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.     

Computation models simulating notochordal cell extinction during early ageing of an intervertebral disc

Lower back pain due to intervertebral disc (IVD) degeneration is a prevalent problem which drastically affects the quality of life of millions of sufferers. Healthy IVDs begin with high populations of notochordal cells in the nucleus pulposus, while by the second stage of degeneration, these cells will be replaced by chondrocyte-like cells. Because the IVD is avascular, these cells rely on passive diffusion of nutrients to survive. It is thought that this transition in cell phenotype causes the shift of the IVD's physical properties, which impede the flow of nutrients. Our computational model of the IVD illustrates its ability to simulate the evolving chemical and mechanical environments occurring during the early ageing process. We demonstrate that, due to the insufficient nutrient supply and accompanying changes in physical properties of the IVD, there was a resultant exponential decay in the number of notochordal cells over time.     

Computation models simulating notochordal cell extinction during early ageing of an intervertebral disc

Lower back pain due to intervertebral disc (IVD) degeneration is a prevalent problem which drastically affects the quality of life of millions of sufferers. Healthy IVDs begin with high populations of notochordal cells in the nucleus pulposus, while by the second stage of degeneration, these cells will be replaced by chondrocyte-like cells. Because the IVD is avascular, these cells rely on passive diffusion of nutrients to survive. It is thought that this transition in cell phenotype causes the shift of the IVD's physical properties, which impede the flow of nutrients. Our computational model of the IVD illustrates its ability to simulate the evolving chemical and mechanical environments occurring during the early ageing process. We demonstrate that, due to the insufficient nutrient supply and accompanying changes in physical properties of the IVD, there was a resultant exponential decay in the number of notochordal cells over time.     

Modeling and simulation of lactic acid fermentation with inhibition effects of lactic acid and glucose

An unstructured mathematical model for lactic acid fermentation was developed. This model was able to predict the inhibition effects of lactic acid and glucose and was confirmed to be valid with various initial concentrations of lactic acid and glucose. Simulation of energy production was made using this mathematical model, and the relationship between the kinetics of energy metabolism and lactic acid production was also analyzed.     

Manganese, superoxide dismutase, and oxygen tolerance in some lactic acid bacteria

A previous study of the aerotolerant bacterium Lactobacillus plantarum, which lacks superoxide dismutase (SOD), demonstrated that it possesses a novel substitute for this defensive enzyme. Thus, L. plantarum contains 20 to 25 mM Mn(II),m in a dialyzable form, which is able to scavenge O2- apparently as effectively as do the micromolar levels of SOD present in most other organisms. This report describes a survey of the lactic acid bacteria. The substitution of millimolar levels of Mn(II) for micromolar levels of SOD is a common occurrence in this group of microorganisms, which contained either SOD or high levels of Mn(II), but not both. Two strains were found which had neither high levels of Mn(II) nor SOD, and they were, as was expected, very oxygen intolerant. Lactic acid bacteria containing SOD grew better aerobically than anaerobically, whereas the organisms containing Mn(II) in place of SOD showed aerobic growth which was best, at best, equal to anaerobic growth. Plumbagin (5-hydroxy-2-methyl-1,4-naphthoquinone) increases the rate of O2- production in these organisms. Lactobacillus strains containing high intracellular Mn(II) were more resistant to the oxygen-dependent toxicity of plumbagin than were strains containing lower levels of Mn(II). The results support the conclusion that a high internal level of Mn(II) provides these organisms with an important defence against endogenous O2-.     

Responses of lactic acid bacteria to oxygen

Abstract A small number of flavoprotein oxidase enzymes are responsible for the direct interaction of lactic acid bacteria (LAB) with oxygen; hydrogen peroxide or water are produced in these reactions. In some cultures exposed to oxygen, hydrogen peroxide accumulates to inhibitory levels.
Through these oxidase enzymes and NADH peroxidase, O₂ and H₂O₂ can accept electrons from sugar metabolism, and thus have a sparing effect on the use of metabolic intermediates, such as pyruvate or acetaldehyde, as electron acceptors. Consequently, sugar metabolism in aerated cultures of LAB can be substantially different from that in unaerated cultures. Energy and biomass yields, end-products of sugar metabolism and the range of substrates which can be metabolised are affected.
Lactic acid bacteria exhibit an inducible oxidative stress response when exposed to sublethal levels of H₂O₂. This response protects them if they are subsequently exposed to lethal concentrations of H₂O₂. The effect appears to be related to other stress responses such as heat-shock and is similar, in some but not all respects, to that previously reported for enteric bacteria.     

