Analysis of cell growth and diffusion in a scaffold for cartilage tissue engineering

Current strategies with implementation of three-dimensional cell culture: the challenge of quantification

From growing cells in spheroids to arranging them on complex engineered scaffolds, three-dimensional cell culture protocols are rapidly expanding and diversifying. While these systems may often improve the physiological relevance of cell culture models, they come with technical challenges, as many of the analytical methods used to characterize traditional two-dimensional (2D) cells must be modified or replaced to be effective. Here we review the advantages and limitations of quantification methods based either on biochemical measurements or microscopy imaging. We focus on the most basic of parameters that one may want to measure, the number of cells. Precise determination of this number is essential for many analytical techniques where measured quantities are only meaningful when normalized to the number of cells (e.g. cytochrome p450 enzyme activity). Thus, accurate measurement of cell number is often a prerequisite to allowing comparisons across different conditions (culturing conditions or drug and treatment screening) or between cells in different spatial states. We note that this issue is often neglected in the literature with little or no information given regarding how normalization was performed, we highlight the pitfalls and complications of quantification and call for more accurate reporting to improve reproducibility.

A combined experimental and computational framework to evaluate the behavior of therapeutic cells for peripheral nerve regeneration

Recent studies have explored the potential of tissue‐mimetic scaffolds in encouraging nerve regeneration. One of the major determinants of the regenerative success of cellular nerve repair constructs (NRCs) is the local microenvironment, particularly native low oxygen conditions which can affect implanted cell survival and functional performance. In vivo, cells reside in a range of environmental conditions due to the spatial gradients of nutrient concentrations that are established. Here we evaluate in vitro the differences in cellular behavior that such conditions induce, including key biological features such as oxygen metabolism, glucose consumption, cell death, and vascular endothelial growth factor secretion. Experimental measurements are used to devise and parameterize a mathematical model that describes the behavior of the cells. The proposed model effectively describes the interactions between cells and their microenvironment and could in the future be extended, allowing researchers to compare the behavior of different therapeutic cells. Such a combinatorial approach could be used to accelerate the clinical translation of NRCs by identifying which critical design features should be optimized when fabricating engineered nerve repair conduits.

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.

Modelling-informed cell-seeded nerve repair construct designs for treating peripheral nerve injuries

Millions of people worldwide are affected by peripheral nerve injuries (PNI), involving billions of dollars in healthcare costs. Common outcomes for patients include paralysis and loss of sensation, often leading to lifelong pain and disability. Engineered Neural Tissue (EngNT) is being developed as an alternative to the current treatments for large-gap PNIs that show underwhelming functional recovery in many cases. EngNT repair constructs are composed of a stabilised hydrogel cylinder, surrounded by a sheath of material, to mimic the properties of nerve tissue. The technology also enables the spatial seeding of therapeutic cells in the hydrogel to promote nerve regeneration. The identification of mechanisms leading to maximal nerve regeneration and to functional recovery is a central challenge in the design of EngNT repair constructs. Using in vivo experiments in isolation is costly and time-consuming, offering a limited insight on the mechanisms underlying the performance of a given repair construct. To bridge this gap, we derive a cell-solute model and apply it to the case of EngNT repair constructs seeded with therapeutic cells which produce vascular endothelial growth factor (VEGF) under low oxygen conditions to promote vascularisation in the construct. The model comprises a set of coupled non-linear diffusion-reaction equations describing the evolving cell population along with its interactions with oxygen and VEGF fields during the first 24h after transplant into the nerve injury site. This model allows us to evaluate a wide range of repair construct designs (e.g. cell-seeding strategy, sheath material, culture conditions), the idea being that designs performing well over a short timescale could be shortlisted for in vivo trials. In particular, our results suggest that seeding cells beyond a certain density threshold is detrimental regardless of the situation considered, opening new avenues for future nerve tissue engineering.

A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.

Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering

BACKGROUND

Advances in cartilage tissue engineering have demonstrated noteworthy potential for developing cartilage for implantation onto sites impacted by joint degeneration and injury. To supplement resource-intensive in vivo and in vitro studies required for cartilage tissue engineering, computational models and simulations can assist in enhancing experimental design.

METHODS

Research articles pertinent to cartilage tissue engineering and computer modeling were identified, reviewed, and summarized. Various applications of computer modeling for cartilage tissue engineering are highlighted, limitations of in silico modeling are addressed, and suggestions for future work are enumerated.

RESULTS

Computational modeling can help better characterize shear stresses generated by bioreactor fluid flow, refine scaffold geometry, customize the mechanical properties of engineered cartilage tissue, and model rates of cell growth and dynamics. Thus, results from in silico studies can help resourcefully enhance in vitro and in vivo studies; however, the limitations of these studies, such as the underlying assumptions and simplifications applied in each model, should always be addressed and justified where applicable. In silico models should also seek validation and verification when possible.

