Nonsymmetrical DRT and Multiple Cole Systems

Davidson and Cole (1951) proposed another version of the Cole—Cole equation  

Havriliak and Negami (1966) and Williams and Watts (1970) proposed even more general versions of the form  

These equations do not correspond to circular arcs in the complex plane, but to a nonsymmetrical DRT with a larger density of relaxation times on the low-frequency side. 

With measured data showing a nonsymmetrical DRT, the choice of model is important for example, a model according to this section or a model with multiple Cole systems (see the next section). 

Parameters similar to those, for example, of the Cole equation, can also be computed without choosing a model. Jossinet and Schmitt (1998) suggested two new parameters that were used to characterize breast tissues. The first parameter was the distance of the 1 MHz impedance point to the low-frequency intercept in the complex impedance plane and the second parameter was the slope of the measured phase angle against frequency at the upper end of the spectrum (200 kHz—1 MHz). Significant differences between carcinoma and other breast tissues were found using these parameters. 

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