A simple correlation for predicting effective diffusivities in immobilized cell systems

Mass Transfers in a Fluidized Bed Bioreactor using Alginate Beads for a Future Bioartificial Liver

Fluidized bed bioreactor with alginate beads may be an alternative to hollow fiber cartridge to host hepatocytes for bioartificial liver purposes. After the bioreactor design and the characterization of fluid mechanics, the present study was aimed at analyzing bi-directional mass transfers of calibrated species between external fluid and empty beads. Static (batch) and dynamic (fluidized bed bioreactor) experimental conditions were analyzed. A simple modelling approach permitted the definition of mass transfer coefficients.

The motion of beads within the bioreactor clearly enhanced mass transfer kinetics, but did not alter the amount exchanged. The shear enhanced diffusion coefficient for VitB12 was 20 times higher in the fluidized bed bioreactor than under batch conditions, proving the efficiency of such a device.

Oxygen consumption by bovine granulosa cells with prediction of oxygen transport in preantral follicles

The rate of oxygen consumption by granulosa cells is a key parameter in mathematical models that describe oxygen transport across ovarian follicles. This work measured the oxygen consumption rate of bovine granulosa cells in vitro to be in the range 2.1–3.3 × 10–16 mol cell–1 s–1 (0.16–0.25 mol m–3 s–1). The implications of the rates for oxygen transport in large bovine preantral follicles were examined using a mathematical model. The results indicate that oocyte oxygenation becomes increasingly constrained as preantral follicles grow, reaching hypoxic levels near the point of antrum formation. Beyond a preantral follicle radius of 134 µm, oxygen cannot reach the oocyte surface at typical values of model parameters. Since reported sizes of large bovine preantral follicles range from 58 to 145 µm in radius, this suggests that oocyte oxygenation is possible in all but the largest preantral follicles, which are on the verge of antrum formation. In preantral bovine follicles, the oxygen consumption rate of granulosa cells and fluid voidage will be the key determinants of oxygen levels across the follicle.

Ethanol fermentation in a magnetically fluidized bed reactor with immobilized Saccharomyces cerevisiae in magnetic particles

Ethanol fermentation by immobilized Saccharomyces cerevisiae cells in magnetic particles was successfully carried out in a magnetically stabilized fluidized bed reactor (MSFBR). These immobilized magnetic particles solidified in a 2 % CaCl(2) solution were stable and had high ethanol fermentation activity. The performance of ethanol fermentation of glucose in the MSFBR was affected by initial particle loading rate, feed sugar concentration and dilution rate. The ethanol theoretical yield, productivity and concentration reached 95.3%, 26.7 g/L h and 66 g/L, respectively, at a particle loading rate of 41% and a feed dilution rate of 0.4 h(-1) with a glucose concentration of 150 g/L when the magnetic field intensity was kept in the range of 85-120 Oe. In order to use this developed MSFBR system for ethanol production from cheap raw materials, cane molasses was used as the main fermentation substrate for continuous ethanol fermentation with the immobilized S. cerevisiae cells in the reactor system. Molasses gave comparative ethanol productivity in comparison with glucose in the MSFBR, and the higher ethanol production was observed in the MSFBR than in a fluidized bed reactor (FBR) without a magnetic field.

Theoretical investigation into the dissolved oxygen levels in follicular fluid of the developing human follicle using mathematical modelling

Oxygen levels in the follicle are likely to be critical to follicle development. However, a quantitative description of oxygen levels in the follicle is lacking. Mathematical modelling was used to predict the dissolved oxygen levels in the follicular fluid of the developing human follicle. The model predictions showed that follicular fluid dissolved oxygen levels are highly variable among follicles, due to the unique geometry of individual follicles. More generally, predictions showed that oxygen levels in follicular fluid increase rapidly during the initial early antral stages of follicle growth before peaking in the later early antral phase. Follicular fluid dissolved oxygen levels then decline through to the beginning of the pre-ovulatory phase, from which they increase through to ovulation. Based on the best available parameter estimates, the model predictions suggest that the mean dissolved oxygen levels in human follicular fluid during the late antral and pre-ovulatory phases range between 11 and 51 mmHg (~1.5–6.7 vol%). These predictions suggest that the human ovarian follicle is a low-oxygen environment that is often challenged by hypoxia, and are in agreement with only some published data on follicular fluid oxygen levels. Predictions are discussed in relation to follicle health and oocyte culture.

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.

