Application of modified superposition model to viscoelastic behavior of periodontal ligament

J. Hazrati, F. Ghalichi, B. Mirzakouchaki

Division of Biomechanics, Mechanical Engineering Department, Sahand University of Technology, Tabriz, Iran..
Division of Orthodontics, School Of Dentistry, Tabriz University of Medical Sciences, Tabriz, Iran.

DOI: 10.4236/jbise.2008.13033                

Abstract

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.

Keywords

periodontal ligament, viscoelasticity, modified superposition method, stress relaxation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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.