Abstract
An auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of the polarization current when the time discretization is short enough. The polarization current density is approached using Lagrange extrapolation polynomial and the fractional derivation is obtained according to Riemann definition of a fractional α-order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found to be in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.
Highlights
In the last two decades there has been a growing interest in the interaction between biological tissues and electromagnetic field at microwave frequencies
A first model of the time response in a time varying electric field of biological tissues was formulated by Debye [6] through a time decaying polarization current jðtÞ
In the case of the biological tissue there is a multiple contribution of each relaxation process resulting in a broadening of the relaxation zone
Summary
In the last two decades there has been a growing interest in the interaction between biological tissues and electromagnetic field at microwave frequencies. This model even if it fits the experimental results in liquids it loses its accuracy when applied over a large band of frequency or in the presence of more than one type of polar molecule. This non-Debye relaxation is attributed to the existence of different relaxation processes [7] each with its own relaxation time τ and its amplitude Δε. The auxiliary differential equation is used to establish the update equation of the polarization currents which are included later in the general structure of the SCN-TLM node
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