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.     

Regulation of lactate production and utilization in rat tumors in vivo

These experiments were performed to determine the factor(s) that regulate lactic acid production and utilization by rat tumors in vivo. Arteriovenous differences for glucose and lactic, pyruvic, 3-OH-butyric, and acetoacetic acids were measured across "tissue-isolated" Walker 256 sarcocarcinomas and Morris 5123C hepatomas in fasted rats anesthetized with sodium pentobarbital. Twenty-six per cent of the sarcocarcinomas (n = 53) and 48% of the hepatomas (n = 29) utilized blood lactic acid. The remainder released lactic acid into the venous blood. The steady-state rate of glucose consumption was similar in both lactate-producing and lactate-utilizing tumors. The range of lactate concentrations in the blood leaving the tumors was narrower than the range of lactate concentrations in the blood entering the tumors. This difference was caused by tumor lactic acid production at low arterial lactate concentrations and tumor lactic acid utilization at high arterial lactate concentrations. Individual tumors changed from lactic acid production to lactic acid utilization in a matter of minutes in response to an increase in the arterial lactic acid concentration. Mean lactic plus pyruvic acid concentrations and lactic/pyruvic acid ratios in the tumor venous blood were 2.15 +/- 0.22 and 23.4 +/- 3.7 mM, respectively, for Walker sarcocarcinoma 256 (n = 18) and 1.28 +/- 0.13 and 48.1 +/- 5.1 mM, respectively, for hepatoma 5123C (n = 11). The results suggest: that a steady-state lactic plus pyruvic acid concentration and lactic/pyruvic acid ratio are maintained in the tumor cell cytoplasm by the active glycolytic pathway and by lactic acid dehydrogenase; that the tumor intracellular concentrations equilibrate with the arterial blood and that the tumor steady state is expressed in the tumor venous blood; and that tumor lactic acid production or utilization results from the equilibration between the variable arterial lactic acid concentration and the more constant tumor intracellular steady-state lactic acid concentration. Since the arterial lactate concentration may be less than, greater than, or equal to the intracellular steady-state concentration, an individual tumor may produce, utilize or neither produce nor utilize lactic acid.     

Effect of acid-base status on plasma phosphorus response to lactate

The mechanism(s) underlying the hyperphosphatemia of lactic acidosis is uncertain. We assessed the interacting influence of the acid anion and acid-base status on plasma phosphorus concentration by administering lactic acid alone, lactic acid plus sodium bicarbonate, sodium bicarbonate alone, and sodium lactate alone to four different groups of dogs. The findings of (1) no increase in plasma phosphorus concentration with lactic acid plus sodium bicarbonate versus a marked increment with lactic acid alone, and (2) no difference in the plasma phosphorus response to sodium lactate versus sodium bicarbonate indicate that acidemia is necessary for the expression of lactate-induced hyperphosphatemia. The apparent greater propensity for marked hyperphosphatemia in lactic acidosis than in other types of metabolic acidosis remains unexplained, but conceivably might relate to differences in intracellular pH and in the rate of glycolysis.     

Reduction of waste product excretion via nutrient control: Possible strategies for maximizing product and cell yields on serum in cultures of mammalian cells

Mammalian cells grown in culture excrete lactic acid and ammonium ions in quantities that may limit growth and reduce product synthesis. Frequent replenishment of the culture medium is often necessary to prevent waste product accumulation which could inhibit cell growth. Since increased medium replenishment results in increased usage of animal serum, the most expensive raw material, excessive production of waste products lowers the cell and product yield on serum, and hence increases production costs. Strategies for reducing the production of lactic acid and ammonium bymammalian cells via controlled addition of glucose and glutamine will be demonstrated. Mathematical relations coupling ammonium and glutamine kinetics will be described. Additionally, a method for automatic on-line estimation of the cell concentration was developed. This method involves calculating the ATP production rate from the oxygen uptake rate and the lactic acid production rate. Automatic online estimation of the cell concentration is critical if nutrient levels in large-scale mammaliancell cultures are to be accurately maintained via process control.     

