title: Estimation of periodontal ligament's equivalent mechanical parameters for finite element modeling.
abstract: BACKGROUND
  Young's modulus (E) and Poisson's ratio (v) of the periodontal ligament are needed in a finite element analysis for investigating the biomechanical behavior of a tooth, periodontal ligament, and bone complex. However, large discrepancies in E (0.01-1,750 MPa) and v (0.28-0.49) were reported previously. The objective of this study was to narrow the ranges and to provide equivalent E and v pairs suitable for finite element modeling of a tooth, periodontal ligament, and bone complex by using a reported crown load-displacement relationship as the criterion.
  
  
  METHODS
  A 3-dimensional finite element model of a 3-tooth, periodontal ligament, and bone complex, consisting of a maxillary central incisor with 2 adjacent teeth, from a cone-beam computed tomography scan was created. The dimensions, constraints, and loading condition were kept similar to those reported in the human study. With the load applied to the crown, both v and E were adjusted independently, and the corresponding crown displacements were calculated. The resulting load-displacement curves were compared with those reported in the human study. The mean absolute displacement difference method was used to find the best fit. The E and v pairs that generated the minimum mean absolute displacement difference were identified.
  
  
  RESULTS
  The finite element model with 1 of the 3 E and v pairs (v = 0.35, E = 0.87 MPa; v = 0.4, E = 0.71 MPa; and v = 0.45, E = 0.47 MPa) simulated the tooth, periodontal ligament, and bone complex well. The mean absolute displacement differences were 0.0135, 0.0138, and 0.0138 mm, respectively; these are less than 8% of 0.175 mm, which was the crown displacement of the tooth, periodontal ligament, and bone complex under the load of 500 cN.
  
  
  CONCLUSIONS
  The E and v values close to the 3 pairs might be used for finite element modeling of the tooth, periodontal ligament, and bone complex.
authors.affiliation: Department of Mechanical Engineering, Indiana University Purdue University, Indianapolis, IN, USA.
authors.forename: Zeyang
authors.initials: Z
authors.lastname: Xia
authors.forename: Feifei
authors.initials: F
authors.lastname: Jiang
authors.forename: Jie
authors.initials: J
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D000539:Alveolar Process / Q000502:physiology; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D054893:Cone-Beam Computed Tomography / Q000379:methods; D003481:Cuspid / Q000502:physiology; D003799:Dental Stress Analysis; D055119:Elastic Modulus; D020342:Finite Element Analysis; D006801:Humans; D007180:Incisor / Q000502:physiology; D008437:Maxilla / Q000502:physiology; D055595:Mechanical Phenomena; D008954:Models, Biological; D010513:Periodontal Ligament / Q000502:physiology*; D014070:Tooth / Q000502:physiology; D019228:Tooth Crown / Q000502:physiology
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