Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.     

组织工程皮肤生物反应器的研究与设计

目的设计一套生物反应器,能针对不同支架材料———细胞复合物进行构建组织工程皮肤。方法根据皮肤的自身生长特点和不同支架材料-细胞复合物的特性,模拟皮肤的生长环境和力学环境,通过生物反应器解决组织工程皮肤构建中支架的装夹和气液界面问题。结果生物反应器由控制系统和生物反应器主体两部分构成,能提供对多种皮肤细胞复合物的动态培养。结论皮肤生物反应器能够满足不同组织工程皮肤产品的需要。能够形成气液界面和模拟生物力学的刺激。     

Hollow-fibre fermenter using ultrafiltration

Summary A novel bioreactor with hollow fibres was developed to facilitate substrate transfer across membrane walls as well as to retain a continuous cell growth in the shell side. Ultrafiltration was induced through membrane by pressurizing feed solution to the inside of a hollow fibre with inlet and outlet pumps. The ultrafiltrate accumulated outside the hollow fibres was recirculated through a reservoir where a part of solution containing cells and substrate was removed to keep the level of reservoir solution constant. Ethanol production by Saccharomyces cerevisiae was carried out to test the feasibility of this reactor. The productivity of this reactor was compared with that of a continuous stirred tank reactor (CSTR).     

Production of recombinant human interleukin-2 with BHK cells in a hollow fibre and a stirred tank reactor with protein-free medium.

For the production of recombinant human interleukin-2 (IL-2) two different culture processes, a 1-2 liter homogeneous stirred bubble-free aerated system and a dense cell hollow fibre bioreactor were compared. Cultivations were carried out with serum- or protein-free medium formulations. In the stirred culture 0.75 mg IL-2 were produced with 1 l of perfused medium at a maximum cell number of 3 X 10(10). The product yield in the hollow fibre module was only 0.23 mg l-1 at a maximum cell number of 6 X 10(10). In contrast to results with hybridoma or EBV-transformed cell lines, in which hollow fibre bioreactors showed comparable efficiency to perfused stirred tank reactors, the tissue-like cell density is disadvantageous as adherent cells tend to stick together leaving insufficient intercellular space for removal of product.     

Membrane process for biological treatment of contaminated gas streams

A hollow fiber membrane bioreactor was investigated for control of air emissions of biodegradable volatile organic compounds (VOCs). In the membrane bioreactor, gases containing VOCs pass through the lumen of microporous hydrophobic hollow fiber membranes. Soluble compounds diffuse through the membrane pores and partition into a VOC degrading biofilm. The hollow fiber membranes serve as a support for the microbial population and provide a large surface area for VOC and oxygen mass transfer. Experiments were performed to investigate the effects of toluene loading rate, gas residence time, and liquid phase turbulence on toluene removal in a laboratory-scale membrane bioreactor. Initial acclimation of the microbial culture to toluene occurred over a period of nine days, after which a 70% removal efficiency was achieved at an inlet toluene concentration of 200 ppm and a gas residence time of 1.8 s (elimination capacity of 20 g m-3 min-1). At higher toluene loading rates, a maximum elimination capacity of 42 g m-3 min-1 was observed. In the absence of a biofilm (abiotic operation), mass transfer rates were found to increase with increasing liquid recirculation rates. Abiotic mass transfer coefficients could be estimated using a correlation of dimensionless parameters developed for heat transfer. Liquid phase recirculation rate had no effect on toluene removal when the biofilm was present, however. Three models of the reactor were created: a numeric model, a first-order flat sheet model, and a zero-order flat sheet model. Only the numeric model fit the data well, although removal predicted as a function of gas residence time disagreed slightly with that observed. A modification in the model to account for membrane phase resistance resulted in an underprediction of removal. Sensitivity analysis of the numeric model indicated that removal was a strong function of the liquid phase biomass density and biofilm diffusion coefficient, with diffusion rates below 10(-9) m2 s-1 resulting in decreased removal rates.     

