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.

The low-frequency dielectric properties of octopus arm muscle measured in vivo.

The conductance and capacitance of octopus arm are measured in vivo over the frequency range 5 Hz to 1 MHz. Measurement of these parameters for a number of electrode separations permits the determination of the variations in tissue conductivity and dielectric constant with frequency. In the range 1-100 kHz the conductivity is independent of the frequency f and the dielectric constant varies as f-1. These results, in conjunction with those reported previously for frog skeletal muscle, are consistent with the fractal model for the dielectric properties of animal tissue proposed by Dissado. Transformation of the results to complex impedance spectra indicates the presence of a dispersion above 100 kHz.

Cell culture dosimetry for low-frequency magnetic fields.

Calculations of the current density and electric field distributions induced in cell cultures by an applied low-frequency magnetic field have assumed that the medium is uniform. This paper calculates these distributions for a more realistic, inhomogeneous, anisotropic model in which the cells are regarded as conducting squares surrounded by insulating membranes. Separate parameters are used to specify the resistivities of the cell interior, the cell membrane parallel to its surface, the cell membrane perpendicular to its surface, and the intercellular junction parallel to the membrane. The presence of gap junctions connecting the interiors of adjacent cells is also considered. For vertical applied magnetic fields, the induced currents and field distributions may deviate considerably from the homogeneous medium model if there is sufficiently tight binding of the cells to each other. The presence of gap junctions can produce relatively large transmembrane electric fields or intracellular current densities. These considerations are generally less important for horizontal applied fields. A simple microscopic model of the cell surface is also discussed.

Spreadsheet method for calculating the induced currents in bone-fracture healing by a low-frequency magnetic field.

A commercially available spreadsheet program is used on a microcomputer to calculate the induced current density and electric field patterns produced in a nonhomogeneous, anisotropic model of tissue by a localized, low-frequency magnetic field source. Specific application is made to coils used to promote the healing of bone fractures in limbs. The variation of the conductivity of the fracture gap during healing causes the induced current density pattern to change correspondingly, whereas the induced electric field remains relatively unchanged. Use of more simplified, isotropic models for the bone and for the soft tissue leads to results that differ significantly from those obtained from the full model. The magnetic field beyond the region of the coils contributes little to the induced currents in the fracture gap if the gap is located near the center of the coils.

In vivo measurement of the low-frequency dielectric spectra of frog skeletal muscle.

Capacitance, conductance and dielectric loss spectra are obtained, in vivo, for a number of electrode separations in the gastrocnemius muscle of a frog. At each frequency the reciprocals of these parameters are plotted versus electrode separation. From the slopes of the resulting lines the complex permittivity and the conductivity of the muscle can be determined, with electrode effects eliminated. The sequence of power-law responses which is found is consistent with the fractal model proposed by Dissado. The electrical properties measured in vivo with needle electrodes are similar to those measured with surface electrodes for frequencies between 1 kHz and 1 MHz.

Use of a spreadsheet program to calculate the electric field/current density distributions induced in irregularly shaped, inhomogeneous biological structures by low-frequency magnetic fields.

A commercially available spreadsheet program is used on a microcomputer to calculate the electric field/current density distributions induced in irregularly shaped, inhomogeneous objects by low-frequency magnetic fields. A finite-difference method is applied to an impedance grid that represents the object being modeled. This approach is validated by comparison with 1) the analytical results of an eccentric cylinder model and 2) measurements made on a square dish containing a saline solution and square, insulating inclusions. Application of the method is also made to a culture dish with a layer of sediment exposed to a horizontal magnetic field.

Electric fields induced in rat and human models by 60-Hz magnetic fields: comparison of calculated and measured values.

The calculated distribution of electric fields induced in homogeneous human and rat models by a 60-Hz magnetic field is compared with values measured in instrumented mannequins. The calculated values agree well with measured values.

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.

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

The current-density distribution produced inside irregularly shaped, homogeneous human and rat models by low-frequency electric fields is obtained by a two-stage finite-difference procedure. In the first stage the model is assumed to be equipotential. Laplace's equation is solved by iteration in the external region to obtain the capacitive-current densities at the model's surface elements. These values then provide the boundary conditions for the second-stage relaxation solution, which yields the internal current-density distribution. Calculations were performed with the Excel spread-sheet program on a Macintosh-II microcomputer. A spread sheet is a two-dimensional array of cells. Each cell of the sheet can represent a square element of space. Equations relating the values of the cells can represent the relationships between the potentials in the corresponding spatial elements. Extension to three dimensions is readily made. Good agreement was obtained with current densities measured on human models with both, one, or no legs grounded and on rat models in four different grounding configurations. The results also compared well with predictions of more sophisticated numerical analyses. Spread sheets can provide an inexpensive and relatively simple means to perform good, approximate dosimetric calculations on irregularly shaped objects.

The extremely low frequency electrical properties of plant stems.

The electrical properties (variation of capacitance and conductance with frequency) of a plant stem can be conveniently measured in vivo by time domain dielectric spectroscopy. In this technique a voltage step is applied to a stem. The resulting polarization current is sampled by a microprocessor and Fourier-transformed to yield these properties. Spectra were obtained for seven electrode separations along a Poinsettia stem. The inverse capacitance and conductance were plotted vs separation for 50 frequencies from .35 to 350 Hz. Least-square fits yielded the effective dielectric constant and conductivity of the stem over this frequency range. In this way electrode effects were eliminated. A similar procedure was carried out for Coleus. A log-log plot of dielectric constant vs frequency shows a two-stage linear decrease for both plants. The conductivity is primarily DC. The dielectric loss decreases smoothly with frequency for Coleus. These results are compared to those for bone and the inorganic material hollandite. The dielectric properties seem best described by a cooperative, many-body approach.

Sensitivity to change in electrical environment: a new bioelectric effect.

The action of a 60-Hz, 5 kV/m electric field on erythrocyte parameters in mice was determined. No effects attributable to the magnitude of the field were found, but a transition either from or to an environment containing the field caused decreased red blood cell concentrations and decreased hematocrits. The failure of others to observe effects on erythrocyte parameters following exposure to low-frequency electric fields may have been due to an inappropriate choice of duration of exposure.

Space osteoporosis: an electromagnetic hypothesis.

Loss of body calcium during spaceflight is a potential problem in long voyages. This loss does not appear to be caused by a deficiency in diet or exercise. The idea is advanced that the altered electromagnetic environment experienced in space may be at least partially responsible. We show that the electric field induced inside astronauts because of their motion in the geomagnetic field is greater than that which has produced a wide variety of biological effects in earth-bound experiments.

In vivo bioelectrochemical changes associated with exposure to extremely low frequency electric fields.

One hundred seventy-four 21- to 24-day-old Sprague-Dawley rats were continuously exposed to a 60 Hz electric field of 150 V/cm for one month in ten separate experiments. Biological effects observed included depressed body weights, serum corticoids, and water consumption. The findings are tentatively in terpreted as indicating that a power frequency electric field is a biological stressor. The observed effects cannot be a consequence of Joule heating and therefore indicate that electric fields can influence biological systems either at the systemic level, or at the cellular level via electrochemical alteration of the microenvironment.