FULL WAVE MODELING OF BRAIN WAVES AS ELECTROMAGNETIC WAVES (Invited Paper)

Abstract

Abstract-This paper describes a novel technique which has the potential to make a significant impact on the mapping of the human brain. This technique has been designed for 3D full-wave electromagnetic simulation of waves at very low frequencies and has been applied to the problem of modeling of brain waves which can be modeled as electromagnetic waves lying in the frequency range of 0.1-100 Hz. The use of this technique to model the brain waves inside the head enables one to solve the problem on a regular PC within 24 hrs, and requires just 1 GB of memory, as opposed to a few years of run time and nearly 200 Terabyte (200,000 GB) needed by the conventional FDTD (Finite Difference Time Domain) methods. The proposed technique is based on scaling the material parameters inside the head and solving the problem at a higher frequency (few tens of MHz) and then obtaining the actual fields at the frequency of interest (0.1-100 Hz) by using the fields computed at the higher frequency. The technique has been validated analytically by using the Mie Series solution for a homogeneous sphere, as well as numerically for a sphere, a finite lossy dielectric slab and the human head using the conventional Finite Difference Time Domain (FDTD) Method. The presented technique is universal and can be used to obtain full-wave solution to low-frequency problems in electromagnetics by using any numerical technique.

Electromagnetic Modeling of Rat’s Head: Comparison of Formulations and Models

“…In order to develop the full-wave time-domain model, the frequency scaling method [11] was applied since the lowfrequency breakdown can occur, and the solution of Maxwell equations can diverge.…”

“…The frequency scaling method [11] is based on scaling the relative permittivity ε rsc of the brain tissue  r rsc r sc…”

“…After the simulation, the resulting quantities have to be recalculated according to the following equation [11]:…”

“…Error of the full-wave time-domain solver is caused by the frequency scaling [11] from 10 Hz to 10 MHz. At this frequency, the wavelength is much smaller and the interaction with the model is stronger.…”

“…Furthermore, a recent paper [11] on the time-domain full-wave formulation of brain waves showed significantly different results compared to quasi-static approximations of a sphere and a slab.…”