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

Optimising cell aggregate expansion in a perfused hollow fibre bioreactor via mathematical modelling

The need for efficient and controlled expansion of cell populations is paramount in tissue engineering. Hollow fibre bioreactors (HFBs) have the potential to meet this need, but only with improved understanding of how operating conditions and cell seeding strategy affect cell proliferation in the bioreactor. This study is designed to assess the effects of two key operating parameters (the flow rate of culture medium into the fibre lumen and the fluid pressure imposed at the lumen outlet), together with the cell seeding distribution, on cell population growth in a single-fibre HFB. This is achieved using mathematical modelling and numerical methods to simulate the growth of cell aggregates along the outer surface of the fibre in response to the local oxygen concentration and fluid shear stress. The oxygen delivery to the cell aggregates and the fluid shear stress increase as the flow rate and pressure imposed at the lumen outlet are increased. Although the increased oxygen delivery promotes growth, the higher fluid shear stress can lead to cell death. For a given cell type and initial aggregate distribution, the operating parameters that give the most rapid overall growth can be identified from simulations. For example, when aggregates of rat cardiomyocytes that can tolerate shear stresses of up to are evenly distributed along the fibre, the inlet flow rate and outlet pressure that maximise the overall growth rate are predicted to be in the ranges to (equivalent to to ) and to (or 15.6 psi to 15.7 psi) respectively. The combined effects of the seeding distribution and flow on the growth are also investigated and the optimal conditions for growth found to depend on the shear tolerance and oxygen demands of the cells.

Computational fluid model incorporating liver metabolic activities in perfusion bioreactor

The importance of in vitro hepatotoxicity testing during early stages of drug development in the pharmaceutical industry demands effective bioreactor models with optimized conditions. While perfusion bioreactors have been proven to enhance mass transfer and liver specific functions over a long period of culture, the flow-induced shear stress has less desirable effects on the hepatocytes liver-specific functions. In this paper, a two-dimensional human liver hepatocellular carcinoma (HepG2) cell culture flow model, under a specified flow rate of 0.03 mL/min, was investigated. Besides computing the distribution of shear stresses acting on the surface of the cell culture, our numerical model also investigated the cell culture metabolic functions such as the oxygen consumption, glucose consumption, glutamine consumption, and ammonia production to provide a fuller analysis of the interaction among the various metabolites within the cell culture. The computed albumin production of our 2D flow model was verified by the experimental HepG2 culture results obtained over 3 days of culture. The results showed good agreement between our experimental data and numerical predictions with corresponding cumulative albumin production of 2.9 × 10(-5) and 3.0 × 10(-5)  mol/m(3) , respectively. The results are of importance in making rational design choices for development of future bioreactors with more complex geometries.

Engineering parameters in bioreactor's design: a critical aspect in tissue engineering

Bioreactors are important inevitable part of any tissue engineering (TE) strategy as they aid the construction of three-dimensional functional tissues. Since the ultimate aim of a bioreactor is to create a biological product, the engineering parameters, for example, internal and external mass transfer, fluid velocity, shear stress, electrical current distribution, and so forth, are worth to be thoroughly investigated. The effects of such engineering parameters on biological cultures have been addressed in only a few preceding studies. Furthermore, it would be highly inefficient to determine the optimal engineering parameters by trial and error method. A solution is provided by emerging modeling and computational tools and by analyzing oxygen, carbon dioxide, and nutrient and metabolism waste material transports, which can simulate and predict the experimental results. Discovering the optimal engineering parameters is crucial not only to reduce the cost and time of experiments, but also to enhance efficacy and functionality of the tissue construct. This review intends to provide an inclusive package of the engineering parameters together with their calculation procedure in addition to the modeling techniques in TE bioreactors.

High-content adhesion assay to address limited cell samples

Cell adhesion is a broad topic in cell biology that involves physical interactions between cells and other cells or the surrounding extracellular matrix, and is implicated in major research areas including cancer, development, tissue engineering, and regenerative medicine. While current methods have contributed significantly to our understanding of cell adhesion, these methods are unsuitable for tackling many biological questions requiring intermediate numbers of cells (10(2)-10(5)), including small animal biopsies, clinical samples, and rare cell isolates. To overcome this fundamental limitation, we developed a new assay to quantify the adhesion of ~10(2)-10(3) cells at a time on engineered substrates, and examined the adhesion strength and population heterogeneity via distribution-based modeling. We validated the platform by testing adhesion strength of cancer cells from three different cancer types (breast, prostate, and multiple myeloma) on both IL-1β activated and non-activated endothelial monolayers, and observed significantly increased adhesion for each cancer cell type upon endothelial activation, while identifying and quantifying distinct subpopulations of cell-substrate interactions. We then applied the assay to characterize adhesion of primary bone marrow stromal cells to different cardiac fibroblast-derived matrix substrates to demonstrate the ability to study limited cell populations in the context of cardiac cell-based therapies. Overall, these results demonstrate the sensitivity and robustness of the assay as well as its ability to enable extraction of high content, functional data from limited and potentially rare primary samples. We anticipate this method will enable a new class of biological studies with potential impact in basic and translational research.

