title: Biomechanical investigation into the role of the periodontal ligament in optimising orthodontic force: a finite element case study.
abstract: OBJECTIVE
  This paper aimed to precisely locate centres of resistance (CRe) of maxillary teeth and investigate optimal orthodontic force by identifying the effective zones of orthodontic tooth movement (OTM) from hydrostatic stress thresholds in the periodontal ligament (PDL).
  
  
  METHODS
  We applied distally-directed tipping and bodily forces ranging from 0.075 N to 3 N (7.5 g to 300 g) onto human maxillary teeth. The hydrostatic stress was quantified from nonlinear finite element analysis (FEA) and compared with normal capillary and systolic blood pressure for driving the tissue remodelling. Two biomechanical stimuli featuring localised and volume-averaged hydrostatic stresses were introduced to describe OTM. Locations of CRe were determined through iterative FEA simulation.
  
  
  RESULTS
  Accurate locations of CRes of teeth and ranges of optimal orthodontic forces were obtained. By comparing with clinical results in literature, the volume average of hydrostatic stress in PDL was proved to describe the process of OTM more indicatively. The optimal orthodontic forces obtained from the in-silico modelling study echoed with the clinical results in vivo.
  
  
  CONCLUSIONS
  A universal moment to force (M/F) ratio is not recommended due to the variation in patients and loading points. Accurate computational determination of CRe location can be applied in practice to facilitate orthodontic treatment. Global measurement of hydrostatic pressure in the PDL better characterised OTM, implying that OTM occurs only when the majority of PDL volume is critically stressed. The FEA results provide new insights into relevant orthodontic biomechanics and help establish optimal orthodontic force for a specific patient.
authors.affiliation: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia.
authors.forename: Zhipeng
authors.initials: Z
authors.lastname: Liao
authors.affiliation: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia.
authors.forename: Junning
authors.initials: J
authors.lastname: Chen
authors.affiliation: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia.
authors.forename: Wei
authors.initials: W
authors.lastname: Li
authors.affiliation: Faculty of Dentistry, The University of Sydney, NSW 2006, Australia.
authors.forename: M Ali
authors.initials: MA
authors.lastname: Darendeliler
authors.affiliation: Faculty of Dentistry, The University of Sydney, NSW 2006, Australia.
authors.forename: Michael
authors.initials: M
authors.lastname: Swain
authors.affiliation: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia. Electronic address: qing.li@sydney.edu.au.
authors.forename: Qing
authors.initials: Q
authors.lastname: Li
mesh_terms: D001696:Biomechanical Phenomena; D016723:Bone Remodeling / Q000502:physiology; D003198:Computer Simulation; D003799:Dental Stress Analysis / Q000379:methods; D020342:Finite Element Analysis; D006801:Humans; D021621:Imaging, Three-Dimensional; D008437:Maxilla / Q000033:anatomy & histology / Q000502:physiology; D008954:Models, Biological; D016910:Orthodontic Brackets; D010513:Periodontal Ligament / Q000033:anatomy & histology / Q000502:physiology*; D015898:Tomography Scanners, X-Ray Computed; D014087:Tooth Movement Techniques / Q000379:methods*
keywords: Hydrostatic stress; Hyperelastic model; Optimal orthodontic forces; Periodontal interstitial fluid; Periodontal ligament