Modeling of bioimpedance for human skin based on fractional distributed-order modified cole model

Abstract

Eksperimentalni podaci otpornosti i računa necelobrojnog reda koriste se za modeliranje bioimpedansnih osobina ljudske kože. Uveli smo i predložili modifikovani Kole model koristeći pri tom operator distribuiranog necelog reda koji je zasnovan na Caputo-Weyl-ovim izvodima necelog reda.Naš predloženi model predstavlja izmenjen jedno-disperzijski Kole model, jer uvodi nove parametre k i σ u jedno-disperzijskoj Kole impedansnoj jednačini. Ovi parametri karakterišu širinu intervala oko frakcionog indeksa α i oni su važni za precizniji opis bioimpedansnih osobina ljudske kože. Predloženi modifikovani Kole model mnogo bolje daje fitovanje date eksperimentalne krive u datom frekventnom opsegu u poređenju sa sa postojećim Kole modelima. Fitovanje je urađeno primenom Levenberg-Marquardt algoritma nelinearnih najmanjih kvadrata.Electrical impedance measurement data and fractional calculus have been utilized for modeling bioimpedance properties of human skin. We introduced and proposed revisited Cole model using modified distributed order operator based on the Caputo-Weyl fractional derivatives. Our proposed model presents essentially modified single-dispersion Cole model, since it introduces a new parameters k and σ in single-dispersion Cole impedance equation. These parameters characterize the width of interval around fractional index α and they are important for more accurate describing bioimpedance properties of human skin. The impedance spectrum was measured in a finite frequency range up to 100 kHz. Our proposed modified Cole model fits much better to experimental curve in a given frequency range compared to existing Cole models. The fitting is done using the Levenberg-Marquardt nonlinear least squares