Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold

Generation and evaluation of input values for computational analysis of transport processes within tissue cultures

Techniques for tissue culture have seen significant advances during the last decades and novel 3D cell culture systems have become available. To control their high complexity, experimental techniques and their Digital Twins (modelling and computational tools) are combined to link different variables to process conditions and critical process parameters. This allows a rapid evaluation of the expected product quality. However, the use of mathematical simulation and Digital Twins is critically dependent on the precise description of the problem and correct input parameters. Errors here can lead to dramatically wrong conclusions. The intention of this review is to provide an overview of the state‐of‐the‐art and remaining challenges with respect to generating input values for computational analysis of mass and momentum transport processes within tissue cultures. It gives an overview on relevant aspects of transport processes in tissue cultures as well as modelling and computational tools to tackle these problems. Further focus is on techniques used for the determination of cell‐specific parameters and characterization of culture systems, including sensors for on‐line determination of relevant parameters. In conclusion, tissue culture techniques are well‐established, and modelling tools are technically mature. New sensor technologies are on the way, especially for organ chips. The greatest remaining challenge seems to be the proper addressing and handling of input parameters required for mathematical models. Following Good Modelling Practice approaches when setting up and validating computational models is, therefore, essential to get to better estimations of the interesting complex processes inside organotypic tissue cultures in the future.

Numerical modelling of osteocyte growth on different bone tissue scaffolds

The most common solution for the regeneration or replacement of damaged bones is the implantation of prostheses comprising ceramic or metallic materials. However, these implants are known to cause problems such as post-operative infections, collapse of the prosthesis, and lack of osseointegration. Consequently, bone tissue engineering was established because of the limitations of such implants. Osteogenic implants offer promising solutions for bone regeneration; however, three-dimensional scaffolds should be used as supportive structures. It is challenging to correctly design these structures and their compositions or properties to provide a microenvironment that promotes tissue regeneration and expedites bone formation. Computational fluid dynamics can be used to model the main phenomena that occur in bioreactors, such as cell metabolism, nutrient transport, and cell culture growth, or to model the influence of several key mechanisms related to the fluid medium, in particular, the wall shear stress. In this work, a new numerical bone cell growth model was developed, which considered the oxygen and nutrient consumption as well as the wall shear stress effect on cell proliferation. The model was implemented using 35 three-dimensional scaffolds of different porosities, and the effect of the main geometrical parameters involved in each scaffold type was analysed. The porosity plays an important role, however, a similar porosity did not guarantee similar shear stress or cell growth among the scaffolds. Randomised trabecular scaffolds, that more closely resembled trabecular bone, showed the highest cell growth values, so these are the best candidates for cell growth in a bioreactor.

A Systematically Reduced Mathematical Model for Organoid Expansion

Organoids are three-dimensional multicellular tissue constructs. When cultured in vitro, they recapitulate the structure, heterogeneity, and function of their in vivo counterparts. As awareness of the multiple uses of organoids has grown, e.g. in drug discovery and personalised medicine, demand has increased for low-cost and efficient methods of producing them in a reproducible manner and at scale. Here we focus on a bioreactor technology for organoid production, which exploits fluid flow to enhance mass transport to and from the organoids. To ensure large numbers of organoids can be grown within the bioreactor in a reproducible manner, nutrient delivery to, and waste product removal from, the organoids must be carefully controlled. We develop a continuum mathematical model to investigate how mass transport within the bioreactor depends on the inlet flow rate and cell seeding density, focusing on the transport of two key metabolites: glucose and lactate. We exploit the thin geometry of the bioreactor to systematically simplify our model. This significantly reduces the computational cost of generating model solutions, and provides insight into the dominant mass transport mechanisms. We test the validity of the reduced models by comparison with simulations of the full model. We then exploit our reduced mathematical model to determine, for a given inlet flow rate and cell seeding density, the evolution of the spatial metabolite distributions throughout the bioreactor. To assess the bioreactor transport characteristics, we introduce metrics quantifying glucose conversion (the ratio between the total amounts of consumed and supplied glucose), the maximum lactate concentration, the proportion of the bioreactor with intolerable lactate concentrations, and the time when intolerable lactate concentrations are first experienced within the bioreactor. We determine the dependence of these metrics on organoid-line characteristics such as proliferation rate and rate of glucose consumption per cell. Finally, for a given organoid line, we determine how the distribution of metabolites and the associated metrics depend on the inlet flow rate. Insights from this study can be used to inform bioreactor operating conditions, ultimately improving the quality and number of bioreactor-expanded organoids.

