Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

References

• Anani Y, Alizadeh Y. 2011. Visco-hyperelastic constitutive law for modeling of foam's behavior. Mater Des. 32(5):2940–2948. doi:10.1016/j.matdes.2010.11.010.
   Web of Science ®Google Scholar
• Ashrafi H, Shariyat M. 2012. A mathematical approach for describing the time-dependent poisson's ratio of viscoelastic periodontal ligaments. J Biomed Phys Eng. 2(3):108–115.
   Google Scholar
• Bäker M, Shrot A. 2013. Inverse parameter identification with finite element simulations using knowledge-based descriptors. Comput Mater Sci. 69(3):128–136.
   Google Scholar
• Cattaneo PM, Dalstra M, Melsen B. 2005. The finite element method: a tool to study orthodontic tooth movement. J Dent Res. 84(5):428–433. doi:10.1177/154405910508400506.
   PubMed Web of Science ®Google Scholar
• Chui C, Kobayashi E, Chen X, Hisada T, Sakuma I. 2004. Combined compression and elongation experiments and non-linear modelling of liver tissue for surgical simulation. Med Biol Eng Comput. 42(6):787–798. doi:10.1007/BF02345212.
   PubMed Web of Science ®Google Scholar
• Dong-Xu L, Hong-Ning W, Chun-Ling W, Hong L, Ping S, Xiao Y. 2011. Modulus of elasticity of human periodontal ligament by optical measurement and numerical simulation. Angle Orthod. 81(2):229–236. doi:10.2319/060710-311.1.
   PubMed Web of Science ®Google Scholar
• Dorow C, Krstin N, Sander FG. 2002. Experiments to determine the material properties of the periodontal ligament. J Orofac Orthop. 63(2):94–104. doi:10.1007/s00056-002-0107-4.
   PubMedGoogle Scholar
• Field C, Ichim I, Swain MV, Chan E, Darendeliler MA, Li W, Li Q. 2009. Mechanical responses to orthodontic loading: a 3-dimensional finite element multi-tooth model. Am J Orthod Dentofacial Orthop. 135(2):174–181. doi:10.1016/j.ajodo.2007.03.032.
   PubMed Web of Science ®Google Scholar
• Fill TS, Carey JP, Toogood RW, Major PW. 2011. Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature. J Dent Biomech. 31(8):1–7.
   Google Scholar
• Fill TS, Toogood RW, Major PW, Carey JP. 2012. Analytically determined mechanical properties of, and models for the periodontal ligament: critical review of literature. J Biomech. 45(1):9–16. doi:10.1016/j.jbiomech.2011.09.020.
   PubMed Web of Science ®Google Scholar
• Fung YC. 1993. Biomechanics: mechanical properties of living tissues. New York: Springer.
   Google Scholar
• Gao Z, Lister K, Desai JP. 2010. Constitutive modeling of liver tissue: experiment and theory. Ann Biomed Eng. 38(2):505–516. doi:10.1007/s10439-009-9812-0.
   PubMed Web of Science ®Google Scholar
• Groves RB, Coulman SA, Birchall JC, Evans SL. 2012. Quantifying the mechanical properties of human skin to optimise future microneedle device design. Comput Methods Biomech Biomed Eng. 15(1):73–82. doi:10.1080/10255842.2011.596481.
   PubMed Web of Science ®Google Scholar
• Herbert EG, Pharr GM, Oliver WC, Lucas BN, Hay JL. 2001. On the measurement of stress-strain curves by spherical indentation. Thin Solid Films. 398–399:331–335. doi:10.1016/S0040-6090(01)01439-0.
   Web of Science ®Google Scholar
• Holzapfel GA. 2001. Nonlinear solid mechanics: a continuum approach for engineering. England: Lohn Wiley & Sons, Ltd.
   Google Scholar
• Komatsu K, Sanctuary C, Shibata T, Shimada A, Botsis J. 2007. Stress-relaxation and microscopic dynamics of rabbit periodontal ligament. J Biomech. 40(3):634–644. doi:10.1016/j.jbiomech.2006.01.026.
   PubMed Web of Science ®Google Scholar
• Limbert G, Middleton J, Laizans J, Dobelis M, Knets I. 2003. A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects. Comput Methods Biomech Biomed Eng. 6(5–6):337–345. doi:10.1080/10255840310001637572.
   PubMedGoogle Scholar
• Lin DC, Shreiber DI, Dimitriadis EK, Horkay F. 2009. Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models. Biomech Model Mechanobiol. 8(5):345–358. doi:10.1007/s10237-008-0139-9.
   PubMed Web of Science ®Google Scholar
• Martínez-Martínez F, Lago MA, Rupérez MJ, Monserrat C. 2013. Analysis of several biomechanical models for the simulation of lamb liver behaviour using similarity coefficients from medical image. Comput Methods Biomech Biomed Eng. 16(7):747–757.
   PubMed Web of Science ®Google Scholar
• Natali AN, Carniel EL, Pavan PG, Bourauel C, Ziegler A, Keilig L. 2007. Experimental-numerical analysis of minipig's multi-rooted teeth. J Biomech. 40(8):1701–1708. doi:10.1016/j.jbiomech.2006.08.011.
   PubMed Web of Science ®Google Scholar
• Natali AN, Pavan PG, Carniel EL, Dorow C. 2004. Viscoelastic response of the periodontal ligament: an experimental-numerical analysis. Connect Tissue Res. 45(4–5):222–230. doi:10.1080/03008200490885742.
   PubMed Web of Science ®Google Scholar
• Oyen ML. 2011. Nanoindentation of biological and biomimetic materials. Exp Tech. 37(1):1–15.
