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Spatially Averaged Values
Differing Views for Assessing Exposure Several present-day limits on maximum permissible exposures (MPEs) to RF fields are based on the spatially averaged value of the power density or the squares of electric or magnetic field strengths. The IEEE, FCC and Canadian RF exposure limits contain this approach to defining exposure. This specification is based on the concept that the exposure limits are based on limiting the whole-body averaged specific absorption rate (SAR) in the exposed subject and that a measure of the spatially averaged field, over the body dimensions, represents the best approximation to the field that would lead to the limiting whole-body averaged SAR, typically either 0.4 W/kg or 0.08 W/kg depending on whether the exposure is controlled or uncontrolled. In the case of the IEEE standard (C95.1-1999), MPE values in terms of electric and magnetic field strengths are the mean values obtained by spatially averaging the squares of the fields over an area equivalent to the vertical cross section of the human body (projected area) or, similarly, by finding the average of the plane wave equivalent power density over the body. While the issue of the most appropriate method for assessing the spatially averaged exposure has been the subject of discussion for several years, the IEEE standard does provide guidance in its Section 6.6 on Measurements where it states "For practical measures of compliance with the standard, the average of a series of ten field strength measurements performed in a vertical line with uniform spacing starting at ground level up to a height of 2 m shall be deemed sufficient.... Additional field strength data, for example, as obtained through the use of data-logging or spatial averaging equipment, obtained at smaller spacings than 20 cm, are acceptable and will provide more detail on the spatial distribution of the fields." In the most recent revision of the Canadian Safety Code 6 on Limits of Human Exposure to Radiofrequency Electromagnetic Fields, Appendix V.A.2 provides guidance on determining the spatially averaged field by using a particular rectangular grid of at least 9 measurement points that lie in a flat plane, approximating the frontal surface of the body. In a project conducted for the Cellular Telecommunications Industry Association, Richard Tell Associates, Inc. studied the difference in assessing exposure based on a simple vertical line average vs. a much more detailed frontal projected area average (see EME Design and Operation Considerations for Wireless Antenna Sites prepared by Richard A. Tell and available from the CTIA). RF exposure fields may be averaged as a straight linear spatial average or they may be averaged over the projected area of the body. The difference in using the projected body area is that nonuniformity in the fields is weighted according to the projected area and, due to the variation of projected area with height, the RF fields are, consequently, not linearly averaged. For example, the projected area of the head represents a relatively small area relative to its vertical extension compared with the torso over an equal vertical dimension. Thus, in cases where the fields may be maximum near the location of the head, and relatively weak over the rest of the body, the projected area average of the fields will result in a smaller value than would occur via simple linear averaging. Of course, for highly variable field levels with spatial maxima corresponding to the torso and lower body, the use of projected area averaging may produce higher spatial averages than simple linear averaging and, hence, the outcome of the averaging process will be dependent on the spatial characteristics of the RF fields in relation to the posture of the exposed subject. The following information contained in the Tell report to the CTIA provides a limited illustration of the use of projected area averaging in comparision with straight linear spatial averaging of RF fields. Of particular utility in this examination are those data collected by A. W. Guy in a series of experiments that addressed the issue of induced current measurements and RF hazards associated with very low frequency exposures.¹ Guy performed physical measurements of body dimensions on 186 subjects consisting of 97 females and 89 males. In each case, the body was assumed to be represented by elliptical cross-section slabs and the major and minor axes were determined at 5 cm intervals from the bottom of the foot to the top of the head. Separate measurements were made for the arms. Using these data, the projected area presented by each of the approximately 5 cm thick slabs of the body could then be calculated. From the large data set collected by Guy, information for a precisely 183 cm tall person was used to explore spatial averaging issues in the context of 6-foot tall individuals. Using Guy's data for this subject, the projected area of the body was analyzed by calculating the accumulative area as a function of height along the body axis to illustrate the nominal relationship between projected area contribution and various parts of the body. This figure below shows the results of this accumulative projected area analysis for the 183 cm tall subject. The plot indicates that the projected area increases most rapidly within the trunk region of the body normalized to 5 cm slabs; in this region, the accumulative projected area curve presents the greatest slope compared to either the region of the lower leg or the head. This simply confirms the obvious insight that relative to constant vertical increments, the lower leg and head will not present as great a projected area because of their width compared to the trunk. In this particular subject, the neck was located at 155 cm above the foot and the integrated projected area of the neck and head region amounted to 515 square centimeters. This area may be contrasted with the total projected area for this subject of 5,728 square centimeters which means that the head represents approximately 9% of the total body projected area.  