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To develop the mathematical model for root canal preparation using Endodontic file. Method: The process of obturation consist of the filling of the root canal cavity using heated and softened guttapercha to get the fluid tight seal in between the canal wall and filled gutta-percha. Any obturation process to perform before it requires the preparation of the root canal which involves the removing dead tissue, substrates and debris from the decayed root canal. The various geometric parameters viz. Taper, relative angle for orientation of cross-section between two planes, pitch and polar symmetry constant of the Endodontic file etc. Geometric parameters are derived. The various performance parameters like Endodontic file life assessment, cutting force components (tangential and normal), substrate removal rate, torque exerted by Endodontic file etc are also derived successfully. The Endodontic file life is estimated based on two approaches viz. speed and volumetric wear approach. Conclusion: The mathematical model described is helpful for the Endodontic experts, researchers, design engineers etc. However the applicability of the described mathematical model limited to assumption of study. The gap between root canal to be prepared and Endodontic file is zero while preparation. The Endodontic file weight, speed of rotation and substrate removal rate is assumed to be constant. The mathematical model for Endodontic file discussed above proved to be efficient tool for studying the root canal preparation. The various geometric parameters and the various performance parameters are derived.

The objective of this review article is to review literature on fatigue analysis and biomaterials studies in Endodontics. The nitinol and gutta-percha are widely used biomaterials in the Endodontic fields. The nitinol is used to manufacture the Endodontic files which are used for preparation of the root canal. The preparation of the root canal consist of removal of dead tissue, substrates and debris from the decayed root canal. During the preparation of root canal shaping of the root canal is done to develop the perfectly prepared cavity. The gutta-percha is used to fill the prepared cavity. The nitinol and gutta-percha are important contributing biomaterial for success of root canal treatment. This review article has been reviewed contemporary studies on nitinol and gutta-percha biomaterials. For the success of root canal treatment the fatigue of Endodontic file and three dimensional filling of root canal are two important aspect. The Endodontic files during the cleaning and shaping of the canal gets subjected to torsion fatigue failure or cyclic fatigue failure. The past studies lacks the exact knowledge about these failures as well as analysis approaches to be followed for correct diagnosis. This review article helps to overcome this difficulties. Moreover, the fatigue factors are discussed so that researcher can get little idea about failure point of the nitinol rotary files. The review consist of A contemporary review of nitinol alloy studies, A review of fatigue failure diagnosis, A contemporary review of gutta-percha quality assessment techniques studies, A novel approach for fatigue analysis of nitinol file and A novel approach for quality assessment of gutta-percha etc.

Regarding the article Numerical simulation and experimentation of endodontic file using Taguchi DoE, Int. J. Simul. Multidisci. Des. Optim. 12, 32 (2021), published November 17 th , 2021, the first name and affiliation of the third co-author were erroneous.