Mass transport and shear stress in a microchannel bioreactor: numerical simulation and dynamic similarity

Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells. In this study, substrate concentrations and shear stresses at the base were computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters were developed from a simplified analysis. The numerical results of substrate concentration were well correlated by the combined parameters. The generalized results may find applications in design analysis of microchannel bioreactors. The mass transport and shear stress were related in a generalized result. Based on the generalized results and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered.     

Numerical simulation of mass transport in a microchannel bioreactor with cell micropatterning

Micropatterning of two different cell types based on surface modification allows spatial control over two distinct cell subpopulations. This study considers a micropatterned coculture system, which has release and absorption parts alternately arranged at the base, and each part has a single cell type. A micropattern unit was defined and within each unit, there are one release part and one absorption part. The cells in the absorption parts consume species, which are secreted by the cells in the release parts. The species concentrations at the micropatterned cell base were computed from a three-dimensional numerical flow model incorporating mass transport. Different combined parameters were developed for the release and absorption parts to make the data collapse in each part. Combination of the collapse data in the release and absorption parts can be used to predict the concentration distribution through the whole channel. The correlated results were applied to predict the critical length ratio of the release and absorption parts for an actual micropatterned system (Bhatia et al., 1999, "Effect of Cell-Cell Interactions in Preservation of Cellular Phenotype: Co-Cultivation of Hepatocytes and Nonparenchymal Cell," FASEB J. 13, pp. 1883-1900) to avoid species insufficiency based on basic fibroblast growth factor (bFGF). The mass transfer effectiveness was found to be higher with more numbers of micropattern units. The optimal condition for micropatterned coculture bioreactors is achieved by having the product of the length ratio and the reaction ratio equal to 1. This condition was used to optimize the mass transfer in the micropatterned system (Bhatia et al., 1999, "Effect of Cell-Cell Interactions in Preservation of Cellular henotype: Co-Cultivation of Hepatocytes and Nonparenchymal Cell," FASEB J. 13, pp. 1883-1900) based on bFGF.     

Mass transport in a microchannel bioreactor with a porous wall

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.     

RWPV bioreactor mass transport: earth-based and in microgravity

Mass transport and mixing of perfused scalar quantities in the NASA Rotating Wall Perfused Vessel bioreactor are studied using numerical models of the flow field and scalar concentration field. Operating conditions typical of both microgravity and ground-based cell cultures are studied to determine the expected vessel performance for both flight and ground-based control experiments. Results are presented for the transport of oxygen with cell densities and consumption rates typical of colon cancer cells cultured in the RWPV. The transport and mixing characteristics are first investigated with a step change in the perfusion inlet concentration by computing the time histories of the time to exceed 10% inlet concentration. The effects of a uniform cell utilization rate are then investigated with time histories of the outlet concentration, volume average concentration, and volume fraction starved. It is found that the operating conditions used in microgravity produce results that are quite different then those for ground-based conditions. Mixing times for microgravity conditions are significantly shorter than those for ground-based operation. Increasing the differential rotation rates (microgravity) increases the mixing and transport, while increasing the mean rotation rate (ground-based) suppresses both. Increasing perfusion rates enhances mass transport for both microgravity and ground-based cases, however, for the present range of operating conditions, above 5-10 cc/min there are diminishing returns as much of the inlet fluid is transported directly to the perfusion exit. The results show that exit concentration is not a good indicator of the concentration distributions in the vessel. In microgravity conditions, the NASA RWPV bioreactor with the viscous pump has been shown to provide an environment that is well mixed. Even when operated near the theoretical minimum perfusion rates, only a small fraction of the volume provides less than the required oxygen levels.     

Modeling of effects of nutrient gradients on cell proliferation in microfluidic bioreactor

Precise control of the microenvironment is highly desirable in cell culture to study the cell biology. Microfluidic based bioreactors provide a promising method for the spatial and temporal control of cell growth and stimuli. A three-dimensional nutrient transport model, incorporating the monolayer cell growth model, has been developed to investigate the influence of gradients of oxygen and epidermal growth factor (EGF) on the cell culture in the continuous-flow microchannel bioreactor. Our results demonstrate that applying inlet concentration gradients of oxygen and EGF can induce variations of cell density in the y-direction. It is further found that compared to the oxygen gradients the EGF concentration gradients are more efficient in regulating the cell growth.     

