An ADE-TLM Modeling of Biological Tissues with Cole-Cole Dispersion Model

In this paper, 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 alpha-order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.