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Electromagnetic Fields in Biological Systems
parameters depend strongly on the frequency and type of the tissues. The dielectric
constant is represented as ε (F/m), and the dielectric constant of free space is ε 0 (=8.854 ×
10 −12 F/m). So, the relative permittivity is defined as ε r = ε/ε 0 . The electrical conductivity
is represented as σ (S/m). The magnetic permeability of free space is μ 0 (=4π × 10 −7 H/m).
The relative magnetic permeability is defined as μ r = μ/μ 0 . The entities ε r and μ r are
the relative permittivity and the relative magnetic permeability of a particular medium,
respectively. At low frequencies, the tissue conductivity is dominant. At high frequencies, the relative permittivity tends to become dominant. The magnetic permeability
of body tissues is almost the same as that in free space and does not change with the
frequency.
The relative permittivity ε r and the electrical conductivity σ of tissues change with
frequency. There are relaxation characteristic regions allowing frequency dispersion.
An overview of the dielectric properties of biological tissues has been presented in
terms of their relaxation mechanisms. The dielectric properties of biological tissues
have been categorized according to relaxation regions that are related to the sizes of
composing cells and ions. For relative permittivity and electrical conductivity, there
are three main relaxation regions: α, β, and γ dispersions for the frequencies ranging from a few hertz to a few gigahertz. They occur (1) at lower frequencies (few kilohertz)—an ionic diffusion process in cellular membrane, which allows the dielectric
relaxation in the α region and (2) at higher frequencies (~10 kHz to ~100 MHz)—the
β dispersion region becomes more evident in response to the relaxation from polarization of cellular membranes and organic macromolecules. The α dispersion is believed
to result mainly due to the relaxation phenomenon of an ionic diffusion process at cellular membrane. Although the origin of β dispersion is less well understood, it stems
due to the blockage of polarization in cellular structural components, including cell
membranes, which act as barriers to ion flow. The β dispersion is also caused by the
polarization of organic polymers and proteins. At gigahertz frequencies, the γ dispersion is caused by the polarization of water molecules, both free and bound ones, which
are common in biological systems.
In the ELF region, human and animal bodies can be considered as conductive
material defined by the relative permittivity and the effective conductivity. There are
a number of published papers on the electrical properties of living tissues (Gabriel,
Gabriel, and Corthout 1996a; Gabriel, Lau, and Gabriel 1996b,c; Gabriel 2005; Gabriel,
Peyman, and Grand 2009; Schwan 1985). Gabriel and coworkers studied electrical
properties in more than 30 animals and in humans in the frequency range of 10 Hz
to 20 GHz, using an automatic swept-frequency network and impedance analyzers
(Gabriel, Gabriel, and Corthout 1996a; Gabriel, Lau, and Gabriel 1996b). Although the
electrical properties of the tissues have been studied extensively through experiments,
studies on the effective conductivity and the relative permittivity are scarce and the
results show wide variations. The reason why there is no accurate data available is
that the electrode polarization errors affect the results below 1 kHz and this source of
errors may influence the permittivity values below 100 Hz by a factor of 2 or 3. From
the electrical point of view, the biological tissues below 100 Hz can be treated as resistance. The permittivity will not play a major role, and the induced current inside the
body is evaluated only by conductivity.