Macro-scale topology optimization for controlling internal shear stress in a porous scaffold bioreactor

Shear stress is an important physical factor that regulates proliferation, migration, and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers to improve upon cell culture protocols. Recent work has focused on optimizing the microstructural parameters of the scaffold to fine tune the shear stress. In this study, we have adopted a different approach whereby flows are redirected throughout the bioreactor along channels patterned in the porous scaffold to yield shear stress distributions that are optimized for uniformity centered on a target value. A topology optimization algorithm coupled to computational fluid dynamics simulations was devised to this end. The channel topology in the porous scaffold was varied using a combination of genetic algorithm and fuzzy logic. The method is validated by experiments using magnetic resonance imaging readouts of the flow field.     

3-D computational modeling of media flow through scaffolds in a perfusion bioreactor

Media perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional (3-D) tissue-engineered constructs cultured in vitro. In addition to enhancing the exchange of nutrients and wastes, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. Local shear stresses are a function of media flow rate and dynamic viscosity, bioreactor configuration, and porous scaffold microarchitecture. We have used the Lattice-Boltzmann method to simulate the flow conditions within perfused cell-seeded cylindrical scaffolds. Microcomputed tomography imaging was used to define the scaffold microarchitecture for the simulations, which produce a 3-D fluid velocity field throughout the scaffold porosity. Shear stresses were estimated at various media flow rates by multiplying the symmetric part of the gradient of the velocity field by the dynamic viscosity of the cell culture media. The shear stress algorithm was validated by modeling flow between infinite parallel plates and comparing the calculated shear stress distribution to the analytical solution. Relating the simulation results to perfusion experiments, an average surface shear stress of 5x10(-5)Pa was found to correspond to increased cell proliferation, while higher shear stresses were associated with upregulation of bone marker genes. This modeling approach can be used to compare results obtained for different perfusion bioreactor systems or different scaffold microarchitectures and may allow specific shear stresses to be determined that optimize the amount, type, or distribution of in vitro tissue growth.     

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.     

Computational simulation modelling of bioreactor configurations for regenerating human bladder

The objective of this study was to investigate a bioreactor suitable for human bladder regeneration. Simulations were performed using the computational fluid dynamic tools. The thickness of the bladder scaffold was 3 mm, similar to the human bladder, and overall hold-up volume within the spherical shape scaffold was 755 ml. All simulations were performed using (i) Brinkman equation on porous regions using the properties of 1% chitosan–1% gelatin structures, (ii) Michaelis–Menten type rate law nutrient consumption for smooth muscle cells (SMCs) and (iii) Mackie–Meares relationship for determining effective diffusivities. Steady state simulations were performed using flow rates from 0.5 to 5 ml/min. Two different inlet shapes: (i) straight entry at the centre (Design 1) and (ii) entry with an expansion (Design 2) were simulated to evaluate shear stress distribution. Also, mimicking bladder shape of two inlets (Design 3) was tested. Design 2 provided the uniform shear stress at the inlet and nutrient distribution, which was further investigated for the effect of scaffold locations within the reactor: (i) attached with a 3-mm open channel (Design 2-A), (ii) flow through with no open channel (Design 2-B) and (iii) porous structure suspended in the middle with 1.5-mm open channel on either side (Design 2-C). In Design 2-A and 2-C, fluid flow occurred by diffusion dominant mechanisms. Furthermore, the designed bioreactor is suitable for increased cell density of SMCs. These results showed that increasing the flow rate is necessary due to the decreased permeability at cell densities similar to the human bladder.     

Flow dynamics in bioreactors containing tissue engineering scaffolds

Bioreactors are widely used in tissue engineering as a way to distribute nutrients within porous materials and provide physical stimulus required by many tissues. However, the fluid dynamics within the large porous structure are not well understood. In this study, we explored the effect of reactor geometry by using rectangular and circular reactors with three different inlet and outlet patterns. Geometries were simulated with and without the porous structure using the computational fluid dynamics software Comsol Multiphysics 3.4 and/or ANSYS CFX 11 respectively. Residence time distribution analysis using a step change of a tracer within the reactor revealed non-ideal fluid distribution characteristics within the reactors. The Brinkman equation was used to model the permeability characteristics with in the chitosan porous structure. Pore size was varied from 10 to 200 microm and the number of pores per unit area was varied from 15 to 1,500 pores/mm(2). Effect of cellular growth and tissue remodeling on flow distribution was also assessed by changing the pore size (85-10 microm) while keeping the number of pores per unit area constant. These results showed significant increase in pressure with reduction in pore size, which could limit the fluid flow and nutrient transport. However, measured pressure drop was marginally higher than the simulation results. Maximum shear stress was similar in both reactors and ranged approximately 0.2-0.3 dynes/cm(2). The simulations were validated experimentally using both a rectangular and circular bioreactor, constructed in-house. Porous structures for the experiments were formed using 0.5% chitosan solution freeze-dried at -80 degrees C, and the pressure drop across the reactor was monitored.     

