Fractional calculus-based modeling of electromagnetic field propagation in arbitrary biological tissue

Pietro Bia, Luciano Mescia, Diego Caratelli

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)
63 Downloads (Pure)


The interaction of electromagnetic fields and biological tissues has become a topic of increasing interest for new research activities in bioelectrics, a new interdisciplinary field combining knowledge of electromagnetic theory, modeling, and simulations, physics, material science, cell biology, and medicine. In particular, the feasibility of pulsed electromagnetic fields in RF and mm-wave frequency range has been investigated with the objective to discover new noninvasive techniques in healthcare. The aim of this contribution is to illustrate a novel Finite-Difference Time-Domain (FDTD) scheme for simulating electromagnetic pulse propagation in arbitrary dispersive biological media. The proposed method is based on the fractional calculus theory and a general series expansion of the permittivity function. The spatial dispersion effects are taken into account, too. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The comparison between simulation results and those evaluated by using an analytical method based on the Fourier transformation demonstrates the accuracy and effectiveness of the developed FDTD model. Five numerical examples showing the plane wave propagation in a variety of dispersive media are examined.

Original languageEnglish
Article number5676903
Number of pages12
JournalMathematical Problems in Engineering
Publication statusPublished - 1 Jan 2016


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