A parametric model was developed to describe the variation of dielectric properties of tissues as a function of frequency. The experimental spectrum from 10 Hz to 100 GHz was modelled with four dispersion regions. The development of the model was based on recently acquired data, complemented by data surveyed from the literature. The purpose is to enable the prediction of dielectric data that are in line with those contained in the vast body of literature on the subject. The analysis was carried out on a Microsoft Excel spreadsheet. Parameters are given for 17 tissue types.

https://iopscience.iop.org/article/10.1088/0031-9155/41/11/003/pdf

The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues

A weakness of the finite-difference-time-domain (FDTD) method is that dispersion of the dielectric properties of the scattering/absorbing body is often ignored and frequency-independent properties are generally taken. While this is not a disadvantage for CW or narrowband irradiation, the results thus obtained may be highly erroneous for short pulses where ultrawide bandwidths are involved. In some recent publications, procedures based on a convolution integral describing D(t) in terms of E(t) are given for media for which the complex permittivity in *( omega ) may be described by a single-order Debye relaxation equation or a modified version thereof. Procedures are, however, needed for general dispersive media for which in *( omega ) and mu *( omega ) may be expressible in terms of rational functions, or for human tissues for which multiterm Debye relaxation equations must generally be used. The authors describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) in terms of E(t) by means of a differential equation involving E, and their time derivatives. The method is illustrated for several examples. >

A frequency-dependent finite-difference time-domain formulation for general dispersive media

For the study of electromagnetic dosimetry and hyperthermia, it is necessary to simulate human biological materials. This can be done by chemical mixtures that are described in this paper. Formulas are presented for simulating bone, lung, brain, and muscle tissue in the frequency range of 100 MHz to 1 GHz. By using these preparations a realistic equivalent to the human body can be constructed.

Simulated biological materials for electromagnetic radiation absorption studies.

A three-dimensional (3D) time-domain numerical scheme for simulation of ground penetrating radar (GPR) on dispersive and inhomogeneous soils with conductive loss is described. The finite-difference time-domain (FDTD) method is used to discretize the partial differential equations for time stepping of the electromagnetic fields. The soil dispersion is modeled by multiterm Lorentz and/or Debye models and incorporated into the FDTD scheme by using the piecewise-linear recursive convolution (PLRC) technique. The dispersive soil parameters are obtained by fitting the model to reported experimental data. The perfectly matched layer (PML) is extended to match dispersive media and used as an absorbing boundary condition to simulate an open space. Examples are given to verify the numerical solution and demonstrate its applications. The 3D PML-PLRC-FDTD formulation facilitates the parallelization of the code. A version of the code is written for a 32-processor system, and an almost linear speedup is observed.

/pdf/finite-difference-time-domain-simulation-of-ground-3mktyd7a25.pdf

Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils

Finite difference time-domain (FDTD) methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium. The temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first-order differential equations. From this, the final equations are temporally advanced using the classical leapfrog method. One-dimensional scattering from a dielectric slab is chosen for a test case. Provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space, as shown in the error analysis, the agreement between the computed and exact solutions will be excellent. The attached data, which are associated with the four pole Lorentz dielectric and the five pole Debye medium, verify this assertion. >

Propagation in linear dispersive media: finite difference time-domain methodologies

A computer program was developed to fit multiple-term Debye-type expressions to published data of permittivity for muscle. The number of terms in this expression was varied and tested for significance. Based on these results, closed form expressions for dielectric permittivity and conductivity are suggested for use as estimators over the 10 Hz-100 GHz range.

William D. Hurt

Papers

Multiterm Debye Dispersion Relations for Permittivity of Muscle