title: Stress distributions in human teeth modeled with a natural graded material distribution.
abstract: OBJECTIVE
  This study aimed to investigate how the structural stress distribution in human teeth could be affected by the presence of a graded material distribution often found in nature using the finite element (FE) method.
  
  
  METHODS
  Hydroxyapatite (HA) tablets with different densities were scanned using a Micro-CT scanner to obtain a relationship between the attenuation coefficient and the elastic modulus via the mineral density. Two maxillary premolars were scanned to provide the geometries and material distributions for constructing the FE models. Stress analyses were then performed to compare the stress distributions between the models with uniform material properties and those with a graded material layout.
  
  
  RESULTS
  The attenuation coefficients and densities of the HA tablets measured ranged from 109.77 to 175.01cm(-1) and 0.99 to 1.54gcm(-3), respectively. A linear relationship was found between them and applied to the premolars to derive the elastic modulus via the mineral density. Stress analysis showed that, with a graded material layout, the peak maximum principal stress in the enamel was reduced by about 50% and the overall stress distribution was more uniform. Along the DEJ, two stress peaks were found near the dentin horns, but again they were much lower in magnitude in the models with a graded material distribution.
  
  
  CONCLUSIONS
  The results from this study support the hypothesis that the material layout in human enamel is optimized for distributing the external load evenly. They also point to the importance of taking into account the graded material distribution in nature when performing stress analysis for tooth structures.
authors.affiliation: Minnesota Dental Research Center for Biomaterials and Biomechanics, School of Dentistry, University of Minnesota, MN, USA. Electronic address: chen1954@umn.edu.
authors.forename: YungChung
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Minnesota Dental Research Center for Biomaterials and Biomechanics, School of Dentistry, University of Minnesota, MN, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Fok
mesh_terms: D000293:Adolescent; D001641:Bicuspid / Q000737:chemistry / Q000502:physiology*; D001696:Biomechanical Phenomena; D003743:Dental Enamel / Q000737:chemistry / Q000502:physiology; D003804:Dentin / Q000737:chemistry / Q000502:physiology; D017886:Durapatite / Q000737:chemistry*; D055119:Elastic Modulus; D020342:Finite Element Analysis; D006801:Humans; D008422:Materials Testing; D008903:Minerals / Q000737:chemistry; D008953:Models, Anatomic; D008954:Models, Biological; D013314:Stress, Mechanical; D014074:Tooth Calcification / Q000502:physiology; D055114:X-Ray Microtomography / Q000379:methods
chemical_list: D008903:Minerals; D017886:Durapatite
keywords: Finite element analysis; Graded material distribution; Tooth structure