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.     

Numerical simulation on mass transport in a microchannel bioreactor for co-culture applications

Microchannel bioreactors have applications for manipulating and investigating the fluid microenvironment on cell growth and functions in either single culture or co-culture. This study considers two different types of cells distributed randomly as a co-culture at the base of a microchannel bioreactor: absorption cells, which only consume species based on the Michaelis-Menten process, and release cells, which secrete species, assuming zeroth order reaction, to support the absorption cells. The species concentrations at the co-culture cell base are computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters are proposed for the co-culture system, developed from a simplified analysis under the condition of decreasing axial-concentration. The numerical results of species concentration at the co-culture cell-base are approximately correlated by the combined parameters under the condition of positive flux-parameter. Based on the correlated results, the critical value of the inlet concentration is determined, which depends on the effective microchannel length. For the flow to develop to the critical inlet concentration, an upstream length consisting only of release cells is needed; this upstream length is determined from an analytical solution. The generalized results may find applications in analyzing the mass transport requirements in a co-culture microchannel bioreactor.     

Characterization of the localized hydrodynamic shear forces and dissolved oxygen distribution in sparged bioreactors

Detailed, high-resolution numerical simulations of the bubbly flows, used for oxygen delivery and mixing in mammalian cell suspensions, have been performed. The hydrodynamics, shear and normal forces, mass transfer and mass transport from and around individual bubbles and bubble clusters were resolved for different operating conditions, that is, Weber, Morton, and Schmidt numbers. Suspended animal (e.g., mammalian, insect) cells are known to be susceptible to damage potentially leading to cell death, caused by hydrodynamic stresses and oxygen deprivation. Better knowledge of the magnitude of the shear forces and the extent of mixing of the dissolved oxygen in sparged bioreactors can have a significant impact on their future design and optimization. Therefore, the computed liquid-phase velocity fields were used to calculate and compare the local shear in different types of single bubble wakes and in bubble clusters. Oxygen mass transfer and dissolved oxygen transport were resolved to examine oxygen supply to the cells in the different types of flows.     

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.     

Solid-state fermentation in rotating drum bioreactors: operating variables affect performance through their effects on transport phenomena

Aspergillus oryzae ACM 4996 was grown on an artificial gel-based substrate and on steamed wheat bran during solid-state fermentations in 18.7 L rotating drum bioreactors. For gel fermentations fungal growth decreased as rotational speed increased, presumably due to increased shear. For wheat bran fermentations fungal growth improved under agitated compared to static culture conditions, due to superior heat and mass transfer. We conclude that the effects of operational variables on the performance of SSF bioreactors are mediated by their effects on transport phenomena such as mixing, shear, heat transfer, and mass transfer within the substrate bed. In addition, the substrate characteristics affect the need for and the rates of these transport processes. Different transport phenomena may be rate limiting with different substrates. This work improves understanding of the effects of bioreactor operation on SSF performance.     

Increased mass transfer to microorganisms with fluid motion

The effect of fluid flow and laminar shear on bacterial uptake was examined under conditions representative of the fluid environment of unattached and attached cells in wastewater treatment bioreactors. Laminar shear rates below 50 s(-1) did not increase leucine uptake by suspended cultures of Zoogloea ramigera. However, leucine uptake by cells fixed in a flow field of approximately 1 mm s(-1) was 55-65% greater than uptake by suspended cells. Enhanced microbial uptake with advective motion is consistent with mass transfer rates calculated using Sherwood number correlations. Advective flow increases microbial uptake by increasing collisions between substrate molecules and cells through compression of the concentration boundary layer surrounding a cell. The rate of leucine uptake suggests that binding proteins used to transport leucine into the cell can occupy approximately 1% of the cell surface area.     

