Is post-contrast MRI a valuable method for the study of the nutrition of the intervertebral disc?

Decreased nutrition has been proposed as a potential mechanism leading to intervertebral disc degeneration. A method to investigate it in vivo is the MRI evaluation of the transport of a paramagnetic contrast agent, which is assumed to diffuse through the endplate to the disc using the same mechanisms as the cell nutrients. However, previous numerical studies questioned the value of this method as a model to investigate disc nutrition. To assess its validity, a parametric osmoporoelastic finite element model of a lumbar intervertebral disc incorporating diffusion and convection of a solute (representing the contrast agent) was developed. A Taguchi sensitivity analysis was performed in order to assess the relevance of various parameters which influence the solute transport. Subsequently, a full-factorial sensitivity analysis was used to investigate specifically the diffusion coefficients of the contrast agent. The most important parameters in determining the results were the disc height, the diffusion coefficients and the pharmacokinetic of the contrast agent. However, diffusion coefficients values as measured in in vitro studies would lead to insubstantial enhancement of the MRI signal. Thus, transport mechanisms other than pure diffusion should be active in in vivo transport of the contrast agent. In conclusion, the study showed that post-contrast MRI may not be suited for a quantitative analysis, but only for a qualitative examination aimed for example to detect endplate lesions. Open questions remain on the use of post-contrast MRI for the investigation of the relevance of reduced nutrition as a trigger to disc degeneration.     

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc.An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa.Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.     

The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes

Intervertebral disc metabolic transport is essential to the functional spine and provides the cells with the nutrients necessary to tissue maintenance. Disc degenerative changes alter the tissue mechanics, but interactions between mechanical loading and disc transport are still an open issue. A poromechanical finite element model of the human disc was coupled with oxygen and lactate transport models. Deformations and fluid flow were linked to transport predictions by including strain-dependent diffusion and advection. The two solute transport models were also coupled to account for cell metabolism. With this approach, the relevance of metabolic and mechano-transport couplings were assessed in the healthy disc under loading-recovery daily compression. Disc height, cell density and material degenerative changes were parametrically simulated to study their influence on the calculated solute concentrations. The effects of load frequency and amplitude were also studied in the healthy disc by considering short periods of cyclic compression. Results indicate that external loads influence the oxygen and lactate regional distributions within the disc when large volume changes modify diffusion distances and diffusivities, especially when healthy disc properties are simulated. Advection was negligible under both sustained and cyclic compression. Simulating degeneration, mechanical changes inhibited the mechanical effect on transport while disc height, fluid content, nucleus pressure and overall cell density reductions affected significantly transport predictions. For the healthy disc, nutrient concentration patterns depended mostly on the time of sustained compression and recovery. The relevant effect of cell density on the metabolic transport indicates the disturbance of cell number as a possible onset for disc degeneration via alteration of the metabolic balance. Results also suggest that healthy disc properties have a positive effect of loading on metabolic transport. Such relation, relevant to the maintenance of the tissue functional composition, would therefore link disc function with disc nutrition.     

Effects of dynamic loading on solute transport through the human cartilage endplate

Nutrient and metabolite transport through the cartilage endplate (CEP) is important for maintaining proper disc nutrition, but the mechanisms of solute transport remain unclear. One unresolved issue is the role of dynamic loading. In comparison to static loading, dynamic loading is thought to enhance transport by increasing convection. However, the CEP has a high resistance to fluid flow, which could limit solute convection. Here we measure solute transport through site-matched cadaveric human lumbar CEP tissues under static vs. dynamic loading, and we determine how the degree of transport enhancement from dynamic loading depends on CEP porosity and solute size. We found that dynamic loading significantly increased small and large solute transport through the CEP: on average, dynamic loading increased the transport of sodium fluorescein (376 Da) by a factor of 1.85 ± 0.64 and the transport of a large dextran (4000 Da) by a factor of 4.97 ± 3.05. Importantly, CEP porosity (0.65 ± 0.07; range: 0.47–0.76) strongly influenced the degree of transport enhancement. Specifically, for both solutes, transport enhancement was greater for CEPs with low porosity than for CEPs with high porosity. This is because the CEPs with low porosity were susceptible to larger improvements in fluid flow under dynamic loading. The CEP becomes less porous and less hydrated with aging and as disc degeneration progresses. Together, these findings suggest that as those changes occur, dynamic loading has a greater effect on solute transport through the CEP compared to static loading, and thus may play a larger role in disc nutrition.     

