Modeling of effects of nutrient gradients on cell proliferation in microfluidic bioreactor

Precise control of the microenvironment is highly desirable in cell culture to study the cell biology. Microfluidic based bioreactors provide a promising method for the spatial and temporal control of cell growth and stimuli. A three-dimensional nutrient transport model, incorporating the monolayer cell growth model, has been developed to investigate the influence of gradients of oxygen and epidermal growth factor (EGF) on the cell culture in the continuous-flow microchannel bioreactor. Our results demonstrate that applying inlet concentration gradients of oxygen and EGF can induce variations of cell density in the y-direction. It is further found that compared to the oxygen gradients the EGF concentration gradients are more efficient in regulating the cell growth.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice–Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice-Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

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.     

Effects of oxygen transport on 3-d human mesenchymal stem cell metabolic activity in perfusion and static cultures: experiments and mathematical model

Human mesenchymal stem cells (hMSCs) have unique potential to develop into functional tissue constructs to replace a wide range of tissues damaged by disease or injury. While recent studies have highlighted the necessity for 3-D culture systems to facilitate the proper biological, physiological, and developmental processes of the cells, the effects of the physiological environment on the intrinsic tissue development characteristics in the 3-D scaffolds have not been fully investigated. In this study, experimental results from a 3-D perfusion bioreactor system and the static culture are combined with a mathematical model to assess the effects of oxygen transport on hMSC metabolism and proliferation in 3-D constructs grown in static and perfusion conditions. Cells grown in the perfusion culture had order of magnitude higher metabolic rates, and the perfusion culture supports higher cell density at the end of cultivation. The specific oxygen consumption rate for the constructs in the perfusion bioreactor was found to decrease from 0.012 to 0.0017 micromol/10(6) cells/h as cell density increases, suggesting intrinsic physiological change at high cell density. BrdU staining revealed the noneven spatial distribution of the proliferating cells in the constructs grown under static culture conditions compared to the cells that were grown in the perfusion system. The hypothesis that the constructs in static culture grow under oxygen limitation is supported by higher Y(L/G) in static culture. Modeling results show that the oxygen tension in the static culture is lower than that of the perfusion unit, where the cell density was 4 times higher. The experimental and modeling results show the dependence of cell metabolism and spatial growth patterns on the culture environment and highlight the need to optimize the culture parameters in hMSC tissue engineering.     

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.     

Design and validation of a dynamic flow perfusion bioreactor for use with compliant tissue engineering scaffolds

In tissue engineering, flow perfusion bioreactors can be used to enhance nutrient diffusion while mechanically stimulating cells to increase matrix production. The goal of this study was to design and validate a dynamic flow perfusion bioreactor for use with compliant scaffolds. Using a non-permanent staining technique, scaffold perfusion was verified for flow rates of 0.1-2.0 mL/min. Flow analysis revealed that steady, pulsatile and oscillatory flow profiles were effectively transferred from the pump to the scaffold. Compared to static culture, bioreactor culture of osteoblast-seeded collagen-GAG scaffolds led to a 27-34% decrease in cell number but stimulated an 800-1200% increase in the production of prostaglandin E(2), an early-stage bone formation marker. This validated flow perfusion bioreactor provides the basis for optimisation of bioreactor culture in tissue engineering applications.     

Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs

Mathematic models help interpret experimental results and accelerate tissue engineering developments. We develop in this paper a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by oxygen concentration were carefully studied. Simplified two-dimensional simulations were performed. Using this model, we investigated the influence of cell migration speed on the overall cell growth within in vitro cell scaffolds. It was found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, intense cell motility with conventional uniform cell seeding method may lead to declined cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Therefore, homogeneous cell seeding may not be a good way of gaining large and uniform cell densities for the final results. We then compared cell growth in scaffolds with various seeding modes, and proposed a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount and uniform cell distribution for tissue engineering construct developments.     

