Biological cell modelling using quasi static FDTD/lumped element method

Several numerical models have been set up in order to understand the modalities of interaction of electromagnetic (EM) fields with biological systems. This paper demonstrates the application of a quasi-static approximate version of the finite-difference time-domain method (FDTD) to modelling a biological cell, represented as a sphere inside the computation domain. The modified Berenger´s perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computation grid, in order to reduce the reflections from the interlace layers. The quasi-static approach is verified at microwave frequencies. The results (induced field distribution) obtained from the simulation are in good agreement with previously published data. In addition, a lumped element finite difference time-domain (LE-FDTD) scheme has been used to model the cell´s membrane, represented by the Hodgkin-Huxley (HH) model on the surface of the biological cell. The implementation of the HH model in FDTD is briefly discussed and validated with results from analytical treatments.