Enhancement of cell growth in tissue-engineering constructs under direct perfusion: Modeling and simulation

Perfusion bioreactors improve mass transfer in cell-scaffold constructs. We developed a mathematical model to simulate nutrient flow through cellular constructs. Interactions among cell proliferation, nutrient consumption, and culture medium circulation were investigated. The model incorporated modified Contois cell-growth kinetics that includes effects of nutrient saturation and limited cell growth. Nutrient uptake was depicted through the Michaelis-Menton kinetics. To describe the culture medium convection, the fluid flow outside the cell-scaffold construct was described by the Navier-Stokes equations, while the fluid dynamics within the construct was modeled by Brinkman's equation for porous media flow. Effects of the media perfusion were examined by including time-dependant porosity and permeability changes due to cell growth. The overall cell volume was considered to consist of cells and extracellular matrices (ECM) as a whole without treating ECM separately. Numerical simulations show when cells were cultured subjected to direct perfusion, they penetrated to a greater extent into the scaffold and resulted in a more uniform spatial distribution. The cell amount was increased by perfusion and ultimately approached an asymptotic value as the perfusion rates increased in terms of the dimensionless Peclet number that accounts for the ratio of nutrient perfusion to diffusion. In addition to enhancing the nutrient delivery, perfusion simultaneously imposes flow-mediated shear stress to the engineered cells. Shear stresses were found to increase with cell growth as the scaffold void space was occupied by the cell and ECM volumes. The macro average stresses increased from 0.2 mPa to 1 mPa at a perfusion rate of 20 microm/s with the overall cell volume fraction growing from 0.4 to 0.7, which made the overall permeability value decrease from 1.35 x 10(-2)cm(2) to 5.51 x 10(-4)cm(2). Relating the simulation results with perfusion experiments in literature, the average shear stresses were below the critical value that would induce the chondrocyte necrosis.     

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.     

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.     

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.     

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.     

Performance evaluation of a novel conceptual bioprocess for clinically-required mass production of hematopoietic cells

Objective

The novel engineered bioprocess, which was designed and modeled to provide the clinically relevant cell numbers for different therapies in our previous work (Kaleybar et al. Food Bioprod Process 122:254–268, https://doi.org/10.1016/j.fbp.2020.04.012, 2020), was evaluated by using U937 as hematopoietic model cells.

Results

The culture system showed a 30-fold expansion of U937 cells in one-step during a 10-day culture period. The cell growth profile, the substrate and oxygen consumptions, and byproduct formations were all in agreement with the model predications during 7 days. The cell proliferation decrease after 7 days was attributed to optional oxygen limiting condition in the last days of culture. The bioreactor culture system revealed also a slight enhancement of lactate dehydrogenase (LDH) production as compared to the 2D conventional culture system, indicating the low impact of shear stress on cellular damage in the dynamic system.

Conclusions

The results demonstrated that the conceptual bioprocess for suspended stem cell production has a great potential in practice although additional experiments are required to improve the system.

     

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.     

A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models

The control of the mechanical stimuli transmitted to the cells is critical for the design of functional scaffolds for tissue engineering. The objective of this study was to investigate the dynamics of the mechanical stimuli transmitted to the cells during tissue differentiation in an irregular morphology scaffold under compressive load and perfusion flow. A calcium phosphate-based glass porous scaffold was used. The solid phase and the fluid flow within the pores were modeled as linear elastic solid material and Newtonian fluid, respectively. In the fluid model, different levels of viscosity were used to simulate tissue differentiation. Compressive strain of 0.5% and fluid flow with constant inlet velocity of 10 μm/s or constant inlet pressure of 3 Pa were applied. Octahedral shear strain and fluid shear stress were used as mechano-regulatory stimuli. For constant inlet velocity, stimuli equivalent to bone were predicted in 80% of pore volume for the case of low tissue viscosity. For the cases of high viscosity, fluctuations between stimuli equivalent to tissue formation and cell death were predicted due to the increase in the fluid shear stress when tissue started to fill pores. When constant pressure was applied, stimuli equivalent to bone were predicted in 62% of pore volume when low tissue viscosity was used and 42% when high tissue viscosity was used. This study predicted critical variations of fluid shear stress when cells differentiated. If these variations are not controlled in vitro, they can impede the formation of new matured tissue.     