Mesenchymal stem cell cultivation in electrospun scaffolds: mechanistic modeling for tissue engineering

Tissue engineering is a multidisciplinary field of research in which the cells, biomaterials, and processes can be optimized to develop a tissue substitute. Three-dimensional (3D) architectural features from electrospun scaffolds, such as porosity, tortuosity, fiber diameter, pore size, and interconnectivity have a great impact on cell behavior. Regarding tissue development in vitro, culture conditions such as pH, osmolality, temperature, nutrient, and metabolite concentrations dictate cell viability inside the constructs. The effect of different electrospun scaffold properties, bioreactor designs, mesenchymal stem cell culture parameters, and seeding techniques on cell behavior can be studied individually or combined with phenomenological modeling techniques. This work reviews the main culture and scaffold factors that affect tissue development in vitro regarding the culture of cells inside 3D matrices. The mathematical modeling of the relationship between these factors and cell behavior inside 3D constructs has also been critically reviewed, focusing on mesenchymal stem cell culture in electrospun scaffolds.     

Three hours of perfusion culture prior to 28 days of static culture, enhances osteogenesis by human cells in a collagen GAG scaffold

In tissue engineering, bioreactors can be used to aid in the in vitro development of new tissue by providing biochemical and physical regulatory signals to cells and encouraging them to undergo differentiation and/or to produce extracellular matrix prior to in vivo implantation. This study examined the effect of short term flow perfusion bioreactor culture, prior to long‐term static culture, on human osteoblast cell distribution and osteogenesis within a collagen glycosaminoglycan (CG) scaffold for bone tissue engineering. Human fetal osteoblasts (hFOB 1.19) were seeded onto CG scaffolds and pre‐cultured for 6 days. Constructs were then placed into the bioreactor and exposed to 3 × 1 h bouts of steady flow (1 mL/min) separated by 7 h of no flow over a 24‐h period. The constructs were then cultured under static osteogenic conditions for up to 28 days. Results show that the bioreactor and static culture control groups displayed similar cell numbers and metabolic activity. Histologically, however, peripheral cell‐encapsulation was observed in the static controls, whereas, improved migration and homogenous cell distribution was seen in the bioreactor groups. Gene expression analysis showed that all osteogenic markers investigated displayed greater levels of expression in the bioreactor groups compared to static controls. While static groups showed increased mineral deposition; mechanical testing revealed that there was no difference in the compressive modulus between bioreactor and static groups. In conclusion, a flow perfusion bioreactor improved construct homogeneity by preventing peripheral encapsulation whilst also providing an enhanced osteogenic phenotype over static controls. Bioeng. 2011; 108:1203–1210. © 2010 Wiley Periodicals, Inc.     

A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.     

Mathematical modeling of cell growth in a 3D scaffold and validation of static and dynamic cultures

Tissue engineering, an immensely important field in contemporary clinical practices, aims at the repair or replacement of damaged tissues. The mathematical model proposed herein shows the distribution and growth of cells in their characteristic time in a 3D scaffold model. This study contributes to the progress of simulation techniques in static and dynamic cultures of bone tissue. Brinkman, nutrient transport, and cell growth equations are brought together to quantify the growth behavior of cells. However, when a static culture is being studied, the Brinkman equation is eliminated. The model was validated by experimental cell culture using 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay and scanning electron microscopy. Then, static and dynamic cultures were compared to assess the cell density and cell distribution in the scaffold. Cell counting after 21 days of cell culture showed that the number of cells increased 42‐fold in static and 53.5‐fold in dynamic cultures, which was in good agreement with our model estimations (37‐fold increase in the number of cells in static and 49‐fold increase in dynamic cultures). In conclusion, our mathematical model could predict cell distribution and growth in the scaffold.     

Rotating versus perfusion bioreactor for the culture of engineered vascular constructs based on hyaluronic acid

It is generally accepted that dynamic culture conditions are required for vascular tissue engineering. We compared the effects of two dynamic culture systems, a perfusion and a rotating bioreactor, using tubular constructs based on hyaluronic acid seeded with porcine aortic smooth muscle cells (SMC), that we recently showed to be adequate for the generation of vascular tissue. In perfused constructs mechanical stimulation importantly affected cell morphology, increased the incidence of cell proliferation and reduced apoptosis. However, extracellular matrix deposition, cytoskeletal organization and mechanical properties were poor. In rotated constructs cell proliferation was also higher and apoptosis lower than in static controls. Rotated constructs showed the highest ultimate stress and the lowest elastic modulus. Our data indicate that the rotating bioreactor is more efficient than the perfusion bioreactor and we then suggest that this method can be considered a valid alternative to complex bioreactor systems described in the literature.     