Immobilized cell microchannel bioreactor for evaluating fermentation characteristics of mixed substrate consumption and product formation

An immobilized cell microchannel bioreactor was designed to test continuous fermentation. The fermentation set-up included a bottom hydrophilic quartz channel to immobilize cells using 0.4 wt% polyethyleneimine and a top channel designed to continuously remove metabolically generated carbon dioxide using hydrophobic polypropylene. To evaluate fermentation characteristics of immobilized cells, ethanol fermentation was carried out using Saccharomyces cerevisiae and Pichia stipitis. The immobilized cell microchannel bioreactor was used to identify long-term activity of immobilized S. cerevisiae cells. The continuous flow microchannel bioreactor was operated stably over a period of 1 month. The immobilized cell microchannel bioreactor was used to examine the characteristics cells that consumed mixed substrates. The concentration ratio of glucose to xylose for simultaneous utilization of hemicellulosic sugars was evaluated using the microchannel bioreactor and the results were compared with those obtained by using conventional batch fermentation with P. stipitis.     

Design of well and groove microchannel bioreactors for cell culture

Microfluidic bioreactors have been shown valuable for various cellular applications. The use of micro-wells/grooves bioreactors, in which micro-topographical features are used to protect sensitive cells from the detrimental effects of fluidic shear stress, is a promising approach to culture sensitive cells in these perfusion microsystems. However, such devices exhibit substantially different fluid dynamics and mass transport characteristics compared to conventional planar microchannel reactors. In order to properly design and optimize these systems, fluid and mass transport issues playing a key role in microscale bioreactors should be adequately addressed. The present work is a parametric study of micro-groove/micro-well microchannel bioreactors. Operation conditions and design parameters were theoretically examined via a numerical model. The complex flow pattern obtained at grooves of various depths was studied and the shear protection factor compared to planar microchannels was evaluated. 3D flow simulations were preformed in order to examine the shear protection factor in micro-wells, which were found to have similar attributes as the grooves. The oxygen mass transport problem, which is coupled to the fluid mechanics problem, was solved for various groove geometries and for several cell types, assuming a defined shear stress limitation. It is shown that by optimizing the groove depth, the groove bioreactor may be used to effectively maximize the number of cells cultured within it or to minimize the oxygen gradient existing in such devices. Moreover, for sensitive cells having a high oxygen demand (e.g., hepatocytes) or low endurance to shear (e.g., human embryonic stem cells), results show that the use of grooves is an enabling technology, since under the same physical conditions the cells cannot be cultured for long periods of time in a planar microchannel. In addition to the theoretical model findings, the culture of human foreskin fibroblasts in groove (30 microm depth) and well bioreactors (35 microm depth) was experimentally examined at various flow rates of medium perfusion and compared to cell culture in regular flat microchannels. It was shown that the wells and the grooves enable a one order of magnitude increase in the maximum perfusion rate compared to planar microchannels. Altogether, the study demonstrates that the proper design and use of microgroove/well bioreactors may be highly beneficial for cell culture assays.     

Mass transport in a microchannel enzyme reactor with a porous wall: Hydrodynamic modeling and applications

A two-dimensional flow model, incorporating mass transport, has been developed to simulate a microchannel enzyme reactor with a porous wall. A two-domain approach based on the finite volume method was implemented. Two parameters are defined to characterize the mass transports in the fluid and porous regions: the porous Damkohler number and the fluid Damkohler number. For reactions close to first-order type (enzyme reactor), the concentration results are found to be well correlated by the use of a reaction–convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection. The reactor efficiency reduces with reaction–convection distance parameter because of reduced reaction (or flux) due to the lower concentration. Increased fluid convection improves the efficiency but it is limited by the diffusion in the fluid region. The correlated results can find applications for the design of enzyme reactors with a porous wall.     