A mechanical composite spheres analysis of engineered cartilage dynamics

In the preparation of bioengineered reparative strategies for damaged or diseased tissues, the processes of biomaterial degradation and neotissue synthesis combine to affect the developing mechanical state of multiphase, composite engineered tissues. Here, cell-polymer constructs for engineered cartilage have been fabricated by seeding chondrocytes within three-dimensional scaffolds of biodegradable polymers. During culture, synthetic scaffolds degraded passively as the cells assembled an extracellular matrix (ECM) composed primarily of glycosaminoglycan and collagen. Biochemical and biomechanical assessment of the composite (cells, ECM, and polymer scaffold) were modeled at a unit-cell level to mathematically solve stress-strain relationships and thus construct elastic properties (n=4 samples per seven time points). This approach employed a composite spheres, micromechanical analysis to determine bulk moduli of: (1) the cellular-ECM inclusion within the supporting scaffold structure; and (2) the cellular inclusion within its ECM. Results indicate a dependence of constituent volume fractions with culture time (p<0.05). Overall mean bulk moduli were variably influenced by culture, as noted for the cell-ECM inclusion (K(c-m)=29.7 kPa, p=0.1439), the cellular inclusion (K(c)=5.5 kPa, p=0.0067), and its surrounding ECM (K(m)=373.9 kPa, p=0.0748), as well as the overall engineered construct (K=165.0 kPa, p=0.6899). This analytical technique provides a framework to describe the time-dependent contribution of cells, accumulating ECM, and a degrading scaffold affecting bioengineered construct mechanical properties.     

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.     

Tissue Engineering of a Human 3D in vitro Tumor Test System

Cancer is one of the leading causes of death worldwide. Current therapeutic strategies are predominantly developed in 2D culture systems, which inadequately reflect physiological conditions in vivo. Biological 3D matrices provide cells an environment in which cells can self-organize, allowing the study of tissue organization and cell differentiation. Such scaffolds can be seeded with a mixture of different cell types to study direct 3D cell-cell-interactions. To mimic the 3D complexity of cancer tumors, our group has developed a 3D in vitro tumor test system.Our 3D tissue test system models the in vivo situation of malignant peripheral nerve sheath tumors (MPNSTs), which we established with our decellularized porcine jejunal segment derived biological vascularized scaffold (BioVaSc). In our model, we reseeded a modified BioVaSc matrix with primary fibroblasts, microvascular endothelial cells (mvECs) and the S462 tumor cell line. For static culture, the vascular structure of the BioVaSc is removed and the remaining scaffold is cut open on one side (Small Intestinal Submucosa SIS-Muc). The resulting matrix is then fixed between two metal rings (cell crowns).Another option is to culture the cell-seeded SIS-Muc in a flow bioreactor system that exposes the cells to shear stress. Here, the bioreactor is connected to a peristaltic pump in a self-constructed incubator. A computer regulates the arterial oxygen and nutrient supply via parameters such as blood pressure, temperature, and flow rate. This setup allows for a dynamic culture with either pressure-regulated pulsatile or constant flow.In this study, we could successfully establish both a static and dynamic 3D culture system for MPNSTs. The ability to model cancer tumors in a more natural 3D environment will enable the discovery, testing, and validation of future pharmaceuticals in a human-like model.     

Mechanobiology of engineered cartilage cultured under a quantified fluid-dynamic environment

Natural cartilage remodels both in vivo and in vitro in response to mechanical forces and hence mechanical stimulation is believed to have a potential as a tool to modulate extra-cellular matrix synthesis in tissue-engineered cartilage. Fluid-induced shear is known to enhance chondrogenesis on animal cells. A well-defined hydrodynamic environment is required to study the biochemical response to shear of three-dimensional engineered cell systems. We have developed a perfused-column bioreactor in which the culture medium flows through chondrocyte-seeded porous scaffolds, together with a computational fluid-dynamic model of the flow through the constructs' microstructure. A preliminary experiment of human chondrocyte growth under static versus dynamic conditions is described. The median shear stress imposed on the cells in the bioreactor culture, as predicted by the CFD model, is 3 × 10⁻³ Pa (0.03 dyn/cm²) at a flow rate of 0.5 ml/min corresponding to an inlet fluid velocity of 44.2 μm/s. Providing a fluid-dynamic environment to the cells yielded significant differences in cell morphology and in construct structure. Received: 22 December 2001 / Accepted: 18 February 2002     

