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.

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SUMMARYAn element-free Galerkin (EFG) method with linear, quadratic and cubic approximations, which can exactly, in a numerical sense, pass the corresponding patch tests is proposed and is named as consistent EFG (CEFG) method. The development of this method is based on the Hu-Washizu three-field variational principle. Numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference. Thus, the method is variationally consistent. The consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated. Numerical results show that the proposed CEFG method greatly improves the numerical performance of the EFG method in terms of accuracy, convergence, efficiency and stability, especially the proposed cubic CEFG method, which shows exceptional accuracy and convergence.

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.

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The study compares the performance of alternative implementations of both time-series and cross-sectional momentum strategies across 24 markets. We find that over our sample period, both types of momentum strategies generate positive returns under the majority of implementations evaluated but that time-series momentum is clearly superior. An important difference between the two momentum strategies is that with time-series momentum, the number of stocks included in the winner and loser portfolios vary with the state of the market. As a consequence, cross-sectional momentum digs deeper to select winning stocks when markets are weak and deeper to select losing stocks when markets are strong. As the information in the momentum signals is concentrated in the tails of the return distribution, it is not that surprising that momentum is best implemented using time-series momentum.