Mathematical modelling of oxygen transport-limited follicle growth

Mathematical modelling was used to investigate oxygen transport in the developing ovarian follicle. In contrast to previous findings, the results show that oxygen can reach the oocyte in large preantral follicles. This is largely due to the inclusion of fluid voidage in the model and improved estimates of oxygen diffusion coefficients through the granulosa. The results also demonstrate that preantral follicles will eventually reach a size beyond which further growth will result in the follicle becoming increasingly anoxic. The predicted size range at which this occurs is consistent with the size range at which antrum formation is observed in many mammals. This suggests that the antrum formation stage of follicular growth may be pivotal to the further development and ultimate fate of the follicle, and that antrum formation itself may represent a mechanism by which the follicle can overcome oxygen limitations. This was supported through extension of the model to the antral follicle, which showed that antrum formation can provide a way in which the follicle can continue to grow and yet avoid becoming hypoxic. The results of the model were consistent with observed follicle development.

Ethanol fermentation from biomass resources: current state and prospects

In recent years, growing attention has been devoted to the conversion of biomass into fuel ethanol, considered the cleanest liquid fuel alternative to fossil fuels. Significant advances have been made towards the technology of ethanol fermentation. This review provides practical examples and gives a broad overview of the current status of ethanol fermentation including biomass resources, microorganisms, and technology. Also, the promising prospects of ethanol fermentation are especially introduced. The prospects included are fermentation technology converting xylose to ethanol, cellulase enzyme utilized in the hydrolysis of lignocellulosic materials, immobilization of the microorganism in large systems, simultaneous saccharification and fermentation, and sugar conversion into ethanol.

Ethanol fermentation in an immobilized cell reactor using Saccharomyces cerevisiae

Fermentation of sugar by Saccharomyces cerevisiae, for production of ethanol in an immobilized cell reactor (ICR) was successfully carried out to improve the performance of the fermentation process. The fermentation set-up was comprised of a column packed with beads of immobilized cells. The immobilization of S. cerevisiae was simply performed by the enriched cells cultured media harvested at exponential growth phase. The fixed cell loaded ICR was carried out at initial stage of operation and the cell was entrapped by calcium alginate. The production of ethanol was steady after 24 h of operation. The concentration of ethanol was affected by the media flow rates and residence time distribution from 2 to 7 h. In addition, batch fermentation was carried out with 50 g/l glucose concentration. Subsequently, the ethanol productions and the reactor productivities of batch fermentation and immobilized cells were compared. In batch fermentation, sugar consumption and ethanol production obtained were 99.6% and 12.5% v/v after 27 h while in the ICR, 88.2% and 16.7% v/v were obtained with 6 h retention time. Nearly 5% ethanol production was achieved with high glucose concentration (150 g/l) at 6 h retention time. A yield of 38% was obtained with 150 g/l glucose. The yield was improved approximately 27% on ICR and a 24 h fermentation time was reduced to 7 h. The cell growth rate was based on the Monod rate equation. The kinetic constants (K(s) and mu(m)) of batch fermentation were 2.3 g/l and 0.35 g/lh, respectively. The maximum yield of biomass on substrate (Y(X-S)) and the maximum yield of product on substrate (Y(P-S)) in batch fermentations were 50.8% and 31.2% respectively. Productivity of the ICR were 1.3, 2.3, and 2.8 g/lh for 25, 35, 50 g/l of glucose concentration, respectively. The productivity of ethanol in batch fermentation with 50 g/l glucose was calculated as 0.29 g/lh. Maximum production of ethanol in ICR when compared to batch reactor has shown to increase approximately 10-fold. The performance of the two reactors was compared and a respective rate model was proposed. The present research has shown that high sugar concentration (150 g/l) in the ICR column was successfully converted to ethanol. The achieved results in ICR with high substrate concentration are promising for scale up operation. The proposed model can be used to design a lager scale ICR column for production of high ethanol concentration.

Modeling pO(2) distributions in the bone marrow hematopoietic compartment. I. Krogh's model

Human bone marrow (BM) is a tissue of complex architectural organization, which includes granulopoietic loci, erythroblastic islets, and lymphocytic nodules. Oxygen tension (pO(2)) is an important determinant of hematopoietic stem and progenitor cell proliferation and differentiation. Thus, understanding the impact of the BM architectural organization on pO(2) levels in extravascular hematopoietic tissue is an important biophysical problem. However, currently it is impossible to measure pO(2) levels and their spatial variations in the BM. Homogeneous Kroghian models were used to estimate pO(2) distribution in the BM hematopoietic compartment (BMHC) and to conservatively simulate pO(2)-limited cellular architectures. Based on biophysical data of hematopoietic cells and characteristics of BM physiology, we constructed a tissue cylinder solely occupied by granulocytic progenitors (the most metabolically active stage of the most abundant cell type) to provide a physiologically relevant limiting case. Although the number of possible cellular architectures is large, all simulated pO(2) profiles fall between two extreme cases: those of homogeneous tissues with adipocytes and granulocytic progenitors, respectively. This was illustrated by results obtained from a parametric criterion derived for pO(2) depletion in the extravascular tissue. Modeling results suggest that stem and progenitor cells experience a low pO(2) environment in the BMHC.