Parametric optimization and kinetic study of l-lactic acid production by homologous batch fermentation of Lactobacillus pentosus cells

Parametric optimization always plays important roles in bioengineering systems to obtain a high product yield under the proper conditions. The parametric conditions of lactic acid production by homologous batch fermentation of Lactobacillus pentosus cells was optimized by the Box-Behnken design. The highest l-lactic acid yield was obtained as 0.836 ± 0.003 g/g glucose with the productivity of 0.906 ± 0.003 g/(L × H) under the optimum conditions of 34.7 °C, pH 6.2, 148 rpm agitation speed, and 9.3 g/L nitrogen source concentration determined by quadratic response surface with high accuracy. The adequate kinetic models of cell growth rate, lactic production rate, and glucose consumption rate were also established to describe the fermentation behavior of L. pentosus cells with the correlation coefficients of 09985, 0.9990, and 0.9989, respectively.

An Introduction to 3D Bioprinting: Possibilities, Challenges and Future Aspects

Bioprinting is an emerging field in regenerative medicine. Producing cell-laden, three-dimensional structures to mimic bodily tissues has an important role not only in tissue engineering, but also in drug delivery and cancer studies. Bioprinting can provide patient-specific spatial geometry, controlled microstructures and the positioning of different cell types for the fabrication of tissue engineering scaffolds. In this brief review, the different fabrication techniques: laser-based, extrusion-based and inkjet-based bioprinting, are defined, elaborated and compared. Advantages and challenges of each technique are addressed as well as the current research status of each technique towards various tissue types. Nozzle-based techniques, like inkjet and extrusion printing, and laser-based techniques, like stereolithography and laser-assisted bioprinting, are all capable of producing successful bioprinted scaffolds. These four techniques were found to have diverse effects on cell viability, resolution and print fidelity. Additionally, the choice of materials and their concentrations were also found to impact the printing characteristics. Each technique has demonstrated individual advantages and disadvantages with more recent research conduct involving multiple techniques to combine the advantages of each technique.

Numerical optimization of cell colonization modelling inside scaffold for perfusion bioreactor: A multiscale model

Part of clinically applicable bone graft substitutes are developed by using mechanical stimulation of flow-perfusion into cell-seeded scaffolds. The role of fluid flow is crucial in driving the nutrient to seeded cells and in stimulating cell colonization. A common numerical approach is to use a multiscale model to link some physical quantities (wall shear stress and inlet flow rate) that act at different scales. In this study, a multiscale model is developed in order to determine the optimal inlet flow rate to cultivate osteoblast-like cells seeded in a controlled macroporous biomaterial inside a perfusion bioreactor system. We focus particularly on the influence of Wall Shear Stress on cell colonization to predict cell colonization at the macroscale. Results obtained at the microscale are interpolated at the macroscale to determine the optimal flow rate. For a macroporous scaffold made of interconnected pores with pore diameters of above 350 μm and interconnection diameters of 150 μm, the model predicts a cell colonization of 325% after a 7-day-cell culture with a constant inlet flow rate of 0.69 mL·min^-1. Furthermore, the strength of this protocol is the possibility to adapt it to most porous biomaterials and dynamic cell culture systems.

Relevant biological processes for tissue development with stem cells and their mechanistic modeling: A review

A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds.

