On the FDTD Formulations for Biological Tissues With Cole–Cole Dispersion

The rationale behind several previously reported FDTD formulations for directly implementing fractional-ordered Cole-Cole models is investigated from another perspective. The explicit expressions of their numerical permittivities are derived, respectively, which makes a quantitative comparison of their modeling ability on a Cole-Cole medium possible and verifies the direct validation of these formulations clearly. Their practical performance, by evaluating implicit effective permittivities after being incorporated into a second-order or fourth-order accurate FDTD algorithm, is also illustrated for the one-dimension FDTD problem of modeling an exemplified human biological medium in order to find the potentially best one among them.