Improved oxygen transfer and increased l-lactic acid production by morphology control of Rhizopus oryzae in a static bed bioreactor

Rhizopus oryzae was immobilized on a cotton matrix in a static bed bioreactor. Compared with free cells in a stirred tank bioreactor, immobilized R. oryzae in this bioreactor gave higher lactic acid production but lower ethanol production. The highest lactic acid production rate (2.09 g/L h) with the final concentration of 37.83 g/L from 70 g/L glucose was achieved when operating the bioreactor at 700 rpm and 0.5 vvm air. To better understand the relationship between shear effects (agitation and aeration) and R. oryzae morphology and metabolism, oxygen transfer rate, fermentation kinetics, and lactate dehydrogenase activity were determined. In immobilized cell culture, higher oxygen transfer rate and lactic acid production were achieved but lower lactate dehydrogenase activity was found as compared with those in free cell culture operated at the same conditions. These results clearly imply that mass transport was the rate controlling step in lactic acid fermentation by R. oryzae.     

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.     

High viable cell concentration fed-batch cultures of hybridoma cells through on-line nutrient feeding

A hybridoma cell line was cultivated in fed-batch cultures using a low-protein, serum-free medium. On-line oxygen uptake rate (OUR) measurement was used to adjust the nutrient feeding rate based on glucose consumption, which was estimated on-line using the stoichiometric relations between glucose and oxygen consumption. Through on-line control of the nutrient feeding rate, not only sufficients were supplied for cell growth and antibody production, but also the concentrations of glucose and other important nutrients such as amino acids were maintained at low levels during the cell growth phase. During the cultivation, cell metabolism changed from high lactate production and low oxygen consumption to low lactate production and high oxygen consumption. As a result the accumulation of lactate was reduced and the growth phase was extended. In comparison with the batch cultures, in which cells reached a concentration of approximately 2 x 10(6) cells/mL, a very high concentration of 1.36 x 10(7) cells/mL with a high cell viability (>90%) was achieved in the fed-batch culture. By considering the consumption of glucose and amino acids, as well as the production of cell mass, metabolites, and antibodies, a well-closed material balance was established. Our results demonstrate the value of coupling on-line OUR measurement and the stoichiometric realations for dynamic nutrient feeding in high cell concentration fed batch cultures. (c) 1995 John Wiley & Sons, Inc.     

Kinetics of Homoacetic Fermentation of Lactate by Clostridium formicoaceticum

Clostridium formicoaceticum homofermentatively converted lactate to acetate at mesophilic temperatures (30 to 42°C) and at pHs between 6.6 and 9.6. The production of acetate was found to be growth associated. Approximately 0.96 g of acetic acid and 0.066 g of cells were formed from each gram of lactic acid consumed at 37°C. The concentration of the substrate (lactate) had little or no effect on the growth rate; however, the fermentation was inhibited by acetic acid. The bacterium grew at an optimal pH of 7.6 and an optimal temperature of 37°C. Small amounts of bicarbonate were stimulatory to bacterial growth. Bacterial growth was enhanced, however, by the use of higher concentrations of bicarbonate in the media, only because higher buffer capacities were obtained and proper medium pH could be maintained for growth. Based on its ability to convert lactate to acetate, this homoacetic bacterium may be important in the anaerobic methanogenic process when lactate is a major intermediary metabolite.     

High-concentration cultivation of Lactococcus cremoris in a cell-recycle reactor

High-cell concentration cultivation of Lactococcus cremoris, a homofermentative lactic acid producer, in a cell-recycle fermentor is described. Cross-flow filtration allowing continuous removal of the inhibitory metabollte, the influence of dilution rate on growth was investigated in total or partial cell-recycle cultures. The dependence of growth characteristics on operating conditions was identified and quantified using lactose as the carbon source. Growth kinetics could be described by both lactate removal efficiency and nutrient availability. Based on physiological observations, biomass and lactic acid productivities were predicted in partial cell-recycle cultures.     

Lactic acid translocation: terminal step in glycolysis by Streptococcus faecalis

Streptococcus faecalis obtains metabolic energy chiefly from the conversion of glucose to lactic acid; the present experiments deal with the mechanism of lactic acid translocation across the cytoplasmic membrane. Efflux of [(14)C]lactate from preloaded cells was accelerated by raising the external pH, and also by the ionophores nigericin and valinomycin. These results suggest that lactate leaves the cell by an electroneutral process, presumably as lactic acid. Further evidence was obtained by studying the entry of [(14)C]lactate into nonmetabolizing cells. It appears that the membrane is essentially impermeable to the lactate anion, but allows passage of lactic acid. The most persuasive evidence is that, upon establishment of a pH gradient such that the cytoplasm was alkaline, l-[(14)C]lactate accumulated in the cells against the concentration gradient. Accumulation was transient, and dissipated in parallel with the collapse of the pH gradient. The concentration gradient attained at the peak was a function of the pH difference. Ionophores which are known to collapse a pH gradient, such as nigericin and valinomycin, abolished accumulation of l-lactate. We infer that lactic acid translocation, whether into the cells or outward, is an electroneutral process and for that reason the distribution of lactic acid across the membrane is a function of the pH of cytoplasm and medium. The specificity of translocation and its kinetic parameters suggest that it is mediated by a carrier of low specificity.     