Efficient Computational Design of a Scaffold for Cartilage Cell Regeneration

Due to the sensitivity of mammalian cell cultures, understanding the influence of operating conditions during a tissue generation procedure is crucial. In this regard, a detailed study of scaffold based cell culture under a perfusion flow is presented with the aid of mathematical modelling and computational fluid dynamics (CFD). With respect to the complexity of the case study, this work focuses solely on the effect of nutrient and metabolite concentrations, and the possible influence of fluid-induced shear stress on a targeted cell (cartilage) culture. The simulation set up gives the possibility of predicting the cell culture behavior under various operating conditions and scaffold designs. Thereby, the exploitation of the predictive simulation into a newly developed stochastic routine provides the opportunity of exploring improved scaffold geometry designs. This approach was applied on a common type of fibrous structure in order to increase the process efficiencies compared with the regular used formats. The suggested topology supplies a larger effective surface for cell attachment compared to the reference design while the level of shear stress is kept at the positive range of effect. Moreover, significant improvement of mass transfer is predicted for the suggested topology.

A mathematical model of tissue-engineered cartilage development under cyclic compressive loading

In this work a coupled model of solute transport and uptake, cell proliferation, extracellular matrix synthesis and remodeling of mechanical properties accounting for the impact of mechanical loading is presented as an advancement of a previously validated coupled model for free-swelling tissue-engineered cartilage cultures. Tissue-engineering constructs were modeled as biphasic with a linear elastic solid, and relevant intrinsic mechanical stimuli in the constructs were determined by numerical simulation for use as inputs of the coupled model. The mechanical dependent formulations were derived from a calibration and parametrization dataset and validated by comparison of normalized ratios of cell counts, total glycosaminoglycans and collagen after 24-h continuous cyclic unconfined compression from another dataset. The model successfully fit the calibration dataset and predicted the results from the validation dataset with good agreement, with average relative errors up to 3.1 and 4.3 %, respectively. Temporal and spatial patterns determined for other model outputs were consistent with reported studies. The results suggest that the model describes the interaction between the simultaneous factors involved in in vitro tissue-engineered cartilage culture under dynamic loading. This approach could also be attractive for optimization of culture protocols, namely through the application to longer culture times and other types of mechanical stimuli.

Automated Assembly of Vascular-Like Microtube With Repetitive Single-Step Contact Manipulation

Fabricated vessel-mimetic microtubes are essential for delivering sufficient nutrient to engineered composite tissues. In this paper, vascular-like microtubes are engineered by automated assembly of donut-shaped micromodules that embed fibroblast cells. A microrobotic system is set up with dual manipulators of 30-nm positioning resolution under an optical microscope. The system assembles the micromodules by repeated single-step pick-up motions. This process is specifically designed to avoid human interference and ensure high reproducibility for automation. We optimized the single-step motion by calibrating the key parameters (the micromodule dimensions) in a force analysis. The optimal motion achieved a 98% pick-up success rate. The automated repetitive single-step assembly is achieved by an algorithm that acquires the 3-D location and tracks the micromanipulator without being affected by low contrast. The accuracy of the acquired 3-D location was experimentally determined as approximately 1 pixel (2 μm under 4× magnification), and the tracking under different observation conditions is proved effective. Finally, we automatically assembled microtubes at 6 micromodules/min, sufficiently fast for fabricating macroscopic vessel-mimetic substitutes in biological applications.

Modeling the fluid-dynamics and oxygen consumption in a porous scaffold stimulated by cyclic squeeze pressure