Hollow fiber culture accelerates differentiation of Caco-2 cells

Caco-2 cells usually require 21 days of culture for developing sufficient differentiation in traditional two-dimensional Transwell culture, deviating far away from the quick differentiation of enterocytes in vivo. The recently proposed three-dimensional cultures of Caco-2 cells, though imitating the villi/crypt-like microstructure of intestinal epithelium, showed no effect on accelerating the differentiation of Caco-2 cells. In this study, a novel culture of Caco-2 cells on hollow fiber bioreactor was applied to morphologically mimic the human small intestine lumen for accelerating the expression of intestine functions. The porous hollow fibers of polyethersulfone (PES), a suitable membrane material for Caco-2 cell culture, successfully promoted cells to form confluent monolayer on the inner surface. The differentiated functions of Caco-2 cells, represented by alkaline phosphatase, γ-glutamyltransferase, and P-glycoprotein activity, were greatly higher in a 10-day hollow fiber culture than in a 21-day Transwell culture. Moreover, the Caco-2 cells on PES hollow fibers expressed higher F-actin and zonula occludens-1 protein than those on Transwell culture, indicative of an increased mechanical stress in Caco-2 cells on PES hollow fibers. The accelerated differentiation of Caco-2 cells on PES hollow fibers was unassociated with membrane chemical composition and surface roughness, but could be stimulated by hollow fiber configuration, since PES flat membranes with either rough or smooth surface failed to enhance the differentiation of Caco-2. Therefore, the accelerated expression of Caco-2 cell function on hollow fiber culture might show great values in simulation of the tissue microenvironment in vivo and guide the construction of intestinal tissue engineering apparatus.     

A multiphase model for chemically- and mechanically- induced cell differentiation in a hollow fibre membrane bioreactor: minimising growth factor consumption

We present a simplified two-dimensional model of fluid flow, solute transport, and cell distribution in a hollow fibre membrane bioreactor. We consider two cell populations, one undifferentiated and one differentiated, with differentiation stimulated either by growth factor alone, or by both growth factor and fluid shear stress. Two experimental configurations are considered, a 3-layer model in which the cells are seeded in a scaffold throughout the extracapillary space (ECS), and a 4-layer model in which the cell–scaffold construct occupies a layer surrounding the outside of the hollow fibre, only partially filling the ECS. Above this is a region of free-flowing fluid, referred to as the upper fluid layer. Following previous models by the authors (Pearson et al. in Math Med Biol, 2013, Biomech Model Mechanbiol 1–16, 2014a, we employ porous mixture theory to model the dynamics of, and interactions between, the cells, scaffold, and fluid in the cell–scaffold construct. We use this model to determine operating conditions (experiment end time, growth factor inlet concentration, and inlet fluid fluxes) which result in a required percentage of differentiated cells, as well as maximising the differentiated cell yield and minimising the consumption of expensive growth factor.     

In silico multi‐scale model of transport and dynamic seeding in a bone tissue engineering perfusion bioreactor

Computer simulations can potentially be used to design, predict, and inform properties for tissue engineering perfusion bioreactors. In this work, we investigate the flow properties that result from a particular poly‐L ‐lactide porous scaffold and a particular choice of perfusion bioreactor vessel design used in bone tissue engineering. We also propose a model to investigate the dynamic seeding properties such as the homogeneity (or lack of) of the cellular distribution within the scaffold of the perfusion bioreactor: a pre‐requisite for the subsequent successful uniform growth of a viable bone tissue engineered construct. Flows inside geometrically complex scaffolds have been investigated previously and results shown at these pore scales. Here, it is our aim to show accurately that through the use of modern high performance computers that the bioreactor device scale that encloses a scaffold can affect the flows and stresses within the pores throughout the scaffold which has implications for bioreactor design, control, and use. Central to this work is that the boundary conditions are derived from micro computed tomography scans of both a device chamber and scaffold in order to avoid generalizations and uncertainties. Dynamic seeding methods have also been shown to provide certain advantages over static seeding methods. We propose here a novel coupled model for dynamic seeding accounting for flow, species mass transport and cell advection‐diffusion‐attachment tuned for bone tissue engineering. The model highlights the timescale differences between different species suggesting that traditional homogeneous porous flow models of transport must be applied with caution to perfusion bioreactors. Our in silico data illustrate the extent to which these experiments have the potential to contribute to future design and development of large‐scale bioreactors. Biotechnol. Bioeng. 2013; 110: 1221–1230. © 2012 Wiley Periodicals, Inc.     

