Abstract
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 (), 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.
Highlights
The interest in the application of fractional calculus, the branch of mathematics concerning integration and differentiation to non-integer orders, to modeling complex biomedical phenomena has increased significantly in recent decades
Entropy 2020, 22, 1117 utilize fewer parameters than the integer-order models traditionally used; offering an opportunity for reduced order modeling without decreases in fitting accuracy
Two age groups were selected in the investigation; 20 (±1) and 50 (±1) years old and five dentin samples were collected from each age group
Summary
The interest in the application of fractional calculus, the branch of mathematics concerning integration and differentiation to non-integer orders, to modeling complex biomedical phenomena has increased significantly in recent decades. This interest stems from the fitting accuracy achieved between experimental data and fractional-order models [1]. Entropy 2020, 22, 1117 utilize fewer parameters than the integer-order models traditionally used; offering an opportunity for reduced order modeling without decreases in fitting accuracy. Recent studies have reported age-related differences in human dental tissue impedance and utilized fractional-order equivalent circuit model parameters to represent these measurements
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