The architecture and dynamic physical environment of tissues can be recreated in-vitro by combining 3D porous scaffolds and bioreactors able to apply controlled mechanical stimuli on cells. In such systems, the entity of the stimuli and the distribution of nutrients within the engineered construct depend on the micro-structure of the scaffolds. In this work, we present a new approach for optimizing computational fluid-dynamics (CFD) models for the investigation of fluid-induced forces generated by cyclic squeeze pressure within a porous construct, coupled with oxygen consumption of cardiomyocytes. A 2D axial symmetric macro-scaled model of a squeeze pressure bioreactor chamber was used as starting point for generating time dependent pressure profiles. Subsequently the fluid movement generated by the pressure fields was coupled with a complete 3D micro-scaled model of a porous protein cryogel. Oxygen transport and consumption inside the scaffold was evaluated considering a homogeneous distribution of cardiomyocytes throughout the structure, as confirmed by preliminary cell culture experiments. The results show that a 3D description of the system, coupling a porous geometry and time dependent pressure driven flow with fluid-structure-interaction provides an accurate and meaningful description of the microenvironment in terms of shear stress and oxygen distribution than simple stationary 2D models.

A triphasic constrained mixture model of engineered tissue formation under in vitro dynamic mechanical conditioning

While it has become axiomatic that mechanical signals promote in vitro engineered tissue formation, the underlying mechanisms remain largely unknown. Moreover, efforts to date to determine parameters for optimal extracellular matrix (ECM) development have been largely empirical. In the present work, we propose a two-pronged approach involving novel theoretical developments coupled with key experimental data to develop better mechanistic understanding of growth and development of dense connective tissue under mechanical stimuli. To describe cellular proliferation and ECM synthesis that occur at rates of days to weeks, we employ mixture theory to model the construct constituents as a nutrient-cell-ECM triphasic system, their transport, and their biochemical reactions. Dynamic conditioning protocols with frequencies around 1 Hz are described with multi-scale methods to couple the dissimilar time scales. Enhancement of nutrient transport due to pore fluid advection is upscaled into the growth model, and the spatially dependent ECM distribution describes the evolving poroelastic characteristics of the scaffold-engineered tissue construct. Simulation results compared favorably to the existing experimental data, and most importantly, distinguish between static and dynamic conditioning regimes. The theoretical framework for mechanically conditioned tissue engineering (TE) permits not only the formulation of novel and better-informed mechanistic hypothesis describing the phenomena underlying TE growth and development, but also the exploration/optimization of conditioning protocols in a rational manner.

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Influence of the scaffold geometry on the spatial and temporal evolution of the mechanical properties of tissue-engineered cartilage: insights from a mathematical model

The production of tissue-engineered cartilage in vitro with inhomogeneous mechanical properties is a problem yet to be solved. Different geometries have been studied to overcome this caveat; however, the reported measurements are limited to average values of some properties and qualitative measures of spatial distributions. We will apply a coupled model to extend knowledge about the introduction of a macrochannel in a scaffold by calculating spatiotemporal patterns for several interest variables related to the remodeling of the mechanical properties. Model parameters were estimated based on experimental data on the temporal patterns of glycosaminoglycans, collagen and compressive Young's modulus for channel-free constructs. The model reproduced the experimental data trends in both geometries, with experimental-numerical correlations between 0.84 and 0.97. The channel had a higher impact on the reduction in spatial heterogeneities and delay of saturation of core properties than in the improvement of average properties. Despite the possible improvement of cell densities for longer periods than 56 days, it is estimated that it will not cause further significant improvements of the mechanical properties. The degrees of spatial heterogeneity of the Young's modulus and permeability in the channeled geometry are 23 and 27 % of the channel-free values. While the average Young's modulus values are in the range of native cartilage, the permeabilities are one to three degrees of magnitude higher than the native cartilage, suggesting that limiting factors such as scaffold porosity and initial permeability are more relevant than scaffold geometry to effectively decrease the tissue permeability.

Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor

Mathematical and computational modeling of the dynamic process where tissue scaffolds are cultured in perfusion bioreactors is able to provide insight into the cell and tissue growth which can facilitate the design of tissue scaffolds and selection of optimal operating conditions. To date, a resolved-scale simulation of cell growth in the culture process, by taking account of the influences of the supply of nutrients and fluid shear stress on the cells, is not yet available in the literature. This paper presents such a simulation study specifically on cartilage tissue regeneration by numerically solving the momentum, scalar transport and cell growth equations, simultaneously, based on the lattice Boltzmann method. The simulation uses a simplified scaffold that consists of two circular strands placed in tandem inside a microchannel, with the object of identifying the effect of one strand on the other. The results indicate that the presence of the front strand can reduce the cell growth rate on the surface of the rear strand, depending on the distance between them. As such, the present study allows for investigation into the influence of the scaffold geometry on the cell growth rate within scaffolds, thus providing a means to improve the scaffold design and the culture process.