Elucidation of the mechanism of lactic acid growth inhibition and production in batch cultures of Lactobacillus rhamnosus

Batch cultures of Lactobacillus rhamnosus were carried out at different pH values in order to study the limitation of growth and lactic acid production by the hydrogen ion, non-dissociated lactic acid and internal lactate concentrations. The effect of pH between 5 and 6.8 was studied at non-limiting concentrations of glucose; this is more significant for the lactic acid fermentation rate than for the maximum specific growth rate, as shown by the incomplete substrate consumption at lower values of medium pH and by the constant maximum cell mass obtained within the range of pH values studied. To check whether these results were a direct consequence of the different concentrations of the non-dissociated form of lactic acid at different external pH values, specific growth rates and lactic acid productions rates were calculated for each external pH value. The same specific growth rates were observed at the same non-dissociated lactic acid concentrations only at pH values of 5 and 5.5. For higher values of pH (pH > 6) the specific growth rate falls to zero as the non-dissociated lactic acid concentration decreases. This shows that generalisations made from studies performed within very narrow ranges of pH are not valid and that the non-dissociated form of lactic acid is not the only inhibiting species. The internal pH was measured experimentally for each external pH value in order to calculate the internal lactate ion concentration. This form is described to be the inhibitory one. The results obtained confirmed that the specific growth rate reached zero at approximately the same lactate concentration for all the pH values studied. Received: 31 January 1997 / Received revision: 15 May 1997 / Accepted: 19 May 1997     

Aeration-controlled formation of acetic acid in heterolactic fermentations

Summary Controlled aeration ofLeuconostoc mesenteroides was studied as a possible mechanism for control of the formation of acetic acid a metabolite of major influence on the taste of lactic fermented foods. Fermentations were carried out in small scale in a medium in which growth was limited by the buffer capacity only. Ethanol and acetic acid formed during the fermentation were analyzed by rapid head space gas chromatography, and the ratio of the molar concentrations of these two volatiles quantitatively predicted the balance between the formation of acetic acid and lactic acid. The oxygen concentration during the fermentations decreased rapidly to zero, meaning that oxygen transfer was limited by the volumetric oxygen transfer rate,k ₁ aC ^*. A linear correlation between k₁aC^* and the quantity of acetic acid produced was established, and it is suggested that such oxygenated heterolactic fermentation processes should be analyzed as fed-batch fermentations with oxygen as the limiting substrate. Addition of fructose in limited amounts leads to the formation of one half mole of acetic acid for each mole fructose, thus offering an alternative mechanism for controlling acetic acid formation.     

Computational modeling of nutrient utilization in engineered cartilage

This study presents a mathematical model for simulating cartilaginous culture of chondrocytes seeded in scaffolds and for investigating the effects of glucose and oxygen concentration and pH value on cell metabolic rates. The model can clearly interpret the unexplained experimental observation (Sengers BG, Heywood HK, Lee DA, Oomens CWJ, Bader DL. Nutrient utilization by bovine articular chondrocytes: A combined experimental and theoretical approach. J Biomech Eng. 2005;127:758–766.), which showed that the oxygen concentration within the scaffold may increase instead of continuously decreasing in static cartilaginous culture of chondrocytes. Results from simulation demonstrate that when cells metabolize glucose and form lactate under high glucose concentration conditions, the acidity in the culture environment increases, inhibiting cell metabolic rates in the process. Consequently, the rate of oxygen consumption decreases in later stages of cell culture. As oxygen can be replenished through the free surface of the culture medium, oxygen concentration within the scaffold increases rather than decreases over time in the acidic environment. Different initial glucose concentration yields different results. In low glucose concentration conditions, oxygen concentration basically keeps decreasing with culture time. This is because the pH in the environment does not significantly change because of slower glycolysis rate in low glucose concentration cases, forming less lactic acid. From the simulation results, additional information regarding in vitro culture of chondrocytes is obtained. The correlations between nutrient consumption, lactate secretion, and pH changes during cell culture are also understood and may serve as a reference for in vitro cell culture research of tissue engineering. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 452–462, 2013     

