A Comparative Study of Two Fractional-Order Equivalent Electrical Circuits for Modeling the Electrical Impedance of Dental Tissues.

Background: Electrical impedance spectroscopy (EIS) is a fast, non-invasive, and safe approach for electrical impedance measurement of biomedical tissues. Applied to dental research, EIS has been used to detect tooth cracks and caries with higher accuracy than visual or radiographic methods. Recent studies have reported age-related differences in human dental tissue impedance and utilized fractional-order equivalent circuit model parameters to represent these measurements. Objective: We aimed to highlight that fractional-order equivalent circuit models with different topologies (but same number of components) can equally well model the electrical impedance of dental tissues. Additionally, this work presents an equivalent circuit network that can be realized using Electronic Industries Alliance (EIA) standard compliant RC component values to emulate the electrical impedance characteristics of dental tissues. Results: To validate the results, the goodness of fits of electrical impedance models were evaluated visually and statistically in terms of relative error, mean absolute error (MAE), root mean squared error (RMSE), coefficient of determination (R2), Nash-Sutcliffe's efficiency (NSE), Willmott's index of agreement (WIA), or Legates's coefficient of efficiency (LCE). The fit accuracy of proposed recurrent electrical impedance models for data representative of different age groups teeth dentin supports that both models can represent the same impedance data near perfectly. Significance: With the continued exploration of fractional-order equivalent circuit models to represent biological tissue data, it is important to investigate which models and model parameters are most closely associated with clinically relevant markers and physiological structures of the tissues/materials being measured and not just "fit" with experimental data. This exploration highlights that two different fractional-order models can fit experimental dental tissue data equally well, which should be considered during studies aimed at investigating different topologies to represent biological tissue impedance and their interpretation.

Accurate Empirical Fractional-Order Electrical Models of Young and Old Dentines.

Electrical impedance spectroscopy (EIS) is a fast, non-invasive, and safe technique for bioimpedance measurement. In dental research, EIS has been used to detect tooth cracks and caries with higher accuracy than visual and radiographic methods. Recently, a study has been reported on effect of age on impedance measurements for two age groups by employing EIS. The aim of that study was to demonstrate the usefulness of fractional calculus in equivalent circuit modeling. In proposed double dispersion Cole impedance (C-C) models, both resistance and pseudo-capacitance values were found to be significantly different for both age groups. However, in our study, the first time it was found out that proposed models' total pseudo-capacitance values of both young and old dentines can be reduced by 34% and 7.5%, respectively, if recurrent electrical impedance model for n = 2 bifurcations to be used. Secondly, new empirical fractional-order electrical models of human tooth using the optimized Valsa network with EIA standard compliant RC values are reported that provide better understanding of the structure of dentine from resistance and capacitance point of view.

2DOF multi-objective optimal tuning of disturbance reject fractional order PIDA controllers according to improved consensus oriented random search method.

This study presents a Fractional Order Proportional Integral Derivative Acceleration (FOPIDA) controller design methodology to improve set point and disturbance reject control performance. The proposed controller tuning method performs a multi-objective optimal fine-tuning strategy that implements a Consensus Oriented Random Search (CORS) algorithm to evaluate transient simulation results of a set point filter type Two Degree of Freedom (2DOF) FOPIDA control system. Contributions of this study have three folds: Firstly, it addresses tuning problem of FOPIDA controllers for first order time delay systems. Secondly, the study aims fine-tuning of 2DOF FOPIDA control structure for improved set point and disturbance rejection control according to transient simulations of implementation models. This enhances practical performance of theoretical tuning method according to implementation requirements. Thirdly, the paper presents a hybrid controller tuning methodology that increases effectiveness of the CORS algorithm by using stabilizing controller coefficients as an initial configuration. Accordingly, the CORS algorithm performs the fine-tuning of 2DOF FOPIDA controllers to achieve an improved set point and disturbance rejection control performances. This fine-tuning is carried out by considering transient simulation results of 2DOF FOPIDA controller implementation model. Moreover, Reference to Disturbance Ratio (RDR) formulation of the FOPIDA controller is derived and used for measurement of disturbance rejection control performance. Illustrative design examples are presented to demonstrate effectiveness of the proposed method.