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.     

Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models

We present a combined macro-scale/micro-scale computational approach to quantify oxygen transport and flow-mediated shear stress to human chondrocytes cultured in three-dimensional scaffolds in a perfusion bioreactor system. A macro-scale model was developed to assess the influence of the bioreactor design and to identify the proper boundary conditions for the micro-scale model. The micro-scale model based on a micro-computed tomography (microCT) reconstruction of a poly(ethylene glycol terephthalate)/poly(butylene terephthalate) (PEGT/PBT) foam scaffold, was developed to assess the influence of the scaffold micro-architecture on local shear stress and oxygen levels within the scaffold pores. Experiments were performed to derive specific oxygen consumption rates for constructs perfused under flow rates of 0.3 and 0.03 ml min(-1). While macro-scale and micro-scale models predicted similar average oxygen levels at different depths within the scaffold, microCT models revealed small local oxygen variations within the scaffold micro-architecture. The combined macro-scale/micro-scale approach indicated that 0.3 ml min(-1), which subjected 95% of the cells to less than 6.3 mPa shear, would maintain the oxygen supply throughout the scaffold above anoxic levels (>1%), with 99.5% of the scaffold supplied with 8-2% O(2). Alternatively, at 0.03 ml min(-1), the macro-scale model predicted 6% of the cells would be supplied with 0.5-1% O(2), although this region of cells was confined to the periphery of the scaffold. Together with local variations predicted by the micro-scale model, the simulations underline that in the current model system, reducing the flow below 0.03 ml min(-1) would likely have dire consequences on cell viability to pronounced regions within the engineered construct. The presented approach provides a sensitive tool to aid efficient bioreactor optimization and scaffold design.     

Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering

Novel tissue‐culture bioreactors employ flow‐induced shear stress as a means of mechanical stimulation of cells. We developed a computational fluid dynamics model of the complex three‐dimensional (3D) microstructure of a porous scaffold incubated in a direct perfusion bioreactor. Our model was designed to predict high shear‐stress values within the physiological range of those naturally sensed by vascular cells (1–10 dyne/cm²), and will thereby provide suitable conditions for vascular tissue‐engineering experiments. The model also accounts for cellular growth, which was designed as an added cell layer grown on all scaffold walls. Five model variants were designed, with geometric differences corresponding to cell‐layer thicknesses of 0, 50, 75, 100, and 125 µm. Four inlet velocities (0.5, 1, 1.5, and 2 cm/s) were applied to each model. Wall shear‐stress distribution and overall pressure drop calculations were then used to characterize the relation between flow rate, shear stress, cell‐layer thickness, and pressure drop. The simulations showed that cellular growth within 3D scaffolds exposes cells to elevated shear stress, with considerably increasing average values in correlation to cell growth and inflow velocity. Our results provide in‐depth analysis of the microdynamic environment of cells cultured within 3D environments, and thus provide advanced control over tissue development in vitro. Biotechnol. Bioeng. 2010; 105: 645–654. © 2009 Wiley Periodicals, Inc.     

Dynamics of diffusivity and pressure drop in flow-through and parallel-flow bioreactors during tissue regeneration

In this study, transport characteristics in flow-through and parallel-flow bioreactors used in tissue engineering were simulated using computational fluid dynamics. To study nutrient distribution and consumption by smooth muscle cells colonizing the 100 mm diameter and 2-mm thick scaffold, effective diffusivity of glucose was experimentally determined using a two-chambered setup. Three different concentrations of chitosan-gelatin scaffolds were prepared by freezing at -80°C followed by lyophilization. Experiments were performed in both bioreactors to measure pressure drop at different flow rates. At low flow rates, experimental results were in agreement with the simulation results for both bioreactors. However, increase in flow rate beyond 5 mL/min in flow-through bioreactor showed channeling at the circumference resulting in lower pressure drop relative to simulation results. The Peclet number inside the scaffold indicated nutrient distribution within the flow-through bioreactor to be convection-dependent, whereas the parallel-flow bioreactor was diffusion-dependent. Three alternative design modifications to the parallel-flow were made by (i) introducing an additional inlet and an outlet, (ii) changing channel position, and (iii) changing the hold-up volume. Simulation studies were performed to assess the effect of scaffold thickness, cell densities, and permeability. These new designs improved nutrient distribution for 2 mm scaffolds; however, parallel-flow configuration was found to be unsuitable for scaffolds more than 4-mm thick, especially at low porosities as tissues regenerate. Furthermore, operable flow rate in flow-through bioreactors is constrained by the mechanical strength of the scaffold. In summary, this study showed limitations and differences between flow-through and parallel-flow bioreactors used in tissue engineering.     

