Quantification of interaction between ELF-LF electric fields and human bodies

Relationship of electric power quality to milk production of dairy herds - field study with literature review

Public Utility Commissions (PUC) in several states adopted 0.5 volt rms (root mean squared) or 1.0 milliampere as the actionable limit for utilities to respond to complaints of uncontrolled voltage. This study clearly shows that the actionable level should be reduced to 10 mV p-p (peak-to-peak), which is 140 times less than the current standard. Dairy farmer complaints that animal behavior and milk production were affected by electrical shocks below adopted standards were investigated on 12 farms in Wisconsin, Michigan, and Minnesota. Milk production per cow was determined from daily tank-weight pickup and number of cows milked. Number of transient events, transients, voltage p-p, waveform phase angle degree, sags, and sag-Vrms were measured from event recorders plugged into milk house wall outlets. Data from 1705 cows and 939 data points were analyzed by multiherd least-squares multiple regression and SAS-ANOVA statistical programs. In five herds for 517 days, milk/cow/day decreased -0.0281 kg/transient event as transient events increased from 0 to 122/day (P<0.02). Negative effects on milk/cow/day from event recorder measurements were significant for eight independent electrical variables. Step-potential voltage and frequency of earth currents were measured by oscilloscope from metal plates grouted into the floor of milking stalls. Milk decreased as number of 3rd, 5th, 7th, 21st, 28th, and 42nd harmonics and the sum of triplen harmonics (3rd, 9th, 15th, 21st, 27th, 33rd, and 39th) increased/day (P<0.003). Event recorder transient events were positively correlated with oscilloscope average V p-p event readings. Steps/min counted from videotapes of a dancing cow with no contact to metal in the barnyard were correlated with non-sinusoidal 8.1 to 14.6 mV p-p impulses recorded by oscilloscope for 5 min from EKG patches on legs. PUC standards and use of 500-Ohm resistors in test circuits underestimate effects of non-sinusoidal, higher frequency voltage/current common on rural power lines.

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.

A three-dimensional method for calculating currents induced in bodies by extremely low-frequency electric fields

A user-friendly, numerical program has been developed to permit the calculation of induced currents in modeled bodies of human and infrahuman subjects. The program is based on a charge-simulation method (CSM), and it takes into account the three-dimensional (3-D) character of the extremely-low-frequency (ELF) electric field and of the models to be exposed. The principle of the method is to simulate a 3-D object, for example, an animal model, by a combination of several parts (blocks) having simple geometric forms such as a sphere, a cylinder, or a cone. This approach permits easy preparation of input data on the dimensions of the blocks and their positions in a 3-D arrangement. Other input data, such as the coordinates of the contour points and the imaginary values of charges inside objects, which are necessary in the calculations by CSM, are produced automatically by selecting an appropriate "level" for each block, according to its importance. To simulate parts having irregular shapes, special blocks may be added. In one series of experiments, induced currents were calculated for a baboon model in various postures: standing upright, positioned on four legs, and sitting on the floor. Calculated currents, the total induced current in particular, agreed very well with experimental values. Local currents in parts of the baboon models were more variable, ranging from 5% to 17% of measured values in the case of induced currents in the head. Some problems with this method, such as the effect of the dimensions of blocks or the choice of block levels, are discussed.

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.

A numerical method for the computation of induced currents inside 3-D heterogeneous biological bodies by ELF--LF electric fields

A numerical technique, based on the combination of surface-charge integral equations (SCIE) and an impedance network method, has been developed to compute internal electric fields and currents inside 3-D heterogeneous biological bodies with arbitrary grounding impedances induced by ELF-LF electric fields. The method has been applied to a biological concentric-sphere and the numerical results agree well with an existing analytical solution. Numerical results of the induced current inside a simplified heterogeneous model of the human head computed by this method are also presented.

Current densities induced in swine and rat models by power-frequency electric fields

Measurements have been made of vector current densities induced by vertical, uniform, 60-Hz electric fields in the torsos of homogeneous models of swine and rats. The observed data were a strong function of the five grounding configurations invested: all four feet grounded, only front feet grounded, only rear feet grounded, left front and right rear feet grounded, and right front and left rear feet grounded. In the first configuration and with an exposure field strength of 10 kV/m, average total current densities induced in the torsos of pigs and rats were 34 nA/cm2 and 20 nA/cm2, respectively. The corresponding value for human exposure is about 250 nA/cm2, 7.3 and 12.5 times larger than for swine and rats, respectively. Current densities measured at 60 Hz can be linearly extrapolated to frequencies in a range extending from at least 1 Hz to 1 MHz. Human and animal current-density data can provide an improved rationale for extrapolating biological data across species. In addition, these data can be used to validate the predictions of numerical models.

Finite difference calculations of current densities in a homogeneous model of a man exposed to extremely low frequency electric fields

This paper presents three-dimensional finite difference calculations of induced current densities in a grounded, homogeneous, realistically human-shaped phantom. Comparison is made with published experimental values of current density at 60 Hz, measured in conducting saline manikins with their arms down by the side. The congruence between calculation and experiment gives confidence in the applicability of the numerical method and phantom shape to other configurations. The effect of raising both arms above the head is to reduce the current densities in the head and neck by approximately 50% and to increase those from the thorax downwards by 20-30%. A sensitivity analysis was performed on the shape and dimensions of the phantom, from a 45-kg, 1.5-m-tall person to a 140-kg, 1.9-m-tall person. When the phantom is grounded through both feet the current densities range from 50 to 90 microAm-2 in the head (all values for a 60-Hz, 1-kVm-1, vertical applied field), 70 to 140 microAm-2 in the thorax, 150 to 440 microAm-2 at the crotch, and 500 to 2,230 microAm-2 in the ankle. When grounded through only one foot the current densities at the crotch range from 400 to 1,000 microAm-2 and from 1,000 to 4,400 microAm-2 in the ankle of the grounded leg. Scale transformations of the short-circuit current with phantom height, weight, and surface area are confirmed.