Perfusion flow bioreactor for 3D in situ imaging: investigating cell/biomaterials interactions

The capability to image real time cell/material interactions in a three-dimensional (3D) culture environment will aid in the advancement of tissue engineering. This paper describes a perfusion flow bioreactor designed to hold tissue engineering scaffolds and allow for in situ imaging using an upright microscope. The bioreactor can hold a scaffold of desirable thickness for implantation (>2 mm). Coupling 3D culture and perfusion flow leads to the creation of a more biomimetic environment. We examined the ability of the bioreactor to maintain cell viability outside of an incubator environment (temperature and pH stability), investigated the flow features of the system (flow induced shear stress), and determined the image quality in order to perform time-lapsed imaging of two-dimensional (2D) and 3D cell culture. In situ imaging was performed on 2D and 3D, culture samples and cell viability was measured under perfusion flow (2.5 mL/min, 0.016 Pa). The visualization of cell response to their environment, in real time, will help to further elucidate the influences of biomaterial surface features, scaffold architectures, and the influence of flow induced shear on cell response and growth of new tissue.     

Modeling fluid flow through irregular scaffolds for perfusion bioreactors

Direct perfusion of 3D tissue engineered constructs is known to enhance osteogenesis, which can be partly attributed to enhanced nutrient and waste transport. In addition flow mediated shear stresses are known to upregulate osteogenic differentiation and mineralization. A quantification of the hydrodynamic environment is therefore crucial to interpret and compare results of in vitro bioreactor experiments. This study aims to deal with the pitfalls of numerical model preparation of highly complex 3D bone scaffold structures and aims to provide more accurate wall shear stress (WSS) estimates. µCT imaging techniques were used to reconstruct the geometry of both a titanium (Ti) and a hydroxyapatite scaffold, starting from 430 images with a resolution of 8 µm. To tackle the tradeoff between model size and mesh resolution we selected two concentric regions of interest (cubes with a volume of 1 and 3.375 mm³, respectively) for both scaffolds. A flow guidance in front of the real inlet surface of the scaffold was designed to mimic realistic inlet conditions. With a flow rate of 0.04 mL/min perfused through a 5 mm diameter scaffold at an inlet velocity of 33.95 µm/s we obtained average WSSs of 1.10 and 1.46 mPa for the 1 mm³ and the 3.375 mm³ model of the hydroxyapatite scaffold compared to 1.40 and 1.95 mPa for the 1 mm³ model and the 3.375 mm³ model of the Ti scaffold, showing the important influence of the scaffold micro‐architecture heterogeneity and the proximity of boundaries. To assess that influence we selected cubic portions, of which the WSS data were analyzed, with the same size and the same location within both 1 and 3.375 mm³ cubic models. Varying the size of the inner portions simultaneously in both model selections gives a quantification of the sensitivity to boundary neighborhood. This methodology allows to get more insight in the complex concept of tissue engineering and will likely help to understand and eventually improve the fluid‐mechanical aspects. Biotechnol. Bioeng. 2009;103: 621–630. © 2009 Wiley Periodicals, Inc.     

High-performance microbial removal of ethanol from contaminated air

Ethanol vapour from air was removed using a bioreactor (2.7 m 3 ) packed with a novel engineered material consisting of a highly porous inorganic matrix coated with activated carbon. The system was operated over a period of two months varying the inlet ethanol between 90 and 2200 mg m –3 . Removal efficiencies ranging from 80 to 99.9% were obtained. A simplified kinetic model of the bioreactor was developed and used to estimate the maximum degradationrate and to predict thermal effects resulting from ethanol oxidation.     