Analysis of nonlinear coupled diffusion of oxygen and lactic acid in intervertebral discs

The transport of oxygen and lactate (i.e., lactic acid) in the human intervertebral disc was investigated accounting for the measured coupling between species via the pH level in the tissue. Uncoupled cases were also analyzed to identify the extent of the effect of such coupling on the solute gradients across the disc. Moreover, nonlinear lactic production rate versus lactic concentration and oxygen consumption rate versus oxygen concentration were considered. The nonlinear coupled diffusion equations were solved using an in-house finite element program and an axisymmetric model of the disc with distinct nucleus and anulus regions. A pseudotransient approach with a backward integration scheme was employed to improve convergence. Coupled simulations influenced the oxygen concentration and lactic acid concentration throughout the disc, in particular the gradient of concentrations along the disc mid-height to the nucleus-anulus boundary where the solutes reached their most critical values; minimum for the oxygen tension and maximum for the lactate. Results suggest that for realistic estimates of nutrient and metabolite gradients across the disc, it could be important to take into account the coupling between the rates of synthesis and overall local metabolite/nutrient concentration.     

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.     

Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc

The present numerical study aims to investigate the disc nutrition and factors affecting it by evaluating the concentrations of oxygen, glucose and lactic acid in the disc while accounting for the coupling between these species via the pH level in the tissue and the nonlinear concentration-consumption (for glucose and oxygen) and concentration-production (for lactate) relations. The effects of changes in the endplate exchange area (EA) adjacent to the nucleus or the inner annulus for the transport of nutrients and in the disc geometry as well as tissue diffusivities under static compression loading on species concentrations are also studied. Moreover, alterations in solute diffusion following a central endplate fracture are investigated. An axisymmetric geometry with four distinct regions is considered. Supply sources are assumed at the outer annulus periphery and disc endplates. Coupling between different solutes, pH level, endplate disruptions (calcifications and fractures) and mechanical loads substantially influenced the distribution of nutrients throughout the disc as well as the magnitude and location of critical concentrations; maximum for the lactic acid and minimum for oxygen and glucose. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid expression, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, thus initiating or accelerating disc degeneration.     

3D finite element analysis of nutrient distributions and cell viability in the intervertebral disc: effects of deformation and degeneration

The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell viability in the degenerated case, in which averaged cell density fell 11% compared with the normal case. This effect was further exacerbated by deformation of the degenerated IVD. Both deformation and disc degeneration altered the glucose distribution in the IVD. For the degenerated case, glucose levels fell below levels necessary for maintaining cell viability, and cell density decreased. This study provides important insight into nutrition-related mechanisms of disc degeneration. Moreover, our model may serve as a powerful tool in the development of new treatments for low back pain.     

Effects of Tobacco Smoking on the Degeneration of the Intervertebral Disc: A Finite Element Study

Tobacco smoking is associated with numerous pathological conditions. Compelling experimental evidence associates smoking to the degeneration of the intervertebral disc (IVD). In particular, it has been shown that nicotine down-regulates both the proliferation rate and glycosaminoglycan (GAG) biosynthesis of disc cells. Moreover, tobacco smoking causes the constriction of the vascular network surrounding the IVD, thus reducing the exchange of nutrients and anabolic agents from the blood vessels to the disc. It has been hypothesized that both nicotine presence in the IVD and the reduced solute exchange are responsible for the degeneration of the disc due to tobacco smoking, but their effects on tissue homeostasis have never been quantified. In this study, a previously presented computational model describing the homeostasis of the IVD was deployed to investigate the effects of impaired solute supply and nicotine-mediated down-regulation of cell proliferation and biosynthetic activity on the health of the disc. We found that the nicotine-mediated down-regulation of cell anabolism mostly affected the GAG concentration at the cartilage endplate, reducing it up to 65% of the value attained in normal physiological conditions. In contrast, the reduction of solutes exchange between blood vessels and disc tissue mostly affected the nucleus pulposus, whose cell density and GAG levels were reduced up to 50% of their normal physiological levels. The effectiveness of quitting smoking on the regeneration of a degenerated IVD was also investigated, and showed to have limited benefit on the health of the disc. A cell-based therapy in conjunction with smoke cessation provided significant improvements in disc health, suggesting that, besides quitting smoking, additional treatments should be implemented in the attempt to recover the health of an IVD degenerated by tobacco smoking.     

Analysis of cell viability in intervertebral disc: Effect of endplate permeability on cell population

Responsible for making and maintaining the extracellular matrix, the cells of intervertebral discs are supplied with essential nutrients by diffusion from the blood supply through mainly the cartilaginous endplates (CEPs) and disc tissue. Decrease in transport rate and increase in cellular activity may adversely disturb the intricate supply–demand balance leading ultimately to cell death and disc degeneration. The present numerical study aimed to introduce for the first time cell viability criteria into nonlinear coupled nutrition transport equations thereby evaluating the dynamic nutritional processes governing viable cell population and concentrations of oxygen, glucose and lactic acid in the disc as CEP exchange area dropped from a fully permeable condition to an almost impermeable one. A uniaxial model of an in vitro cell culture analogue of the disc is first employed to examine and validate cell viability criteria. An axisymmetric model of the disc with four distinct regions was subsequently used to investigate the survival of cells at different CEP exchange areas.In agreement with measurements, predictions of the diffusion chamber model demonstrated substantial cell death as essential nutrient concentrations fell to levels too low to support cells. Cells died away from the nutrient supply and at higher cell densities. In the disc model, the nucleus region being farthest away from supply sources was most affected; cell death initiated first as CEP exchange area dropped below ～40% and continued exponentially thereafter to depletion as CEP calcified further. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid outflow, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, resulting in cell death and disc degeneration.     