Oxygen transport and cell viability in an annular flow bioreactor: comparison of laminar Couette and Taylor-vortex flow regimes

Rotating wall vessel bioreactors have been proposed as a means of controlling the fluid dynamic environment during long-term culture of mammalian cells and engineered tissues. In this study, we show how the delivery of oxygen to cells in an annular flow bioreactor is enhanced by the forced convective transport afforded by Taylor vortex flows. A fiberoptic oxygen probe with negligible lag time was used to measure the dissolved oxygen concentration in real time and under carefully controlled aeration conditions. From these data, the overall mass transfer coefficients were calculated and mass transport correlations determined under laminar Couette flow conditions and discrete Taylor vortex flow regimes, including laminar, wavy, and turbulent flows. While oxygen transport in Taylor vortex flows was significantly greater, and the available oxygen exceeded that consumed by murine fibroblasts in free suspension, the proportion of cells that remained viable decreased with increasing Reynolds number (101.8 < Rei < 1018), which we attribute to the action of fluid shear stresses on the cells as opposed to any limitation in mass transport. Nevertheless, the results of this study suggest that laminar Taylor-vortex flow regimes provide an effective means of maintaining the levels of oxygen transport required for long-term cell culture.     

Comparison of substrate utilization and growth kinetics between immobilized and suspended Pseudomonas cells

A methodology is described for measurement if immobilized and suspended cell growth and substrate utilization kinetics parameters. Substrate utilization and growth kinetics were compared between immobilized and suspended cells for toluene degrading Pseudomonas strains K3-2 and 2,4-dichlorophenoxyacetic acid (2,4-D) degrading strain DBO131(pR0101), respectively. Kinetic parameters were estimated using nonlinear parameter estimation methods and compared between the immobilized and suspended Pseudomonas cells to determine the effect of immobilization on cellular growth and substrate utilization. Factors influencing the experimental design included calculated oxygen flux rates, primary carbon substrate flux rates, and shear stresses on the immobilize cell. Statistical interpretation of the cellular reaction rate parameters indicates that only the growth kinetics of the toluene system were significantly altered upon immobilization. Substrate utilization kinetics remained unchanged upon immobilization. The substrate growth associated half-saturation constant (K(g)) for the toluene system increased by 30-fold and the maximum specific growth rate (mu(max)) decreased by 2-fold upon immobilization. Implication of these results for experimental determination of cellular kinetic parameters and for immobilization cell bioreactors design are discussed. (c) 1993 John Wiley & Sons, Inc.     

Model of oxygen transport limitations in hollow fiber bioreactors

Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.     

Theoretical analysis of engineered cartilage oxygenation: influence of construct thickness and media flow rate

A novel parallel-plate bioreactor has been shown to modulate the mechanical and biochemical properties of engineered cartilage by the application of fluid-induced shear stress. Flow or perfusion bioreactors may improve tissue development via enhanced transport of nutrients or gases as well as the application of mechanical stimuli, or a combination of these factors. The goal of this study was to complement observed experimental responses to flow by simulating oxygen transport within cartilage constructs of different thicknesses (250 μm or 1 mm). Using numerical computation of convection–diffusion equations, the evaluation of the tissue oxygenation is performed. Four culture conditions are defined based on tissue thickness and flow rates ranging from 0 to ∼25 mL min⁻¹. Under these experimental conditions results show a mean oxygen concentration within the tissue varying from 0.01 to 0.19 mol m⁻³ as a function of the tissue thickness and the magnitude of the applied shear stress. More generally, the influence of shear stress varying (via flow rate modification) from 10⁻³ to 10 dynes cm⁻² on the tissue oxygenation is studied. The influence on the results of important physical parameters such as the maximal oxygen consumption rate of cells is discussed. Lastly, the importance of oxygen concentration in the lower chamber and its relevance to tissue oxygenation are highlighted by the model results.     

A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor

Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications.     

Non‐Newtonian rheology in suspension cell cultures significantly impacts bioreactor shear stress quantification