The effect of oxygen tension on human articular chondrocyte matrix synthesis: integration of experimental and computational approaches

Significant oxygen gradients occur within tissue engineered cartilaginous constructs. Although oxygen tension is an important limiting parameter in the development of new cartilage matrix, its precise role in matrix formation by chondrocytes remains controversial, primarily due to discrepancies in the experimental setup applied in different studies. In this study, the specific effects of oxygen tension on the synthesis of cartilaginous matrix by human articular chondrocytes were studied using a combined experimental-computational approach in a “scaffold-free” 3D pellet culture model. Key parameters including cellular oxygen uptake rate were determined experimentally and used in conjunction with a mathematical model to estimate oxygen tension profiles in 21-day cartilaginous pellets. A threshold oxygen tension (pO₂ ≈ 8% atmospheric pressure) for human articular chondrocytes was estimated from these inferred oxygen profiles and histological analysis of pellet sections. Human articular chondrocytes that experienced oxygen tension below this threshold demonstrated enhanced proteoglycan deposition. Conversely, oxygen tension higher than the threshold favored collagen synthesis. This study has demonstrated a close relationship between oxygen tension and matrix synthesis by human articular chondrocytes in a “scaffold-free” 3D pellet culture model, providing valuable insight into the understanding and optimization of cartilage bioengineering approaches. Biotechnol. Bioeng. 2014;111: 1876–1885.

Concise review: optimizing expansion of bone marrow mesenchymal stem/stromal cells for clinical applications

Bone marrow-derived mesenchymal stem/stromal cells (MSCs) have demonstrated success in the clinical treatment of hematopoietic pathologies and cardiovascular disease and are the focus of treating other diseases of the musculoskeletal, digestive, integumentary, and nervous systems. However, during the requisite two-dimensional (2D) expansion to achieve a clinically relevant number of cells, MSCs exhibit profound degeneration in progenitor potency. Proliferation, multilineage potential, and colony-forming efficiency are fundamental progenitor properties that are abrogated by extensive monolayer culture. To harness the robust therapeutic potential of MSCs, a consistent, rapid, and minimally detrimental expansion method is necessary. Alternative expansion efforts have exhibited promise in the ability to preserve MSC progenitor potency better than the 2D paradigm by mimicking features of the native bone marrow niche. MSCs have been successfully expanded when stimulated by growth factors, under reduced oxygen tension, and in three-dimensional bioreactors. MSC therapeutic value can be optimized for clinical applications by combining system inputs to tailor culture parameters for recapitulating the niche with probes that nondestructively monitor progenitor potency. The purpose of this review is to explore how modulations in the 2D paradigm affect MSC progenitor properties and to highlight recent efforts in alternative expansion techniques.

In silico prediction of the cell proliferation in porous scaffold using model of effective pore

The mathematical prediction of cell proliferation in porous scaffold still remains a challenge. The analysis of existing models and experimental data confirms a need for a new solution, which takes into account cells" development on the scaffold pore walls as well as some additional parameters such as the pore size, cell density in cellular layers, the thickness of the growing cell layer and others. The simulations, presented below, are based on three main approaches. The first approach takes into account multilayer cell growth on the pore walls of the scaffold. The second approach is a simulation of cell proliferation in a discrete process as a continuous one. The third one is the representation of scaffold structure as a system of cylindrical channels. Oxygen (nutrient) mass transfer is realized inside these channels. The model, described below, proposes the new solution to time dependent description of cell proliferation in porous scaffold and optimized trophical conditions for tissue development.