Microencapsulation technology: a powerful tool for integrating expansion and cryopreservation of human embryonic stem cells

The successful implementation of human embryonic stem cells (hESCs)-based technologies requires the production of relevant numbers of well-characterized cells and their efficient long-term storage. In this study, cells were microencapsulated in alginate to develop an integrated bioprocess for expansion and cryopreservation of pluripotent hESCs. Different three-dimensional (3D) culture strategies were evaluated and compared, specifically, microencapsulation of hESCs as: i) single cells, ii) aggregates and iii) immobilized on microcarriers. In order to establish a scalable bioprocess, hESC-microcapsules were cultured in stirred tank bioreactors.The combination of microencapsulation and microcarrier technology resulted in a highly efficient protocol for the production and storage of pluripotent hESCs. This strategy ensured high expansion ratios (an approximately twenty-fold increase in cell concentration) and high cell recovery yields (>70%) after cryopreservation. When compared with non-encapsulated cells, cell survival post-thawing demonstrated a three-fold improvement without compromising hESC characteristics.Microencapsulation also improved the culture of hESC aggregates by protecting cells from hydrodynamic shear stress, controlling aggregate size and maintaining cell pluripotency for two weeks.This work establishes that microencapsulation technology may prove a powerful tool for integrating the expansion and cryopreservation of pluripotent hESCs. The 3D culture strategy developed herein represents a significant breakthrough towards the implementation of hESCs in clinical and industrial applications.     

Shear flow affects selective monocyte recruitment into MCP‐1‐loaded scaffolds

Novel cardiovascular replacements are being developed by using degradable synthetic scaffolds, which function as a temporary guide to induce neotissue formation directly in situ. Priming of such scaffolds with fast‐releasing monocyte chemoattractant protein‐1 (MCP‐1) was shown to improve the formation of functional neoarteries in rats. However, the underlying mechanism has not been clarified. Therefore, the goal of this study was to investigate the effect of a burst‐release of MCP‐1 from a synthetic scaffold on the local recruitment of circulating leucocytes under haemodynamic conditions. Herein, we hypothesized that MCP‐1 initiates a desired healing cascade by recruiting favourable monocyte subpopulations into the implanted scaffold. Electrospun poly(ε‐caprolactone) scaffolds were loaded with fibrin gel containing various doses of MCP‐1 and exposed to a suspension of human peripheral blood mononuclear cells in static or dynamic conditions. In standard migration assay, a dose‐dependent migration of specific CD14⁺ monocyte subsets was observed, as measured by flow cytometry. In conditions of pulsatile flow, on the other hand, a marked increase in immediate monocyte recruitment was observed, but without evident selectivity in monocyte subsets. This suggests that the selectivity was dependent on the release kinetics of the MCP‐1, as it was overruled by the effect of shear stress after the initial burst‐release. Furthermore, these findings demonstrate that local recruitment of specific MCP‐1‐responsive monocytes is not the fundamental principle behind the improved neotissue formation observed in long‐term in vivo studies, and mobilization of MCP‐1‐responsive cells from the bone marrow into the bloodstream is suggested to play a predominant role in vivo.     

Ultra scale‐down prediction using microwell technology of the industrial scale clarification characteristics by centrifugation of mammalian cell broths