Effect of bench-scale culture conditions on murine IgG heterogeneity

A stable murine hybridoma cell line, secreting IgG1 antibodies (7H3) against the soluble type I receptor for Tumor Necrosis Factor (sTNF-R1), was cultivated in two different bioreactor systems, a hollow fiber and a stirred tank fermentor, in order to evaluate the effect of culture conditions on antibody structural and functional heterogeneity. Conventional serum-supplemented and serum-free media were chosen for fermentation in stirred tank bioreactor, whereas only serum-supplemented media were used for hollow fiber cultivation. Extent of glycosylation, determined by lectin binding assays, and charge heterogeneity of murine monoclonal antibodies displayed relevant variations according to the fermentation system used. After complete sugars removal by N-glycosidase F treatment, charge heterogeneity were still observed suggesting the occurrence of additional modifications at the protein level. In vitro culture in serum-supplemented media carried out with the hollow fibre system led to higher productivity but greater antibody charge heterogeneity and differences in lectin-binding profile than cultivation in the stirred tank bioreactor.Results cumulatively indicated that hybridoma cultivation methods, but also cultivation time, influence antibody heterogeneity, both in the protein and sugar moieties. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 17-25, 1997.     

Modeling,simulations, and optimization of smooth muscle cell tissue engineering for the production of vascular grafts

The paper presents a transient, continuum, two-phase model of the tissue engineering in fibrous scaffolds, including transport equations for the flowing culture medium, nutrient and cell concentration with transverse and in-plane diffusion and cell migration, a novel feature of local in-plane transport across a phenomenological pore and innovative layer-by-layer cell filling approach. The model is successfully validated for the smooth muscle cell tissue engineering of a vascular graft using crosslinked, electrospun gelatin fiber scaffolds for both static and dynamic cell culture, the latter in a dynamic bioreactor with a rotating shaft on which the tubular scaffold is attached. Parametric studies evaluate the impact of the scaffold microstructure, cell dynamics, oxygen transport, and static or dynamic conditions on the rate and extent of cell proliferation and depth of oxygen accessibility. An optimized scaffold of 75% dry porosity is proposed that can be tissue engineered into a viable and still fully oxygenated graft of the tunica media of the coronary artery within 2 days in the dynamic bioreactor. Such scaffold also matches the mechanical properties of the tunica media of the human coronary artery and the suture retention strength of a saphenous vein, often used as a coronary artery graft.     

Twitch and tetanic tension during culture of mature Xenopus laevis single muscle fibres

Investigation of the mechanisms of muscle adaptation requires independent control of the regulating factors. The aim of the present study was to develop a serum-free medium to culture mature single muscle fibres of Xenopus laevis. As an example, we used the culture system to study adaptation of twitch and tetanic force characteristics, number of sarcomeres in series and fibre cross-section. Fibres dissected from m. iliofibularis (n = 10) were kept in culture at a fibre mean sarcomere length of 2.3 microm in a culture medium without serum. Twitch and tetanic tension were determined daily. Before and after culture the number of sarcomeres was determined by laser diffraction and fibre cross-sectional area (CSA) was determined by microscopy. For five fibres twitch tension increased during culture and tetanic tension was stable for periods varying from 8 to 14 days ('stable fibres'), after which fibres were removed from culture for analysis. Fibre CSA and the number of sarcomeres in series remained constant during culture. Five other fibres showed a substantial reduction in twitch and tetanic tension within the first five days of culture ('unstable fibres'). After 7-9 days of culture, three of these fibres died. For two of the unstable fibres, after the substantial force reduction, twitch and tetanic tension increased again. Finally at day 14 and 18 of culture, respectively, the tensions attained values higher than their original values. For stable fibres, twitch contraction time, twitch half-relaxation time and tetanus 10%-relaxation time increased during culture. For unstable fibres these parameters fluctuated. For all fibres the stimulus threshold fluctuated during the first two days, and then remained constant, even for the fibres that were cultured for at least two weeks. It is concluded that the present culture system for mature muscle fibres allows long-term studies within a well-defined medium. Unfortunately, initial tetanic and twitch force are poor predictors of the long-term behaviour of the fibres.     

