228
Electromagnetic Fields in Biological Systems
In addition, the equation for the electric fields was transformed into a scalar potential
form, which then was solved using finite differences. The SPFD method was used to
model induced electric fields and current densities during the exposure to ELF magnetic fields. First, Stuchly’s group at University of Victoria developed and used simple
geometric shapes, spheres and ellipsoids, to assess the accuracy of the SPFD method
against analytic solutions. They applied detailed calculations to an anatomically MRIbased human model with voxels of 3.6 and 7 mm exposed to uniform magnetic field.
Dawson and Stuchly (1998c) presented the results of the calculation in terms of the
effect of skeletal muscle anisotropy on the induced current densities and electric fields
under conditions of 60 Hz uniform magnetic field exposures. As they mentioned in
their research paper, the numerical estimations were based on an isotropic conductivity model for all body components. In reality, the anisotropy of biological tissues, skeletal muscle, should affect the estimation of induced electrical values. The comparison
was made between the magnetic induced electrical quantities in the full human body
model under several assumptions of anisotropy ratios and those in the isotropic case.
The anisotropy of skeletal muscle is the key factor in the numerical modeling of the
human body.
In order to compare the dosimetry of a child and that of an adult and to evaluate
the accuracy of linear scaling of organ dosimetry between species, Dawson, Caputa,
and Stuchly (2002b) evaluated electric fields in high-resolution, anatomically based
inhomogeneous models of a human male adult (77-kg weight, 175-cm length, 3.6-mm
voxel size). Other models were a male child (17 kg, 110 cm, 3.2 mm), a male rat (591 g,
27.4 cm, 0.8 mm), a female rat (284 g, 23.8 cm, 0.8 mm), a male mouse (45 g, 11.6 cm,
0.34 mm), and a female mouse (23 g, 8.8 cm, 0.35 mm) exposed to 60 Hz, 1-μT uniform magnetic fields with three different orientations. The calculation included the
tissue average, voxel maximum, and 99th percentile values of the electric fields and current densities in organs. Organs included the brain, fat, liver, and lung. The numerical
method was based on the quasistatic approximation. The averaged and 99th percentile
values of the induced electric fields in the child’s brain exposed to 1 μT from side to side
were 9.38 μV/m and 26.8 μV/m, respectively. The conclusions are (1) child-to-adult and
mouse-to-rat organ dosimetry shows linear dependence on the geometric scale factor
between models and (2) postural and individual organ differences have a significant
effect when mouse and human child models are compared. The latter conclusion attracts
much attention to scaling-based extrapolation of rodent experimental results versus
results of human models.
Stuchly and Gandhi (2000) compared the induced electric fields and current densities during exposure to 60 Hz electric and magnetic fields on different models from
three laboratories. The Utah group used the FDTD method scaled in frequency on
6-mm resolution of their phantom model. The Uvic group used the quasistatic hybrid
SPFD on 7.2-mm resolution of their model and the SPFD on 3.6-mm resolution. The
averaged electric field in the brain in the phantom model for 60 Hz, 1 mT from front
to back was 11.5 mV/m (σ = 0.17 S/m), and 10.6 mV/m (σ = 0.11 S/m) for the Uvic
model with 3.6-mm resolution. They showed that for the average induced electric
fields, maximum differences were as low as 60%, and for the average current densities,
maximum differences were up to 110%. They concluded that the differences between