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Interaction of Extremely Low–Frequency Electromagnetic Fields
induced current densities in small voxels of tissues. The numerical calculation method has
been progressively developed for numerical dosimetry in bioelectromagnetics. The commonly used methods are as follows: FEM, IM, FDTD, and SPFD. For ELF electric fields,
several numerical methods have been used: BEM, Space Charge Method (SCM), FEM,
FDM, FDTD, spread sheet, hybrid quasistatic FDTD with SPFD, and MoM. The most
computationally efficient method is quasistatic FDTD. This quasistatic FDTD is hybridized with SPFD. For ELF magnetic fields, two calculation methods have mainly been used:
IM and SPFD. The IM is a vector, and the SPFD method is scalar. Dimbylow (1998) compared the efficiency of the two methods and indicated that the SPFD method requires less
memory for the same size of voxels and is much quicker than IM (1.5–11 times).
For the accuracy of voxel models of human body, Dawson, Potter, and Stuchly (2001b)
verified the numerical techniques for the computations of the induced currents in anatomically heterogeneous voxel models of the human body exposed to uniform ELF
electric and magnetic fields. For comparison, three numerical methods, the SPFD, the
quasi-static FDTD, and the hybrid method, are used for simple body models with different voxel sizes, from 1.8 to 7.2 mm. For uniform magnetic field exposure of 60 Hz,
1 μT, four human body models were considered: (1) simple homogeneous spheres and
ellipsoids, (2) double-layered spheres, (3) a sphere with equatorially varying conductivity, and (4) infinite square base and other infinite right cylinders. For uniform electric
field exposure of 60 Hz, 1 kV/m, two models, homogeneous and layered spheres, are
considered. Errors have been evaluated by comparing induced electric fields in human
body models computed by numerical methods with values obtained from analytical
solutions. Errors of 1%–2% are typical for both electric and magnetic field exposures.
However, large errors over 250% occur in maximum induced electric fields values in a
homogeneous sphere with 3.6-mm voxel model. This is the result of singularities introduced by the staircasing smooth surface. These errors are inherent in the voxel human
body model and are the greatest at the air-conductive interface of the body. The errors
are smaller for interfaces between conductors having different conductivity values. The
smaller the conductivity contrast, the smaller the errors. In calculations using the voxel
human body model, the error associated with the staircase approximation of a smooth
surface becomes a problem for the evaluation of the induced electric fields. Staircase
approximation is a common problem when modeling curved structures. The approach
to solve this error has not been established until now. Error introduced by staircasing
smooth surfaces will always exist while using the voxel human body model. To avoid the
inherent error in the voxel human body model, methods that will reduce error should be
proposed. The development and application of new numerical methods without using
voxel models is one of the options for the future. The differences in calculated data can
be explained in terms of the accuracy of applied numerical method, voxel size, human
body model size, posture, organ size and shape, and dielectric properties.
4.6 Conclusion
This chapter summarizes many state-of-the-art examples of numerical calculation of
the electric fields and current densities induced in both very simple human body models and anatomically realistic, high-resolution human body models exposed to ELF