In this study, a new cell density model was developed and incorporated into the formulation of the mechano-electrochemical mixture theory to investigate the effects of deprivation of nutrition supply at boundary source, degeneration, and dynamic loading on the cell viability of intervertebral disc (IVD) using finite element methods. The deprivation of nutrition supply at boundary source was simulated by reduction in nutrition level at CEP and AF boundaries. Cases with 100%, 75%, 60%, 50% and 30% of normal nutrition level at both CEP and AF boundaries were modeled. Unconfined axial sinusoidal dynamic compressions with different combinations of amplitude (u=10%±2.5%, ±5%) and frequency (f=1, 10, 20 cycle/day) were applied. Degenerated IVD was modeled with altered material properties. Cell density decreased substantially with reduction of nutrition level at boundaries. Cell death was initiated primarily near the NP–AF interface on the mid-plane. Dynamic loading did not result in a change in the cell density in non-degenerated IVD, since glucose levels did not fall below the minimum value for cell survival; in degenerated IVDs, we found that increasing frequency and amplitude both resulted in higher cell density, because dynamic compression facilitates the diffusion of nutrients and thus increases the nutrition level around IVD cells. The novel computational model can be used to quantitatively predict both when and where cells start to die within the IVD under various kinds of nutritional and mechanical conditions.

Study Design Simulate the progression of human disc degeneration. Objective The objective of this study was to quantitatively analyze and simulate the changes in cell density, nutrition level, proteoglycan content, water content, and volume change during human disc degeneration using a numerical method. Summary of Background Data Understanding the etiology and progression of intervertebral disc (IVD) degeneration is crucial for developing effective treatment strategies for IVD-degeneration related diseases. During tissue degeneration, the disc undergoes losses of cell viability and activities, changes in extracellular matrix composition and structure, and compromise of the tissue-level integrity and function, which is significantly influenced by the inter-coupled biological, chemical, electrical, and mechanical signals in the disc. Characterizing these signals in human discs in vivo is difficult. Methods A realistic 3D finite element model of the human IVD was developed based on biomechano-electrochemical continuum mixture theory. The theoretical framework and the constitutive relationships were all biophysics based. All the material properties were obtained from experimental results. The cell-mediated disc degeneration process caused by lowered nutrition levels at disc boundaries was simulated and validated by comparing with experimental results. Results Cell density reached equilibrium state in 30 days after reduced nutrition supply at the disc boundary, while the proteoglycan (PG) and water contents reached a new equilibrium state in 55 years. The simulated results for the distributions of PG and water contents within the disc were consistent with the results measured in the literature, except for the distribution of PG content in the sagittal direction. Conclusions Poor nutrition supply has a long-term effect on disc degeneration.

In this study, a three-dimensional finite element model was used to investigate the changes in tissue composition and mechanical signals within human lumbar intervertebral disc during the degenerative progression. This model was developed based on the cell-activity coupled mechano-electrochemical mixture theory. The disc degeneration was simulated by lowering nutrition levels at disc boundaries, and the temporal and spatial distributions of the fixed charge density, water content, fluid pressure, Von Mises stress, and disc deformation were analyzed. Results showed that fixed charge density, fluid pressure, and water content decreased significantly in the nucleus pulposus (NP) and the inner to middle annulus fibrosus (AF) regions of the degenerative disc. It was found that, with degenerative progression, the Von Mises stress (relative to that at healthy state) increased within the disc, with a larger increase in the outer AF region. Both the disc volume and height decreased with the degenerative progression. The predicted results of fluid pressure change in the NP were consistent with experimental findings in the literature. The knowledge of the variations of temporal and spatial distributions of composition and mechanical signals within the human IVDs provide a better understanding of the progression of disc degeneration.

Study Design Investigation of the effects of the impairment of different nutritional pathways on the intervertebral disc degeneration patterns in terms of spatial distributions of cell density, glycosaminoglycan content, and water content. Objective To test the hypothesis that impairment of different nutritional pathways would result in different degenerative patterns in human discs. Summary of Background Data Impairment of nutritional pathways has been found to affect cell viability in the disc. However, details on how impairment of different nutritional pathways affects the disc degeneration patterns are unknown. Methods A 3D finite element model was used for this study. This finite element method was based on the cell-activity-coupled mechano-electrochemical theory for cartilaginous tissues. Impairment of the nutritional pathways was simulated by lowering the nutrition level at the disc boundaries. Effects of the impartment of cartilaginous endplate-nucleus pulposus (CEP-NP) pathway only (Case 1), annulus fibrosus (AF) pathway only (Case 2), and both pathways (Case 3) on disc degeneration patterns were studied. Results The predicted critical level of nutrition for Case 1, Case 2, and Case 3 were around 30%, 20%, and 50% of the reference values, respectively. Below this critical level, the disc degeneration would occur. Disc degeneration appeared mainly in the NP for Case 1, in the outer AF for Case 2, and in both the NP and inner to middle AF for Case 3. For Cases 1 and 3, the loss of water content was primarily located in the mid-axial plane, which is consistent with the horizontal gray band seen in some T2-weighted MRI images. For the disc geometry used in this study, it was predicted that there existed a High Intensity Zone (for Case 3), as seen in some T2-weighted MRI images. Conclusion Impairment of different nutrition pathways results in different degenerative patterns.

