Document Type : Full Research Paper

Authors

1 Associate Professor, Biomechanics Research Lab, Mechanical Engineering School, Iran University of Science and Technology

2 PhD Candidate, Biomechanics Research Lab, Mechanical Engineering School, Iran University of Science and Technology

3 Nonomedicine and Tissue Engineering Research Center, Shahid Beheshti University of Medical Science and Health Services

10.22041/ijbme.2008.13458

Abstract

According to mechanobilogical studies as an infrastructure for tissue engineering researches, this paper presents a triphasic finite element modeling of intervertebral discs such a hydrated porous soft tissue. First, the governmental equations were derived on the basis of the laws of continuum mechanics. Then the standard Galerkin weighted residual method was used to form the finite element model. The implicit time integration schemes were applied to solve the nonlinear equations. The formulation accuracy and convergence for one dimensional case were examined with Simon's and Sun's analytical solutions and also Drost's experimental Data. It was shown that the mathematical model is in excellent agreement and has the capability to simulate the intervertebral disc response under different types of mechanical and electrochemical loading conditions. Finally, to have a short review of the capability of the model, a homogenous two dimensional version of the model was applied to simulate the response of a simple sagittal slice of the intervertebral disc. 

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[1]     Mow V.C., Kuei S.C., Lai W.M., Armstrong C.G., Biphasic creep and stress relaxation of articular cartilage: Theory and experiments; Journal of Biomechanical Engineering; 1980; 102: 73-84.
[2]     Spilker R.L., Suh J.K., Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissue, Computers & Structures; 1990; 35; No. 4:425-439.
[3]     Suh J.K., Spilker R.L., Holmes M.H., A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation; International Journal for Numerical Methods in Engineering; 1991; 32: 1411-1439.
[4]     Suh J.K., Bai S.; Finite element formulation of biphasic poroviscoelastic model for articular cartilage; Journal of Biomechanical Engineering; 1998; 120:195- 201.
[5]     Suh J.K., DiSilvestro M.R., Biphasic poroviscoelastic behavior of hydrated biological soft tissue; Journal of Applied Mechanics; 1999; 66: 528-535.
[6]     Simon B.R., Wu J.S.S., Carlton M.W., Evans J.H., Kazarian L.E., Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disc; Journal of Biomechanical Engineering; 1985; 107: 327-335.
[7]     Simon B.R., Wu J.S.S., Carlton M.W., Poroelastic dynamic structural models of Rhesus spinal motion segments; Spine; 1985; 10: 494-507.
[8]     Yang Z., Smolinsky P.; Dynamic finite element modeling of poroviscoelastic soft tissue; Computer Methods in Biomechanics and Biomedical Engineering; 2006; 9: 7-16.
[9]     Lai W.M., Hou J.S., Mow V.C., A triphasic theory for the swelling and deformation behavior of articular cartilage; Journal of Biomechanical Engineering; 1991; 113: 245-258.
[10] Gu W.Y., Lai W.M., Mow V.C., A mixture theory for charged-hydrated soft tissues containing multielectrolytes: passive transport and swelling behaviors; Journal of Biomechanical Engineering; 1998; 120: 169-180
[11] Sun D.N., Gu W.Y., Guo X.E., Lai W.M., and V.C. Mow; A mixed finite element formulation of Triphasic mechano electrochemical theory for charged, hydrated biological soft tissues; International Journal of Numerical Methods in Engineering; 1999; 45: 1375- 1402.
[12] Simon B.R., Multiphase poroelastic finite element models for soft tissue structures; Applied Mechanics Reviews; 1992; 45: 191-218.
[13] Simon B.R., Liable J.P., Yuan Y., Krag M.H.; A poroelastic finite element formulation including transport and swelling in soft tissue structures; Journal of Biomechanical Engineering; 1996; 118: 1-9.
[14] 14- Laible J.P., Pflaster D.S., Krag M.H., A poroelastic-swelling finite element model with application to the intervertebral disc; Spine; 1993; 18: 659-670.
[15] Iatridis J.C., Laible J.P., Krag M.H.; Influence of fixed charge density magnitude and distribution on the intervertebral disc: applications of a poroelastic and chemical electric (PEACE) model; Journal of Biomechanical Engineering; 2003; 125: 12-24.
[16] Nikkhoo M., Haghpanahi M., Peirovi H., Ghanavi J., Mathematical model for tissue engineered intervertebral disc as a saturated porous media; Proceedings of the 3rd International Conference on Applied and Theoretical Mechanics; Spain; 2007: 197- 201.
[17] Bathe K.J., Finite Element Procedure; Prentice Hall; 1995.
[18] Duffy D.G., Advanced Engineering Mathematics with MATLAB; Chapman and Hall/CRC; 2003.
[19] Drost M.R., Willems P., Snijders H., Huyghe J.M., Janssen J.D., Huson A., Confined Compression of Canine Annulus Fibrosus Under Chemical and Mechanical Loads; Journal of Biomechanical Engineering; 1995; 117: 390– 396.
[20] Matsumoto T., Kawakami M., Kuribayashi K., Takenaka T., Tamaki T., Cyclic mechanical stretch stress increases the growth rate and collagen synthesis of nucleus pulposus cells in vitro; Spine; 1999; 24:315- 319.