A frequency-dependent finite-difference time-domain formulation for induced current calculations in human beings

The finite-difference time-domain (FDTD) method has been used to calculate SARs and induced currents involving whole-body or partial-body exposures of models to spatially uniform or nonuniform (far-field or near-field), to sinusoidally varying EM fields, or to transient fields such as those associated with electromagnetic pulses. However, a weakness of the FDTD algorithm is that the dispersion of the tissue's dielectric properties is ignored and frequency-independent properties are assumed. Although this is permissible for continuous-wave or narrow-band irradiation, the results may be highly erroneous for short pulses, in which ultra-wide bandwidths are involved. In some recent publications, procedures are described for one- and two-dimensional problems for media in which the complex permittivity epsilon * (omega) may be described by a single-order Debye relaxation equation or a modified version thereof. These procedures based on a convolution integral describing D(t) in terms of E(t) cannot be extended to human tissues for which multiterm Debye relaxation equations must generally be used. We describe here a new differential-equation approach that can be used for general dispersive media. We illustrate the use of this approach by one- and three-dimensional examples of media for which epsilon * (omega) is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body. Based on a single run involving a Gaussian pulse, the frequency-dependent FDTD [(FD)2TD] method allows calculations of SARs and induced currents at various frequencies by taking the Fourier components of the induced E fields. The (FD)2TD method can also be used to calculate coupling of the short (ultra-wideband) pulses to the human body.