Electrical Model of Tissue
Tissue can be modeled as an electrical circuit with resistive and capacitive properties:
Its dispersion and absorption are represented by the empirical formula:
In this equation is the complex dielectric constant, and are the "static" and "infinite frequency" dielectric constants, times the frequency, and is a generalized relaxation time. The parameter can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. This expression requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below the axis.
It is worth emphasizing that the Cole–Cole model is an empirical model of the measured data. It has been successfully applied to a wide variety of tissues over the past 60 years, but it does not give any information about the underlying causes of the phenomena being measured.
Several references in the literature use a form of the Cole equation written in terms of impedance instead of a complex permittivity. The impedance is given by:
Where and are the resistances at zero frequency (i.e. DC) and infinity, respectively. is often referred to as the characteristic frequency. It should be emphasized that the characteristic frequency is not the same when the analysis is carried out in terms of the complex permittivity. A simple interpretation of the above equation is in terms of a circuit where a resistance is in series with a capacitor and this combination is placed in parallel with a resistance . In this case and . It can be shown that is given by
Read more about this topic: Kenneth Stewart Cole
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