CONCLUSION

Future studies may adopt similar approaches to supplement in vitro trials and further investigate effects of mechanical stimulation on chondrocyte and stem cell dynamics. Additionally, as precision medicine, machine learning, and powerful open-source software become more popular and accessible, applications of multi-scale and multiphysics computational models in cartilage tissue engineering are expected to increase.

Modeling, simulations, and optimization of smooth muscle cell tissue engineering for the production of vascular grafts

The paper presents a transient, continuum, two-phase model of the tissue engineering in fibrous scaffolds, including transport equations for the flowing culture medium, nutrient and cell concentration with transverse and in-plane diffusion and cell migration, a novel feature of local in-plane transport across a phenomenological pore and innovative layer-by-layer cell filling approach. The model is successfully validated for the smooth muscle cell tissue engineering of a vascular graft using crosslinked, electrospun gelatin fiber scaffolds for both static and dynamic cell culture, the latter in a dynamic bioreactor with a rotating shaft on which the tubular scaffold is attached. Parametric studies evaluate the impact of the scaffold microstructure, cell dynamics, oxygen transport, and static or dynamic conditions on the rate and extent of cell proliferation and depth of oxygen accessibility. An optimized scaffold of 75% dry porosity is proposed that can be tissue engineered into a viable and still fully oxygenated graft of the tunica media of the coronary artery within 2 days in the dynamic bioreactor. Such scaffold also matches the mechanical properties of the tunica media of the human coronary artery and the suture retention strength of a saphenous vein, often used as a coronary artery graft.

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 for cell infiltration and proliferation in a chondral defect

We develop a mathematical model to describe the regeneration of a hydrogel inserted into an ex vivo osteochondral explant. Specifically we use partial differential equations to describe the evolution of two populations of cells that migrate from the tissue surrounding the defect, proliferate, and compete for space and resources within the hydrogel. The two cell populations are chondrocytes and cells that infiltrate from the subchondral bone. Model simulations are used to investigate how different seeding strategies and growth factor placement within the hydrogel affect the spatial distribution of both cell types. Since chondrocyte migration is extremely slow, we conclude that the hydrogel should be seeded with chondrocytes prior to culture in order to obtain zonal chondrocyte distributions typical of those associated with healthy cartilage.

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.

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.

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.

A comparative study of oxygen diffusion in tissue engineering scaffolds

Tissue engineering scaffolds are designed to support tissue self-healing within physiological environments by promoting the attachment, growth and differentiation of relevant cells. Newly formed tissue must be supplied with sufficient levels of oxygen to prevent necrosis. Oxygen diffusion is the major transport mechanism before vascularization is completed and oxygen is predominantly supplied via blood vessels. The present study compares different designs for scaffolds in the context of their oxygen diffusion ability. In all cases, oxygen diffusion is confined to the scaffold pores that are assumed to be completely occupied by newly formed tissue. The solid phase of the scaffolds acts as diffusion barrier that locally inhibits oxygen diffusion, i.e. no oxygen passes through the scaffold material. As a result, the oxygen diffusivity is determined by the scaffold porosity and pore architecture. Lattice Monte Carlo simulations are performed to compare the normalized oxygen diffusivities in scaffolds obtained by the foam replication (FR) method, robocasting and sol-gel foaming. Scaffolds made by the FR method were found to have the highest oxygen diffusivity due to their high porosity and interconnected pores. These structures enable the best oxygen supply for newly formed tissue among the scaffold types considered according to the present numerical predictions.

Computational analysis of cartilage implants based on an interpenetrated polymer network for tissue repairing

Interpenetrated polymer networks (IPNs), composed by two independent polymeric networks that spatially interpenetrate, are considered as valuable systems to control permeability and mechanical properties of hydrogels for biomedical applications. Specifically, poly(ethyl acrylate) (PEA)-poly(2-hydroxyethyl acrylate) (PHEA) IPNs have been explored as good hydrogels for mimicking articular cartilage. These lattices are proposed as matrix implants in cartilage damaged areas to avoid the discontinuity in flow uptake preventing its deterioration. The permeability of these implants is a key parameter that influences their success, by affecting oxygen and nutrient transport and removing cellular waste products to healthy cartilage. Experimental try-and-error approaches are mostly used to optimize the composition of such structures. However, computational simulation may offer a more exhaustive tool to test and screen out biomaterials mimicking cartilage, avoiding expensive and time-consuming experimental tests. An accurate and efficient prediction of material's permeability and internal directionality and magnitude of the fluid flow could be highly useful when optimizing biomaterials design processes. Here we present a 3D computational model based on Sussman-Bathe hyperelastic material behaviour. A fluid structure analysis is performed with ADINA software, considering these materials as two phases composites where the solid part is saturated by the fluid. The model is able to simulate the behaviour of three non-biodegradable hydrogel compositions, where percentages of PEA and PHEA are varied. Specifically, the aim of this study is (i) to verify the validity of the Sussman-Bathe material model to simulate the response of the PEA-PHEA biomaterials; (ii) to predict the fluid flux and the permeability of the proposed IPN hydrogels and (iii) to study the material domains where the passage of nutrients and cellular waste products is reduced leading to an inadequate flux distribution in healthy cartilage tissue. The obtained results show how the model predicts the permeability of the PEA-PHEA hydrogels and simulates the internal behaviour of the samples and shows the distribution and quantification of fluid flux.