The fields of regenerative medicine and tissue engineering require large‐scale manufacturing of stem cells for both therapy and recombinant protein production, which is often achieved by culturing cells in stirred suspension bioreactors. The rheology of cell suspensions cultured in stirred suspension bioreactors is critical to cell growth and protein production, as elevated exposure to shear stress has been linked to changes in growth kinetics and genetic expression for many common cell types. Currently, little is understood on the rheology of cell suspensions cultured in stirred suspension bioreactors. In this study, we present the impact of three common cell culture parameters, serum content, cell presence, and culture age, on the rheology of a model cell line cultured in stirred suspension bioreactors. The results reveal that cultures containing cells, serum, or combinations thereof are highly shear thinning, whereas conditioned and unconditioned culture medium without serum are both Newtonian. Non‐Newtonian viscosity was modeled using a Sisko model, which provided insight on structural mechanisms driving the rheological behavior of these cell suspensions. A comparison of shear stress estimated by using Newtonian and Sisko relationships demonstrated that assuming Newtonian viscosity underpredicts both mean and maximum shear stress in stirred suspension bioreactors. Non‐Newtonian viscosity models reported maximum shear stresses exceeding those required to induce changes in genetic expression in common cell types, whereas Newtonian models did not. These findings indicate that traditional shear stress quantification of cell or serum suspensions is inadequate and that shear stress quantification methods based on non‐Newtonian viscosity must be developed to accurately quantify shear stress.     

Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.     

Novel mechanical bioreactor for concomitant fluid shear stress and substrate strain

The two main types of mechanical stimuli used in cellular-level bone mechanotransduction studies are substrate strain and flow-induced shear stress. A subset of studies has investigated which of these stimuli induces the primary mechanotransduction effect on bone cells. The shortcomings of these experiments are twofold. First, in some experiments the magnitude of one loading type is able to be quantitatively measured while the other loading mode is only estimated. Second, the two loading modes are compared using different bioreactors, representing different cellular environments and substrates to which the cells are attached. In addition, none of these studies utilized bioreactors which apply controlled magnitudes of substrate strain and flow-induced shear stress differentially and simultaneously. This study presents the design of a multimodal loading device which can apply substrate stretch and fluid flow simultaneously while allowing for real-time cell imaging. The mechanical performance of the bioreactor is validated in this study by correlating the output levels of flow-induced shear stress and substrate strain with the input levels of displacement and displacement rate. The magnitudes of cross-talk loading (i.e. flow-induced strain, and strain-induced fluid flow) are also characterized and shown to be magnitudes lower than physiological levels of loading estimated to occur in bone in vivo.     

Modeling particle transport by bubbles for performance guidelines in airlift fermentors

A calculation method has been developed to model the statistical transport of biological particles in bubble-driven flows, with special reference to the biokinetics of environmental excursions experienced by individual cells, aggregated cells, or immobilization beads in airlift bioreactors. Interim developments on modeling the transport of such particles in concentric tube devices are reported. The calculation is driven by user-prescribed global parameters for the bioreactor geometry, bulk air flow rate, and particle parameters (size and slip speed). The algorithm calls on empirical data correlations for void fraction, bulk liquid flow rate, and bubble sizes and slip speeds, optimally selected from a large bibliographic database. The Monte Carlo algorithm concentrates on simulating particle transport in the bubbly riser flows.The packaged family of correlations and calculations represents, in effect, an expert system augmented by a transport simulation suited to characterizing the biokinetic response of cells cultured in airlift bioreactors.     

Experimental and computational characterization of mass transfer in high turndown bioreactors

Single-use bioreactors (SUBs, or disposable bioreactors) are extensively used for the clinical and commercial production of biologics. Despite widespread application, minimal results have been reported utilizing the turndown ratio; an operation mode where the working range of the bioreactor can be expanded to include low fluid volumes. In this work, a systematic investigation into free surface mass transfer and cell growth in high turndown single-use bioreactors is presented. This approach, which combines experimental mass transfer measurements with numerical simulation, deconvolutes the combined effects of headspace mixing and the free surface convective mass transfer on cell growth. Under optimized conditions, mass transfer across the interface alone may be sufficient to satisfy oxygen demands of the cell culture. Within the context of high turndown bioreactors, this finding provides a counterpoint to traditional sparge-based bioreactor operational philosophy. Multiple monoclonal antibody-producing cell lines grown using this high turndown approach showed similar viable cell densities to those cells expanded using a traditional cell bag rocker. Furthermore, cells taken directly from the turndown expansion and placed into production showed identical growth characteristics to traditionally expanded cultures. Taken together, these results suggest that the Xcellerex SUB can be run at a 5:1 working volume as a seed to itself, with no need for system modifications, potentially simplifying preculture operations.     

