Comparison of Electrical Equivalent Circuits of Human Tooth used for Measuring the Root Canal Length

An accurate determination of the root canal length, which is the most critical procedure in the endodontic treatment of a tooth, is commonly performed nowadays by electronic apex locators which are based on electrical impedance measurements. In this paper tooth impedances were measured in vitro on extracted tooth in alginate material using HP 4284A LCR meter and a specially designed stalk with a micrometer for precise file positioning. In order to develop a more accurate measurement procedure human tooth was modeled by electrical equivalent circuit. Four new equivalent circuits comprising of resistors, capacitors and constant-phase elements were proposed in this paper and compared with four previously suggested circuits. Elements of equivalent circuits were determined by complex nonlinear least squares fitting using LEVM software. Different quality factors were defined to describe the fit quality of a certain equivalent circuit at each file position. The overall fitting efficiency in the region of file positions of interest was calculated as well. A detailed discussion was given on equivalent circuit parameters that can be used to measure the root canal length. Upon these results the most appropriate equivalent circuit was selected and a new measurement procedure was proposed.