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

• Published in: Computers in biology and medicine Vol. 191; p. 110189
• Main Authors: Wei Chan, Chloe Xiao, Leow, Wee Kheng, Cheng, Alan Ho-lun, Chiong Foong, Kelvin Weng
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.06.2025
• Subjects: 3D tooth models; Adult; Algorithms; External apical root resorption; Humans; Imaging, Three-Dimensional; Internal Medicine; Male; Mandible - anatomy & histology; Mandible - diagnostic imaging; Models, Dental; Molar - anatomy & histology; Molar - diagnostic imaging; Other; Python algorithm; Root cross-sectional area; Root length; Root surface area; Tooth Root - anatomy & histology; Tooth Root - diagnostic imaging; Root cross-sectional area; 3D tooth models; Root surface area; External apical root resorption; Python algorithm; Root length
• ISSN: 0010-4825; 1879-0534; 1879-0534
• DOI: 10.1016/j.compbiomed.2025.110189

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. •A novel Python algorithm analysed root surface area (RSA).•Up to 20 % apical root length loss retains more than 90 % of RSA.•Root length (RL) reduction beyond 8 mm significantly reduces RSA.•Cross-sectional root area is an important consideration in assessing RL loss.•3D anatomic tooth models are appropriate alternatives for RSA measurement.