Bioflocculation as a microbial response to substrate limitations

Previous theories of nutrient supply to microbial floes assumed that transport within the flocs was by molecular diffusion, and they predict that overall nutrient uptake is reduced in floes compared to dispersed cells. Calculations, supported by recent advances in understanding fluid flow through suspended aggregates, however, have shown that substantial fluid flow may occur through highly permeable bacterial floes. Since bioflocculation of microorganisms in bioreactors is known to occur under conditions of low substrate availability, the rate of substrate uptake is assumed to be mass transfer limited. The hydrodynamic environment of a cell then determines cellular uptake rates. Through development of a relative uptake factor, the overall uptake by cells in flocs in sheared fluids and floes attached to bubbles are compared with the uptake by an identical quantity of dispersed cells. Bioflocculation is found to increase the rate of substrate transport to cells in permeable floes compared to dispersed cells, particularly for large-molecular-weight substrates and when bubbles are present.     

Substrate mass transport in two-phase partitioning bioreactors employing liquid and solid non-aqueous phases

The mass transfer of phenol and butyl acetate to/from water was studied in two-phase partitioning bioreactors using immiscible organic solvents and solid polymer beads as the partitioning phases in a 5-L stirred tank bioreactor. Virtually instantaneous mass transfer was observed with phenol in water/2-undecanone, and with butyl acetate in water/silicone oil systems. The mass transfer of butyl acetate to silicone oil was rapid irrespective of the viscosity of the partitioning phase. When Hytrel(?) polymer beads were employed as the partitioning phase, substrate transport to the polymer was found not to be externally mass transfer limited, but rather internally by substrate diffusion into the polymer. In contrast to gaseous, poorly soluble substrates studied in other works, mass transfer of soluble substrates such as phenol and butyl acetate to the polymer was unaffected by impeller speed but rather by polymer mass fraction.     

Analysis and simulation of hollow-fiber bioreactor dynamics

A flexible and economical computer simulation model for the process analysis, parameter prediction, and optimal design of hollow-fiber biochemical reactors (HFBRs) has been developed. The validity and predictive capability of the HFBR simulator was successfully tested with two independent laboratory case studies. Of particular interest are the transient transport and bioconversion mechanisms including the effect of radial mass convection on the substrate uptake in the lumen. The portable computer code is an efficient tool to aid in theoretical and experimental investigations. The underlying principles used for the model development are applicable to a broad family of (membrane) bioreactors.     

Shear rate and microturbulence effects on the synthesis of proteases by Jacaratia mexicana cells cultured in a bubble column, airlift, and stirred tank bioreactors

Cysteine proteases from Jacaratia mexicana, an endemic Mexican plant, could compete in industrial applications with papain. Currently the only way to obtain these proteases is by extracting them from the wild plant. An alternative source of these enzymes is by J. mexicana suspension culture. In this work, this culture was carried out in airlift, bubble column and stirred tank bioreactors, and the effects of shear rate and microturbulence on cell growth, protein accumulation and proteolytic activity were determined. The shear rates in the stirred tank, bubble column and airlift bioreactors were 274 1/s, 13 1/s and 36 1/s respectively, and microturbulences (symbolized by λ, in units of μm) were 46, 79, and 77 μm, respectively. Protein levels and proteolytic activity were linearly correlated with both shear rate and microturbulence. A higher shear rate and a more intensive microturbulence occurred in the stirred tank, producing higher protein accumulation and higher proteolytic activity compared with those of the other two bioreactor systems. Higher shear rate and microturbulence had an elicitor effect on protease synthesis, because microturbulence in stirred tank bioreactors was lower than the average length of J. mexicana cells. Furthermore, cells in the stirred tank were smaller and thinner than those grown in shake flask, bubble column and airlift bioreactors. In summary, proteases were produced by J. mexicana cell cultures in a stirred tank under conditions of high shear rate and intensive microturbulence, which are similar to those which occur in industrial stirred tanks. These results encourage continuation of the process development for large scale production of these proteases by this technology.