Fluid forces control endothelial sprouting

During angiogenesis, endothelial cells (ECs) from intact blood vessels quickly infiltrate avascular regions via vascular sprouting. This process is fundamental to many normal and pathological processes such as wound healing and tumor growth, but its initiation and control are poorly understood. Vascular endothelial cell growth factor (VEGF) can promote vessel dilation and angiogenic sprouting, but given the complex nature of vascular morphogenesis, additional signals are likely necessary to determine, for example, which vessel segments sprout, which dilate, and which remain quiescent. Fluid forces exerted by blood and plasma are prime candidates that might codirect these processes, but it is not known whether VEGF cooperates with mechanical fluid forces to mediate angiogenesis. Using a microfluidic tissue analog of angiogenic sprouting, we found that fluid shear stress, such as exerted by flowing blood, attenuates EC sprouting in a nitric oxide-dependent manner and that interstitial flow, such as produced by extravasating plasma, directs endothelial morphogenesis and sprout formation. Furthermore, positive VEGF gradients initiated sprouting but negative gradients inhibited sprouting, promoting instead sheet-like migration analogous to vessel dilation. These results suggest that ECs integrate signals from fluid forces and local VEGF gradients to achieve such varied goals as vessel dilation and sprouting.

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.

Fundamentals of microfluidic cell culture in controlled microenvironments

Microfluidics has the potential to revolutionize the way we approach cell biology research. The dimensions of microfluidic channels are well suited to the physical scale of biological cells, and the many advantages of microfluidics make it an attractive platform for new techniques in biology. One of the key benefits of microfluidics for basic biology is the ability to control parameters of the cell microenvironment at relevant length and time scales. Considerable progress has been made in the design and use of novel microfluidic devices for culturing cells and for subsequent treatment and analysis. With the recent pace of scientific discovery, it is becoming increasingly important to evaluate existing tools and techniques, and to synthesize fundamental concepts that would further improve the efficiency of biological research at the microscale. This tutorial review integrates fundamental principles from cell biology and local microenvironments with cell culture techniques and concepts in microfluidics. Culturing cells in microscale environments requires knowledge of multiple disciplines including physics, biochemistry, and engineering. We discuss basic concepts related to the physical and biochemical microenvironments of the cell, physicochemical properties of that microenvironment, cell culture techniques, and practical knowledge of microfluidic device design and operation. We also discuss the most recent advances in microfluidic cell culture and their implications on the future of the field. The goal is to guide new and interested researchers to the important areas and challenges facing the scientific community as we strive toward full integration of microfluidics with biology.

The influence of flow cell geometry related shear stresses on the distribution, structure and susceptibility of Pseudomonas aeruginosa 01 biofilms

The effects of non-uniform hydrodynamic conditions resulting from flow cell geometry (square and rectangular cross-section) on Pseudomonas aeruginosa 01 (PAO1) biofilm formation, location, and structure were investigated for nominally similar flow conditions using a combination of confocal scanning laser microscope (CSLM) and computational fluid dynamics (CFD). The thickness and surface coverage of PAO1 biofilms were observed to vary depending on the location in the flow cell and thus also the local wall shear stress. The biofilm structure in a 5:1 (width to height) aspect ratio rectangular flow cell was observed to consist mainly of a layer of bacterial cells with thicker biofilm formation observed in the flow cell corners. For square cross-section (1:1 aspect ratio) flow cells, generally thicker and more uniform surface coverage biofilms were observed. Mushroom shaped structures with hollow centers and wall breaks, indicative of 'seeding' dispersal structures, were found exclusively in the square cross-section tubes. Exposure of PAO1 biofilms grown in the flow cells to gentamicin revealed a difference in susceptibility. Biofilms grown in the rectangular flow cell overall exhibited a greater susceptibility to gentamicin compared to those grown in square flow cells. However, even within a given flow cell, differences in susceptibility were observed depending on location. This study demonstrates that the spanwise shear stress distribution within the flow cells has an important impact on the location of colonization and structure of the resultant biofilm. These differences in biofilm structure have a significant impact on the susceptibility of the biofilms grown within flow channels. The impact of flow modification due to flow cell geometry should be considered when designing flow cells for laboratory investigation of bacterial biofilms.

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.

Cell culture chip using low-shear mass transport

We have developed a flow cell that allows culturing adherent cells as well as suspended cells in a stable, homogeneous, and low-shear force environment. The device features continuous medium supply and waste exchange. In this paper, a simple and fast protocol for device design, fabrication, and assembly (sealing) based on a poly(dimethylsiloxane) (PMDS)/glass slide hybrid structure is described. The cell culture system performance was monitored, and the effective shear force inside the culture well was also determined. By manipulating the device dimensions and volumetric flow rate, shear stress was controlled during experiments. Cell adhesion, growth, proliferation, and death over long-term culture periods were observed by microscopy. The growth of both endothelial and suspension cells in this device exhibited comparable characteristics to those of traditional approaches. The low-shear culture device significantly reduced shear stress encountered in microfluidic systems, allowing both adherent and suspended cells to be grown in a simple device.