Biomanufacturing versus Superficial Cell Seeding: Simulation of Chondrocyte Proliferation in a Cylindrical Cartilage Scaffold

Local volume averaging approach was used for modeling and simulation of cell growth and proliferation, as well as glucose transfer within a cylindrical cartilage scaffold during cell cultivation. The scaffold matrix including the nutrient solution filling spaces among seeded cell colonies was treated as a porous medium. Applying differential mass balance of cells and glucose to a representative elementary volume of the scaffold, two diffusional mass transfer models were developed based on local volume averaged properties. The derived governing equations take into account time-dependent glucose diffusion, glucose consumption by cells, cell migration, apoptosis, and cell reproduction within the scaffold. Since the volumetric fraction of cells in the scaffold relies on cell growth, which strongly depends on glucose concentration in the scaffold, the governing equations were solved simultaneously using implicit finite difference method and Gauss-Seidel technique. Simulation results showed that cell volumetric fraction of the scaffold can reach about 45% after 50 days if a culture medium with a glucose concentration of 45 kgm−3 is used. Also, simulation results indicate that more uniform and higher average cell volume fraction of the scaffold can be obtained if biomanufacturing-based cell seeding is used across the scaffold rather than cell seeding on the scaffold surface.

A multi-paradigm modeling framework to simulate dynamic reciprocity in a bioreactor

Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications.

Computational modeling of nutrient utilization in engineered cartilage

This study presents a mathematical model for simulating cartilaginous culture of chondrocytes seeded in scaffolds and for investigating the effects of glucose and oxygen concentration and pH value on cell metabolic rates. The model can clearly interpret the unexplained experimental observation (Sengers BG, Heywood HK, Lee DA, Oomens CWJ, Bader DL. Nutrient utilization by bovine articular chondrocytes: A combined experimental and theoretical approach. J Biomech Eng. 2005;127:758-766.), which showed that the oxygen concentration within the scaffold may increase instead of continuously decreasing in static cartilaginous culture of chondrocytes. Results from simulation demonstrate that when cells metabolize glucose and form lactate under high glucose concentration conditions, the acidity in the culture environment increases, inhibiting cell metabolic rates in the process. Consequently, the rate of oxygen consumption decreases in later stages of cell culture. As oxygen can be replenished through the free surface of the culture medium, oxygen concentration within the scaffold increases rather than decreases over time in the acidic environment. Different initial glucose concentration yields different results. In low glucose concentration conditions, oxygen concentration basically keeps decreasing with culture time. This is because the pH in the environment does not significantly change because of slower glycolysis rate in low glucose concentration cases, forming less lactic acid. From the simulation results, additional information regarding in vitro culture of chondrocytes is obtained. The correlations between nutrient consumption, lactate secretion, and pH changes during cell culture are also understood and may serve as a reference for in vitro cell culture research of tissue engineering.

Mathematical model of growth factor driven haptotaxis and proliferation in a tissue engineering scaffold

Motivated by experimental work (Miller et al. in Biomaterials 27(10):2213-2221, 2006, 32(11):2775-2785, 2011) we investigate the effect of growth factor driven haptotaxis and proliferation in a perfusion tissue engineering bioreactor, in which nutrient-rich culture medium is perfused through a 2D porous scaffold impregnated with growth factor and seeded with cells. We model these processes on the timescale of cell proliferation, which typically is of the order of days. While a quantitative representation of these phenomena requires more experimental data than is yet available, qualitative agreement with preliminary experimental studies (Miller et al. in Biomaterials 27(10):2213-2221, 2006) is obtained, and appears promising. The ultimate goal of such modeling is to ascertain initial conditions (growth factor distribution, initial cell seeding, etc.) that will lead to a final desired outcome.

