A Multi-Phase Media Formulation for Biomechanical Analysis of Periodontal Ligament*

A numerical analysis of the biomechanical response of the periodontal ligament is presented. A multi-phase media formulation is developed for representing soft tissue constitutive models, and implemented in a specific finite element code. It is possible to simulate the presence of liquid phase permeating the extra-cellular material and to interpret the consequent time-dependent behaviour due to the fluid flux through periodontal ligament. The analysis of the mobility of human upper incisor, under the application of short time transversal forces, is reported. The numerical results are compared with in vivo experimental data. The agreement of different approaches confirms the effectiveness of the proposed model for investigation of the biomechanical behaviour of periodontal ligament under application of low magnitude forces, and represents the basis for the definition of a general multi-phase constitutive model.

[1]  B. Schrefler,et al.  The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media , 1998 .

[2]  J S Wu,et al.  Clarification of the mechanical behaviour of spinal motion segments through a three-dimensional poroelastic mixed finite element model. , 1996, Medical engineering & physics.

[3]  V. Kafka.  On hydraulic strengthening of bones. , 1993, Journal of biomechanics.

[4]  Hiroyuki Ishikawa,et al.  P011 The relationships between tissue response and stress distribution in the periodontal ligament during orthodontic tooth movement , 1998 .

[5]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[6]  V C Mow,et al.  A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. , 1992, Journal of biomechanical engineering.

[7]  W D van Driel,et al.  Time-dependent mechanical behaviour of the periodontal ligament , 2000, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[8]  R. Dillaman,et al.  Fluid movement in bone: theoretical and empirical. , 1991, Journal of biomechanics.

[9]  K. Komatsu,et al.  Mechanical responses of the periodontal ligament in the transverse section of the rat mandibular incisor at various velocities of loading in vitro. , 1993, Journal of biomechanics.

[10]  A. Sanders,et al.  Stiffening of the femoral head due to inter-trabecular fluid and intraosseous pressure. , 1991, Journal of biomechanical engineering.

[11]  E. Dill,et al.  An Introduction to the Mechanics of Solids , 1972 .

[12]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[13]  A Shirazi-Adl,et al.  A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression. , 2000, Journal of biomechanics.

[14]  B. K. B. Berkovitz,et al.  The Periodontal ligament in health and disease , 1982 .

[15]  B. Schrefler,et al.  A Porous Media Approach to Finite Deformation Behaviour in Soft Tissues. , 1999, Computer methods in biomechanics and biomedical engineering.

[16]  W M Lai,et al.  A triphasic theory for the swelling and deformation behaviors of articular cartilage. , 1991, Journal of biomechanical engineering.

[17]  R. Spilker,et al.  Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I - Alternate Formulations. , 1997, Computer methods in biomechanics and biomedical engineering.

[18]  P H Jacobsen,et al.  Elastic modulus of the periodontal ligament. , 1997, Biomaterials.

[19]  D. Winter,et al.  A comparison of three muscle pennation assumptions and their effect on isometric and isotonic force. , 1991, Journal of biomechanics.

[20]  R. Spilker,et al.  Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues , 1998 .

[21]  A Shirazi-Adl,et al.  Poroelastic creep response analysis of a lumbar motion segment in compression. , 1996, Journal of biomechanics.

[22]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[23]  C S Lear,et al.  Modeling the lateral movement of teeth. , 1976, Journal of biomechanics.

[24]  L. Blankevoort,et al.  Time dependent displacement of the tooth in response to orthodontic forces , 1998 .

[25]  S L Woo,et al.  Application of the u-p finite element method to the study of articular cartilage. , 1991, Journal of biomechanical engineering.

[26]  J. Z. Zhu,et al.  The finite element method , 1977 .