Model of the mass transport to the surface of animal cells cultured in a rotating bioreactor operated in micro gravity

A mathematical model is used to investigate the transport of dissolved oxygen from the bulk fluid to the surface of aggregates of animal cells cultured in a rotating bioreactor. These aggregates move through different regions of the bioreactor with a local flow field and concentration distribution that vary with time. The time variation of the Sherwood number and the surface concentration for a range of parameters typical of a cell science experiment executed in the Rotating Wall Perfused Vessel (RWPV) bioreactor in space are investigated. The Reynolds numbers experienced by the aggregate are generally low (Re < 1) and the Peclet numbers range from O(1) to O(100). Comparison of the results from the numerical solution of the mathematical model with those from a quasi-steady model, using a steady-state correlation for mass transport on a sphere, indicate that the quasi-steady assumption is not a good model to compute the instantaneous Sherwood number. This indicates a significant history effect in the Sherwood number response to the variations of acceleration of the aggregates in the bioreactor. A high resistance to the mass transport from the bulk fluid to the surface of the aggregate exists for the bioreactor operated in micro gravity. The difference between the surface concentration and the free stream concentration was as high as 30% for aggregates larger than 3 mm. Diffusion reduces the variations of the free stream concentration resulting in a nearly constant value for the concentration at the surface of the aggregates.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

Surface transformation of bioactive glass in bioreactors simulating microgravity conditions. Part II: numerical simulations

The effects of simulated microgravity on the surface modification of bioactive glass (BG) in solution were studied using a numerical method. Models were developed for estimating the mass transfers of different chemical species from the surface of bioactive glass particles (microcarriers) suspended in the rotating liquid medium of a NASA-designed high aspect ratio vessel (HARV) bioreactor and on the bottom surface of a static vial. The concentration profiles resulting from chemical reactions and ionic transports were ascertained. Numerical results for the transport under simulated microgravity in the HARV and at normal gravity in the static vial were compared. These results were also compared with those of experiments to verify the enhancement of the reaction kinetics under simulated microgravity conditions. The experimental and numerical studies confirm that simulated microgravity conditions lead to the quick achievement of bioactive glass surface modification.     

Next-generation polymerized human hemoglobins in hepatic bioreactor simulations

Hepatic hollow fiber (HF) bioreactors can be used to provide temporary support to patients experiencing liver failure. Before being connected to the patient's circulation, cells in the bioreactor must be exposed to a range of physiological O₂ concentrations as observed in the liver sinusoid to ensure proper performance. This zonation in cellular oxygenation promotes differences in hepatocyte phenotype and may better approximate the performance of a real liver within the bioreactor. Polymerized human hemoglobin (PolyhHb) locked in the tense quaternary state (T-state) has the potential to both supply and regulate O₂ transport to cultured hepatocytes in the bioreactor due to its low O₂ affinity. In this study, T-state PolyhHb production and purification processes were optimized to minimize the concentration of low-molecular-weight PolyhHb species in solution. Deconvolution of size-exclusion chromatography spectra was performed to calculate the distribution of polymeric Hb species in the final product. Fluid flow and mass transport within a single fiber of a hepatic HF bioreactor was computationally modeled with finite element methods to simulate the effects of employing T-state PolyhHb to facilitate O₂ transport in a hepatic bioreactor system. Optimal bioreactor performance was defined as having a combined hypoxic and hyperoxic volume fraction in the extracapillary space of less than 0.05 where multiple zones were observed. The Damköhler number and Sherwood number had strong inverse relationships at each cell density and fiber thickness combination. These results suggest that targeting a specific Damköhler number may be beneficial for optimal hepatic HF bioreactor operation.     

Development of a novel bioreactor system for treatment of gaseous benzene

A novel, continuous bioreactor system combining a bubble column (absorption section) and a two-phase bioreactor (degradation section) has been designed to treat a gas stream containing benzene. The bubble column contained hexadecane as an absorbent for benzene, and was systemically chosen considering physical, biological, environmental, operational, and economic factors. This solvent has infinite solubility for benzene and very low volatility. After absorbing benzene in the bubble column, the hexadecane served as the organic phase of the two-phase partitioning bioreactor, transferring benzene into the aqueous phase where it was degraded by Alcaligenes xylosoxidans Y234. The hexadecane was then continuously recirculated back to the absorber section for the removal of additional benzene. All mass transfer and biodegradation characteristics in this system were investigated prior to operation of the integrated unit, and these included: the mass transfer rate of benzene in the absorption column; the mass transfer rate of benzene from the organic phase into the aqueous phase in the two-phase bioreactor; the stripping rate of benzene out of the two-phase bioreactor, etc. All of these parameters were incorporated into model equations, which were used to investigate the effects of operating conditions on the performance of the system. Finally, two experiments were conducted to show the feasibility of this system. Based on an aqueous bioreactor volume of 1 L, when the inlet gas flow and gaseous benzene concentration were 120 L/h and 4.2 mg/L, respectively, the benzene removal efficiency was 75% at steady state. This process is believed to be very practical for the treatment of high concentrations of gaseous pollutants, and represents an alternative to the use of biofilters.     

