Realization of Cole–Davidson Function-Based Impedance Models: Application on Plant Tissues

Stavroula Kapoulea,Costas Psychalinos,Ahmed S Elwakil

doi:10.3390/fractalfract4040054

Stavroula Kapoulea, Costas Psychalinos + Show 1 more

Open Access

https://doi.org/10.3390/fractalfract4040054

Copy DOI

Abstract

The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with simulation results verifying the validity of the introduced procedure.

Highlights

Electrical Impedance Spectroscopy (EIS) is a scientific field of great interest with a wide range of applications, in characterizing biological tissues as well as different materials and interfaces [1,2,3,4,5,6,7,8,9]
It must be mentioned at this point that in [34] the measured spectral impedance data have been fitted to the Cole–Davidson model using a suitable optimization algorithm in order for the model parameters (Z0, τm, α) to be identified
Electrical circuit approximations of biological tissue models based on using Constant Phase Elements (CPEs) are already known in the literature

Summary

Introduction

Electrical Impedance Spectroscopy (EIS) is a scientific field of great interest with a wide range of applications, in characterizing biological tissues as well as different materials and interfaces [1,2,3,4,5,6,7,8,9]. Despite its usefulness and popularity, this function does not take into consideration the dispersive nature of many materials, which is a result of distributed time-constants that represent the inherent built-in memory in these materials For this reason, improved versions of the Debye function have been introduced; the first of which is the single-dispersion Cole–Cole model described by the expression in (2). The non-integer exponent α ∈ (0, 1) is known as the dispersion coefficient and is related to the fractal structure (geometry and morphology) of the material and to its memory behavior Because of this exponent, the Cole–Cole model is fractional-order and its circuit implementation requires using Constant Phase Elements (CPEs; known as fractional-order capacitors) [19,20,21,22,23,24,25].

Approximation and Implementation of the Cole–Davidson Impedance Function

Design Equations

Application Example

Discussion and Conclusions

%% IMPLEMENTATION PROCEDURE