Quantitative Study of the Effect of Tissue Microstructure on Contraction in a Computational Model of Rat Left Ventricle

Tissue microstructure, in particular the alignment of myocytes (fibre direction) and their lateral organisation into sheets, is fundamental to cardiac function. We studied the effect of microstructure on contraction in a computational model of rat left ventricular electromechanics. Different fibre models, globally rule-based or locally optimised to DT-MRI data, were compared, in order to understand whether a subject-specific fibre model would enhance the predictive power of our model with respect to the global ones. We also studied the impact of sheets on ventricular deformation by comparing: (a) a transversely isotropic versus an orthotropic material law and (b) a linear model with a bimodal model of sheet transmural variation. We estimated ejection fraction, wall thickening and base-to-apex shortening and compared them with measures from cine-MRI. We also evaluated Lagrangian strains as local metrics of cardiac deformation. Our results show that the subject-specific fibre model provides little improvement in the metric predictions with respect to global fibre models while material orthotropy allows closer agreement with measures than transverse isotropy. Nonetheless, the impact of sheets in our model is smaller than that of fibres. We conclude that further investigation of the modelling of sheet dynamics is necessary to fully understand the impact of tissue structure on cardiac deformation.     

Culture of primary rat hepatocytes within a flat hollow fibre cassette for potential use as a component of a bioartificial liver support system

Primary rat hepatocytes were cultured in a flat, hollow-fibre cassette, `The Tecnomouse', which provided direct oxygenation and a homogeneous environment for cells within the cassette. Most hollow fibre systems utilise media oxygenators to provide O₂ to cells; in the Tecnomouse cassette, cells are provided with direct oxygenation via gas channels in the silicone membrane surrounding the hollow fibres. Hepatocyte functionality was monitored by following urea production, albumin production and cytochrome P-450 enzyme activities. The system could maintain cells in a viable state and the presence of specific hepatocyte functions including albumin production and cytochrome P-450 activity. Electron microscopy showed aggregated spherical hepatocytes and apparent high extent of necrosis.     

Optimal design of bio-hybrid systems with a hollow fiber scaffold: model analysis of oxygen diffusion/consumption

The oxygen distribution in various bio-hybrid systems composed of cellular tissue on an artificial scaffold was estimated by mathematically modeling the oxygen consumption and diffusion. Mathematical models were established for practical systems such as bio-hybrid artificial liver (BAL) and bio-hybrid blood vessels, and the calculated results were compared with corresponding experimental data. Analysis of a spherical organoid (“spheroid”) composed of hepatic cells suggested that the oxygen consumption rate in hepatocyte spheroids incubated in a BAL is one or two orders of magnitude larger than the total average value that had been calculated for various organs. A model was established for a BAL system on a scaffold of commercially available hollow fiber (typical inner and outer radii of 150 and 200 μm) to determine the optimal conditions under which the hepatocytes can be packed as closely as possible into the hollow fiber lumen while still maintaining viability without falling into oxygen deficiency. A model of bio-hybrid blood vessels formed by vascular endothelial cells incubated on the inner wall of a hollow fiber scaffold was used to estimate the maximum thickness of viable endothelial tissue under various conditions of outer partial oxygen pressure and different sizes and permeabilities of the hollow fiber scaffold. The model suggested that the oxygen supply becomes quite restricted when the hollow fiber membrane is thicker than 100 μm; the thickness of the endothelium in a 500 μm-thick hollow fiber membrane was estimated to be 7 μm at most, even when the membrane permeability was as large as that of the culture medium.     

