Qiaoqiao Zhu

Cell viability in intervertebral disc under various nutritional and dynamic loading conditions: 3d finite element analysis.

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.

Simulation of the progression of intervertebral disc degeneration due to decreased nutritional supply.

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, nutritional level, proteoglycan (PG) content, water content, and volume during human disc degeneration using a numerical method. Summary of Background Data. Understanding the cause and progression of intervertebral disc degeneration is crucial for developing effective treatment strategies for intervertebral disc 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 intercoupled biological, chemical, electrical, and mechanical signals in the disc. Characterizing these signals in human discs in vivo is difficult. Methods. A realistic 3-dimensional finite element model of the human intervertebral disc was developed on the basis of biomechanoelectrochemical 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 nutritional levels at disc boundaries was simulated and validated by comparing with experimental results. Results. Cell density reached equilibrium state in 30 days after reduced nutritional supply at the disc boundary, whereas the 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. Conclusion. Poor nutritional supply has a long-term effect on disc degeneration. Level of Evidence: N/A

Temporal changes of mechanical signals and extracellular composition in human intervertebral disc during degenerative progression

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.

Analyzing the effects of mechanical and osmotic loading on glycosaminoglycan synthesis rate in cartilaginous tissues

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.

Influences of Nutrition Supply and Pathways on the Degenerative Patterns in Human Intervertebral Disc.

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. The aim of this study was 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 levels 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 magnetic resonance imaging (MRI). 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. Level of Evidence: N/A

Simulation of biological therapies for degenerated intervertebral discs

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.

Kinetics of charged antibiotic penetration into human intervertebral discs: A numerical study

Little quantitative information exists on the kinetics of charged antibiotic penetration into human intervertebral discs (IVD). This information is crucial for determining the dosage to use, timing of administration, and duration of treatment for infected IVDs. The objective of this study was to quantitatively analyze the transport of various charged antibiotics into human lumbar IVDs. Penetration of charged and uncharged antibiotics into a human lumbar disc was analyzed using a 3D finite element model. The valence (z) of the electrical charge of antibiotics varied from z=+2 (positively charged) to z=-2 (negatively charged). An uncharged antibiotic (z=0) was used as a control. Cases with intravenous (IV) administrations of different charged antibiotics were simulated. Our results showed that the electrical charge had great effects on kinetics of an antibiotic penetration into the IVD; with higher concentrations and uptakes for positively charged antibiotics than those for negatively charged ones. This study provides quantitative information on selecting antibiotics for treating intervertebral disc infections.

Simulation of water content distributions in degenerated human intervertebral discs.

The objective of this study was to investigate the spatial and temporal variations of water content in intervertebral discs during degeneration and repair processes. We hypothesized that the patterns of water content distribution in the discs are related to the intensity patterns observed in T2‐weighted MRI images. Water content distributions in the mildly (e.g., 80% viable cells in the disc, 2.3% decrease in disc height) and moderately (e.g., 40% viable cells in the disc, 9.3% decrease in disc height) degenerated discs were predicted using a finite element model. The variation of water content in the degenerated discs treated with three biological therapies (i.e., increasing the cell density in the nucleus pulposus [Case I], increasing glycosaminoglycan synthesis rate in the nucleus pulposus [Case II], and decreasing glycosaminoglycan degradation rate in the nucleus pulposus [Case III]) were also predicted. It was found that two patterns of water content distributions, a horizontal region with lower water content at the mid‐axial plane of nucleus pulposus and a spot with higher water content at the posterior region, were shown during the degeneration progress for the disc simulated in this study. These two patterns disappeared after treatment in Case I, but in Case II and Case III. The implication of these patterns for the horizontal gray band and high intensity zone in T2‐weighted MRI images was discussed. This study provided new guidance to develop a novel method for diagnosing disc degeneration and assessing outcomes of biological therapies with MRI techniques.

Prediction of glycosaminoglycan synthesis in intervertebral disc under mechanical loading

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 (0.2MPa) and diurnal loads (0.1/0.3MPa and 0.15/0.25MPa in 12/12 hours shift with an average of 0.2MPa 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.

An Anisotropic Multiphysics Model for Intervertebral Disk

Intervertebral disk (IVD) is the largest avascular structure in human body, consisting of three types of charged hydrated soft tissues. Its mechanical behavior is nonlinear and anisotropic, due mainly to nonlinear interactions among different constituents within tissues. In this study, a more realistic anisotropic multiphysics model was developed based on the continuum mixture theory and employed to characterize the couplings of multiple physical fields in the IVD. Numerical simulations demonstrate that this model is capable of systematically predicting the mechanical and electrochemical signals within the disk under various loading conditions, which is essential in understanding the mechanobiology of IVD.