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.     

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.     

Modeling particle transport by bubbles for performance guidelines in airlift fermentors

A calculation method has been developed to model the statistical transport of biological particles in bubble-driven flows, with special reference to the biokinetics of environmental excursions experienced by individual cells, aggregated cells, or immobilization beads in airlift bioreactors. Interim developments on modeling the transport of such particles in concentric tube devices are reported. The calculation is driven by user-prescribed global parameters for the bioreactor geometry, bulk air flow rate, and particle parameters (size and slip speed). The algorithm calls on empirical data correlations for void fraction, bulk liquid flow rate, and bubble sizes and slip speeds, optimally selected from a large bibliographic database. The Monte Carlo algorithm concentrates on simulating particle transport in the bubbly riser flows.The packaged family of correlations and calculations represents, in effect, an expert system augmented by a transport simulation suited to characterizing the biokinetic response of cells cultured in airlift bioreactors.     

A simple eccentric stirred tank mini‐bioreactor: Mixing characterization and mammalian cell culture experiments

In industrial practice, stirred tank bioreactors are the most common mammalian cell culture platform. However, research and screening protocols at the laboratory scale (i.e., 5–100 mL) rely primarily on Petri dishes, culture bottles, or Erlenmeyer flasks. There is a clear need for simple—easy to assemble, easy to use, easy to clean—cell culture mini‐bioreactors for lab‐scale and/or screening applications. Here, we study the mixing performance and culture adequacy of a 30 mL eccentric stirred tank mini‐bioreactor. A detailed mixing characterization of the proposed bioreactor is presented. Laser induced fluorescence (LIF) experiments and computational fluid dynamics (CFD) computations are used to identify the operational conditions required for adequate mixing. Mammalian cell culture experiments were conducted with two different cell models. The specific growth rate and the maximum cell density of Chinese hamster ovary (CHO) cell cultures grown in the mini‐bioreactor were comparable to those observed for 6‐well culture plates, Erlenmeyer flasks, and 1 L fully instrumented bioreactors. Human hematopoietic stem cells were successfully expanded tenfold in suspension conditions using the eccentric mini‐bioreactor system. Our results demonstrate good mixing performance and suggest the practicality and adequacy of the proposed mini‐bioreactor. Biotechnol. Bioeng. 2013; 110: 1106–1118. © 2012 Wiley Periodicals, Inc.     

CFD simulation coupled with population balance equations for aerated stirred bioreactors

Mammalian cells have been widely used to produce therapeutic proteins in stirred bioreactors in suspension culture. Local hydrodynamics can have a great impact on cell proliferation and protein synthesis, but there are few reports on spatial heterogeneity of nutrients, gas bubbles, and mass transfer coefficients. We have employed computational fluid dynamics (CFD) coupled with population balance equations to study local hydrodynamics in a 20 L stirred bioreactor. The flow patterns, energy dissipation rates, gas volume fraction, gas bubble size distribution and local mass transfer coefficient have been displayed throughout the whole bioreactor. Their implications for mammalian cell culture have been discussed. This study provides an insight into rational design and optimum operation conditions in a stirred bioreactor for mammalian cell cultivation.     

Coupled metabolic-hydrodynamic modeling enabling rational scale-up of industrial bioprocesses

Metabolomics aims to address what and how regulatory mechanisms are coordinated to achieve flux optimality, different metabolic objectives as well as appropriate adaptations to dynamic nutrient availability. Recent decades have witnessed that the integration of metabolomics and fluxomics within the goal of synthetic biology has arrived at generating the desired bioproducts with improved bioconversion efficiency. Absolute metabolite quantification by isotope dilution mass spectrometry represents a functional readout of cellular biochemistry and contributes to the establishment of metabolic (structured) models required in systems metabolic engineering. In industrial practices, population heterogeneity arising from fluctuating nutrient availability frequently leads to performance losses, that is reduced commercial metrics (titer, rate, and yield). Hence, the development of more stable producers and more predictable bioprocesses can benefit from a quantitative understanding of spatial and temporal cell-to-cell heterogeneity within industrial bioprocesses. Quantitative metabolomics analysis and metabolic modeling applied in computational fluid dynamics (CFD)-assisted scale-down simulators that mimic industrial heterogeneity such as fluctuations in nutrients, dissolved gases, and other stresses can procure informative clues for coping with issues during bioprocessing scale-up. In previous studies, only limited insights into the hydrodynamic conditions inside the industrial-scale bioreactor have been obtained, which makes case-by-case scale-up far from straightforward. Tracking the flow paths of cells circulating in large-scale bioreactors is a highly valuable tool for evaluating cellular performance in production tanks. The “lifelines” or “trajectories” of cells in industrial-scale bioreactors can be captured using Euler-Lagrange CFD simulation. This novel methodology can be further coupled with metabolic (structured) models to provide not only a statistical analysis of cell lifelines triggered by the environmental fluctuations but also a global assessment of the metabolic response to heterogeneity inside an industrial bioreactor. For the future, the industrial design should be dependent on the computational framework, and this integration work will allow bioprocess scale-up to the industrial scale with an end in mind.     

