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The aims of this study were to develop a three-dimensional (3D) mathematical model of a typical root resorption crater and to correlate two-dimensional (2D) surface area measurements to 3D volumetric measurements of root resorption craters created under light and heavy orthodontic forces. Data were obtained from a previous study of 36 first premolars from 16 subjects requiring extraction of these teeth as part of their orthodontic treatment. Buccal tipping forces of 25 or 225 g were applied for an experimental period of 28 days. After extraction, the samples were prepared for scanning electron microscopy (SEM) imaging, image processing and analysis. Surface area (2D) and volumetric (3D) measurements of all craters were obtained. A mathematical analysis of the 2D/3D relationship enabled the determination of an appropriate digital model for the shape, type and dimensions of resorption craters, which was also able to distinguish between a 'hemispheric' model versus a 'layered' model of craters. The results demonstrated that 2D and 3D measurements were strongly correlated (r = 0.991**). Within the light and heavy force groups, the measurements were also strongly correlated (r = 0.978** and r = 0.994**, respectively). For a 28 day experimental period, 2D measurements of root resorption craters were found to be as reliable as 3D measurements.

Validation of two-dimensional measurements of root resorption craters on human premolars after 28 days of force application