2-D coupled computational model of biological cell proliferation and nutrient delivery in a perfusion bioreactor

Tissue engineering aims to regenerate, repair or replace organs or tissues which have become defective due to trauma, disease or age related degeneration. This engineering may take place within the patient's body or tissue can be regenerated in a bioreactor for later implantation into the patient. Regeneration of soft tissue is one of the most demanding applications of tissue engineering. Producing proper nutrient supply, uniform cell distribution and high cell density are the important challenges. Many experimental models exist for tissue growth in a bioreactor. It is important to put experiments into a theoretical framework. Mathematical modelling in terms of physical and biochemical mechanisms is the best tool to understand experimental results. In this work a mathematical model of convective and diffusive transport of nutrients and cell evolution in a perfusion bioreactor is developed. A cell-seeded porous scaffold is placed in a perfusion bioreactor and fluid delivers the nutrients to the cells for their growth. The model describes the key features of the tissue engineering processes which includes the interaction between the cell growth, variation of material permeability due to cell proliferation, flow of fluid through the material and delivery of nutrients to the cells. The fluid flow through the porous scaffold is modelled by Darcy's law, and the delivery of nutrients to the cells is modelled by the advection-diffusion equation. A non-linear reaction diffusion system is used to model the cell growth. The growth of cells is modelled by logistic growth. COMSOL (a commercial finite element solver) is used to numerically solve the model. The results show that the distribution of cells and total cell number in the scaffold does not depend on the initial cell density but depend on the material permeability.

Enhanced cell viability via strain stimulus and fluid flow in magnetically actuated scaffolds

A novel magnetically actuated scaffold was used to explore the effects of strain stimulus on the proliferation and spatial distribution of smooth muscle cells and improve cell viability in the scaffold interior by pumping nutrients throughout the structure. Magnetically actuable scaffolds were fabricated in a tube shape by winding electrospun sheets of a biodegradable polymer modified with magnetic Fe(2)O(3) nanoparticles. Prior to rolling, the sheets were seeded with smooth muscle cells and wound into tubes with diameter 5.2 mm and wall thickness 0.2 mm. The tubular scaffolds were actuated by a magnetic field to induce a cyclic crimping deformation, which applies strain stimulus to the cells and pumps nutrient fluid through the porous tube walls. Comparison with non-actuated controls shows that magnetic actuation increases the total cell count throughout the scaffold after 14 days of incubation. Furthermore, whereas cell density as a function of position through the tube wall thickness showed a minimum in the mid-interior in the controls after 14 days due to cell starvation, the actuated scaffolds displayed a maximum cell density. Comparison of cell distributions with the expected spatial variations in strain amplitude and nutrient flux implies that both strain stimulus and nutrient pumping are significant factors in cell proliferation.

Modeling of cell cultures in perfusion bioreactors

Cultivating cells and tissues in bioreactors is a critical step in forming artificial tissues or organs prior to transplantation. Among various bioreactors, the perfusion bioreactor is known for its enhanced convection through the cell-scaffold constructs. Knowledge of mass transfer is essential for controlling the cell culture process; however, obtaining this information remains a challenging task. In this research, a novel mathematical model is developed to represent the nutrient transport and cell growth in a 3-D scaffold cultivated in a perfusion bioreactor. Numerical methods are employed to solve the equations involved, with a focus on identifying the effect of factors such as porosity, culturing time, and flow rate, which are controllable in the scaffold fabrication and culturing process, on cell cultures. To validate the new model, the results from the model simulations were compared to the experimental results extracted from the literature. With the validated model, further simulations were carried out to investigate the glucose and oxygen distribution and the cell growth within the cell-scaffold construct in a perfusion bioreactor, thus providing insight into the cell culture process.

