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Original Articles

Parametric Finite Element Analysis and Closed-formSolutions in Orthodontics

Pages 101-112 | Published online: 14 Sep 2010

  • Yettram , A.L. , Wright , K.W.J. and Houston , W.J.B. 1977 . Centre of rotation of a maxillary central incisor under orthodontic loading . British Journal of Orthodontics , 4 (1} ) : 23 – 27 .
  • Williams , K.R. and Edmundson , J.T. 1984 . Orthodontic tooth movement analysed by the Finite Element Method . Biomaterials , 5 : 347 – 351 .
  • Williams , K.R. , Edmundson , J.T. , Morgan , G. , Jones , M.L. and Richmond , S. 1986 . Orthodontic movement of a canine into an adjoining extraction site . Journal of Biomedical Engineering , 8 : 115 – 120 .
  • Matsuura , T. 1984 . Mechanical study on initial changes during canine retraction . Journal of Japanese Orthodontics Society , 43 : 33 – 52 .
  • Tanne , K. , Sakuda , M. and Burstone , C.J. 1987 . Three-dimensional finite element analysis for stress in the periodontal ligament by orthodontic forces . American Journal of Orthodontics and Dentofacial Orthopedics , 92 : 499 – 505 .
  • Tanne , K. , Koenig , H.A. and Burstone , C.J. 1988 . Moment to force ratios and the center of rotation . American Journal of Orthodontics and Dentofacial Orthopedics , 94 : 426 – 431 .
  • Tanne , K. , Nagataki , T. , Inoue , Y. , Sakuda , M. and Burstone , C.J. 1991 . Patterns of initial tooth displacements associated with various root lengths alveolar bone heights . American Journal of Orthodontics and Dentofacial Orthopedics , 100 : 66 – 71 .
  • Middleton , J. , Jones , M.L. and Wilson , A.N. 1990 . Three-dimensional analysis of orthodontic tooth movement . Journal of Biomedical Engineering , 12 : 319 – 327 .
  • McGuiness , N.J.P. , Wilson , A.N. , Jones , M.L. and Middleton , J. 1992 . A stress analysis of the periodontal ligament under various orthodontic loadings . European Journal of Orthodontics , 13 : 115 – 120 .
  • Cobo , J. , Sicilia , A. , Arguelles , J. , Suarez , D. and Vijande , M. 1993 . Initial stress induced in periodontal tissue with diverse degrees of bone loss by an orthodontic force: Tridimensional analysis by means of the finite element method . American Journal of Orthodontics and Dentofacial Orthopedics , 104 : 448 – 454 .
  • Jones , M.L. , Middleton , J. , Hickman , J. , Volp , C. and Knox , J. 1998 . The development of a validated model of orthodontic tooth movement of the maxillary central incisor in the human subject . Russian Journal of Biomechanics , 2 : 36 – 44 .
  • Provatidis , C. 1999 . Numerical estimation of the centres of rotation and resistance in orthodontic tooth movement . Computer Methods in Biomechanics and Biomedical Engineering , 2 : 149 – 156 .
  • Nikolai , R.J. and Schweiker , J.W. 1972 . Investigation of root-periodontium interface stresses and displacements for orthodontic application . Experimental Mechanics , 12 : 406 – 413 .
  • Caputo , A.A. , Chaconas , S.J. and Hayashi , R.K. 1974 . Photoelastic visualisation of orthodontic forces during canine retraction . American Journal of Orthodontics , 65 : 250 – 259 .
  • Pedersen , E. , Andersen , K. and Gjessing , P.E. 1990 . Electronic determination of centres of rotation produced by orthodontic force systems . European Journal of Orthodontics , 12 : 272 – 280 .
  • Burstone , C.J. and Pryputniewicz , R.J. 1980 . Holographic determination of centres of rotation produced by orthodontic forces . American Journal of Orthodontics , 77 : 396 – 409 .
  • Reitan , K. 1957 . Some factors determining the evaluation of force in orthodontics . American Journal of Orthodontics , 43 : 32 – 45 .
  • Picton , D.C.A. and Davies , W.I.R. 1967 . Dimensional changes in the periodontal membrane of monkeys due to horizontal thrusts applied to teeth . Archives of Oral Biology , 12 : 1635 – 1643 .
  • Rygh , P. 1974 . Elimination of hyalinized periodontal tissues associated with orthodontic tooth movement . Scandinavian Journal of Dental Research , 82 : 57 – 73 .
  • Rygh , P. 1977 . Orthodontic root resorption studied by electron microscopy . Angle Orthodontist , 47 : 1 – 66 .
  • Hong , R.K. 1990 . Effect of experimental tooth movement on the mechanical properties of the periodontal ligament in the rat maxillary molars . American Journal of Orthodontics and Dentofacial Orthopedics , 98 : 543 – 553 .
  • Provatidis , Ch. and Toutountzakis , N. 1998 . A critical review of older and contemporary applications of biomechanical methods in orthodontics . Hellenic Orthodontic Review , 1 : 27 – 49 .
  • Synge , J.L. 1933a . The tightness of the teeth, considered as a problem concerning the equilibrium of a thin elastic membrane . Philosophical Transactions Royal Society London , 231A : 435 – 477 .
