Mathematical Model for Tissue Engineered Intervertebral Disc as a Saturated Porous Media MOHAMMAD NIKKHOO 1,* , MOHAMMAD HAGHPANAHI 1 , HABIBALLAH PEIROVI 2 , JALAL-EDIN GHANAVI 3 1 Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, IRAN 2 Nanomedicine and Tissue Engineering Research Center, Tehran, IRAN 3 National Research Institute of Tuberculosis and Lung Disease, Tehran, IRAN Abstract: - Success of the intervertebral disc tissue engineering approach depends on the restoration of its mechanical function and proposing a suitable model as an infrastructure for a better understanding of its mechanobiological behavior is a major requirement. This paper presents a finite element formulation including the chemical behaviour, inertia terms and viscoelasticity which can be used in our predicted tissue engineering procedure as a powerful model. After derivation of the governmental equations, implicit time integration schemes are applied to solve the nonlinear equations. The formulation accuracy and convergence for 1D case are examined with Sun's and Simon's analytical solution and Drost's experimental Data. It is shown that the mathematical model is in excellent agreement and can be used for simulation of the IVD response under different types of mechanical and electrochemical loading conditions. Key-Words: - Mechanobiology, Finite element, Porous media, Intervertebral disc, Tissue engineering 1 Introduction The intervertebral disc can be described as a charged, hydrated and permeable material which is comprised largely of collagen and elastic fibers embedded in a proteoglycan gel to form a solid matrix. As an infrastructure for studying the biomechanics of the intervertebral disc tissue engineering, it is so vital to propose suitable mechanobiological models. During the last decade, several researches have been proposed the multiphasic computational models to study mechanics of the soft tissues (such as articular cartilage, intervertebral disc, vascular vessel and skin). Mow et al. [1] first presented the biphasic theory in which the material was modeled as a mixture of two distinct phases and later it was extended by Spilker et al. [2]. On the basis of the Biot theorem, Simon et al. [3, 4] considered the soft tissues in the spinal motion segment as poroelastic materials which was later extended by Yang et al.[5]. Since significant deformations resulting from loading and inherent swelling mechanisms in the soft tissues have been described, Mow et al. [6] developed a triphasic model to consider the effects of swelling and transport in descriptions of soft tissue mechanics. Then Gu et al. [7] and Sun et al. [8] extended triphasic theory to model the mechano- electrochemical behaviors of charged hydrated soft tissues containing electrolytes. Later, Simon et al. [9, 10] and Laible et al. [11, 12] extended poroelastic model to poroelastic transport swelling model which includes chemical effects. It is so clear that all these models tried to incorporate the features of actual biological tissue but there are some limitations that should be improved for better understanding of the intervertebral disc biomechanics. Except for the model of Simon [3, 4] and Yang [5], the previous models are quasi static which means that the inertia is ignored. Actually, the inertia terms can be significant when the external forces vary rapidly. Also the construction of biological tissue such as collagen fibers and proteoglycan gel are highly viscoelastic, but only the models of Huang [13], Suh [14], and Yang [5] considered this point. Additionally, some limited models considered the chemical and electrical effects (Sun [8], Simon [9, 10] and Iatridis [12]), which is so important for us in our predicted tissue engineering procedure. So based on the work of Sun, Simon and Yang, this paper presents a novel mixed finite element formulation including the chemical behaviour, inertia terms and viscoelasticity which can simulate intervertebral disc response regarding to the different types of mechanical, electrical and physicochemical loading conditions. 2 Mechanobiological Model This mechanobiological model considers a charged hydrated tissue engineered intervertebral disc as a mixture consisting of: (1) a porous, permeable, charged solid phase; (2) an incompressible fluid phase; and (3) ion phase with two ion species, i.e., 3rd WSEAS International Conference on APPLIED and THEORETICAL MECHANICS, Spain, December 14-16, 2007 197