Cell viability in intervertebral disc under various nutritional and dynamic loading conditions: 3d Finite element analysis
Introduction
The intervertebral disc (IVD) cells play a vital role in maintaining IVD health and function. Not only do cells synthesize the extracellular matrix (ECM), a significant structure helping sustain the mechanical force for the IVD in the spine, but they also synthesize catabolic molecules responsible for matrix breakdown. A disruption in the delicate balance between anabolic and catabolic activities leads to alteration of ECM, which is strongly correlated with structural remodeling, leading to tissue disorganization and, resultantly, IVD dysfunction and degeneration (Adams and Roughley, 2006, Bibby and Urban, 2004).
Degenerative changes to IVD include decreased nutrients levels, reduced cell density, reduced proteoglycan synthesis and alteration in collagen distribution (Maroudas, 1975, Maroudas et al., 1975, Oegema, 1993, Roberts et al., 1989, Urban and Roberts, 2003). Reduction of cell density in degenerated IVD tissue greatly diminishes the ability of the cells to synthesize and maintain the ECM structure, deterioration of which further exacerbates the degeneration of IVD tissues.
Due to the avascular nature of the tissue, essential nutrients (e.g., glucose and oxygen) are transported in and metabolic wastes (e.g., lactic acid) out of the tissue through the dense ECM by diffusion (mainly for small molecules) and convection (mainly for large molecules) from the peripheral and endplate vasculatures. Most of the nucleus pulposus (NP) cells rely on nutrients supplied through the cartilaginous endplate (CEP) route while the cells in the annulus fibrosus (AF) region are mainly nurtured through the annulus peripheral pathway (Bibby and Urban, 2004, Maroudas, 1975, Nachemson et al., 1970, Roberts et al., 1989, Urban and Roberts, 2003, Urban et al., 2000). Adequate nutrient supply has long been regarded as a crucial factor for maintaining normal activities of IVD cells (Bibby et al., 2002, Bibby and Urban, 2004, Horner and Urban, 2001, Nachemson et al., 1970, Oegema, 1993, Urban et al., 2000). It has been shown that the density of IVD cells is mainly dependent on glucose concentration (Bibby et al., 2002, Bibby and Urban, 2004, Horner and Urban, 2001, Jackson et al., 2011a, Shirazi-Adl et al., 2010).
In patients with cigarette smoking, malnutrition, or disorders like blood aneurysms, nutrition levels from the boundary vasculatures tends to decrease accordingly, which could lead to cell death and the development of IVD degeneration (Frymoyer et al., 1983, Gyntelbe, 1974, Holm and Nachemson, 1988). Mechanical loading has been shown not only to directly affect the intrinsic cellular activity (Huang et al., 2004, Kasra et al., 2003, Kroeber et al., 2005, MacLean et al., 2004, Ohshima et al., 1995, Wang et al., 2007, Wuertz et al., 2009), but also to influence the transport of nutrients through the ECM of the IVD tissue (Huang and Gu, 2007, Huang et al., 2012, Jackson et al., 2011b, Jackson et al., in press, Jackson et al., 2008, Malandrino et al., 2011, Yao and Gu, 2006, Yao and Gu, 2007, Yuan et al., 2009). Knowledge of changes in cell viability and metabolism in the IVD under various biological, physical and chemical signals is essential for understanding IVD degeneration.
However, it is difficult to study the complicated cellular environment in IVD in vivo experimentally. Numerical methods therefore have been increasingly used to investigate the transport of nutrients and cell viability within the IVDs (Huang and Gu, 2008, Huang et al., 2012, Jackson et al., 2011a, Sélard et al., 2003, Shirazi-Adl et al., 2010, Soukane et al., 2005, Soukane et al., 2007, Soukane et al., 2009). Shirazi-Adl et al. (2010) were the first to introduce a theoretical model to describe the coupling of cell viability and nutrition level in IVD. In this model (Shirazi-Adl et al., 2010), it is assumed that cell density varies instantaneously with glucose concentration. This model has also been used in our previous study on cell viability in IVD (Jackson et al., 2011a). One of the disadvantages of this model is that the resurrection of dead cells would occur when the glucose level recovers after falling below certain critical level for cell survival (e.g., 0.5 mM (Bibby and Urban, 2004)). Another problem of this model is that it cannot be used to analyze cell viability in a time-dependent process under dynamic situations. In fact, to date, there is no theoretical model that is capable of adequately describing the effect of nutrition levels on cell viability in a time-dependent manner.
Therefore, the objectives of this study were to develop (1) a novel constitutive model for IVD cell viability and (2) a comprehensive numerical tool to analyze and predict how cell viability was affected by the alteration in the extracellular microenvironment that results from disturbances in nutrition deprivation, degeneration, and dynamic loading in the realistic, human IVDs in a time-dependent manner.
Section snippets
Theoretical model
The IVD is assumed as a mixture of intrinsically incompressible elastic solid phase (denoted as ‘s’), water phase (denoted as ‘w’), and charged (Na+ and Cl−) and uncharged (glucose, oxygen, lactate) solute (denoted as ‘α’) phases. The governing equations for the mixture are summarized as follows (Ateshian, 2007, Gu et al., 1998, Lai et al., 1991):where σ is the total stress of the mixture, vs is the velocity of the solid phase, Jw is the volume flux of
Finite element analysis
A realistic, three-dimensional IVD geometry was generated based on an L2-L3 human disc (41 years old, male, healthy), see Fig. 2a. The IVD was modeled with three distinct regions: nucleus pulposus (NP), annulus fibrosus (AF), and cartilaginous endplate (CEP). Because of symmetry, only the upper right quarter of IVD (Fig. 2b) was modeled and meshed with 13,981 quadratic Lagrange tetrahedral elements (Fig. 2d) using COMSOL software (COMSOL 4.2a, COMSOL, Inc., Burlington, MA). The convergence
Results
The mechanical signals (stress, strain, fluid pressure, fluid flux, etc.), chemical signals (sodium and chloride ion concentrations, oxygen, glucose, and lactate concentrations, and pH value), electrical signals, and cell density distributions within the IVD were calculated. Because of page limitation, only results relevant to cell density (normalized by its initial value in each region) and glucose level were reported.
Discussion
In this study, the effects of reduction of nutrition levels at boundaries, degeneration, and dynamic compression on cell viability in IVDs in a time-dependent manner were investigated. To this end, a novel constitutive model for cell viability was developed based on the experimental data (Bibby et al., 2002, Bibby and Urban, 2004, Horner and Urban, 2001), and incorporated into the mechano-electrochemical mixture theory to regulate the cell density.
This new constitutive model can more
Conflict of interest statement
No financial support or benefits have been or will be received from any commercial source related directly or indirectly to the scientific work reported in this manuscript.
Acknowledgments
This study was supported by a research Grant from NIH/NIBIB (EB008653).
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