An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters

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Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals.


Two extracted human lower molars were radiographed in the occlusal direction using micro–computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model.


The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry.


With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes.

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