The efficacy of biological therapies on intervertebral disc repair was quantitatively studied using a three-dimensional finite element model based on a cell-activity coupled multiphasic mixture theory. In this model, cell metabolism and matrix synthesis and degradation were considered. Three types of biological therapies-increasing the cell density (Case I), increasing the glycosaminoglycan (GAG) synthesis rate (Case II), and decreasing the GAG degradation rate (Case III)-to the nucleus pulposus (NP) of each of two degenerated discs [one mildly degenerated (e.g., 80% viable cells in the NP) and one severely degenerated (e.g., 30% viable cells in the NP)] were simulated. Degenerated discs without treatment were also simulated as a control. The cell number needed, nutrition level demanded, time required for the repair, and the long-term outcomes of these therapies were analyzed. For Case I, the repair process was predicted to be dependent on the cell density implanted and the nutrition level at disc boundaries. With sufficient nutrition supply, this method was predicted to be effective for treating both mildly and severely degenerated discs. For Case II, the therapy was predicted to be effective for repairing the mildly degenerated disc, but not for the severely degenerated disc. Similar results were predicted for Case III. No change in cell density for Cases II and III were predicted under normal nutrition level. This study provides a quantitative guide for choosing proper strategies of biological therapies for different degenerated discs.

The loss of glycosaminoglycan (GAG) content is a major biochemical change during intervertebral disc (IVD) degeneration. Abnormal mechanical loading is one of the major factors causing disc degeneration. In this study, a multiscale mathematical model was developed to quantify the effect of mechanical loading on GAG synthesis. This model was based on a recently developed cell volume dependent GAG synthesis theory that predicts the variation of GAG synthesis rate of a cell under the influence of mechanical stimuli, and the biphasic theory that describes the deformation of IVD under mechanical loading. The GAG synthesis (at the cell level) was coupled with the mechanical loading (at the tissue level) via a cell-matrix unit approach which established a relationship between the variation of cell dilatation and the local tissue dilatation. This multiscale mathematical model was used to predict the effect of static load (creep load) on GAG synthesis in bovine tail discs. The predicted results are in the range of experimental results. This model was also used to investigate the effect of static (0.2 MPa) and diurnal loads (0.1/0.3 MPa and 0.15/0.25 MPa in 12/12 hours shift with an average of 0.2 MPa over a cycle) on GAG synthesis. It was found that static load and diurnal loads have different effects on GAG synthesis in a diurnal cycle, and the diurnal load effects depend on the amplitude of the load. The model is important to understand the effect of mechanical loading at the tissue level on GAG synthesis at the cellular level, as well as to optimize the mechanical loading in growing engineered tissue.

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The glycosaminoglycan (GAG) plays an important role in cartilaginous tissues to support and transmit mechanical loads. Many extracellular biophysical stimuli could affect GAG synthesis by cells. It has been hypothesized that the change of cell volume is a primary mechanism for cells to perceive the stimuli. Experimental studies have shown that the maximum synthesis rate of GAG is achieved at an optimal cell volume, larger or smaller than this level the GAG synthesis rate decreases. Based on the hypothesis and experimental findings in the literature, we proposed a mathematical model to quantitatively describe the cell volume dependent GAG synthesis rate in the cartilaginous tissues. Using this model, we investigated the effects of osmotic loading and mechanical loading on GAG synthesis rate. It is found our proposed mathematical model is able to well describe the change of GAG synthesis rate in isolated cells or in cartilage with variations of the osmotic loading or mechanical loading. This model is important for evaluating the GAG synthesis activity within cartilaginous tissues as well as understanding the role of mechanical loading in tissue growth or degeneration. It is also important for designing a bioreactor system with proper extracellular environment or mechanical loading for growing tissue at the maximum synthesis rate of the extracellular matrix.