title: Biology of biomechanics: Finite element analysis of a statically determinate system to rotate the occlusal plane for correction of a skeletal Class III open-bite malocclusion.
abstract: BACKGROUND
  In the absence of adequate animal or in-vitro models, the biomechanics of human malocclusion must be studied indirectly. Finite element analysis (FEA) is emerging as a clinical technology to assist in diagnosis, treatment planning, and retrospective analysis. The hypothesis tested is that instantaneous FEA can retrospectively simulate long-term mandibular arch retraction and occlusal plane rotation for the correction of a skeletal Class III malocclusion.
  
  
  METHODS
  Seventeen published case reports were selected of patients treated with statically determinate mechanics using posterior mandible or infrazygomatic crest bone screw anchorage to retract the mandibular arch. Two-dimensional measurements were made for incisor and molar movements, mandibular arch rotation, and retraction relative to the maxillary arch. A patient with cone-beam computed tomography imaging was selected for a retrospective FEA.
  
  
  RESULTS
  The mean age for the sample was 23.3 ± 3.3 years; there were 7 men and 10 women. Mean incisor movements were 3.35 ± 1.55 mm of retraction and 2.18 ± 2.51 mm of extrusion. Corresponding molar movements were retractions of 4.85 ± 1.78 mm and intrusions of 0.85 ± 2.22 mm. Retraction of the mandibular arch relative to the maxillary arch was 4.88 ± 1.41 mm. Mean posterior rotation of the mandibular arch was -5.76° ± 4.77° (counterclockwise). The mean treatment time (n = 16) was 36.2 ± 15.3 months. Bone screws in the posterior mandibular region were more efficient for intruding molars and decreasing the vertical dimension of the occlusion to close an open bite. The full-cusp, skeletal Class III patient selected for FEA was treated to an American Board of Orthodontics Cast-Radiograph Evaluation score of 24 points in about 36 months by en-masse retraction and posterior rotation of the mandibular arch: the bilateral load on the mandibular segment was about 200 cN. The mandibular arch was retracted by about 5 mm, posterior rotation was about 16.5°, and molar intrusion was about 3 mm. There was a 4° decrease in the mandibular plane angle to close the skeletal open bite. Retrospective sequential iterations (FEA animation) simulated the clinical response, as documented with longitudinal cephalometrics. The level of periodontal ligament stress was relatively uniform (<5 kPa) for all teeth in the mandibular arch segment.
  
  
  CONCLUSIONS
  En-masse retraction of the mandibular arch is efficient for conservatively treating a skeletal Class III malocclusion. Posterior mandibular anchorage causes intrusion of the molars to close the vertical dimension of the occlusion and the mandibular plane angle. Instantaneous FEA as modeled here could be used to reasonably predict the clinical results of an applied load.
authors.affiliation: Professor emeritus of orthodontics and adjunct professor of mechanical engineering, Indiana University and Purdue University at Indianapolis, Indianapolis, Ind, and visiting professor, Department of Orthodontics, School of Dentistry, Loma Linda University, Loma Linda, Calif. Electronic address: werobert@iu.edu.
authors.forename: W Eugene
authors.initials: WE
authors.lastname: Roberts
authors.affiliation: Associate professor, Center for Dental Research and Department of Orthodontics, School of Dentistry, Loma Linda University, Loma Linda, Calif.
authors.forename: Rodrigo F
authors.initials: RF
authors.lastname: Viecilli
authors.affiliation: Founder and director, Beethoven Orthodontic Center, and Newton's A, Hsinchu, Taiwan.
authors.forename: Chris
authors.initials: C
authors.lastname: Chang
authors.affiliation: Associate professor, Departments of Orthodontics and Oral Facial Genetics, and Mechanical Engineering, Indiana University and Purdue University at Indianapolis, Indianapolis, Ind.
authors.forename: Thomas R
authors.initials: TR
authors.lastname: Katona
authors.affiliation: Chancellor, Indiana University and Purdue University at Indianapolis; executive vice president, and professor of mechanical engineering and informatics and computing, Indiana University, Indianapolis, Ind.
authors.forename: Nasser H
authors.initials: NH
authors.lastname: Paydar
mesh_terms: D000328:Adult; D001696:Biomechanical Phenomena; D001863:Bone Screws; D002508:Cephalometry / Q000379:methods; D003198:Computer Simulation; D054893:Cone-Beam Computed Tomography / Q000379:methods; D003724:Dental Arch / Q000473:pathology; D005260:Female; D020342:Finite Element Analysis; D005500:Follow-Up Studies; D006801:Humans; D007180:Incisor / Q000473:pathology; D008137:Longitudinal Studies; D008297:Male; D008313:Malocclusion, Angle Class III / Q000628:therapy*; D008334:Mandible / Q000473:pathology; D008437:Maxilla / Q000473:pathology; D008954:Models, Biological; D008963:Molar / Q000473:pathology; D024343:Open Bite / Q000628:therapy*; D052280:Orthodontic Anchorage Procedures / Q000295:instrumentation; D016382:Orthodontic Appliance Design; D012189:Retrospective Studies; D012399:Rotation; D014716:Vertical Dimension; D055815:Young Adult