Reduction of extraction times in liquid-phase microextraction

Recently, we introduced a simple and inexpensive disposable device for liquid-phase microextraction (LPME) based on porous polypropylene hollow fibres. In the present paper, extraction times were significantly reduced by an increase in the surface of the hollow fibres. The model compounds methamphetamine and citalopram, were extracted from 2.5 ml of urine, plasma, and whole blood after dilution with water and alkalisation with 125 μl of 2 M NaOH though a porous polypropylene hollow fibre impregnated with hexyl ether and into an aqueous acceptor phase consisting of 0.1 M HCl. Two commercially available hollow fibres, which differed in surface area, wall thickness and internal diameter, were compared. An increase in the contact area of the hollow fibre with the sample solution by a factor of approximately two resulted in reduction in equilibrium times by approximately the same factor. Thus, the model compounds were extracted to equilibrium within 15 min from both urine and plasma, and within 30 min from whole blood. For the first time LPME was utilised to extract drugs from whole blood, and the extracts were comparable with plasma both with regard to sample clean-up and extraction recoveries. Extraction recoveries for methamphetamine and citalopram varied from 60 to 100% using the two fibres and the different matrices.     

The effect of hydrodynamic shear on 3D engineered chondrocyte systems subject to direct perfusion

Bioreactors allowing direct-perfusion of culture medium through tissue-engineered constructs may overcome diffusion limitations associated with static culturing, and may provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed on cells within scaffolds is directly dependent on scaffold microstructure and on bioreactor configuration. Aim of this study is to investigate optimal shear stress ranges and to quantitatively predict the levels of hydrodynamic shear imposed to cells during the experiments. Bovine articular chondrocytes were seeded on polyestherurethane foams and cultured for 2 weeks in a direct perfusion bioreactor designed to impose 4 different values of shear level at a single flow rate (0.5 ml/min). Computational fluid dynamics (CFD) simulations were carried out on reconstructions of the scaffold obtained from micro-computed tomography images. Biochemistry analyses for DNA and sGAG were performed, along with electron microscopy. The hydrodynamic shear induced on cells within constructs, as estimated by CFD simulations, ranged from 4.6 to 56 mPa. This 12-fold increase in the level of applied shear stress determined a 1.7-fold increase in the mean content in DNA and a 2.9-fold increase in the mean content in sGAG. In contrast, the mean sGAG/DNA ratio showed a tendency to decrease for increasing shear levels. Our results suggest that the optimal condition to favour sGAG synthesis in engineered constructs, at least at the beginning of culture, is direct perfusion at the lowest level of hydrodynamic shear. In conclusion, the presented results represent a first attempt to quantitatively correlate the imposed hydrodynamic shear level and the invoked biosynthetic response in 3D engineered chondrocyte systems.     

Towards Self‐Regulated Bioprocessing: A Compact Benchtop Bioreactor System for Monitored and Controlled 3D Cell and Tissue Culture

Bioreactors are crucial tools for the manufacturing of living cell‐based tissue engineered products. However, to reach the market successfully, higher degrees of automation, as well as a decreased footprint still need to be reached. In this study, the use of a benchtop bioreactor for in vitro perfusion culture of scaffold‐based tissue engineering constructs is assessed. A low‐footprint benchtop bioreactor system is designed, comprising a single‐use fluidic components and a bioreactor housing. The bioreactor is operated using an in‐house developed program and the culture environment is monitored by specifically designed sensor ports. A gas‐exchange module is incorporated allowing for heat and mass transfers. Titanium‐based scaffolds are seeded with human periosteum‐derived cells and cultured up to 3 weeks. The benchtop bioreactor constructs are compared to benchmark perfusion systems. Live/Dead stainings, DNA quantifications, glucose consumption, and lactate production assays confirm that the constructs cultured in the benchtop bioreactor grew similarly to the benchmark systems. Manual regulation of the system set points enabled efficient alteration of the culture environment in terms of temperature, pH, and dissolved oxygen. This study provides the necessary basis for the development of low‐footprint, automated, benchtop perfusion bioreactors and enables the implementation of active environment control.