References
- M. Bergomi, J. Cugnoni, M. Galli, J. Botsis, U.C. Belser and H.W.A. Wiskott. Hydro-mechanical coupling in the periodontal ligament: A porohyperelastic finite element model. J. Biomech., 44(1):34–38, 2011. http://dx.doi.org/10.1016/j.jbiomech.2010.08.019.
- S.M. Bosiakov and G.I. Mikhasev. The analytical model of the initial translational displacements of the tooth root in the linear elastic periodontal ligament. Mech. Mach. Mechan. Mat., 3(28):68–72, 2014. (in Russian)
- S.M. Bosiakov and K.S. Yurkevich. Mathematical modelling of initial tooth root displacements in bone tissue under action of instant static loading. Russ. J. Biomech., 15:22–29, 2011.
- C. Bourauel, D. Vollmer and A. Jager. Application of bone remodeling theories in the simulation of orthodontic tooth movements. J. Orofac. Orthop., 61(4):266–279, 2000. http://dx.doi.org/10.1007/s000560050012.
- R. Clement, J. Schneider, H.-J. Brambs, A. Wunderlich, M. Geiger and F.G. Sander. Quasi-automatic 3d finite element model generation for individual singlerooted teeth and periodontal ligament. Comp. Meth. Progr. Biomed., 73:135–144, 2004. http://dx.doi.org/10.1016/S0169-2607(03)00027-0.
- M. Cronau, D. Ihlow, D. Kubein-Meesenburg, J. Fanghanel, H. Dathe and H. Nagerl. Biomechanical features of the periodontium: An experimental pilot study in vivo. Am. J. Orthod. Dentofacial Orthop., 129:599.e13–599. e21, 2006. http://dx.doi.org/10.1016/j.ajodo.2005.11.030.
- C. Dorow and F.G. Sander. Development of a model for the simulation of orthodontic load on lower first premolars using the finite element method. J. Orofac. Orthop., 66:208–218, 2005. http://dx.doi.org/10.1007/s00056-005-0416-5.
- O.I. Dudar, I.P. Kosterina, L.V. Mayorova and N.A. Fateeva. Distribution of masticatory load over dental arch during central occlusion. Russ. J. Biomech., 13:56–62, 2009.
- T.S. Fill, J.P. Carey, R.W. Toogood and P.W. Major. Experimentally determined mechanical properties of, and models for, the periodontal ligament: Critical review of current literature. J. Dent. Biomech., 2(1), 2011. http://dx.doi.org/10.4061/2011/312980.
- T.S. Fill, R.W. Toogood, P.W. Major and J.P. Carey. Analytically determined mechanical properties of, and models for the periodontal ligament: Critical review of literature. J. Biomech., 45(1):9–16, 2012. http://dx.doi.org/10.1016/j.jbiomech.2011.09.020.
- P.D. Jeon, P.K. Turley, H.B Moon and K. Ting. Analysis of stress in the periodontium of the maxillary first molar with a three-dimensional finite element model. Am. J. Orthod. Dentofacial Orthop., 115:267–274, 1999. http://dx.doi.org/10.1016/S0889-5406(99)70328-8.
- R.S. Masella and M. Meister. Current concepts in the biology of orthodontic tooth movement. Am. J. Orthod. Dentofacial Orthop., 129(4):458–468, 2006. http://dx.doi.org/10.1016/j.ajodo.2005.12.013.
- G.I. Mikhasev, S. Ermochenko and M. Bornitz. On the strain-stress state of the reconstructed middle ear after inserting a malleusincus prosthesis. Math. Med. Biol., 27(4):289–312, 2010. http://dx.doi.org/10.1093/imammb/dqp020.
- H. Nagerl and D. Kubein-Meesenburg. Discussion: A fem study for the biomechanical comparison of labial and palatal force application on the upper incisors. Fortschritte der Kieferorthopadie, 54:229–230, 1993. doi: 10.1007/BF02341469
- A. Nanci and A.R. Ten Cate. Periodontium. Mosby Elsevier, St. Louis, 2008.
- A.N. Natali, P.G. Pavan, B.A. Schrefler and S. Secchi. A multi-phase media formulation for biomechanical analysis of periodontal ligament. Meccanica, 37(4–5):407–418, 2002. http://dx.doi.org/10.1023/A:1020895906292.
