A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.     

Influence of flow rate and scaffold pore size on cell behavior during mechanical stimulation in a flow perfusion bioreactor

Mechanically stimulating cell-seeded scaffolds by flow-perfusion is one approach utilized for developing clinically applicable bone graft substitutes. A key challenge is determining the magnitude of stimuli to apply that enhances cell differentiation but minimizes cell detachment from the scaffold. In this study, we employed a combined computational modeling and experimental approach to examine how the scaffold mean pore size influences cell attachment morphology and subsequently impacts upon cell deformation and detachment when subjected to fluid-flow. Cell detachment from osteoblast-seeded collagen-GAG scaffolds was evaluated experimentally across a range of scaffold pore sizes subjected to different flow rates and exposure times in a perfusion bioreactor. Cell detachment was found to be proportional to flow rate and inversely proportional to pore size. Using this data, a theoretical model was derived that accurately predicted cell detachment as a function of mean shear stress, mean pore size, and time. Computational modeling of cell deformation in response to fluid flow showed the percentage of cells exceeding a critical threshold of deformation correlated with cell detachment experimentally and the majority of these cells were of a bridging morphology (cells stretched across pores). These findings will help researchers optimize the mean pore size of scaffolds and perfusion bioreactor operating conditions to manage cell detachment when mechanically simulating cells via flow perfusion.     

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

     

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.     

Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue engineering

The shear stresses in printed scaffold systems for tissue engineering depend on the flow properties and void volume in the scaffold. In this work, computational fluid dynamics (CFD) is used to simulate flow fields within porous scaffolds used for cell growth. From these models the shear stresses acting on the scaffold fibres are calculated. The results led to the conclusion that the Darcian (k ₁) permeability constant is a good predictor for the shear stresses in scaffold systems for tissue engineering. This permeability constant is easy to calculate from the distance between and thickness of the fibres used in a 3D printed scaffold. As a consequence computational effort and specialists for CFD can be circumvented by using this permeability constant to predict the shear stresses. If the permeability constant is below a critical value, cell growth within the specific scaffold design may cause a significant increase in shear stress. Such a design should therefore be avoided when the shear stress experienced by the cells should remain in the same order of magnitude.     

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.     

A prediction of cell differentiation and proliferation within a collagen–glycosaminoglycan scaffold subjected to mechanical strain and perfusive fluid flow

Mesenchymal stem cell (MSC) differentiation can be influenced by biophysical stimuli imparted by the host scaffold. Yet, causal relationships linking scaffold strain magnitudes and inlet fluid velocities to specific cell responses are thus far underdeveloped. This investigation attempted to simulate cell responses in a collagen–glycosaminoglycan (CG) scaffold within a bioreactor. CG scaffold deformation was simulated using μ-computed tomography (CT) and an in-house finite element solver (FEEBE/linear). Similarly, the internal fluid velocities were simulated using the afore-mentioned μCT dataset with a computational fluid dynamics solver (ANSYS/CFX). From the ensuing cell-level mechanics, albeit octahedral shear strain or fluid velocity, the proliferation and differentiation of the representative cells were predicted from deterministic functions. Cell proliferation patterns concurred with previous experiments. MSC differentiation was dependent on the level of CG scaffold strain and the inlet fluid velocity. Furthermore, MSC differentiation patterns indicated that specific combinations of scaffold strains and inlet fluid flows cause phenotype assemblies dominated by single cell types. Further to typical laboratory procedures, this predictive methodology demonstrated loading-specific differentiation lineages and proliferation patterns. It is hoped these results will enhance in-vitro tissue engineering procedures by providing a platform from which the scaffold loading applications can be tailored to suit the desired tissue.     

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.     

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.     

Computational models for wall shear stress estimation in scaffolds: a comparative study of two complete geometries

Fluid mechanical stimuli are known to upregulate cell differentiation and matrix formation. Since wall shear stress plays an important role various studies tried to estimate the scaffold fluid dynamic environment. However, because of the geometrical complexity, nearly all studies created their CFD model based on a submodel of the entire scaffold assuming that the model covers heterogeneity sufficiently. However to the authors' knowledge no study exist providing guidelines in this matter. In a previous study we demonstrated that submodels are influenced by the boundary conditions, inevitable when flow channels are chopped off. For the current study we therefore developed μCT based models of two complete scaffold geometries (one titanium and one hydroxyapatite). Imposing a 0.04 ml/min flow rate resulted in a surface area averaged wall shear stress of 1.41 mPa for titanium and 1.09 mPa for hydroxyapatite. In order to get insight in required model size we subdivided the domain in regions of different size. From our results we propose a model size between 6 and 10 times the average pore size. The wall shears stress should be calculated on a region at least one pore size away from the boundaries. These guidelines could be of use for computationally more costly simulations where it is not possible to simulate the complete scaffold domain.     

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.     