Effects of mechanical compression on metabolism and distribution of oxygen and lactate in intervertebral disc

The objective of this study was to examine the effects of mechanical compression on metabolism and distributions of oxygen and lactate in the intervertebral disc (IVD) using a new formulation of the triphasic theory. In this study, the cellular metabolic rates of oxygen and lactate were incorporated into the newly developed formulation of the mechano-electrochemical mixture model [Huang, C.-Y., Gu, W.Y., 2007. Effect of tension-compression nonlinearity on solute transport in charged hydrated fibrosus tissues under dynamic unconfined compression. Journal of Biomechanical Engineering 129, 423-429]. The model was used to numerically analyze metabolism and transport of oxygen and lactate in the IVD under static or dynamic compression. The theoretical analyses demonstrated that compressive loading could affect transport and metabolism of nutrients. Dynamic compression increased oxygen concentration, reduced lactate accumulation, and promoted oxygen consumption and lactate production (i.e., energy conversion) within the IVD. Such effects of dynamic loading were dependent on strain level and loading frequency, and more pronounced in the IVD with less permeable endplate. In contrast, static compression exhibited inverse effects on transport and metabolism of oxygen and lactate. The theoretical predictions in this study are in good agreement with those in the literature. This study established a new theoretical model for analyzing cellular metabolism of nutrients in hydrated, fibrous soft tissues under mechanical compression.     

Non-competitive product inhibition in lactic acid fermentation from glucose

Summary A kinetic study regarding product inhibition in lactic acid fermentation by Streptococcus faecalis, which produces l-lactic acid, was performed in a chemostat at various feed concentrations of glucose (10, 20, and 30 g/l) at pH 7.0. Steady-state kinetic constants for the specific consumption rate of glucose and the specific production rate of lactic acid were determined at a residual glucose concentration below 2 g/l, which was accomplished in a chemostat. All the parameters, the specific growth rate, the specific consumption rate of glucose, and the specific production rate of lactic acid, were definitely related to non-competitive inhibition with regard to the concentration of the product, lactic acid.Offprint requests to: K. Hiyama     

Growth related increase in an intervertebral disc space in rats

Methods have been developed that permit repetitive radiographic measurement of the lumbar L4-5 intervertebral disc space area in the laboratory rat. In using this approach, the coefficient of variation in repetitive determinations was 7.6 +/- 0.7%. Normal rats have been shown to manifest statistically significant increase in disc space area size between 2.5 and 5 months of age.     

The influence of serum,glucose and oxygen on intervertebral disc cell growth <Emphasis Type="Italic">in vitro</Emphasis>: implications for degenerative disc disease

Introduction  

The avascular nature of the human intervertebral disc (IVD) is thought to play a major role in disc pathophysiology by limiting nutrient supply to resident IVD cells. In the human IVD, the central IVD cells at maturity are normally chondrocytic in phenotype. However, abnormal cell phenotypes have been associated with degenerative disc diseases, including cell proliferation and cluster formation, cell death, stellate morphologies, and cell senescence. Therefore, we have examined the relative influence of possible blood-borne factors on the growth characteristics of IVD cells in vitro.     

