The geometric relationship between root length and root surface area determined from digital tooth models

This study investigated the correlation between root length (RL) and root surface area (RSA) in permanent maxillary and mandibular teeth to understand the impact of external apical root resorption.

Three-dimensional (3D) models of human teeth, representing a Japanese male adult population, were sourced from a commercial provider and segmented into individual roots. A Python algorithm calculated root surface area (RSA) at simulated root lengths by virtually shortening the roots in 1 mm increments. The total RSA (tRSA) was determined by combining the circumferential root surface area (cRSA) with the cross-sectional area (CSA).

Maxillary and mandibular first molars exhibited the largest tRSAs in their respective arches. In the initial 3 mm of simulated root shortening, five of seven maxillary and mandibular tooth types exhibited minimal tRSA reduction, averaging less than 7 %. Beyond 3 mm, tRSA reduction became more pronounced, an average of 19.4 % for maxillary teeth and 27.77 % for mandibular teeth. CSA significantly contributes to tRSA; the average CSA proportion increases progressively with greater root length reduction, particularly when it exceeds 8 mm.

RSA together with CSA, not just root length, is a crucial consideration when assessing the clinical impact from root length reduction. Generally, when root length loss is up to 20 % (∼3 mm), more than 90 % of the tRSA remains. Teeth with higher CSA proportions, such as molars, are better equipped to retain periodontal support despite substantial RL loss, owing to their broader girth.