- A.N. Natali, P.G. Pavan, C. Venturato and K. Komatsu. Constitutive modeling of the non-linear visco-elasticity of the periodontal ligament. Comp. Meth. Prog. Biomed., 104(2):193–198, 2011. http://dx.doi.org/10.1016/j.cmpb.2011.03.014.
- R.J. Nikolai and J.W. Schweiker. Investigation of root-periodontium interface stresses and displacements for orthodontic application. Exp. Mech., 12(9):406–413, 1972. http://dx.doi.org/10.1007/BF02318551.
- G. Pietrzak, A. Curnier, J. Botsis, S. Scherrer, A. Wiskott and U. Belser. A nonlinear elastic model of the periodontal ligament and its numerical calibration for the study of tooth mobility. Comput. Meth. Biomech. Biomed. Eng., 5:91–100, 2002. http://dx.doi.org/10.1080/10255840290032117.
- C.G. Provatidis. A comparative fem-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Med. Eng. Phys., 22:359–370, 2000. http://dx.doi.org/10.1016/S1350-4533(00)00055-2.
- C.G. Provatidis. An analytical model for stress analysis of a tooth in translation. Int. J. Eng. Sci., 39:1361–1381, 2001. http://dx.doi.org/10.1016/S0020-7225(00)00098-7.
- L. Qian, M. Todo, Y. Morita, Y. Matsushita and K. Koyano. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dent. Mat., 25(10):1285–1292, 2009. http://dx.doi.org/10.1016/j.dental.2009.03.014.
- Y. Qian, Y. Fan, Zh. Liu and M. Zhang. Numerical simulation of tooth movement in a therapy period. Clin. Biomech., 23(Supplement 1):S48–S52, 2008. http://dx.doi.org/10.1016/j.clinbiomech.2007.08.023.
- J.S. Rees and P.H. Jacobsen. Elastic modulus of the periodontal ligament. Biomat., 18(14):995–999, 1997. http://dx.doi.org/10.1016/S0142-9612(97)00021-5.
- S. Reimann, L. Keilig, A. Jager and C. Bourauel. Biomechanical finite-element investigation of the position of the centre of resistance of the upper incisors. Eur. J. Orthod., 29:219–224, 2007. http://dx.doi.org/10.1093/ejo/cjl086.
- A. Van Schepdael, L. Geris and J. Van der Sloten. Analytical determination of stress patterns in the periodontal ligament during orthodontic tooth movement. Med. Eng. Phys., 35:403–410, 2013. http://dx.doi.org/10.1016/j.medengphy.2012.09.008.
- K. Tanne, T. Nagataki, Y. Inoue, M. Sakuda and C. J. Burstone. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am. J. Orthod. Dentofacial Orthop., 100:66–71, 1991. http://dx.doi.org/10.1016/0889-5406(91)70051-W.
- S.P. Timoshenko and I.N. Goodier. Theory of Elasticity. McGraw-Hill Book Co., New York, 1970.
- S.R. Toms, J.E. Lemons, A.A. Bartolucci and A.W. Eberhardt. Nonlinear stressstrain behavior of periodontal ligament under orthodontic loading. Am. J. Orthod. Dentofacial Orthop., 122(2):174–179, 2002. http://dx.doi.org/10.1067/mod.2002.124997.
- R.F. Viecilli, A. Budiman and C.J. Burstone. Axes of resistance for tooth movement: Does the center of resistance exist in 3-dimensional space? Am. J. Orthod. Dentofacial Orthop., 143:163–172, 2013. http://dx.doi.org/10.1016/j.ajodo.2012.09.010.
- D. Vollmer, C. Bourauel, K. Maier and A. Jager. Determination of the centre of resistance in an upper human canine and idealized tooth model. Eur. J. Orthod., 21:633–648, 1999. http://dx.doi.org/10.1093/ejo/21.6.633.
- A. Ziegler, L. Keilig, A. Kawarizadeh, A. Jager and C. Bourauel. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. Eur. J. Orthod., 27:333–339, 2005. http://dx.doi.org/10.1093/ejo/cji020.