- 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 .
Parametric Finite Element Analysis and Closed-formSolutions in Orthodontics
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.