Improved recellularization of ex vivo vascular scaffolds using directed transport gradients to modulate ECM remodeling

The regeneration of functional, clinically viable, tissues from acellular ex vivo tissues has been problematic largely due to poor nutrient transport conditions that limit cell migration and integration. Compounding these issues are subcellular pore sizes that necessarily requires extracellular matrix (ECM) remodeling in order for cells to migrate and regenerate the tissue. The aim of the present work was to create a directed growth environment that allows cells to fully populate an ex vivo‐derived vascular scaffold and maintain viability over extended periods. Three different culture conditions using single (one nutrient source) or dual perfusion bioreactor systems (two nutrients sources) were designed to assess the effect of pressure and nutrient gradients under either low (50/30 mmHg) or high (120/80) relative pressure conditions. Human myofibroblasts were seeded to the ablumenal periphery of an ex vivo‐derived vascular scaffold using a collagen/hydrogel cell delivery system. After 30 days culture, total cell density was consistent between groups; however, significant variation was noted in cell distribution and construct mechanics as a result of differing perfusion conditions. The most aggressive transport gradient was developed by the single perfusion low‐pressure circuits and resulted in a higher proportion of cells migrating across the scaffold toward the vessel lumen (nutrient source). These investigations illustrate the influence of directed nutrient gradients where precisely controlled perfusion conditions significantly affects cell migration, distribution and function, resulting in pronounced effects on construct mechanics during early remodeling events. Biotechnol. Bioeng. 2013; 110: 2035–2045. © 2013 Wiley Periodicals, Inc.     

A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor

In vitro tissue engineering is investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors, where an interstitial fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of cells, provided that the shear stress level is appropriately tuned. In this complex environment, mathematical and computational modeling can help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions, where nutrient concentration, fluid dynamic field and cell growth are consistently coupled. The biomass growth model is calibrated with respect to the shear stress dependence on experimental data using a simplified short-time analysis in which the nutrient concentration and the fluid-induced shear stress are assumed constant in time and uniform in space. Volume averaging techniques are used to derive effective parameters that allow to upscale the microscopic structural properties to the macroscopic level. The biomass growth predictions obtained in this way are significant for long times of culture.     

New miniaturized hollow-fiber bioreactor for in vivo like cell culture, cell expansion, and production of cell-derived products

We have developed a miniaturized hollow-fiber bioreactor system for mammalian cell culture with a volume of 1 mL. Cell and medium compartments of the bioreactor are separated by a semipermeable membrane, and oxygenation of the cell compartment is accomplished using an oxygenation membrane. As a result of the geometry of the transparent housing, cells can be observed by microscopy during culture. The leukemic cell lines CCRF-CEM, HL-60, and REH were cultivated up to densities of 3.5 x 10(7)/mL without medium change or manipulation of the cells. As shown using CCRF-CEM cells, growth in the bioreactor was strongly influenced and could be controlled by the medium flow rate. As a consequence, consumption of glucose and generation of lactate varied with flow rate. Depending on the molecular size cutoff of the membranes used, added growth factors such as GM-CSF, as well as factors secreted from the cells, are retained in the cell compartment for up to 1 week. This new miniaturized hollow-fiber bioreactor offers advantages in tissue engineering by continuous nutrient supply for cells in high density, retention of added or autocrine produced factors, and undisturbed long-term culture in a closed system.     

