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

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Abstract
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.