Quantification of fluid shear stress in bone tissue engineering scaffolds with spherical and cubical pore architectures

Recent studies have shown that mechanical stimulation, in the form of fluid perfusion and mechanical compression, can enhance osteogenic differentiation of mesenchymal stem cells and bone cells within tissue engineering scaffolds in vitro. The precise nature of mechanical stimulation within tissue engineering scaffolds is not only dictated by the exogenously applied loading regime, but also depends on the geometric features of the scaffold, in particular architecture, pore size and porosity. However, the precise contribution of each geometric feature towards the resulting mechanical stimulation within a scaffold is difficult to characterise due to the wide range of interacting parameters. In this study, we have applied a fluid–structure interaction model to investigate the role of scaffold geometry (architecture, pore size and porosity) on pore wall shear stress (WSS) under a range of different loading scenarios: fluid perfusion, mechanical compression and a combination of perfusion and compression. It is found that scaffold geometry (spherical and cubical pores), in particular the pore size, has a significant influence on the stimulation within scaffolds. Furthermore, we observed an amplified WSS within scaffolds under a combination of fluid perfusion and mechanical compression, which exceeded that caused by individual fluid perfusion or mechanical compression approximately threefold. By conducting this comprehensive parametric variation study, an expression was generated to allow the design and optimisation of 3D TE scaffolds and inform experimental loading regimes so that a desired level of mechanical stimulation, in terms of WSS is generated within the scaffold.     

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.     

Modeling and design of optimal flow perfusion bioreactors for tissue engineering applications

Perfusion bioreactors have been used in different tissue engineering applications because of their consistent distribution of nutrients and flow-induced shear stress within the tissue-engineering scaffold. A widely used configuration uses a scaffold with a circular cross-section enclosed within a cylindrical chamber and inlet and outlet pipes which are connected to the chamber on either side through which media is continuously circulated. However, fluid-flow experiments and simulations have shown that the majority of the flow perfuses through the center. This pattern creates stagnant zones in the peripheral regions as well as in those of high flow rate near the inlet and outlet. This non-uniformity of flow and shear stress, owing to a circular design, results in limited cell proliferation and differentiation in these areas. The focus of this communication is to design an optimized perfusion system using computational fluid dynamics as a mathematical tool to overcome the time-consuming trial and error experimental method. We compared the flow within a circular and a rectangular bioreactor system. Flow simulations within the rectangular bioreactor are shown to overcome the limitations in the circular design. This communication challenges the circular cross-section bioreactor configuration paradigm and provides proof of the advantages of the new design over the existing one.     

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 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.     

Investigations into the rheological characteristics of bovine amniotic fluid

The rheological characteristics of bovine amniotic fluid have been studied at different shear rates. The viscosity of bovine amniotic fluid at 20°C was found to increase with time at a constant low shear rate during the measurement. Additionally, the viscosity was observed to decrease with increasing shear rate, indicating that a shear thinning behaviour of the fluid was occurring. The log-log plot of shear stress versus shear rate yielded a straight line, consistent with non-Newtonian behaviour of the fluid and characteristic of pseudoplastic liquids. The data of shear stress versus shear rate could be represented by a power law model. The treatment of amniotic fluid with cetylpyridinium chloride (CPC) resulted in the precipitation of a mixture of components, including complex sulphated polysaccharides and extracellular proteoglycans, with the viscosity of the resulting liquid similar to that of water at 20°C. In addition, the viscosity of the CPC-pretreated fluid did not increase with time at constant shear rate and remained constant with the increase in shear rate. The apparent increase in viscosity with time and the shear thinning behaviour of the amniotic fluid can thus be attributed to pseudoplastic liquid behaviour associated with the presence of structurally complex polysaccharides and extracellular proteoglycans. The implications of this fluid viscosity behaviour are discussed in terms of their impact on the operation of packed or expanded (fluidized) chromatographic bed systems when amniotic fluid biofeed-stocks are used as a source of commercially important proteins.     

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.     

Fluid-induced low shear stress improves cartilage like tissue fabrication by encapsulating chondrocytes

In the recent years, there has been considerable development in the regenerative medicine, which aims to repair, regenerate, and improve injured articular cartilage. The aim of the present study was to investigate the effect of flow-induced shear stress in perfusion bioreactor on alginate encapsulating chondrocytes. The shear stress imposed on the cells in the culture chamber of bioreactor was predicted with computational fluid dynamic. Bovine nasal chondrocytes were isolated and expanded to obtain a pellet. The cell pellet was resuspends in alginate solution, transferred to the culture chamber, and dynamically cultured under direct perfusion. At the end of culture, tissue constructs were examined histologically and by immunohistochemistry. The results of computational fluid dynamic modeling revealed that maximum wall shear stress was 4.820 × 10^?3 Pascal. Macroscopic views of the alginate/chondrocyte beads suggested that it possessed constant shape but were flexible. Under inverted microscope, round shape of chondrocyte observed. Cell distribution was homogeneous throughout the scaffold. Tissue construct subjected to shear showed morphological features, which are characteristic for natural cartilage. Immunohistochemistry results revealed immunopositivity for type II collagens in tissue constructs samples. Flow induced shear stress in the perfusion bioreactor and chnondrocyte encapsulation provide environment to support cell growth, and tissue regeneration and improve cartilage like tissue fabrication.     

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.