56

Bioelectromagnetism

tissues from kHz to about 100 kHz. Afer World War II, the data was extended from below the kHz range

to the microwave frequency range. From these investigations, the concept of dispersion was developed.

Te dielectric (electric) properties of tissues are usually described in terms of electrical conductivity

and the relative dielectric constant called permittivity. Tese two parameters depend strongly on the

frequency and type of tissues. Te dielectric constant is represented as ɛ (F/m), and since the dielectric

constant of free space is ε0 (= 8.854 × 10⁻¹² F/m), the relative permittivity is defned as εγ = ε/ε0. Te elec­

trical conductivity is represented as σ (S/m). Tere are various electrical properties related to biological

cells and tissues, which can help in understanding the characteristics of them. Te relative permittivity

εγ and the electrical conductivity σ of tissues change with frequency. An overview of the dielectric prop­

erties of biological tissues has been presented in terms of their relaxation mechanisms. Te dielectric

properties of biological tissues have been categorized according to relaxation regions that are related to

the sizes of the composing cells and ions. Trough the measurements of the conductive and capacitive

properties of biological tissues, Schwan introduced frst the concept of dispersion. Tere are relaxation

characteristic regions allowing the frequency of dispersion.

Figure 2.11 shows data on the dielectric properties of muscular tissue as a function of frequency which

indicates three unusual features. For relative dielectric constants of biological tissues, there are three

break points; and they occur: (1) below a few kHz, (2) in the frequency range from tens of kHz to tens

of MHz, and (3) in the microwave range, about 20 GHz. At each of these frequencies, a dispersion phe­

nomenon of a rapid decline of relative dielectric constant and rapid increase in electrical conductivity

occur. Tese are referred to, respectively, as α-, β-, and γ-dispersions. At frequencies below a few kHz,

an ionic difusion process in cellular membranes occur which allows the dielectric relaxation in the

α-dispersion. Bioelectric studies of biological tissues below a few kHz were difcult because electrode

polarization at these frequency regions is signifcant. For this reason, the mechanism of the α-dispersion

of biological tissues was not well understood. It is believed to be associated with a counterion layer

(electrical double layer) polarization in the tissues (Foster and Schwan, 1989). Te high dielectric con­

stant observed at low frequencies is a result of the complex and non-uniform structure of biological

organisms. Te origin of the α-dispersion is a relaxation phenomenon of cell membranes; it is related

to the permeability of membranes and to the difusion process of ions in these complex structures. In

the frequency range from tens of kHz to tens of MHz, the β-dispersion region becomes more evident in

response to the relaxation from the polarization of cellular membranes and organic macromolecules.

Although the origin of the β-dispersion is not well understood, it is due to the inability of the polariza­

tion of cellular structural components, including cell membrane, which act as barriers of ion fow. Te

β-dispersion also comes from the polarization of organic polymers and proteins. At the GHz regions,

about 20 GHz, the γ-dispersion is caused by the polarization of water molecules, both free and bound

ones, which are common in biological systems.

FIGURE 2.11 Te dielectric constant ε and the conductivity σ of muscle are shown as a function of frequency of

electromagnetic radiation (From Schwan, 1988.)