Use of a spread sheet to calculate the current-density distribution produced in human and rat models by low-frequency electric fields

Modelling the anisotropic electrical properties of skeletal muscle

We present a numerical model used to analyse the anisotropic electrical properties of frog muscle, measured in vivo. The model represents the anisotropic, irregularly shaped muscle as a set of cubic elements. We develop a finite difference method to calculate the electrical resistance between two electrodes inserted longitudinally or transversely into the muscle in terms of longitudinal and transverse muscle conductivities. Comparison of the measured impedance values with the calculated resistances yields the separate variation with frequency of the two conductivity components. We also compare the results of the numerical, finite difference method with those of two simple, analytical models.

Determination of the induced ELF electric field distribution in a two layer in vitro system simulating biological cells in nutrient solution

In-vitro studies of biological effects of electromagnetic fields are often conducted with cultured cells either in suspension or grown in a monolayer. In the former case, the exposed medium can be assumed to be homogeneous; however, eventually the cells settle to the bottom of the container forming a two layer system with different dielectric and conductive properties. In the present work the effect of this separation on the electric field distribution is calculated and experimentally measured at selected positions for a commonly used exposure configuration. The settled cell suspension is modeled by a well-defined two layer system placed in a rectangular container with the base of the container parallel to the direction of the magnetic field. Theoretical calculations based on numerical techniques are done for various two layer systems with different conductivities in each layer. The agreement between the theoretical calculations and the experimental measurements is within +/- 1.5 mV/m, or 10% of the maximum induced field when the conductivity of the lower layer is ten times that of the upper layer. This result is well within experimental error. When the thickness of one of the layers is small compared to the thickness of the other layer, it is found that the electric field distribution is essentially that of the homogeneous case. The latter situation corresponds to a typical cell exposure condition.

Numerical and analytical methods to determine the current density distributions produced in human and rat models by electric and magnetic fields

Some numerical and analytical methods used to estimate the internal electric fields and current densities produced within human and animal models by low-frequency electric and magnetic fields are surveyed. A major goal of such modeling is the design of laboratory experiments on cellular systems or animal models to produce a dosage comparable to that experienced by humans in a particular situation. Specific comparisons are made between the results of ellipsoidal approximations and finite-difference methods applied to irregularly-shaped, homogeneous, human and rat models for applied 60 Hz electric (10 kV/m) and magnetic (10(-4) T) fields. For scaling purposes, the induced current densities in various parts of the body are compared for rat and human models for both types of field. In addition, the current density distribution induced in rectangular culture dishes by applied magnetic fields is also described. The extension of these methods to inhomogeneous models and localized sources may not be simple.