Stable hybridoma cultivation in a pilot-scale acoustic perfusion system: long-term process performance and effect of recirculation rate

Perfusion systems have the possibility to be operated continuously for several months. It is important that the performance of the cell retention device does not limit the operation time of a perfusion process used in the production of active pharmaceutical ingredients. Therefore, the aim of this study was to investigate the reliability and long-term stability of an acoustic perfusion process using the 200 L/d BioSep. As the BioSep is an external device, it is possible that dependent on the recirculation rate nutrient gradients occur in the external loop, which could affect the cell metabolism. Therefore, the effect of possible nutrient gradients on cell metabolism, viability and productivity was studied by varying the recirculation rate. In this study, it is shown that a perfusion process using a pilot-scale acoustic cell-retention device (200 L/d) is reliable and simple to operate, resulting in a stable 75-day cultivation of a hybridoma cell line producing a monoclonal antibody. The recirculation rate had a significant effect on the oxygen concentration in the external loop, with oxygen being depleted within the cell-retention device at recirculation rates below 6 m3/m(reactor)3.d (=600 L/d). The oxygen depletion at low circulation rates correlated with a slightly increased lactate production rate. For all other parameters no effect of the recirculation rate was observed, including cell death measured through the release of lactate dehydrogenase and specific productivity. A maximum specific productivity of 12 pg/cell.d was reached.     

Nutrient gradients in engineered cartilage: metabolic kinetics measurement and mass transfer modeling

Since tissue-engineered cartilage is avascular, both nutrient supply and metabolic waste removal rely on diffusion. As a result, gradients of nutrients and wastes exist through the construct. Previous models usually calculate gradients of oxygen, glucose, and lactic acid separately, without taking into account the complex interdependence between concentrations of these substrates and rates of metabolism. In this study, these interactions were experimentally examined and incorporated into diffusion models. One-dimensional diffusion-reaction models were developed for three typical culture conditions, that is, static culture, perfusion culture, and suspended culture. The profiles of oxygen, glucose, lactic acid, and pH in the cultured constructs were calculated simultaneously using measured metabolic rates. The maximum construct size and cell density which could be supported before nutrients were depleted in the construct center was identified; a function predicting the relationship between construct dimension and the maximum viable cell density was developed. For constructs incubated under static culture the model demonstrated that the gradients which developed through the medium could not be neglected. Perfusion cultures could support a considerably higher cell density than static cultures, while for batch cultures in a rotating bioreactor, the volume of medium also influences the maximum cell density that could be supported. This study provides useful guidance for design of engineered cartilage constructs.     

Examination of Lactobacillus plantarum lactate metabolism side effects in relation to the modulation of aeration parameters

AIMS: The characterization of global aerobic metabolism of Lactobacillus plantarum LP652 under different aeration levels, in order to optimize acetate production kinetics and to suppress H2O2 toxicity. METHODS AND RESULTS: Cultures of L. plantarum were grown on different aeration conditions. After sugar exhaustion and in the presence of oxygen, lactate was converted to acetate, H2O2 and carbon dioxide with concomitant ATP production. Physiological assays were performed at selected intervals in order to assess enzyme activity and vitality of the strain during lactic acid conversion. The maximal aerated condition led to fast lactate-to-acetate conversion kinetics between 8 and 12 h, but H2O2 immediately accumulated, thus affecting cell metabolism. Pyruvate oxidase activity was highly enhanced by oxygen tension and was responsible for H2O2 production after 12 h of culture, whereas lactate oxidase and NADH-dependent lactate dehydrogenase activities were not correlated to metabolite production. Limited NADH oxidase (NOX) and NADH peroxidase (NPR) activities were probably responsible for toxic H2O2 levels in over-aerated cultures. CONCLUSION: Modulating initial airflow led to the maximal specific activity of NOX and NPR observed after 24 h of culture, thus promoting H2O2 destruction and strain vitality at the end of the process. SIGNIFICANCE AND IMPACT OF THE STUDY: Optimal aeration conditions were determined to minimize H2O2 concentration level during growth on lactate.     

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.     

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.