Smart Search 

Title of the article



Bosiakov S.M., Candidate of Physical and Mathematical Sciences, Associate Professor, Associate Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
Mselati A.F., Postgraduate Student, Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus

In the section  
Year 2013 Issue 4 Pages 7-11
Type of article RAR Index UDK 539.3+612.311 Index BBK  

In present paper the simulation of the initial tooth translational displacement on the periodontal linearly elastic shell are performed. The geometric shape of the tooth root is described by equations of the circular hyperboloid. The outer surface of the periodontal ligament fixed in the dental alveoli. The inner surface of the periodontal ligament coincides with the outer surface of the tooth root. The relationship between displacement and deformation of periodont is defined taking into account the incompressibility of the periodontal tissues. The coordinates of the root center of resistance and the line a concentrated load angles of orientation action is defined for a of single"root tooth. A comparative analysis of the results of the calculation сoordinates of the centers of resistance on the basis of analytical and finite-element model.

Keywords finite-element model, properties of tissues, periodont, stress field, bony tissue, biology
  You can access full text version of the article
  • Abolmasov N.G., Abolmasov N.N. Ortodontija [Orthodontia]. Moscow, MEDpress-inform, 2008. 424 p.
  • Thurow R.C. Edgewise Orthodontics. Michigan, C.V. Mosby Company. 1982, pp. 351.
  • Viecilli R.F., Budiman A., Burstone J.C. Axes of resistance for tooth movement: Does the center of resistance exist in 3-dimensional space. Am. J. Orthod. Dentofacial Orthop., 2013, vol. 143, pp. 163-172.
  • Reimann S. [et al.]. Biomechanical finite-element investigation of the position of the centre of resistance of the upper incisors. European Journal of Orthodontics, 2007, vol. 29, pр. 219-224.
  • Jeon P.D. [et al.]. Analysis of stress in the periodontium of the maxillary first molar with a three-dimensional finite element model. Am. J. Orthod. Dentofacial Orthop., 1999, vol. 115, pр. 267-274.
  • Cronau M. [et al.]. Biomechanical features of the periodontium: An experimental pilot study in vivo. Am. J. Orthod. Dentofacial Orthop., 2006, vol. 129, pp. 599.e13–599.e21.
  • Ren Y., Jaap C., Kuijpers-Jagtman A. Optimum force magnitude for orthodontic tooth movement: a systematic literature review. Angle Orthod., 2003, vol. 73, pр. 86-92.
  • Tanne K. [et al.]. Patterns of initial tooth displacement associated with various root lengths and alveolar bone heights. Am. J. Dentofacial Orthop., 1991, vol. 100, pр. 66-71.
  • Ziegler A. [et al.]. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. European Journal of Orthodontics, 2005, vol. 27, pр. 333-339.
  • Bourauel C. [et al.]. Simulation of orthodontic tooth movements - a comparison of numerical models. J. Orofacial Orthoped, 1999, vol. 60, pр. 136-151.
  • Nagerl H., Kubein-Meesenburg D. Discussion: A FEM study for the biomechanical comparison of labial and palatal force application on the upper incisors. Fortschritte der Kieferorthopadie, 1993, vol. 54, pр. 229-230.
  • Nikolai R.J., Schweiker J.W. Investigation of Root-Periodontium Interface Stresses and Displacements for Orthodontic Application. Experimental Mechanics, 1972, pр. 406-413.
  • Dorow C., Sander F.G. Development of a model for the simulation of orthodontic load on lower first premolars using the finite element method. J. Orofac. Orthop., 2005, vol. 66, pр. 208-218.
  • 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. Orthodont, 2003, vol. 25, pр. 569-578.
  • Provatidis C.G. A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Med. Eng. Physics., 2000, vol. 22, pр. 359-370.
  • Jones M.L. [et al.]. A validated finite element method study of orthodontic tooth movement in the human subject. J. Orthod., 2001, vol. 28, pр. 29-38.
  • Cattaneo P.M., Dalstra M., Melsen B. The finite element method: a tool to study orthodontic tooth movement. J. Den.t Res., 2005, vol. 84, pр. 428-433.
  • Pietrzak G. [et al.]. A nonlinear elastic model of the periodontal ligament and its numerical calibration for the study of tooth mobility. Comput. Methods Biomech. Biomed. Eng., 2002, vol. 5, pр. 91-100.
  • Clement R. [et al.]. Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament. Comput. Methods Programs Biomed, 2004, vol. 73, pр. 135-144.
  • Provatidis C.G. An analytical model for stress analysis of a tooth in translation. Int. J. Eng. Sci., 2001, vol. 39, pр. 1361-1381.
  • Van Schepdael A., Geris L., Van der Sloten J. Analytical determination of stress patterns in the periodontal ligament during orthodontic tooth movement. Med. Eng. Phys., 2013, vol. 35, pр. 403-410.
  • Vollmer D. [et al.]. Determination of the center of resistance in an upper human canine and idealized tooth model. Eur. J. Orthod., 1999, vol. 21, pр. 633-648.
  • Naumovich S.A., Krushevskij A.E. Biomehanika sistemy “zub – periodont” [Biomechanics of the system "tooth - periodontal"]. Minsk, Jekonomich. tehnologii, 2000. 132 p.
  • Hohmann A. [et al.]. Influence of different modeling strategies for the periodontal ligament on finite element simulation results. Am. J. Orthod. Dentofacial. Orthop., 2011, vol. 139, pр. 775-783.
  • TetGen. A Quality Tetrahedral Mesh Generator and a 3D Delaunay Triangulator. Available at: (accessed 06 June 2013).
  • Dennis Roddeman ed. TOCHNOG User's manual — a free explicit/implicit FE program. Available at: (accessed: 06 June 2013).
  • Middleton J., Jones M., Wilson A. The role of the periodontal ligament in bone modeling: the initial development of a timedependent finite element model. Am. J. Orthod. Dentofacial Orthop., 1996, vol. 109, pр. 155-162.
  • De Pauw G., Dermaut L., De Bruyn H. The value of the centre of rotation in initial and longitudinal tooth and bone displacement. Eur. J. Orthodont., 2003, vol. 25, pр. 285-291.