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Electromagnetic Fields in Biological Systems
on a homogeneous ellipsoidal model of the rat carcasses. Furthermore, they measured
the complex electric fields in anesthetized rats using a miniaturized electric field probe.
In living animals, the natural endogenous electric fields exist internally and are readily
detected as an electrocardiogram waveform. If the magnetic field is applied externally to
living animals, an electric field, which is induced by a 60 Hz magnetic field, is added to
endogenous physiological electric fields. Miller and Creim (1997) compared the endogenous electric fields and 60 Hz magnetically induced electric fields. The induced electric
fields were reduced within the body, or in different directions on the body surface. It is
well known that the induced electric fields gradually decrease from a maximum at the
body surface to zero at the center of the body.
Table 4.4 gives examples of the calculated and measured current densities in a realistic human model exposed to uniform and nonuniform ELF magnetic fields.
Baraton and Hutzler (1995) reported FEM calculations on induced current densities in three different human model configurations, both in uniform and nonuniform
magnetic fields. They analyzed induced currents in the human body through either the
TRIFOU (three-dimensional eddy current) code or a simple formula. TRIFOU code is
the three-dimensional field calculation techniques using the FEM (Bossavit and Vérité
1983). This code solves the Maxwell equation within the body by an iterative process.
The inside body is meshed with tetrahedron, while the space around the body remains
unmeshed. The boundary conditions on the body surface are factored in using the
boundary integrals. Dawson and Stuchly (1997) and Dawson (1997) considered the analytic solution to the problems of electric fields and current densities induced by applied
magnetic fields. The analytical solution can be applied to the problem of ELF induction
in an equatorially stratified sphere by using axial uniform magnetic fields. This solution
is formulated through Green’s function.
Gandhi, Deford, and Kanai (1984) introduced the IM for the calculations of current
densities inside the human body exposed to ELF magnetic fields. The IM by Gandhi and
Chen (1992) has been applied to calculations in an anatomically voxel-based human
body model. The human body was based on a semirealistic voxel model. In that calculation, the voxels were differentiated into a three-dimensional network of impedance.
Applied ELF magnetic fields inside the human body were researched.
The IM suggested that when representing the biological body as a three-dimensional
network of impedance whose individual values are obtained through the conductivities,
a system equation was derived using Kirchhoff’s law around each loop in this threedimensional network. As an example, using the quasistatic IM, Gandhi et al. (2001)
calculated the induced currents in the nominal 2 × 2 × 3 and 6-mm resolution, anatomically based human body model exposed to 60 Hz magnetic fields. In the first
calculation, the induced electric fields or current densities for the various glands and
organs of the body including pineal gland were obtained in the context of exposure to
uniform magnetic fields of various orientations and a magnitude of 0.1 mT (50 Hz) or
1 mT (60 Hz). These values are the safety guideline levels set by the ICNIRP (1998a,b)
and the American Conference of Industrial Hygienists (ACGIH 1997). The maximum
1-cm 2 -averaged induced current densities in the brain and spinal cord were within the
basic restriction level of 10 mA/m 2 according to the ICNIRP guidelines for occupational
exposure. Furthermore, the maximum 1-cm 2 -averaged current densities and electric