The investigation of the influence of both forms of spatial averaging was pursued by correlating computed RF power densities as a function of height above ground with the individual body-slab projected areas. The power density present at each slab height was multiplied by the slab's projected area. To find the spatial average based on projected area, the sum of all these products was divided by the total body projected area. For example, if the applied power density were to have been uniform (no spatial variation), then the projected area spatial averaging would yield the same value as if the power densities had been linearly averaged. But if the applied power density were to be nonuniform over the body's height, the projected area spatial average power density would deviate from the straight linear averaging according to the product of power density and slab area along the body. The projected area for each 5 cm slab thickness for the subject represented in the figure above is also displayed in the figure below vs. height. The region of the ankle can be readily identified because of the relatively narrow aspect of the ankle compared to other body regions. Also, this figure clearly shows the lesser magnitude of the head's projected area.  A total of five comparisons of linear vs. projected area spatial averaging of power density were made that are relevant to commonly used cellular telephone base station antennas that are typically roof-mounted. First, the spatial field distributions calculated at one foot adjacent to an eight element collinear dipole antenna, for mounting heights of 0, 4 and 6 feet, were used. These particular RF field conditions were used since they represent a cross-section of the kinds of spatial distributions that can commonly be found adjacent to such antennas. The 0 foot mounting height represents a reasonably uniform field along the height of the 6 foot tall individual. But, mounting heights of 4 feet and 6 feet produce alternative field distributions with significantly higher power densities in the region of the head and could be representative of the fields found near smaller, directional but elevated antennas mounted close to head level. A second comparison was performed by making use of actual field measurements made adjacent to a smaller, directional type of wireless antenna (a Decibel Products Model DB-833). These measurements, made with the antenna mounted at 6.0 or 7.4 feet above ground, shown in this figure, show a very strong dependence of power density on measurement height as the measurement probe comes near the antenna.  In this figure, the measured power densities have been normalized to unity near the main beam. In one case, the relative power densities as actually measured (with the antenna mounted at 7.4 feet) were used in the spatial averaging comparison while in another case, the measurement heights were adjusted to place the main beam at the head. This situation would more closely mimic the case of a very localized exposure from an antenna mounted on a roof at head height and should more dramatically highlight any differences between the two alternative spatial averaging techniques. The results of the comparisons are summarized in the chart below:
These results validate the concept that using the projected body area method of spatial averaging of RF fields can result in lower values than simple linear averaging for highly nonuniform field distributions. With the simulated, head height antenna configuration, the projected area averaging resulted in an averaged power density almost 29% less than linear averaging. But, for field distributions producing stronger fields only slightly higher in elevation, the reduction was determined to be nominally less, about 8% and 1% respectively. However, for the field distributions of the collinear antennas with 0 and 4 foot mounting heights, wherein most of the body is more uniformly exposed, the projected area approach actually resulted in slightly higher values for the spatially averaged power density, being 7% and 15% greater. These findings are not surprising based on the considerably complex situation of reflected fields encountered at telecommunications antenna sites. If the local field power density is relatively high in those regions of the body trunk, the increased body projected areas throughout the trunk region can result in weighted power densities that are actually greater than if the fields were simply linearly averaged. On the other hand, it is clear that basing spatial averaging on the body's projected area can result, in some cases, especially with highly localized fields, in notably lower values of exposure. While the IEEE standard specifies MPEs in terms of spatial averages based on projected areas, the practical complication that this presents to compliance studies is recognized in section 6 of the standard, yielding to the acceptability of performing simple, linear averaging. Individuals involved in compliance studies at telecommunications sites should be aware of the possible differences that either technique can have in evaluation results. ¹ Personal communication with A. W. Guy, Ph.D., consultant in bioelectromagnetics, 18122 Sixtieth Place, N.E., Seattle, WA 98155, December 1995. |
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