19
Coupling of Electromagnetic Fields into Biological Systems
It is important to note that when applying Equations 1.24 and 1.42 to estimate induced
fields inside a body (animals, humans, or tissue preparations), any significant deviations from homogeneity or circular cylindrical symmetry must be taken into account.
Equations 1.24 and 1.42 should be applied to each region inside the body with a different
conductivity, which behaves as a unit with its own body center and radius or an equivalent radius. However, due to opposing field orientations and current paths inside the
body, the highest field and current densities tend to occur with the large dimensions associated with the outer layers of a body or a tissue preparation as long as the conductivities
are not grossly different and the regions are not separated by nonconducting materials.
1.9.3 Combined Quasistatic Electric and Magnetic Fields
It is noteworthy that when both fields are present the relative significance of electrically
or magnetically induced coupling in humans and animals is a function of body size and
the ratio of applied E 1 /H 1 such that
E e /E h = (2ε 0 /σμ 0 r)(E 1 /H 1 )
(1.43a)
where E e and E h are the electrically and magnetically induced inside electric fields,
respectively. For σ = 0.1 S/m at 60 Hz,
E e /E h = 20(E 1 /H 1 )/[(120π) 2 r] (1.43b)
Accordingly, the magnetically induced field in a human head of radius 10 cm is a factor
of 2 (0.6π) greater than the electrically induced field for a ratio of applied fields E 1 /H 1 =
120π. The electric and magnetic fields induced would be equally significant if the applied
electric field strength is 0.6π times stronger than the applied magnetic field. The same is
true if the size of the body is 1/(6π) of 1 m. Thus, for an isolated cell or an aggregate of
cells whose radius is smaller than 1/(6π) of a meter, the electrically induced field is the
predominant factor when the ratio of applied fields is E 1 /H 1 = 120π. This size dependence illustrates the need for scaling extrapolation results from animals to humans or
from cell preparations to whole-body systems. Substantive adjustment is required when
comparable induced fields inside different animals are to be obtained by applying external fields at low frequencies.
1.9.4 Summary of Quasistatic and Low-Frequency
Field Coupling
The coupling and distribution characteristics of low-frequency electric and magnetic
fields in biological tissue are summarized in this section. The results apply to frequencies
at which the wavelength is long or the largest dimension of the body is small compared
with a wavelength, including ELF and quasistatic electric and magnetic fields:
• Exposures to low-frequency electric and magnetic fields occur in the near zone or
inductive region of a source.
• Induced electric and magnetic fields inside animals and humans are quasistatic
in nature.
Coupling of Electromagnetic Fields into Biological Systems
It is important to note that when applying Equations 1.24 and 1.42 to estimate induced
fields inside a body (animals, humans, or tissue preparations), any significant deviations from homogeneity or circular cylindrical symmetry must be taken into account.
Equations 1.24 and 1.42 should be applied to each region inside the body with a different
conductivity, which behaves as a unit with its own body center and radius or an equivalent radius. However, due to opposing field orientations and current paths inside the
body, the highest field and current densities tend to occur with the large dimensions associated with the outer layers of a body or a tissue preparation as long as the conductivities
are not grossly different and the regions are not separated by nonconducting materials.
1.9.3 Combined Quasistatic Electric and Magnetic Fields
It is noteworthy that when both fields are present the relative significance of electrically
or magnetically induced coupling in humans and animals is a function of body size and
the ratio of applied E 1 /H 1 such that
E e /E h = (2ε 0 /σμ 0 r)(E 1 /H 1 )
(1.43a)
where E e and E h are the electrically and magnetically induced inside electric fields,
respectively. For σ = 0.1 S/m at 60 Hz,
E e /E h = 20(E 1 /H 1 )/[(120π) 2 r] (1.43b)
Accordingly, the magnetically induced field in a human head of radius 10 cm is a factor
of 2 (0.6π) greater than the electrically induced field for a ratio of applied fields E 1 /H 1 =
120π. The electric and magnetic fields induced would be equally significant if the applied
electric field strength is 0.6π times stronger than the applied magnetic field. The same is
true if the size of the body is 1/(6π) of 1 m. Thus, for an isolated cell or an aggregate of
cells whose radius is smaller than 1/(6π) of a meter, the electrically induced field is the
predominant factor when the ratio of applied fields is E 1 /H 1 = 120π. This size dependence illustrates the need for scaling extrapolation results from animals to humans or
from cell preparations to whole-body systems. Substantive adjustment is required when
comparable induced fields inside different animals are to be obtained by applying external fields at low frequencies.
1.9.4 Summary of Quasistatic and Low-Frequency
Field Coupling
The coupling and distribution characteristics of low-frequency electric and magnetic
fields in biological tissue are summarized in this section. The results apply to frequencies
at which the wavelength is long or the largest dimension of the body is small compared
with a wavelength, including ELF and quasistatic electric and magnetic fields:
• Exposures to low-frequency electric and magnetic fields occur in the near zone or
inductive region of a source.
• Induced electric and magnetic fields inside animals and humans are quasistatic
in nature.