Computational modeling of adherent cell growth in a hollow-fiber membrane bioreactor for large-scale 3-D bone tissue engineering

The use of hollow-fiber membrane bioreactors (HFMBs) has been proposed for three-dimensional bone tissue growth at the clinical scale. However, to achieve an efficient HFMB design, the relationship between cell growth and environmental conditions must be determined. Therefore, in this work, a dynamic double-porous media model was developed to determine nutrient-dependent cell growth for bone tissue formation in a HFMB. The whole hollow-fiber scaffold within the bioreactor was treated as a porous domain in this model. The domain consisted of two interpenetrating porous regions, including a porous lumen region available for fluid flow and a porous extracapillary space filled with a collagen gel that contained adherent cells for promoting long-term growth into tissue-like mass. The governing equations were solved numerically and the model was validated using previously published experimental results. The contributions of several bioreactor design and process parameters to the performance of the bioreactor were studied. The results demonstrated that the process and design parameters of the HFMB significantly affect nutrient transport and thus cell behavior over a long period of culture. The approach presented here can be applied to any cell type and used to develop tissue engineering hollow-fiber scaffolds.

MECHANICS OF ACTIVE POROUS MEDIA: BONE TISSUE ENGINEERING APPLICATION

In orthopedics, a currently developed technique for large graft hybrid implants consists of using porous and biocompatible scaffolds seeded with a patient's bone cells. Successful culture in such large implants remains a challenge for biologists, and requires strict control of the physicochemical and mechanical environments achieved by perfusion within a bioreactor for several weeks. This perfusion, with a nutritive fluid carrying solute ingredients, is necessary for the active cells to grow, proliferate, differentiate, and produce extracellular matrices. An understanding and control of these processes, which lead to substrate degradation and extracellular matrix remodeling during the in vitro culture phase, depend widely on the success in the realization of new orthopedic biomaterials. Within this context, the analysis of the interactions between convective phenomena of hydrodynamic origin and chemical reactions of biological order which are associated to these processes is a fundamental challenge in the framework of bone tissue engineering. In order to better account for the different intricate processes taking place in such a sample and to design a relevant experimental protocol leading to the definition of an optimal tissue implant, we propose one- and two-dimensional theoretical models based on transport phenomena in porous active media.

COMPUTATIONAL FLUID DYNAMICS FOR TISSUE ENGINEERING APPLICATIONS

Hydrodynamic cellular environment plays an important role in translating engineered tissue constructs into clinically useful grafts. However, the cellular fluid dynamic environment inside bioreactor systems is highly complex and it is normally impractical to experimentally characterize the local flow patterns at the cellular scale. Computational fluid dynamics (CFD) has been recognized as an invaluable and reliable alternative to investigate the complex relationship between hydrodynamic environments and the regeneration of engineered tissues at both the macroscopic and microscopic scales. This review describes the applications of CFD simulations to probe the hydrodynamic environment parameters (e.g., flow rate, shear stress, etc.) and the corresponding experimental validations. We highlight the use of CFD to optimize bioreactor design and scaffold architectures for improved ex-vivo hydrodynamic environments. It is envisioned that CFD could be used to customize specific hydrodynamic cellular environments to meet the unique requirements of different cell types in combination with advanced manufacturing techniques and finally facilitate the maturation of tissue-engineered constructs.

Musculoskeletal tissue engineering with human umbilical cord mesenchymal stromal cells

Multipotent mesenchymal stromal cells (MSCs) hold tremendous promise for tissue engineering and regenerative medicine, yet with so many sources of MSCs, what are the primary criteria for selecting leading candidates? Ideally, the cells will be multipotent, inexpensive, lack donor site morbidity, donor materials should be readily available in large numbers, immunocompatible, politically benign and expandable in vitro for several passages. Bone marrow MSCs do not meet all of these criteria and neither do embryonic stem cells. However, a promising new cell source is emerging in tissue engineering that appears to meet these criteria: MSCs derived from Wharton's jelly of umbilical cord MSCs. Exposed to appropriate conditions, umbilical cord MSCs can differentiate in vitro along several cell lineages such as the chondrocyte, osteoblast, adipocyte, myocyte, neuronal, pancreatic or hepatocyte lineages. In animal models, umbilical cord MSCs have demonstrated in vivo differentiation ability and promising immunocompatibility with host organs/tissues, even in xenotransplantation. In this article, we address their cellular characteristics, multipotent differentiation ability and potential for tissue engineering with an emphasis on musculoskeletal tissue engineering.