FDTD Modeling of Biological Tissues Cole–Cole Dispersion for 0.5–30 GHz Using Relaxation Time Distribution Samples—Novel and Improved Implementations

In this paper, novel finite-difference time-domain implementations of the Cole-Cole dispersion model for biological tissues, from 0.5 to 30 GHz, based on the sampling of the distribution of relaxation time, and the convolution integral formulation, are provided and verified. Moreover, shortcomings of the original relaxation time sampling implementation, with polarization formulation, were identified, and the improved polarization implementation is provided as well. These implementations are compared with the implementation utilizing the fractional derivative formulation. All compared implementations require storing the electric field and some related auxiliary quantities for only the previous time step. It is observed that, for a single-term Cole-Cole relation, relaxation time sampling implementations can provide accuracy, storage requirement, and simulation time comparable to the ones for the fractional derivative implementation. However, the latter does not exist for the more general multiterm Cole-Cole dispersion relation, for which the implementations based on the relaxation time sampling could be easily extended to.

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