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

Knowledge of the three-dimensional (3D) morphology of root canals is import ant for successful endodontic treatment. The objective of the present study was to determine the 3D root canal axis mathematically. Two views (mesiodi stal and buccolingual) of digitized images were taken from extracted natura l human teeth. Geometric reconstruction to standardize projection geometry was conducted on images. Because 90-degree turnaround image pairs are Monge images of a given root canal, these Monge images were positioned using pho togrammetric 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 clinici ans in choosing the optimal instruments and shaping techniques. The root ca nal axis that is described by the 3D function forms a basis for determinati on of curvature values and torsion values in each of the axis points. Evalu ating these values may also yield a new type of classification.