For example, using ADI-FDTD in bioelectromagnetics, quantities like Specific Absorption Rates (SAR) and total induced currents can be computed over models with fine geometrical resolutions without decreasing the time step proportionally.

In this work, the volume of neurons excited (recruitment volume) inside a human body due to external electric or magnetic stimulation is computed using the D-H formulation of ADI-FDTD method. The electric stimulation considered is through current injection by contact electrodes of a Human Electro-Muscular Incapacitative (HEMI) device. For magnetic stimulation, two high frequency current pulses flowing in opposite directions in circular coils are considered. A neuron can be excited if the electric field or the gradient of the electric field along its length exceeds the nerve threshold value. These modes of excitation are termed as `end mode' and `center mode' respectively. The nerve excitation threshold values are decided based on experimental investigations on laboratory animals found in the literature.

Memory and simulation time requirements are reduced by employing expanding grid techniques and DFT averaging. The uniform grid of a 1 mm resolution model is logarithmically expanded to 5 mm in region far from source such as head, lower legs and arms. This reduces the computational size of the model by 90\%. For HEMI current source stimulations, Discrete Fourier Transform (DFT) is used to find the induced electric fields due to the dominant frequencies in the current source. By using quasi-static assumptions, the DFT is evaluated for duration substantially lesser than the time period of the different frequencies. The field values are then obtained as the ratios to the fields at the source and then scaled depending upon the magnitude of the source.

This study builds upon the efficient use of use of ADI-FDTD method for the solution of the low frequency bioelectromagnetics problems by employing expanding grid techniques and DFT averaging. Recruitment volumes due to a HEMI current source device are computed. A novel stimulation technique of magnetic stimulation is investigated.