[en] A dedicated software package that allows simulation of tooth movement can lead to shortening of the treatment program in orthodontics. A first step in the development of this software is the modelling of the movement of a single tooth. Forces applied to the crown of the tooth are transmitted to the alveolar bone through the periodontal ligament, stretching, and compressing the ligament, eventually resulting in tooth movement. This paper presents an analytical model that predicts stresses and strains inside this ligament by approximating the shape of the root as an elliptic paraboloid. The model input consists of 2 material parameters and 4 geometrical parameters. To assess the accuracy of the model a finite element model (FEM) was constructed to compare the results and the influence of the eccentricity of the root was studied. The results show that the model is able to successfully describe the global behavior of the PDL and, except at a region near the alveolar crest, the differences between analytical and FEM results are small. In contrast to FEM, the analytical model does not require setting up a 3D-model and creating a mesh, allowing for significantly lower computational times and reducing cost when implementing in clinical practice.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Van Schepdael, An ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique
Geris, Liesbet ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique
Vander Sloten, Jos
Language :
English
Title :
Analytical determination of stress patterns in the periodontal ligament during orthodontic tooth movement.
Publication date :
2013
Journal title :
Medical Engineering and Physics
ISSN :
1350-4533
eISSN :
1873-4030
Publisher :
Elsevier, Oxford, United Kingdom
Volume :
35
Issue :
3
Pages :
403-10
Peer reviewed :
Peer Reviewed verified by ORBi
Commentary :
Copyright (c) 2012 IPEM. Published by Elsevier Ltd. All rights reserved.
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Krishnan V., Davidovitch Z. Cellular, molecular, and tissue-level reactions to orthodontic force. Am J Orthod Dentofacial Orthop 2006, 129(4):469.
Masella R.S., Meister M. Current concepts in the biology of orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2006, 129(4):458-468.
Wise G.E., King G.J. Mechanisms of tooth eruption and orthodontic tooth movement. J Dent Res 2008, 87(5):414-434.
Provatidis C.G. An analytical model for stress analysis of a tooth in translation. Int J Eng Sci 2001, 39:1361-1381.
Haack D.C., Haft E.E. An analysis of stresses in a model of the periodontal ligament. Int J Eng Sci 1972, 10:1093-1106.
Bourauel C., Vollmer D., Jäger A. Application of bone remodeling theories in the simulation of orthodontic tooth movements. J Orofac Orthop 2000, 61(4):266-279.
Burstone C.J., Pryputniewicz R.J. Holographic determination of centers of rotation produced by orthodontic forces. Am J Orthod 1980, 77(4):396-409.
Reimann S., Keilig L., Jager A., Bourauel C. Biomechanical finite-element investigation of the position of the centre of resistance of the upper incisors. Eur J Orthod 2007, 29(3):219-224.
Zhurov A.I., Limbert G., Aeschlimann D.P., Middleton J. A constitutive model for the periodontal ligament as a compressible transversely isotropic visco-hyperelastic tissue. Comput Methods Biomech Biomed Engin 2007, 10(3):223-235.
Provatidis C.G. A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Finite element method. Med Eng Phys 2000, 22(5):359-370.
Schneider J., Geiger M., Sander F.-G. Numerical experiments on long-time orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2002, 121(3):257-265.
Ziegler A., Keilig L., Kawarizadeh A., Jäger A., Bourauel C. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. Eur J Orthod 2005, 27(4):333-339.
Cattaneo P.M., Dalstra M., Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res 2005, 84(5):428-433.
Qian H., Chen J., Katona T.R. The influence of PDL principal fibers in a 3-dimensional analysis of orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2001, 120(3):272-279.
Pietrzak G., Curnier A., Botsis J., Scherrer S., Wiskott A., Belsen U. A nonlinear elastic model of the periodontal ligament and its numerical calibration for the study of tooth mobility. Comput Methods Biomech Biomed Engin 2002, 5(2):91-100.
Yoshida N., Koga Y., Peng C.L., Tanaka E., Kobayashi K. In vivo measurement of the elastic modulus of the human periodontal ligament. Med Eng Phys 2001, 23(8):567-572.
Poppe M., Bourauel C., Jager A. Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth a study of autopsy specimens and their conversion into finite element models. J Orofac Orthop 2002, 63(5):358-370.
Kawarizadeh A., Bourauel C., Jager A. Experimental and numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar specimens. Eur J Orthod 2003, 25(6):569-578.
Dong-Xu L., Hong-Ning W., Chun-Ling W., Hong L., Ping S., Xiao Y. Modulus of elasticity of human periodontal ligament by optical measurement and numerical simulation. Angle Orthod 2011, 81(2):229-236.
Parfitt G.J. Measurement of the physiological mobility of individual teeth in an axial direction. J Dent Res 1960, 39:608-618.
Jones M.L., Hickman J., Middleton J., Knox J., Volp C. A validated finite element method study of orthodontic tooth movement in the human subject. J Orthod 2001, 28(1):29-38.
Tanne K., Yoshida S., Kawata T., Sasaki A., Knox J., Jones M.L. An evaluation of the biomechanical response of the tooth and periodontium to orthodontic forces in adolescent and adult subjects. Br J Orthod 1998, 25(2):109-115.
De Bondt K., Van Schepdael A., Vander Sloten J. A mesh-based model for prediction of initial tooth movement. IFMBE Proc 2009, 22:2592-2595.
Kawarizadeh A., Bourauel C., Zhang D., Götz W., Jäger A. Correlation of stress and strain profiles and the distribution of osteoclastic cells induced by orthodontic loading in rat. Eur J Oral Sci 2004, 112(2):140-147.
Middleton J., Jones M., Wilson A. The role of the periodontal ligament in bone modeling: the initial development of a time-dependent finite element model. Am J Orthod Dentofacial Orthop 1996, 109(2):155-162.
Frost H.M. Vital biomechanics: proposed general concepts for skeletal adaptations to mechanical usage. Calcif Tissue Int 1988, 42(3):145-156.
Carano A., Siciliani G. Effects of continuous and intermittent forces on human fibroblasts in vitro. Eur J Orthod 1996, 18(1):19-26.
Kimoto S., Matsuzawa M., Matsubara S., Komatsu T., Uchimura N., Kawase T., Saito S. Cytokine secretion of periodontal ligament fibroblasts derived from human deciduous teeth: effect of mechanical stress on the secretion of transforming growth factor-beta 1 and macrophage colony stimulating factor. J Periodontal Res 1999, 34(5):235-243.
Wescott D.C., Pinkerton M.N., Gaffey B.J., Beggs K.T., Milne T.J., Meikle M.C. Osteogenic gene expression by human periodontal ligament cells under cyclic tension. J Dent Res 2007, 86(12):1212-1216.
Pinkerton M.N., Wescott D.C., Gaffey B.J., Beggs K.T., Milne T.J., Meikle M.C. Cultured human periodontal ligament cells constitutively express multiple osteotropic cytokines and growth factors, several of which are responsive to mechanical deformation. J Periodontal Res 2008, 43(3):343-351.
Yamaguchi M., Aihara N., Kojima T. RANKL increase in compressed periodontal ligament cells from root resorption. J Dent Res 2006, 85(8):751-756.
Natali A.N., Pavan P.G., Scarpa C. Numerical analysis of tooth mobility: formulation of a non-linear constitutive law for the periodontal ligament. Dent Mater 2004, 20(7):623-629.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.