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Interaction of Extremely Low–Frequency Electromagnetic Fields
two laboratories could be explained by factors such as the accuracy of the numerical
method, dielectric properties, conductivity of the organ, human model differences,
and voxel size.
In order to compare the computational efficiency between SPFD and IM, Dimbylow
(1998) calculated current densities in a fine-resolution (2 mm), anatomically realistic
voxel phantom called NORMAN with a height of 1.76 m and a mass of 73 kg exposed to
uniform magnetic fields at frequencies ranging from 50 Hz to 10 MHz. In NORMAN,
there were 8.3 million voxels in the body, differentiated into 38 tissue types. Using the
same voxel size, the SPFD method required 14% less memory and was much quicker
than IM (1.5–11 times faster). Two calculation methods at 50 Hz agreed with each other
within 2% for AP (applied from front), 3% for LAT (applied from the side), and 1% for
TOP (applied from above) orientation.
Barchanski et al. (2005a, 2006a, 2007) extended the classical SPFD approach to the
extended SPFD (Ex-SPFD) method. This Ex-SPFD method can treat the arbitrarily
shaped, time harmonic, magnetic field source and highly conductive material inside
the computational domain. This method was applied to compute the induced currents
inside a human body model exposed to electric blankets. Very high resolution was
needed to model the human body because of the geometrical complexity. This human
model, Hugo model, based on the Visible Human Project represents a 38-year-old male
(187-cm height and 113-kg weight), offers a voxel resolution ranging from 8 × 8 × 8 mm 3
to 1 × 1 × 1 mm 3 , and has a total of 32 different tissue types. This human model was
discretized with 200 million grid cells, which correspond to a resolution of 1.5 mm. The
authors proposed a new method for calculating current density distribution within this
human model using FIT. This new method may be performed with higher accuracy due
to an increased local grid resolution only in the areas of interest in the human voxel
model. As an application example, they simulated the current densities induced by an
electric blanket with two different configurations that generate magnetic fields of 73.7
and 78.1 μT. The induced current densities in the whole body due to the magnetic field
originating from two electric blankets are 7.02 × 10 and 3.13 × 10 −4 mA/m 2 . In order
to resolve small organs, they refined a local grid for ELF current calculation, which
allows one to finely resolve areas of particular interest in three-dimensional human
anatomy models (Barchanski et al. 2006b). Eberdt, Brown, and Lazzi (2003) developed
two-dimensional, SPICE-linked, multisolution IM for ELF electromagnetic interactions. The IM with high-resolution models has been hampered by the time required to
solve the equations. The authors have implemented a multiresolution, two-dimensional
mesh generation scheme for the IM to reduce the number of equations. Then, the proposed method can be linked with SPICE (circuit simulator) and can be applied to threedimensional problems.
In order to clear the uncertainty in calculation, Caputa et al. (2002) presented a
comparison of anatomically realistic human models and numerical codes in ELF
magnetic fields. Using models from the University of Victoria, Uvic model, and NRPB,
NORMAN model, an evaluation has been performed for uniform 60 Hz magnetic fields.
The comparison of average (E avg ), maximum (E max ), and 99th percentile (E 99 ) electric
fields for all the organs in the models was made. The effect of model size, shape, and
resolution with the conductivity values kept constant was also given. These approaches