This article describes how a combination of an ultra scale‐down (USD) shear device feeding a microwell centrifugation plate may be used to provide a prediction of how mammalian cell broth will clarify at scale. In particular a method is described that is inherently adaptable to a robotic platform and may be used to predict how the flow rate and capacity (equivalent settling area) of a centrifuge and the choice of feed zone configuration may affect the solids carry over in the supernatant. This is an important consideration as the extent of solids carry over will determine the required size and lifetime of a subsequent filtration stage or the passage of fine particulates and colloidal material affecting the performance and lifetime of chromatography stages. The extent of solids removal observed in individual wells of a microwell plate during centrifugation is shown to correlate with the vertical and horizontal location of the well on the plate. Geometric adjustments to the evaluation of the equivalent settling area of individual wells (Σ_M) results in an improved prediction of solids removal as a function of centrifuge capacity. The USD centrifuge settling characteristics need to be as for a range of equivalent flow rates as may be experienced at an industrial scale for a machine of different shear characteristics in the entry feed zone. This was shown to be achievable with two microwell‐plate based measurements and the use of varying fill volumes in the microwells to allow the rapid study of a fivefold range of equivalent flow rates (i.e., at full scale for a particular industrial centrifuge) and the effect of a range of feed configurations. The microwell based USD method was used to examine the recovery of CHO‐S cells, prepared in a 5 L reactor, at different points of growth and for different levels of exposure to shear post reactor. The combination of particle size distribution measurements of the cells before and after shear and the effect of shear on the solids remaining after centrifugation rate provide insight into the state of the cells throughout the fermentation and the ease with which they and accumulated debris may be removed by continuous centrifugation. Hence bioprocess data are more readily available to help better integrate cell culture and cell removal stages and resolve key bioprocess design issues such as choice of time of harvesting and the impact on product yield and contaminant carry over. Operation at microwell scale allows data acquisition and bioprocess understanding over a wide range of operating conditions that might not normally be achieved during bioprocess development. Biotechnol. Bioeng. 2009; 104: 321–331 © 2009 Wiley Periodicals, Inc.     

Model-based workflow for scale-up of process strategies developed in miniaturized bioreactor systems

Miniaturized bioreactor (MBR) systems are routinely used in the development of mammalian cell culture processes. However, scale-up of process strategies obtained in MBR- to larger scale is challenging due to mainly non-holistic scale-up approaches. In this study, a model-based workflow is introduced to quantify differences in the process dynamics between bioreactor scales and thus enable a more knowledge-driven scale-up. The workflow is applied to two case studies with antibody-producing Chinese hamster ovary cell lines. With the workflow, model parameter distributions are estimated first under consideration of experimental variability for different scales. Second, the obtained individual model parameter distributions are tested for statistical differences. In case of significant differences, model parametric distributions are transferred between the scales. In case study I, a fed-batch process in a microtiter plate (4 ml working volume) and lab-scale bioreactor (3750 ml working volume) was mathematically modeled and evaluated. No significant differences were identified for model parameter distributions reflecting process dynamics. Therefore, the microtiter plate can be applied as scale-down tool for the lab-scale bioreactor. In case study II, a fed-batch process in a 24-Deep-Well-Plate (2 ml working volume) and shake flask (40 ml working volume) with two feed media was investigated. Model parameter distributions showed significant differences. Thus, process strategies were mathematically transferred, and model predictions were simulated for a new shake flask culture setup and confirmed in validation experiments. Overall, the workflow enables a knowledge-driven evaluation of scale-up for a more efficient bioprocess design and optimization.     

A method for the design of 3D scaffolds for high-density cell attachment and determination of optimum perfusion culture conditions

The application of in vitro cultured cells in tissue engineering or drug screening, aimed at complex soft tissues such as liver, requires in vivo physiological function of the cultured cells. For this purpose, the scaffold in which cells are cultured should provide a microenvironment similar to an in vivo one with a three-dimensional extracellular matrix, a high supply capacity of O₂ and nutrients, and high cell density. In this paper, we propose a method to design (1) the geometry of the scaffold, with a surface/volume ratio optimized to allow high-density (5×10⁷ cells/mL) cell culture and (2) culture conditions that will supply optimal quantities of oxygen and nutrients. CFD modeling of mass transport was used to determine the shear stress as well as O₂ and glucose metabolism in the scaffold (20 mm width–35 mm length) for various flow rates. Validation of the model was done through comparison with flow resistance and micro-PIV experiments. CFD analysis showed the maximum metabolic rate densities for this scaffold are 6.04×10⁻³ mol/s/m³ for O₂ at 0.71 mL/min and 1.91×10⁻² mol/s/m³ for glucose at 0.35 mL/min.     

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.