Mathematical Modeling of Flexural Behavior of Rotary Nickel-Titanium Endodontic Instruments

The aim of the present study was to establish a mathematical model to characterize the flexural behavior of nickel-titanium (NiTi) rotary instruments. The bending behavior of ProFile (0.06 and 0.04 tapers), K-3 (0.06 taper), Quantec (0.04 taper) with tip size of ISO 25, was assessed by pressing the tip of the static rotary file against a smooth, freely movable, glass surface. The deflected instrument was photographed digitally, and the deflection path was digitized in software, to which data a function was fitted that best described the bending behavior of the instrument. It was found that all instruments deflected in a manner closely resembling a negative exponential function: y=A⋅e−x/b. The present approach indicated that the analytical difficulties of handling the complex cross-section in tapering spirals in beam-bending theory may be circumvented by a practical and elementary curve-fitting method.