Nutrient gradients in engineered cartilage: metabolic kinetics measurement and mass transfer modeling

Since tissue-engineered cartilage is avascular, both nutrient supply and metabolic waste removal rely on diffusion. As a result, gradients of nutrients and wastes exist through the construct. Previous models usually calculate gradients of oxygen, glucose, and lactic acid separately, without taking into account the complex interdependence between concentrations of these substrates and rates of metabolism. In this study, these interactions were experimentally examined and incorporated into diffusion models. One-dimensional diffusion-reaction models were developed for three typical culture conditions, that is, static culture, perfusion culture, and suspended culture. The profiles of oxygen, glucose, lactic acid, and pH in the cultured constructs were calculated simultaneously using measured metabolic rates. The maximum construct size and cell density which could be supported before nutrients were depleted in the construct center was identified; a function predicting the relationship between construct dimension and the maximum viable cell density was developed. For constructs incubated under static culture the model demonstrated that the gradients which developed through the medium could not be neglected. Perfusion cultures could support a considerably higher cell density than static cultures, while for batch cultures in a rotating bioreactor, the volume of medium also influences the maximum cell density that could be supported. This study provides useful guidance for design of engineered cartilage constructs.     

A mathematical model for fluid shear-sensitive 3D tissue construct development

This research studies dynamic culture for 3D tissue construct development with computational fluid dynamics. It proposes a mathematical model to evaluate the impact of flow rates and flow shear stress on cell growth in 3D constructs under perfusion. The modeling results show that dynamic flow, even at flow rate as low as 0.002 cm/s, can support much better mass exchange, higher cell number, and more even cell and nutrient distribution compared to static culture. Higher flow rate can further improve nutrient supply and mass exchange in the construct, promoting better nutritious environment and cell proliferation compared to lower flow rate. In addition, consideration of flow shear stress predicts much higher cell number in the construct compared to that without shear consideration. While the nutrient can dominate shear stress in influencing cell proliferation, the shear effect increases with flow rate. The proposed model helps tissue engineers better understand the cell-flow relationship at the molecular level during dynamic culture.     

Oxygen transport and consumption by suspended cells in microgravity: a multiphase analysis

A rotating bioreactor for the cell/tissue culture should be operated to obtain sufficient nutrient transfer and avoid damage to the culture materials. Thus, the objective of the present study is to determine the appropriate suspension conditions for the bead/cell distribution and evaluate oxygen transport in the rotating wall vessel (RWV) bioreactor. A numerical analysis of the RWV bioreactor is conducted by incorporating the Eulerian-Eulerian multiphase and oxygen transport equations. The bead size and rotating speed are the control variables in the calculations. The present results show that the rotating speed for appropriate suspensions needs to be increased as the size of the bead/cell increases: 10 rpm for 200 microm; 12 rpm for 300 microm; 14 rpm for 400 microm; 18 rpm for 600 microm. As the rotating speed and the bead size increase from 10 rpm/200 microm to 18 rpm/600 microm, the mean oxygen concentration in the 80% midzone of the vessel is increased by approximately 85% after 1-h rotation due to the high convective flow for 18 rpm/600 microm case as compared to 10 rpm/200 microm case. The present results may serve as criteria to set the operating parameters for a RWV bioreactor, such as the size of beads and the rotating speed, according to the growth of cell aggregates. In addition, it might provide a design parameter for an advanced suspension bioreactor for 3-D engineered cell and tissue cultures.     

Visualizing medium and biodistribution in complex cell culture bioreactors using in vivo imaging

There is a dearth of technology and methods to aid process characterization, control and scale‐up of complex culture platforms that provide niche micro‐environments for some stem cell‐based products. We have demonstrated a novel use of 3d in vivo imaging systems to visualize medium flow and cell distribution within a complex culture platform (hollow fiber bioreactor) to aid characterization of potential spatial heterogeneity and identify potential routes of bioreactor failure or sources of variability. This can then aid process characterization and control of such systems with a view to scale‐up. Two potential sources of variation were observed with multiple bioreactors repeatedly imaged using two different imaging systems: shortcutting of medium between adjacent inlet and outlet ports with the potential to create medium gradients within the bioreactor, and localization of bioluminescent murine 4T1‐luc2 cells upon inoculation with the potential to create variable seeding densities at different points within the cell growth chamber. The ability of the imaging technique to identify these key operational bioreactor characteristics demonstrates an emerging technique in troubleshooting and engineering optimization of bioreactor performance. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 30:256–260, 2014