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.     

Numerical exploration of the combined effect of nutrient supply,tissue condition and deformation in the intervertebral disc

Novel strategies to heal discogenic low back pain could highly benefit from comprehensive biophysical studies that consider both mechanical and biological factors involved in intervertebral disc degeneration. A decrease in nutrient availability at the bone–disc interface has been indicated as a relevant risk factor and as a possible initiator of cell death processes. Mechanical behaviour of both healthy and degenerated discs could highly interact with cell death in these compromised situations. In the present study, a mechano-transport finite element model was used to investigate the nature of mechanical effects on cell death processes via load-induced metabolic transport variations. Cycles of static sustained compression were chosen to simulate daily human activity. Healthy and degenerated cases were simulated as well as a reduced supply of solutes and an increase in solute exchange area at the bone–disc interface. Results showed that a reduction in metabolite concentrations at the bone–disc boundaries induced cell death, even when the increased exchange area was simulated. Slight local mechanical enhancements of glucose in the disc centre were capable of decelerating cell death but occurred only with healthy mechanical properties. However, mechanical deformations were responsible for a worsening in terms of cell death in the inner annulus, a disadvantaged zone far from the boundary supply with both an increased cell demand and a strain-dependent decrease of diffusivity. Such adverse mechanical effects were more accentuated when degenerative properties were simulated. Overall, this study paves the way for the use of biophysical models for a more integrated understanding of intervertebral disc pathophysiology.     

Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition [e.g., water content and fixed charge density (FCD)] on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.     

Effect of intervertebral disc degeneration on disc cell viability: a numerical investigation

Degeneration of the intervertebral disc may be initiated and supported by impairment of the nutrition processes of the disc cells. The effects of degenerative changes on cell nutrition are, however, only partially understood. In this work, a finite volume model was used to investigate the effect of endplate calcification, water loss, reduction of disc height and cyclic mechanical loading on the sustainability of the disc cell population. Oxygen, lactate and glucose diffusion, production and consumption were modelled with non-linear coupled partial differential equations. Oxygen and glucose consumption and lactate production were expressed as a function of local oxygen concentration, pH and cell density. The cell viability criteria were based on local glucose concentration and pH. Considering a disc with normal water content, cell death was initiated in the centre of the nucleus for oxygen, glucose, and lactate diffusivities in the cartilaginous endplate below 20% of the physiological values. The initial cell population could not be sustained even in the non-calcified endplates when a reduction of diffusion inside the disc due to water loss was modelled. Alterations in the disc shape such as height loss, which shortens the transport route between the nutrient sources and the cells, and cyclic mechanical loads, could enhance cell nutrition processes.     

Effect of Cartilage Endplate on Cell Based Disc Regeneration: A Finite Element Analysis

This study examines the effects of cartilage endplate (CEP) calcification and the injection of intervertebral disc (IVD) cells on the nutrition distributions inside the human IVD under physiological loading conditions using multiphasic finite element modeling. The human disc was modeled as an inhomogeneous mixture consisting of a charged elastic solid, water, ions (Na⁺ and Cl⁻), and nutrient solute(oxygen,glucose and lactate) phases. The effect of the endplate calcification was simulated by a reduction of the tissue porosity (i.e., water volume faction) from 0.60 to 0.48. The effect of cell injection was simulated by increasing the cell density in the nucleus pulposus (NP) region by 50%, 100%, and 150%. Strain-dependent transport properties(e.g., hydraulic permeability and solute diffusivities) were considered to couple the solute transport and the mechanical loading. The simulation results showed that nutrient solute distribution inside the discis maintained at a stable state during the day and night. The physiological diurnal cyclic loading does not change the nutrient environment in the human IVD. The cartilage endplate plays a significant role in the nutrient supply to human IVD. Calcification of the cartilage endplate significantly reduces the nutrient levels in human IVD. Therefore, in cell based therapy for IVD regeneration, theincreased nutrient demand as a result of cell injection needs to be addressed. Excessive numbers of injected cells may cause further deterioration of the nutrient environment in the degenerated disc. This study is important for understanding the pathology of IVD degeneration and providing new insights into cell based therapies for low back pain.     