Model of oxygen transport limitations in hollow fiber bioreactors

Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.     

Computational fluid dynamics modeling of steady-state momentum and mass transport in a bioreactor for cartilage tissue engineering

Computational fluid dynamics (CFD) models to quantify momentum and mass transport under conditions of tissue growth will aid bioreactor design for development of tissue-engineered cartilage constructs. Fluent CFD models are used to calculate flow fields, shear stresses, and oxygen profiles around nonporous constructs simulating cartilage development in our concentric cylinder bioreactor. The shear stress distribution ranges from 1.5 to 12 dyn/cm(2) across the construct surfaces exposed to fluid flow and varies little with the relative number or placement of constructs in the bioreactor. Approximately 80% of the construct surface exposed to flow experiences shear stresses between 1.5 and 4 dyn/cm(2), validating the assumption that the concentric cylinder bioreactor provides a relatively homogeneous hydrodynamic environment for construct growth. Species mass transport modeling for oxygen demonstrates that fluid-phase oxygen transport to constructs is uniform. Some O(2) depletion near the down stream edge of constructs is noted with minimum pO(2) values near the constructs of 35 mmHg (23% O(2) saturation). These values are above oxygen concentrations in cartilage in vivo, suggesting that bioreactor oxygen concentrations likely do not affect chondrocyte growth. Scale-up studies demonstrate the utility and flexibility of CFD models to design and characterize bioreactors for growth of tissue-engineered cartilage.     

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.     

Location of scaffolds in bioreactors modulates the hydrodynamic environment experienced by engineered tissues

Physical forces experienced by engineered-tissues during in vitro cultivation influence tissue growth and function. The hydrodynamic environment within bioreactors plays a decisive role in providing the necessary physical stimuli and nutrient transport to support tissue development. Our overall goal is to investigate interrelationships between the local hydrodynamic environment in the bioreactor and the structural and functional tissue properties in order to optimize the production of clinically relevant engineered-tissues. To this end, we used computational fluid dynamics (CFD) modeling to characterize the complex hydrodynamic environment in a wavy-walled bioreactor used for cultivation of tissue-engineered cartilage constructs and examined the changes in the flow field due to the presence of constructs. The flow-induced shear stress range experienced by engineered constructs cultivated in the wavy-walled bioreactor (0-0.67 dyn/cm(2)) was found to be significantly lower than that in the spinner flask (0-1.2 dyn/cm(2)), and to be modulated by the radial or axial position of the constructs. These CFD results are validated by experimental particle-image velocimetry (PIV) measurements previously reported by our group. Results from the present study indicate that the location of constructs in the bioreactor not only affected the magnitude and distribution of the shear stresses on the constructs, but also other hydrodynamic parameters, such as the directional distribution of the fluid velocity and the degree of fluid recirculation, all of which may differentially influence the development of tissue-engineered constructs.     

Computational fluid dynamics modeling,a novel,and effective approach for developing scalable cell therapy manufacturing processes

Induced pluripotent stem cells (iPSCs) hold great potential to generate novel, curative cell therapy products. However, current methods to generate these novel therapies lack scalability, are labor-intensive, require a large footprint, and are not suited to meet clinical and commercial demands. Therefore, it is necessary to develop scalable manufacturing processes to accommodate the generation of high-quality iPSC derivatives under controlled conditions. The current scale-up methods used in cell therapy processes are based on empirical, geometry-dependent methods that do not accurately represent the hydrodynamics of 3D bioreactors. These methods require multiple iterations of scale-up studies, resulting in increased development cost and time. Here we show a novel approach using computational fluid dynamics modeling to effectively scale-up cell therapy manufacturing processes in 3D bioreactors. Using a GMP-compatible iPSC line, we translated and scaled-up a small-scale cardiomyocyte differentiation process to a 3-L computer-controlled bioreactor in an efficient manner, showing comparability in both systems.     