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.     

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.     

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.     

Numerical simulation of fluid field and in vitro three-dimensional fabrication of tissue-engineered bones in a rotating bioreactor and in vivo implantation for repairing segmental bone defects

In this paper, two-dimensional flow field simulation was conducted to determine shear stresses and velocity profiles for bone tissue engineering in a rotating wall vessel bioreactor (RWVB). In addition, in vitro three-dimensional fabrication of tissue-engineered bones was carried out in optimized bioreactor conditions, and in vivo implantation using fabricated bones was performed for segmental bone defects of Zelanian rabbits. The distribution of dynamic pressure, total pressure, shear stress, and velocity within the culture chamber was calculated for different scaffold locations. According to the simulation results, the dynamic pressure, velocity, and shear stress around the surface of cell-scaffold construction periodically changed at different locations of the RWVB, which could result in periodical stress stimulation for fabricated tissue constructs. However, overall shear stresses were relatively low, and the fluid velocities were uniform in the bioreactor. Our in vitro experiments showed that the number of cells cultured in the RWVB was five times higher than those cultured in a T-flask. The tissue-engineered bones grew very well in the RWVB. This study demonstrates that stress stimulation in an RWVB can be beneficial for cell/bio-derived bone constructs fabricated in an RWVB, with an application for repairing segmental bone defects.     

Numerical simulation of hemodynamics in stented internal carotid aneurysm based on patient-specific model

There is still a considerable lack of quantitative information concerning the effects of stent structures on blood flow in an aneurismal cavity. In this paper, five virtual stents with different structures and wire cross-sections were designed for incorporation into the same patient-specific aneurysm model. Computational fluid dynamics simulations were performed so as to study how these five types of stents modified hemodynamic parameters. Numerical results demonstrated that the mean flow rate in the aneurismal cavity decreased the most in the model that used a stent with a rectangular wire cross-section, and that the wall shear stresses at the dome and neck of the aneurysm decreased more in models that used a stent with a circular wire cross-section or a spiral stent with a rectangular wire cross-section compared to other models. In addition, the wall pressure on the aneurysm increased slightly after implantation of the stent in all five models. This result differs from that previously published, and may help guide the design and assist clinicians in selecting an appropriate stent for treating cerebral aneurysms.     

Flow modeling in a novel non-perfusion conical bioreactor

We have developed a bioreactor vessel design which has the advantages of simplicity and ease of assembly and disassembly, and with the appropriately determined flow rate, even allows for a scaffold to be suspended freely regardless of its weight. This article reports our experimental and numerical investigations to evaluate the performance of a newly developed non-perfusion conical bioreactor by visualizing the flow through scaffolds with 45 degrees and 90 degrees fiber lay down patterns. The experiments were conducted at the Reynolds numbers (Re) 121, 170, and 218 based on the local velocity and width of scaffolds. The flow fields were captured using short-time exposures of 60 microm particles suspended in the bioreactor and illuminated using a thin laser sheet. The effects of scaffold fiber lay down pattern and Reynolds number were obtained and correspondingly compared to results obtained from a computational fluid dynamics (CFD) software package. The objectives of this article are twofold: to investigate the hypothesis that there may be an insufficient exchange of medium within the interior of the scaffold when using our non-perfusion bioreactor, and second, to compare the flows within and around scaffolds of 45 degrees and 90 degrees fiber lay down patterns. Scaffold porosity was also found to influence flow patterns. It was therefore shown that fluidic transport could be achieved within scaffolds with our bioreactor design, being a non-perfusion vessel. Fluid velocities were generally same of the same or one order lower in magnitude as compared to the inlet flow velocity. Additionally, the 90 degrees fiber lay down pattern scaffold was found to allow for slightly higher fluid velocities within, as compared to the 45 degrees fiber lay down pattern scaffold. This was due to the architecture and pore arrangement of the 90 degrees fiber lay down pattern scaffold, which allows for fluid to flow directly through (channel-like flow).     

Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: a micro-CT based model

Natural cartilage remodels both in vivo and in vitro in response to mechanical stresses, hence mechanical stimulation is believed to be a potential tool to modulate extra-cellular matrix synthesis in tissue-engineered cartilage. Fluid-induced shear is known to enhance chondrogenesis in engineered cartilage constructs. The quantification of the hydrodynamic environment is a condition required to study the biochemical response to shear of 3D engineered cell systems. We developed a computational model of culture medium flow through the microstructure of a porous scaffold, during direct- perfused culture. The 3D solid model of the scaffold micro-geometry was reconstructed from 250 micro-computed tomography (micro-CT) images. The results of the fluid dynamic simulations were analyzed at the central portions of the fluid domain, to avoid boundary effects. The average, median and mode shear stress values calculated at the scaffold walls were 3.48, 2.90, and 2.45 mPa respectively, at a flow rate of 0.5 cm(3)/min, perfused through a 15 mm diameter scaffold, at an inlet fluid velocity of 53 microm/s. These results were compared to results estimated using a simplified micro-scale model and to results estimated using an analytical macro-scale porous model. The predictions given by the CT-based model are being used in conjunction with an experimental bioreactor model, in order to quantify the effects of fluid-dynamic shear on the growth modulation of tissue-engineered cartilage constructs, to potentially enhance tissue growth in vitro.     

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.     

Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors

Bioreactors allowing culture medium perfusion overcome diffusion limitations associated with static culturing and provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed to cells will depend not only on the culture medium flow rate, but also on the scaffold three-dimensional (3D) micro-architecture. We developed a CFD model of the flow of culture medium through a 3D scaffold of homogeneous geometry, with the aim of predicting the shear stress acting on cells as a function of parameters that can be controlled during the scaffold fabrication process, such as the scaffold porosity and the pore size, and during the cell culture, such as the medium flow rate and the diameter of the perfused scaffold section. We built three groups of models corresponding to three pore sizes: 50, 100 and 150 microm. Each group was made of four models corresponding to 59%, 65%, 77%, and 89% porosity. A commercial finite-element code was used to set up and solve the problem and to analyze the results. The mode value of shear stress varied between 2 and 5 mPa, and was obtained for a circular scaffold of 15.5 mm diameter, perfused by a flow rate of 0.5 ml/min. The simulations showed that the pore size is a variable strongly influencing the predicted shear stress level, whereas the porosity is a variable strongly affecting the statistical distribution of the shear stresses, but not their magnitude. Our results provide a basis for the completion of more exhaustive quantitative studies to further assess the relationship between perfusion, at known micro-fluid dynamic conditions, and tissue growth in vitro.     

Numerical model of fluid flow and oxygen transport in a radial-flow microchannel containing hepatocytes

The incorporation of monolayers of cultured hepatocytes into an extracorporeal perfusion system has become a promising approach for the development of a temporary bioartificial liver (BAL) support system. In this paper we present a numerical investigation of the oxygen tension, shear stress, and pressure drop in a bioreactor for a BAL composed of plasma-perfused chambers containing monolayers of porcine hepatocytes. The chambers consist of microfabricated parallel disks with center-to-edge radial flow. The oxygen uptake rate (OUR), measured in vitro for porcine hepatocytes, was curve-fitted using Michaelis-Menten kinetics for simulation of the oxygen concentration profile. The effect of different parameters that may influence the oxygen transport inside the chambers, such as the plasma flow rate, the chamber height, the initial oxygen tension in the perfused plasma, the OUR, and K(m) was investigated. We found that both the plasma flow rate and the initial oxygen tension may have an important effect upon oxygen transport. Increasing the flow rate and/or the inlet oxygen tension resulted in improved oxygen transport to cells in the radial-flow microchannels, and allowed significantly greater diameter reactor without oxygen limitation to the hepatocytes. In the range investigated in this paper (10 microns < H < 100 microns), and for a constant plasma flow rate, the chamber height, H, had a negligible effect on the oxygen transport to hepatocytes. On the contrary, it strongly affected the mechanical stress on the cells that is also crucial for the successful design of the BAL reactors. A twofold decrease in chamber height from 50 to 25 microns produced approximately a fivefold increase in maximal shear stress at the inlet of the reactor from 2 to 10 dyn/cm2. Further decrease in chamber height resulted in shear stress values that are physiologically unrealistic. Therefore, the channel height needs to be carefully chosen in a BAL design to avoid deleterious hydrodynamic effects on hepatocytes.