Model-based analysis and design of a microchannel reactor for tissue engineering

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.     

Biological phenol degradation in a gas-liquid-solid fluidized bed reactor

Biological phenol degradation was performed experimentally in a gas-liquid-solid fluidized bed bioreactor using a mixed culture of living cells immobilized on activated carbon particles. A comprehensive model was developed for this system utilizing double-substrate limiting kinetics. The model was used to simulate the effects of changing inlet phenol concentration and biofilm thickness on the rate of biodegradation for two different types of support particles. The model shows that gas-liquid mass transfer is the limiting step in the rate of phenol biodegradation when the phenol loading is high.     

Modeling multiphase fluid flow,mass transfer,and chemical reactions in bioreactors using large-eddy simulation

We present a transient large eddy simulation (LES) modeling approach for simulating the interlinked physics describing free surface hydrodynamics, multiphase mixing, reaction kinetics, and mass transport in bioreactor systems. Presented case-studies include non-reacting and reacting bioreactor systems, modeled through the inclusion of uniform reaction rates and more complex biochemical reactions described using Contois type kinetics. It is shown that the presence of reactions can result in a non-uniform spatially varying species concentration field, the magnitude and extent of which is directly related to the reaction rates and the underlying variations in the local volumetric mass transfer coefficient.     

A bioactive foamed emulsion reactor for the treatment of benzene-contaminated air stream

An adapted bioactive foamed emulsion bioreactor for the treatment of benzene vapor has been developed. In this reactor, bed clogging was resolved by bioactive foam as a substitute of packing bed for interfacial contact of liquid to gaseous phase. The pollutant solubility has been increased using biocompatible organic phase in liquid phase and this reactor can be applied for higher inlet benzene concentration. Experimental results showed a benzene elimination capacity (EC) of 220 g m⁻³ h⁻¹ with removal efficiency (RE) of 85% for benzene inlet concentration of 1–1.2 g m⁻³ at 15 s gas residence time in bioreactor. Assessment of benzene concentration in liquid phase showed that a significant amount of transferred benzene mass has been biodegraded. By optimizing the operational parameters of bioreactor, continuous operation of bioreactor with high EC and RE was demonstrated. With respect to the results, this reactor has the potential to be applied instead of biofilter and biotrickling filters.     

Toluene removal from waste air using a flat composite membrane bioreactor

In this report, gaseous toluene biodegradation results in a flat composite membrane reactor inoculated with Pseudomonas putida TVA8 are presented. Preliminary abiotic experiments showed that transport of toluene through the membrane was linearly and negatively correlated with the gas residence time (tau). During a 339-day biofiltration experiment, the influence of gas residence time (2-24 sec) and mass loading rate (B(v); 10-483 g x m(-3) h(-1)) on the toluene elimination capacity was investigated. A maximum elimination capacity (EC(max)) of 397 g x m(-3) h(-1) was achieved at tau = 24 sec and B(v) = 473 g x m(-3) h(-1). Expressed per unit membrane area, the EC(m,max) was 0.793 g x m(-2) h(-1), which is five times higher than results obtained with other membrane bioreactor experiments in the same range of loading rates. At low gas residence times, reactor performance was limited by mass transfer. Toluene concentration profiles along the membrane were measured for several biotic and abiotic conditions. For inlet concentrations (C(in)) up to 1 g x m(-3), more than 90% was eliminated at 15 cm from the reactor inlet. For C(in) > 1.65 g x m(-3), longer membranes are necessary to obtain these high removal efficiencies.     

Bioartificial kidney. II. A convective flow model of a hollow fiber bioartificial renal tubule

An existing model for volume transport in the rat proximal tubule was modified and applied to a bioartificial renal tubule. The predicted volume transport agrees well with experimental data. The volume transport model was coupled to the analytic solutions of flow in the bioartificial renal tubule bioreactor, operated in the open-shell mode with perfusion in both the lumen and surrounding shell. The results suggest that the performance of a multifiber bioreactor can be improved by controlling shell inlet conditions and fiber spacing. These results have important implications for the design and analysis not only for the bioartificial renal tubule bioreactor but also for the general case of hollow fiber bioreactors operated in the open-shell mode with perfusion in both the lumen and surrounding shell.