Scale-up analysis of geometrically dissimilar single-use bioreactors

Cell culture scale-up is a challenging task due to the simultaneous change of multiple hydrodynamic process characteristics and their different dependencies on the bioreactor size as well as variation in the requirements of individual cell lines. Conventionally, the volumetric power input is the most common parameter to select the impeller speed for scale-up, however, it is well reported that this approach fails when there are huge differences in bioreactor scales. In this study, different scale-up criteria are evaluated. At first, different hydrodynamic characteristics are assessed using computational fluid dynamics data for four single-use bioreactors, the Mobius® CellReady 3 L, the Xcellerex™ XDR-10, the Xcellerex™ XDR-200, and the Xcellerex™ XDR-2000. On the basis of this numerical data, several potential scale-up criteria such as volumetric power input, impeller tip speed, mixing time, maximum hydrodynamic stress, and average strain rate in the impeller zone are evaluated. Out of all these criteria, the latter is found to be most appropriate, and the successful scale-up from 3 to 10 L bioreactor and to 200 L bioreactor is confirmed with cell culture experiments using Chinese Hamster Ovary cell cultivation.     

Engineering stem cell niches in bioreactors

Stem cells, including embryonic stem cells, induced pluripotent stem cells, mesenchymal stem cells and amniotic fluid stem cells have the potential to be expanded and differentiated into various cell types in the body. Efficient differentiation of stem cells with the desired tissue-specific function is critical for stem cell-based cell therapy, tissue engineering, drug discovery and disease modeling. Bioreactors provide a great platform to regulate the stem cell microenvironment, known as “niches”, to impact stem cell fate decision. The niche factors include the regulatory factors such as oxygen, extracellular matrix (synthetic and decellularized), paracrine/autocrine signaling and physical forces (i.e., mechanical force, electrical force and flow shear). The use of novel bioreactors with precise control and recapitulation of niche factors through modulating reactor operation parameters can enable efficient stem cell expansion and differentiation. Recently, the development of microfluidic devices and microbioreactors also provides powerful tools to manipulate the stem cell microenvironment by adjusting flow rate and cytokine gradients. In general, bioreactor engineering can be used to better modulate stem cell niches critical for stem cell expansion, differentiation and applications as novel cell-based biomedicines. This paper reviews important factors that can be more precisely controlled in bioreactors and their effects on stem cell engineering.     

Dynamic modeling and simulation of continuous airlift bioreactors

For dynamic behaviors of continuous airlift bioreactors, a mathematical model based on a tanks-in-series model with backflow has been developed. The equations describing the dynamics of airlift bioreactors are material balances for micro-organism, substrate, dissolved oxygen and oxygen in gas-phase and heat balances. Non-ideal mixing of liquid and gas phases is taken into account using a tanks-in-series model with backflow. The batch operation, startup operation and the consequence of plant failure were simulated and the effects of design and operating parameters for an airlift bioreactor on its dynamic behaviors were discussed. The concentration profiles of micro-organism, substrate, dissolved oxygen and oxygen in gas-phase and the temperature profile in an airlift bioreactors and their dynamics were obtained. The computational results indicate that the transients of a chemostat in the case of bubble column bioreactor are slower compared with those in the case of airlift bioreactor. The proposed simulator is more precise as compared with models published previously in the literature and therefore provides more reliable and rational examination of continuous airlift bioreactor performance.     

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.     

Correlating single cell motility with population growth dynamics for flagellated bacteria

Many bacteria used for biotechnological applications are naturally motile. Their "bio-nanopropeller" driven movement allows searching for better environments in a process called chemotaxis. Since bacteria are extremely small in size compared to the bulk fluid volumes in bioreactors, single cell motility is not considered to influence bioreactor operations. However, with increasing interest in localized fluid flow inside reactors, it is important to ask whether individual motility characteristics of bacteria are important in bioreactor operations. The first step in this direction is to try to correlate single cell measurements with population data of motile bacteria in a bioreactor. Thus, we observed the motility behavior of individual bacterial cells, using video microscopy with 33 ms time resolution, as a function of population growth dynamics of batch cultures in shake flasks. While observing the motility behavior of the most intensively studied bacteria, Escherichia coli, we find that overall bacterial motility decreases with progression of the growth curve. Remarkably, this is due to a decrease in a specific motility behavior called "running". Our results not only have direct implications on biofilm formations, but also provide a new direction in bioprocess design research highlighting the role of individual bacterial cell motility as an important parameter.