Determination of root canal curvatures before and after canal preparation (part II): A method based on numeric calculus.

The aim of this paper is to present a new method based on numeric calculus to provide data on any type of root canal curvature at any point of the long axis of the canal. Twenty severely curved, simulated root canals were prepared with rotary FlexMaster and Profile instruments in the crown-down technique and manually in the step-back technique. The inner and outer curvatures were registered in a system of coordinates before and after preparation in increments of 0.5 mm. Using an equalising function, the curvatures were first represented in graphic and algebraic form. The maximum and the mean curvature as well as the length of the arc from the apical foramen to the point of maximum curvature were determined mathematically. An increase in maximum curvature was registered for all four shaping systems investigated. The radius of the inner curvature decreased by 0.5-1.2 mm in the manual systems as a result of the preparation. The Profile system displayed the smallest changes in radius (-0.9 mm) even with the outer curvature, and manual preparation with stainless steel files the most pronounced change (-1.8 mm). The point of maximum curvature at the inner curvature was displaced by 1.6 mm to the apical foramen through manual preparation with Ni-Ti files. At the outer curvature, the maximum displacement (1.8 mm) recorded was also the result of preparation with Ni-Ti hand files, while a displacement of only 0.3 mm to the apical foramen was recorded with the other systems. The method offers a means of determining curvatures precisely without random specification of reference points. The method is also capable of registering only minor changes in curvature in the two-dimensional long axis of the canal.