  • Provatidis , Ch. and Kanarachos , A. 2000 . A boundary-type hydrodynamic analysis of tooth movement . Engineering Analysis with Boundary Elements , 24 (9} ) : 661 – 669 .
  • Synge , J.L. 1933b . The equilibrium of a tooth with a general conical root . Philosophical Magazine S.7 , 15 (101} ) : 969 – 996 .
  • Synge , J.L. 1937 . The equilibrium of a thin flat membrane of compressible material . Transactions Royal Society of Canada , 31 : 57 – 81 .
  • Hay , G.E. 1939a . The equilibrium of a thin compressible membrane . Canadian Journal of Research , 17 : 106 – 121 .
  • Hay , G.E. 1939b . The equilibrium of a thin compressible membrane with application to the periodontal membrane . Canadian Journal of Research , 17 (7} ) : 123 – 140 .
  • Burstone , C.J. 1962 . “ The biomechanics of tooth movement . In: Vistas in orthodontics ” . In Philadelphia, Lea and Febiger Edited by: Kraus , B.S. and Riedel , R.A. 197 – 213 .
  • Christiansen , R.L. and Burstone , C.J. 1969 . Centers of rotation within the periodontal space . American Journal of Orthodontics , 55 (4} ) : 353 – 369 .
  • Haack , D.C. and Weinstein , S. 1963 . Geometry and mechanics as related to tooth movement studied by means of two-dimensional model . Journal of American Dental Association , 66 : 157 – 164 .
  • Nikolai , R.J. 1974 . Periodontal ligament reaction and displacements of a maxillary central incisor subjected to transverse crown loading . Journal of Biomechanics , 7 : 93 – 99 .
  • Davidian , E.J. 1971 . Use of a computer model to study the force distribution on the root of a maxillary central incisor . American Journal of Orthodontics , 59 : 581 – 588 .
  • Steyn , C.L. , Verwoerd , W.S. , van der Merwe , E.J. and Fourie , O.L. 1978 . Calculation of the position of the axis of rotation when single-rooted teeth are orthodontically tipped . British Journal of Orthodontics , 5 : 153 – 156 .
  • Sutcliffe , W.J. and Atherton , J.D. 1980 . The mechanics of tooth mobility . British Journal of Orthodontics , 7 : 171 – 178 .
  • Haack , D.C. and Heft , E.E. 1972 . An analysis of stresses in a model of the periodontal ligament . International Journal of Engineering Science , 10 : 1093 – 1106 .
  • Zienkiewicz , O.C. 1977 . The Finite Element Method , London : McGraw-Hill .
  • Smith , R.J. and Burstone , C.J. 1984 . Mechanics of tooth movement . American Journal of Orthodontics , 85 : 294 – 307 .
  • Provatidis , Ch. 1998 . “ Bone remodelling in orthodontics ” . In Computer Methods in Biomechanics and Biomedical Engineering--2 , Edited by: Middleton , J. , Jones , M.L. and Pande , G.M. 655 – 661 . Australia : Gordon and Breach Publishers .
  • Cameron , A. 1976 . Basic Lubrication Theory , Chichester : Ellis Horwood: John Wiley .
  • Hamrock , B.J. 1994 . Fundamentals of Fluid Film Lubrication , London : McGraw-Hill .
  • Timoshenko , S.P. and Goodier , J.N. 1970 . Theory of Elasticity , Tokyo : McGraw-Hill Kogakusha .
  • Wilson , A.N. , Middleton , J. and Jones , M.L. 1992 . “ The role of the periodontal ligament in bone remodelling ” . In Proc. Recent Advances in Computer Methods and Biomedical Engineering , Edited by: Middleton , J. , Jones , M.L. and Pande , G.N. 150 – 158 . Swansea : Publ. Books and Journals International .
  • Middleton , J. , Jones , M.L. and Wilson , A. 1996 . The role of the periodontal ligament in bone modeling: The initial development of a time-dependent finite element model . American Journal of Orthodontics and Dentofacial Orthopedics , 109 : 155 – 162 .
  • Atmaram , G.H. and Mohammed , H. 1980 . Estimation of physiological stresses with a natural tooth considering fibrous PDL structure . Journal of Dental Research , 60 : 873 – 877 .
  • Provatidis , Ch. 2001 . An analytical model for stress analysis of a tooth in translational . International Journal of Engineering Science , (in press}
  • Provatidis , Ch. 2000 . A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament . Medical Engineering and Physics , 22 (5} ) : 359 – 370 .
  • Burstone , C.J. , Pryputniewicz , R.J. and Bowley , W.W. 1978 . Holographic measurement of tooth mobility in three dimensions . J. Periodont. Res. , 13 : 283 – 294 .
  • Provatidis , Ch. Validation of analytical formulas during the intrusion of a central incisor using the Finite Element Method . 6th FEM Workshop in Biomechanics and Biomedical Engineering, CD Proceedings . July . pp. 19 – 20 . Germany : University of Ulm .
  • Provatidis , Ch. On the numerical estimation of tooth flexibilities . 4th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering . October , Lisbon. pp. 13 – 16 .

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