Eremophila glabra is an Australian plant that reduces lactic acid accumulation in an in vitro glucose challenge designed to simulate lactic acidosis in ruminants

Lactic acidosis is a major welfare issue affecting animal health and production systems such as dairy and feedlot beef. We used two bioassays to identify bioactive plants of Australia with the potential to prevent acidosis in ruminants. In the first bioassay, a potentially acidotic environment was induced by adding glucose to rumen fluid and pH and gas production were used to estimate the effect on acid production and microbial fermentation after 5-h incubation. Australian plants (n = 104) were screened for their ability to prevent a decline in the pH without inhibiting normal gas production, and five plants namely Eremophila glabra, Kennedia eximia, Acacia saligna, Acacia decurrens and Kennedia prorepens with such properties were identified. We investigated further the two top ranking plants, E. glabra and K. prorepens, in the second bioassay to determine the extent of their effect in vitro, by extending the incubation to 24 h and measuring d-lactate, and volatile fatty acids (VFA) in addition to pH and gas production. These were measured at 0, 5, 10, 16 and 24 h after inoculation. Eremophila glabra maintained pH values that were higher and d-lactate concentrations that were lower than the control (P < 0.001), and comparable to the antibiotic-protected environment (AB; 12 μg of virginiamycin/ml). Eremophila glabra and AB treatments did not restrict fermentation, as judged by gas production and VFA. Kennedia prorepens slowed the decline in pH and reduced the accumulation of lactate but inhibited gas production. We concluded that, in vitro, E. glabra was effective at controlling events that can lead to acidosis and the effect was comparable to that of virginiamycin, while K. prorepens was less effective than E. glabra and also inhibited fermentation.     

Diffusion of antibiotics in intervertebral disc

Delivering charged antibiotics to the intervertebral disc is challenging because of the avascular, negatively charged extracellular matrix (ECM) of the tissue. The purpose of this study was to measure the apparent diffusion coefficient of two clinically relevant, charged antibiotics, vancomycin (positively charged) and oxacillin (negatively charged) in IVD. A one-dimensional steady state diffusion experiment was employed to measure the apparent diffusion coefficient of the two antibiotics in bovine coccygeal annulus fibrosus (AF) tissue. The averaged apparent diffusion coefficient for vancomycin under 20% compressive strain was 7.94 ± 2.00 × 10⁻¹² m²/s (n = 10), while that of oxacillin was 2.26 ± 0.68 × 10⁻¹⁰ m²/s (n = 10). A student’s t-test showed that the diffusivity of vancomycin was significantly lower than that of oxacillin. This finding may be attributed to two factors: solute size and possible binding effects. Vancomycin is approximately 3 times larger in molecular weight than oxacillin, meaning that steric hindrance likely plays a role in the slower transport. Reversible binding between positive vancomycin and the negative ECM could also slow down the rate of diffusion. Therefore, more investigation is necessary to determine the specific relationship between net charge on antibiotic and diffusion coefficients in IVD. This study provides essential quantitative information regarding the transport rates of antibiotics in the IVD, which is critical in using computational modeling to design effective strategies to treat disc infection.     

Efficient conversion of lactic acid to butanol with pH-stat continuous lactic acid and glucose feeding method by Clostridium saccharoperbutylacetonicum

In order to achieve high butanol production by Clostridium saccharoperbutylacetonicum N1-4, the effect of lactic acid on acetone–butanol–ethanol fermentation and several fed-batch cultures in which lactic acid is fed have been investigated. When a medium containing 20 g/l glucose was supplemented with 5 g/l of closely racemic lactic acid, both the concentration and yield of butanol increased; however, supplementation with more than 10 g/l lactic acid did not increase the butanol concentration. It was found that when fed a mixture of lactic acid and glucose, the final concentration of butanol produced by a fed-batch culture was greater than that produced by a batch culture. In addition, a pH-controlled fed-batch culture resulted in not only acceleration of lactic acid consumption but also a further increase in butanol production. Finally, we obtained 15.5 g/l butanol at a production rate of 1.76 g/l/h using a fed-batch culture with a pH-stat continuous lactic acid and glucose feeding method. To confirm whether lactic acid was converted to butanol by the N1-4 strain, we performed gas chromatography–mass spectroscopy (GC-MS) analysis of butanol produced by a batch culture during fermentation in a medium containing [1,2,3-¹³C₃] lactic acid as the initial substrate. The results of the GC-MS analysis confirmed the bioconversion of lactic acid to butanol.