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.

Numerical simulation of global hydro-dynamics in a pulsatile bioreactor for cardiovascular tissue engineering

Previous numerical simulations of the hydro-dynamic response in the various bioreactor designs were mostly concentrated on the local flow field analysis using computational fluid dynamics, which cannot provide the global hydro-dynamics information to assist the bioreactor design. In this research, a mathematical model is developed to simulate the global hydro-dynamic changes in a pulsatile bioreactor design by considering the flow resistance, the elasticity of the vessel and the inertial effect of the media fluid in different parts of the system. The developed model is used to study the system dynamic response in a typical pulsatile bioreactor design for the culturing of cardiovascular tissues. Simulation results reveal the detailed pressure and flow-rate changes in the different positions of the bioreactor, which are very useful for the evaluation of hydro-dynamic performance in the bioreactor designed. Typical pressure and flow-rate changes simulated agree well with the published experimental data, thus validates the mathematical model developed. The proposed mathematical model can be used for design optimization of other pulsatile bioreactors that work under different experimental conditions and have different system configurations.

Fabrication of a multiple-diameter branched network of microvascular channels with semi-circular cross-sections using xenon difluoride etching

The majority of microfluidic devices employ networks of channels that have rectangular cross-sections. At the microvascular scale of 30 to 300 microm in diameter, however, the distribution of fluid mechanical stresses and the induced shape of cultured cells will be quite different in a rectangular channel from the near-circular cross-sections seen in vivo. While round-cross-section channels have been produced before by wet etching, fine control of feature size has not been demonstrated, and prior work has only produced channels of a single diameter on a given device. In this work, the xenon difluoride process for isotropic etching of silicon was optimized for production of channels with semicircular cross-sections. This process was then used to produce a network of microvessel-scale semicylindrical channels on a silicon chip, the diameter of which was decreased with each level of branching. Additionally, it was demonstrated that endothelial cells will adhere to both the bottom and sides of these channels, indicating that such chips may be useful in the future for culturing in vitro models of the microvasculature.

Three-dimensional modeling of transport of nutrients for multicellular tumor spheroid culture in a microchannel

The growth dynamics of avascular tumors in a microchannel bioreactor is investigated. A three-dimensional flow and nutrient transport model, incorporating the multicellular tumor spheroid (MTS) growth model, has been developed to study the influence of nutrients (oxygen and glucose) supply and distribution on the MTS growth. Numerical simulations based on the EMT6/Ro tumor cells show that the continuous-flow perfusion is more efficient to deliver nutrients to the MTS than the diffusion-only static culture. It is further demonstrated that as long as there is bulk flow, the growth of a single tumor spheroid at the early stage is insensitive to the flow velocity and the channel size. For multiple tumor spheroids in the same microchannel, however, increasing the perfusion velocity can improve the nutrient environment for the disadvantageous downstream tumor spheroid. The flow shear stress exerting on the MTSs in the current microchannel bioreactor is estimated to be far below the critical value to affect the MTS growth, which means that there is still much room for increasing perfusion velocity to satisfy the higher nutrient requirement by the growing tumor spheroids.

A parametric study of human fibroblasts culture in a microchannel bioreactor

The culture of cells in a microbioreactor can be highly beneficial for cell biology studies and tissue engineering applications. The present work provides new insights into the relationship between cell growth, cell morphology, perfusion rate, and design parameters in microchannel bioreactors. We demonstrate the long-term culture of mammalian (human foreskin fibroblasts, HFF) cells in a microbioreactor under constant perfusion in a straightforward simple manner. A perfusion system was used to culture human cells for more than two weeks in a plain microchannel (130 microm x 1 mm x 2 cm). At static conditions and at high flow rates (>0.3 ml h(-1)), the cells did not grow in the microchannel for more than a few days. For low flow rates (<0.2 ml h(-1)), the cells grew well and a confluent layer was obtained. We show that the culture of cells in microchannels under perfusion, even at low rates, affects cell growth kinetics as well as cell morphology. The oxygen level in the microchannel was evaluated using a mass transport model and the maximum cell density measured in the microchannel at steady state. The maximum shear stress, which corresponds to the maximum flow rate used for long term culture, was 20 mPa, which is significantly lower than the shear stress cells may endure under physiological conditions. The effect of channel size and cell type on long term cell culture were also examined and were found to be significant. The presented results demonstrate the importance of understanding the relationship between design parameters and cell behavior in microscale culture system, which vary from physiological and traditional culture conditions.

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.