   Google Scholar
• Papadopoulou K, Hasan I, Keilig L, Reimann S, Eliades T, Jäger A, Deschner J, Bourauel C. 2013. Biomechanical time dependency of the periodontal ligament: a combined experimental and numerical approach. Eur J Orthod. 35(6):811–818. doi:10.1093/ejo/cjs103.
   PubMed Web of Science ®Google Scholar
• Penedo ND, Elias CN, Pacheco MCT, Gouvêa JP. 2010. 3D simulation of orthodontic tooth movement. Dent Press J Orthod. 15(5):98–108. doi:10.1590/S2176-94512010000500012.
   Google Scholar
• Provatidis CG. 2000. A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Med Eng Phys. 22(5):359–370. doi:10.1016/S1350-4533(00)00055-2.
   PubMed Web of Science ®Google Scholar
• Provatidis CG. 2001. An analytical model for stress analysis of a tooth in translation. Int J Eng Sci. 39:1361–1381. doi:10.1016/S0020-7225(00)00098-7.
   Web of Science ®Google Scholar
• Qian LH, Todo M, Morita Y, Matsushita Y, Koyano K. 2009. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dent Mater. 25(10):1285–1292. doi:10.1016/j.dental.2009.03.014.
   PubMed Web of Science ®Google Scholar
• Ren Y, Maltha JC, Van't Hof MA, Kuijpers-Jagtman AM. 2004. Optimum force magnitude for orthodontic tooth movement: a mathematic model. Am J Orthod Dentofacial Orthop. 125(1):71–77. doi:10.1016/j.ajodo.2003.02.005.
   PubMed Web of Science ®Google Scholar
• Roan E, Vemaganti K. 2011. Strain rate-dependent viscohyperelastic constitutive modeling of bovine liver tissue. Med Biol Eng Comput. 49(4):497–506. doi:10.1007/s11517-010-0702-2.
   PubMed Web of Science ®Google Scholar
• Sanctuary CS, Wiskott HWA, Justiz J, Botsis J, Belser UC. 2005. In vitro time-dependent response of periodontal ligament to mechanical loading. J Appl Physiol. 99(6):2369–2378. doi:10.1152/japplphysiol.00486.2005.
   PubMed Web of Science ®Google Scholar
• Schneider J, Geiger M, Sander FG. 2002. Numerical experiments on long-time orthodontic tooth movement. Am J Orthod Dentofacial Orthop. 121(3):257–265. doi:10.1067/mod.2002.121007.
   PubMed Web of Science ®Google Scholar
• Shibata T, Botsis J, Bergomi M, Mellal A, Komatsu K. 2006. Mechanical behavior of bovine periodontal ligament under tension-compression cyclic displacements. Eur J Oral Sci. 114(1):74–82. doi:10.1111/j.1600-0722.2006.00269.x.
   PubMed Web of Science ®Google Scholar
• Tanaka E, Inubushi T, Takahashi K, Shirakura M, Sano R, Dalla-Bona DA, Nakajima A, Van Eijden TM, Tanne K. 2007. Dynamic shear properties of the porcine molar periodontal ligament. J Biomech. 40(7):1477–1483. doi:10.1016/j.jbiomech.2006.06.022.
   PubMed Web of Science ®Google Scholar
• Toms SR, Dakin GJ, Lemons JE, Eberhardt AW. 2002. Quasi-linear viscoelastic behavior of the human periodontal ligament. J Biomech. 35(10):1411–1415. doi:10.1016/S0021-9290(02)00166-5.
   PubMed Web of Science ®Google Scholar
• Toms SR, Eberhardt AW. 2003. A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading. Am J Orthod Dentofacial Orthop. 123(6):657–665. doi:10.1016/S0889-5406(03)00164-1.
   PubMed Web of Science ®Google Scholar
• Veronda DR, Westmann RA. 1970. Mechanical characterization of skin—finite deformations. J Biomech. 3(1):111–124. doi:10.1016/0021-9290(70)90055-2.
   PubMed Web of Science ®Google Scholar
• Weiss JA, Maker BN, Govindjee S. 1996. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng. 135(1–2):107–128. doi:10.1016/0045-7825(96)01035-3.
   Web of Science ®Google Scholar
• Yan WJ, Jiao XH, Shao P, Cai W. 2012. Stress distribution in the mandibular central incisor and periodontal ligament while opening the bite: a finite element analysis. Biomed Res. 23(2):343–348.
   Google Scholar
• Yang LM, Shim VPW. 2004. A visco-hyperelastic constitutive description of elastomeric foam. Int J Impact Eng. 30(8-9):1099–1110. doi:10.1016/j.ijimpeng.2004.03.011.
   Web of Science ®Google Scholar
• Yoshida N, Koga Y, Peng CL, Tanaka E, Kobayashi K. 2001. In vivo measurement of the elastic modulus of the human periodontal ligament. Med Eng Phys. 23(8):567–572. doi:10.1016/S1350-4533(01)00073-X.
   PubMed Web of Science ®Google Scholar
• Zhurov AI, Limbert G, Aeschlimann DP, Middleton J. 2007. A constitutive model for the periodontal ligament as a compressible transversely isotropic visco-hyperelastic tissue. Comput Methods Biomech Biomed Eng. 10(3):223–235. doi:10.1080/13639080701314894.
   PubMedGoogle Scholar
• Ziegler A, Keilig L, Kawarizadeh A, Jäger A, Bourauel C. 2005. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. Eur J Orthod. 27(4):333–339. doi:10.1093/ejo/cji020.
   PubMed Web of Science ®Google Scholar