Sox9治疗兔椎间盘退变的效果及机制研究

目的:探究Sox9用于治疗椎间盘退变的效果及调控机制。方法:将Ad-sox9和Ad-GFP各20μL分别转染至椎间盘退变兔的髓核组织中,转染后3、7、30、60天取材,采用免疫组化、免疫荧光和MRI等研究方法检测椎间盘髓核组织中II型胶原、蛋白多糖的表达情况,并分析对椎间盘退变的改善情况。结果:免疫组化染色显示sox9组中椎间盘髓核组织中II型胶原、蛋白多糖的表达明显升高,MRI显示sox9组椎间盘T2像信号有明显改善(P<0.05)。结论:体内转染腺病毒介导的sox9基因能够增加椎间盘内II型胶原和蛋白多糖的表达,并抑制椎间盘的退变进程。     

Expression of the two pore domain potassium channel TREK-1 in human intervertebral disc cells

Potassium channels play a major role in intracellular homeostasis and regulation of cell volume. Intervertebral disc cells respond to mechanical loading in a complex manner. Mechanical loading may play a role in disc degeneration. Lumbar intervertebral disc samples from 5 patients (average age: 47 years, range: 25-64 years) were used for this study, investigating cells from the nucleus pulposus and the annulus fibrosus duplicate samples to determine RNA expression and protein expression. Analysis of mRNA expression by RT-PCR demonstrated that TREK 1 was expressed by nucleus pulposus (n=5) and annulus fibrosus (n=5) cells. Currently, TREK-1 is the only potassium channel known to be activated by intracellular acidosis, and responds to mechanical and chemical stimuli. Whilst the precise role of potassium channels in cellular homeostasis remains to be determined, TREK-1 may be important to protect disc cells against ischaemic damage, and subsequent disc degeneration, and may also play a role in effecting mechanotransduction. Further research is required to fully elucidate the role of the TREK-1 ion channel in intervertebral disc cells.     

IL-13抑制剂在损伤大鼠尾椎间盘退变中的作用研究

为了探讨IL-13细胞因子在损伤后大鼠椎间盘退变中的影响,建立了大鼠尾椎间盘退变模型,给予IL-13抑制剂sIL-13Rα2-Fc进行干预,将实验分为空白、对照、低剂量、中剂量、高剂量干预组。分别于4周及6周后通过HE染色和Masson染色观察椎间盘形态变化并评分;DMMB法定量分析椎间盘中的糖胺多糖(glycosaminoglycan,GAG)、硫酸软骨素(chondroitin sulfate,CS)、硫酸角质素(keratan sulfate,KS)、透明质酸(hyaluronic acid,HA)含量变化;RT-PCR分析Ⅰ型和Ⅱ型胶原蛋白的mRNA表达水平;蛋白质印迹分析Ⅰ型和Ⅱ型胶原蛋白含量。HE和Masson染色显示与对照组相比,干预组椎间盘病理改变减小,纤维环排列更规则,破裂部位减小,NP细胞数量增加,胶原纤维减少。sIL-13Rα2-Fc干预增加了糖胺多糖、透明质酸含量,增加了硫酸软骨素/硫酸角质素比,减少了Ⅰ型胶原蛋白的表达,并增加了Ⅱ型胶原蛋白。结果表明IL-13抑制剂sIL-13Rα2-Fc可有效减轻椎间盘退变,并且与作用时间和浓度成正相关。     

Computational pharmacokinetics of solute penetration into human intervertebral discs-Effects of endplate permeability, solute molecular weight and disc size

A finite element model is developed to predict the penetration time-history of three different solutes into the human lumbar disc following intravenous injection. Antibiotics are routinely administered intravenously in spinal surgery to prevent disc infection. Successful prophylaxis requires antibiotics to reach adequate inhibitory levels. Here, the transient diffusion of cephazolin is investigated over 10h post-injection in a human disc model subject to reported concentrations in the blood stream as the prescribed boundary sources. Post-injection variation of cephazolin concentrations in the disc adjacent to supply sources closely followed the decay curve in the blood stream and fell sharply with time. Much lower concentrations were computed in the inner annulus and nucleus; much of the disc (80% at 1h and 49% at 4h) experienced concentrations below required inhibitory level of 1mg/L in agreement with measurements. Changes in endplate permeability, disc size, and solute molecular weight had profound effects on concentration profiles at all times and regions, especially in the disc centre, demonstrating their crucial roles on the adequate delivery of drugs. Larger solutes markedly slow transport into the disc. The failure to reach critical therapeutic levels in the central disc regions, especially when endplates calcify and in larger discs, raises concerns and calls for caution in attempts to extrapolate findings of studies on animals with much smaller and non degenerate discs to the human discs. The current study also demonstrates the capability of computational models in predicting the transport of intravenously injected solutes into the disc.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.