Application of modified superposition model to viscoelastic behavior of periodontal ligament

DOI: 10.4236/jbise.2008.13033   PDF   HTML     5,319 Downloads   10,044 Views   Citations


The periodontal ligament (PDL) is a soft bio-logical tissue which shows a strongly nonlinear and time dependent mechanical behavior. Re-cent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be de-scribed well by the separable quasi linear vis-coelasticity theory which is usually used in tis-sue biomechanics. Therefore, PDL requires a more general description which considers this nonlinearity and time dependency. The purpose of this study was to model strain dependent stress relaxation behavior of PDL using modi-fied superposition method. It is shown herein that modified superposition method describes viscoelastic nonlinearties well and shows a good compatibility with available experimental PDL data. Hence, the modified superposition model is suggested to describe periodontal ligament data, because it can suitably demon-strate both elastic nonlinearity and strain-dependent stress relaxation behavior of PDL.

Share and Cite:

Hazrati, J. , Ghalichi, F. and Mirzakouchaki, B. (2008) Application of modified superposition model to viscoelastic behavior of periodontal ligament. Journal of Biomedical Science and Engineering, 1, 195-199. doi: 10.4236/jbise.2008.13033.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] B.KB. Berkovitz, B.J. Moxham, et al. (Eds.).( 1982) The Perio-dontal Ligament in Health and Disease. Pergamon Press, Elms-ford, NY.
[2] S.R. Toms, G.J. Dakin, J.E. Lemons, A.W. Eberhardt, (2002) Quasi linear viscoelastic behavior of the human periodontal ligament. Journal of Biomechanics. 35, 1411–1415.
[3] Nishihira, M., Yamamoto, K., Sato, Y., Ishikawa, H., Natali, A.N. (2003) Mechanics of periodontal ligament. In: Natali, A.N. (Ed.), Dental Biomechanics. Taylor & Francis, London, 20–34.
[4] C. Dorow, N. Krstin, F.G Sander. (2002) Determination of the Mechanical Properties of the Periodontal Ligament in a Uniaxial Tensional Experiment. Journal of Orofacial Orthopedics, 64, 100–7.
[5] A.N. Natali, E.L. Carniel, P.G. Pavan, C. Bourauel, A. Ziegler, L. Keilig, (2006) Experimental–numerical analysis of minipig’s multi-rooted teeth. Journal of Biomechanics, 37, article in press, 1-8.
[6] A. Kawarizadeh, C. Bourauel, D. Zhang, W. Gotz, A. Jager, (2004) Correlation of stress and strain profiles and the distribution of os-teoclastic cells induced by orthodontic loading in rat. European Journal of Oral Science, 112, 140–147.
[7] P. Provenzano, R. Lakes, R. Vanderby, (2002) Application of nonlinear viscoelastic models to describe ligament behavior. Bio-mechan Model Mechanobiol. 1, 45–57.
[8] G.A. Ateshian, W.H. Warden, J.J. Kim, R.P. Grelsamer, V.C. Mow, (1997) Finite Deformation Biphasic Material Properties of Bovine Articular Cartilage From Confined Compression Experiments. J. Biomech, 30, 1157–1164.
[9] J.J. Garc齣a, D.H. Cortes, A nonlinear viscohyperelastic model for articular cartilage. Journal of Biomechanics. 2006; 39, 2991?998.
[10] A.N. Natali, E.L. Carniel, P.G. Pavan, A. Gasparetto, F.G. Sander, C. Dorow, M. Geiger. (2006) Constitutive formulation for numeri-cal analysis of visco-hyperelastic damage phenomena in soft bio-logical tissues. 8th Biennial ASME Conference on Engineering Systems Design and Analysis. Proceedings of ESDA.
[11] K. Komatsu, C. Sanctuary, T. Shibata, A. Shimada, J. Botsis. (2007) Stress–relaxation and microscopic dynamics of rabbit periodontal ligament. Journal of Biomechanics. 40, 634–644.
[12] Fung, Y.C. Biomechanics, (1993) Mechanical Properties of Living Tissues, second ed. Springer, New York.
[13] A.N. Natali, P.G. Pavan, E.L. Carniel, C. Dorow, (2004) Visco-elastic response of the periodontal ligament: an experimental-numerical analysis. Connective Tissue Research, 45, 222–230.
[14] J.E. Bischoff, E.M. Arruda, K. Grosh. (2004) A rheological net-work model for the continuum anisotropic and viscoelastic behav-ior of soft tissue. Biomechanics Model Mechanobiol, 3, 56–65.
[15] M. Pini, H.W.A. Wiskott, S.S. Scherrer, J. Botsis, U.C. Belser, (2002) Mechanical characterization of bovine periodontal liga-ment. Journal of Periodontal Research, 37, 237–244.
[16] C. Dorow, N. Krstin, F.G. Sander. (2001) Experiments to Deter-mine the Material Properties of the Periodontal Ligament. Journal of Orofacial Orthopedics, 63, 94–104.
[17] Findley, W.N., Lai, J.S., Onaran, K. (1976) Creep and relaxation of nonlinear viscoelastic materials. Dover, NewYork.
[18] Lakes, R.S., (1998) Viscoelastic solids. CRC Press, New York.
[19] M. Pini, P. Zysset, J. Botsis, R. Contro, (2004) Tensile and com-pressive behaviour of the bovine periodontal ligament. Journal of Biomechanics, 37, 111–119.
[20] P. Provenzano, R. Lakes, T. Keenan, R. Vanderby, (2001) Nonlin-ear ligament viscoelasticity. Annals of Biomedical Engineering. 29, 908–914.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.