DRAFT Recommended Practice for Measurements and ...

1/29/98 119 C95.3-1991 Revision — 2 nd Draft
10/98 Draft
D5.2 Extended-Boundary-Condition Method (EBCM).
The EBCM is a matrix formulation based on an integral equation and expansion of the
EM-fields in spherical harmonics. This method was developed by Waterman [D21] and
has subsequently been used to calculate the SAR in prolate spheroidal models of
humans and animals [D1]. The EBCM is exact within the limits of numerical computation
capabilities, but numerical problems presently limit the method to frequencies below
about 80 MHz for prolate spheroidal models of humans. In SAR calculations for prolate
spheroidal models of humans, the long-wavelength approximation and the EBCM give
identical results up to about 30 MHz, where the long-wavelength approximation begins to
become inaccurate.
D5.3 Iterative Extended-Boundary-Condition Method (IEBCM).
The EBCM has been extended [D11] to a technique called the IEBCM, that is capable of
SAR calculations in prolate spheroidal models of man up to at least 400 MHz. The
IEBCM is different from the EBCM in two main respects. It makes use of more than one
spheroidal harmonic expansion, which allows better convergence for elongated bodies at
higher frequencies, and it uses iteration, beginning with an approximate solution, to
converge to the solution. These two features of the IEBCM have significantly extended
the range of calculations over that of the EBCM.
D5.4 The Cylindrical Approximation.
The SAR calculated for an appropriately long section of an infinitely long cylinder is a
good approximation to the SAR of spheroids in the frequency range where the
wavelength is very short compared with the length of the spheroid. The lowest frequency
at which the approximation is useful depends both on the length of the spheroid and on
the ratio of the major axis to the minor axis. For man-sized spheroids, the lower
frequency limit occurs for E-polarization when the wavelength is about four-tenths of the
length of the spheroid [D14].
D5.5 Moment-Method Solution.
A moment-method solution of a Green's-function integral equation for the electric field
has been used to calculate the internal electric field in block models, so-called because
the mathematical cells of which the model is composed are cubes [D4, D6]. Wholebody
average SARs calculated by this method are very close to those calculated for
spheroidal models. Although the block model has the advantage that it resembles the
human body better than a spheroid because it has simulated arms, legs, and head, the
calculations of the spatial distribution of the internal fields made with the above method
have been found to be of varying accuracy depending on the location of the cell in
question [D15]. Apparently, the calculations are of limited accuracy because the electric
field in each mathematical cell is approximated by a constant, and this approximate field
cannot satisfy the boundary conditions for cells that touch the curved surface of
interfaces between two dissimilar dielectric materials, or the surface of the body (airtissue
boundary). An improved moment-method uses tetrahedra as mathematical cells
[D18]. Special basis functions are defined within the tetrahedral volume elements to
insure that the normal electric field satisfies the correct conditions at interfaces between
different dielectric media.
Hagmann [D7] has developed improved means for predicting regionally averaged SAR
using the block model of man, with the moment-method technique. Since individual
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subject to change.