A computerized method for mathematical description of three-dimensional root canal axis.

Knowledge of the three-dimensional (3D) morphology of root canals is important for successful endodontic treatment. The objective of the present study was to determine the 3D root canal axis mathematically. Two views (mesiodistal and buccolingual) of digitized images were taken from extracted natural human teeth. Geometric reconstruction to standardize projection geometry was conducted on images. Because 90-degree turn-around image pairs are Monge images of a given root canal, these Monge images were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in 3D polynomial function of the actual root canal. On the basis of the results gained using 10 samples evaluated with the Friedman statistical test, this description seems to be reproducible. The 3D representation of the root canal may help the clinicians in choosing the optimal instruments and shaping techniques. The root canal axis that is described by the 3D function forms a basis for determination of curvature values and torsion values in each of the axis points. Evaluating these values may also yield a new type of classification.

[Mathematical description of human root canal curvatures]. / Az emberi fogak gyökércsatorna-görbületének matematikai leírása.

There is a necessity of a mathematical formula for the description of root canal curvatures. The aim of this study was to give a mathematical description of root canal forms. The measurements of 60 roots were conducted on isometric radiographs taken from the clinical view. Seven points of the imaginary axis were approximated using fourth-degree polynomial functions. Fourth-degree approximation for the description of the shape of root canal curvatures proved to be exact and reliably repeatable. This method may serve the classification of root canal forms as well as the description of the spatial curve of root canals.