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Calculation of simplified single-root surface area from simulated X-ray projection
Ssu-Kuang Chen1, Chung-Ming Chen, Jeng-Ywan Jeng
1Division of Oral and Maxillofacial Imaging, Dentistry, NTUH, College of Medicine, National Taiwan University, Taipei. cskchen@ccms.ntu.edu.tw
Background:
The prognosis of a tooth affected by periodontitis might depend on the amount of bone remaining around the root surface. The surface area of a single tooth root relates to a simulated x-ray projection.
Methods:
The aim of the study was to determine root surface area from radiographs. Two methods were used. In the first, cross-sections of a single-tooth root were simulated using ellipses with different eccentricities. Projection data from 90 directions at 1 degrees intervals were obtained, which were then used to estimate circumferences that were then compared with the known circumference. In the second model, circumference was estimated from projection data derived from the projection of an ellipse with the central ray parallel to the long axis. The estimated circumference was compared with possible circumferences resulting from this projection data.
Results:
In the first model, all estimated circumferences are less than the true circumferences. The largest error in each case decreased rapidly as the eccentricity of the simulated ellipse decreased. Less than 6% of the largest errors were found when the eccentricity is 0.83. In the second model, the estimation should be within less than 2% of error when the asymmetry factor is less than 0.6.
Conclusions:
The circumference of an elliptical object can be approximated from the projection data of this ellipse. Therefore, the surface area of a single tooth root may be estimated with clinically useful accuracy from the projection data.