A diffusion model and optimal cell loading for immobilized cell biocatalysts

A diffusion model based on the random pore model is derived for immobilized cell biocatalysts and verified with 19 sets of experimental diffusion data. The predicted effective diffusivity relative to that for the support matrix reflects a quadratic dependence on the cell loading and contains a single parameter that depends on the intracellular diffusivity and the chemical partitioning coefficient. The model is used to predict optimal cell loadings that maximize the total reaction rate in an immobilized cell biocatalyst. A rule of thumb based on the diffusion model is obtained to the effect that the cell loading should be at least (1/3) for single reactions regardless of the kinetics and diffusional resistances. A means of calculating improved lower bounds is provided for cases where the cellular diffusional resistance is known but the kinetics are not. The optimal cell loadings for reversible first-order and for Michaelis-Menten kinetics are presented and demonstrated to be within the range of conditions of practical interest.

Characterisation of small molecules diffusion in hydrogel-membrane liquid-core capsules

The overall diffusion coefficients for several low molecular weight solutes, such as glucose, fructose, sucrose, lactose, and vitamin B(12) have been determined in Ca-alginate membrane liquid-core capsules using the unsteady-state method following the release of solutes from the capsules to a well-stirred solution of limited volume. The diffusion coefficients obtained for saccharides were 5-20% lower than the corresponding diffusivity in water while for vitamin B(12) about 50% that of water. The diffusion coefficients of the investigated capsules were not influenced by the change in alginate concentration in the capsule membrane from 0.5 to 1.0%. Lower diffusivities and higher deviations from the diffusivity in water were obtained for higher molecular weight solutes.

Diffusion in cell-free and cell immobilising kappa-carrageenan gel beads with and without chemical reaction

Diffusion into and from kappa-carrageenan gel beads was studied, both in the absence and presence of bacterial cells, both with and without biochemical reaction. The solutes were indole, L-serine, and L-tryptophan. The reaction was that of indole and L-serine to give L-tryptophan. Established theory concerning diffusion of a single solute in cell-free gels was found to describe well the effect of the gel on diffusivity. Simultaneous diffusion of the three solutes resulted in lower diffusivities than those for individual solutes, suggesting the need to use multicomponent diffusion theory. The effect of cells on diffusion could only be accounted for by models assuming permeable cells. Diffusion with chemical reaction was reasonably well described by an effectiveness factor calculated using an effective diffusivity estimated from diffusion data without reaction. Copyright 1999 John Wiley & Sons, Inc.

A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms

Experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms are reviewed. Effective diffusive permeabilities, the parameter appropriate to the analysis of reaction-diffusion interactions, depend on solute type and biofilm density. Three categories of solute physical chemistry with distinct diffusive properties were distinguished by the present analysis. In order of descending mean relative effective diffusive permeability (De/Daq) these were inorganic anions or cations (0.56), nonpolar solutes with molecular weights of 44 or less (0.43), and organic solutes of molecular weight greater than 44 (0.29). Effective diffusive permeabilities decrease sharply with increasing biomass volume fraction suggesting a serial resistance model of diffusion in biofilms as proposed by Hinson and Kocher (1996). A conceptual model of biofilm structure is proposed in which each cell is surrounded by a restricted permeability envelope. Effective diffusion coefficients, which are appropriate to the analysis of transient penetration of nonreactive solutes, are generally similar to effective diffusive permeabilities in biofilms of similar composition. In three studies that examine diffusion of very large molecular weight solutes (>5000) in biofilms, the average ratio of the relative effective diffusion coefficient of the large solute to the relative effective diffusion coefficient of either sucrose or fluorescein was 0.64, 0.61, and 0.36. It is proposed that large solutes are effectively excluded from microbial cells, that small solutes partition into and diffuse within cells, and that ionic solutes are excluded from cells but exhibit increased diffusive permeability (but decreased effective diffusion coefficients) due to sorption to the biofilm matrix.