Mathematical modelling of glycosaminoglycan production by stem cell aggregates incorporated with growth factor-releasing polymer microspheres

Systems composed of high density cells incorporated with growth factor-releasing polymer microspheres have recently been shown to promote chondrogenic differentiation and cartilage formation. Within these systems, the effects of spatial and temporal patterning of growth factor release on hyaline cartilage-specific extracellular matrix production have been examined. However, at present, it is unclear which microsphere densities and growth factor delivery profiles are optimal for inducing human mesenchymal stem cell differentiation and glycosaminoglycan production. A mathematical model to describe glycosaminoglycan production as a function of initial microsphere loading and microsphere degradation rate over a period of 3 weeks is presented. Based on predictions generated by this model, it may be feasible to design a bioactive microsphere system with specific spatiotemporal growth factor presentation characteristics to promote glycosaminoglycan production at controllable rates. Copyright © 2014 John Wiley & Sons, Ltd.

Engineering parameters in bioreactor's design: a critical aspect in tissue engineering

Bioreactors are important inevitable part of any tissue engineering (TE) strategy as they aid the construction of three-dimensional functional tissues. Since the ultimate aim of a bioreactor is to create a biological product, the engineering parameters, for example, internal and external mass transfer, fluid velocity, shear stress, electrical current distribution, and so forth, are worth to be thoroughly investigated. The effects of such engineering parameters on biological cultures have been addressed in only a few preceding studies. Furthermore, it would be highly inefficient to determine the optimal engineering parameters by trial and error method. A solution is provided by emerging modeling and computational tools and by analyzing oxygen, carbon dioxide, and nutrient and metabolism waste material transports, which can simulate and predict the experimental results. Discovering the optimal engineering parameters is crucial not only to reduce the cost and time of experiments, but also to enhance efficacy and functionality of the tissue construct. This review intends to provide an inclusive package of the engineering parameters together with their calculation procedure in addition to the modeling techniques in TE bioreactors.

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.

Bioreactor-Induced Chondrocyte Maturation Is Dependent on Cell Passage and Onset of Loading

OBJECTIVE

To explore the effect of shifting in vitro culture conditions regarding cellular passage and onset of loading within matrix-associated bovine articular chondrocytes cultured under free-swelling and/or dynamical loading conditions on general chondrocyte maturation.

METHODS

Primary or passage 3 bovine chondrocytes were seeded in fibrin-polyurethane scaffolds. Constructs were cultured either free-swelling for 2 or 4 weeks, under direct mechanical loading for 2 or 4 weeks, or free swelling for 2 weeks followed by 2 weeks of loading. Samples were collected for glycosaminoglycan (GAG) quantification, mRNA expression of chondrogenic genes, immunohistochemistry, and histology.

RESULTS

Mechanical loading generally stimulated GAG synthesis, up-regulated chondrogenic genes, and improved the accumulation of matrix in cell-laden constructs when compared with free-swelling controls. Primary chondrocytes underwent more effective cartilage maturation when compared with passaged chondrocytes. Constructs of primary chondrocytes that were initially free-swelling followed by 2 weeks of mechanical load (delayed) had overall highest GAG with strongest responsiveness to load regarding matrix synthesis. Constructs that experienced the delayed loading regime also demonstrated most favorable chondrogenic gene expression profiles in both primary and third passage cells. Furthermore, most intense matrix staining and immunostaining of collagen type II and aggrecan were visualized in these constructs.

CONCLUSIONS

Primary chondrocytes were more effective than passage 3 chondrocytes when chondrogenesis was concerned. The most efficient chondrogenesis resulted from primary articular chondrocytes, which were initially free-swelling followed by a standardized loading protocol.

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.

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.

Mass transfer trends occurring in engineered ex vivo tissue scaffolds

In vivo the vasculature provides an effective delivery system for cellular nutrients; however, artificial scaffolds have no such mechanism, and the ensuing limitations in mass transfer result in limited regeneration. In these investigations, the regional mass transfer properties that occur through a model scaffold derived from the human umbilical vein (HUV) were assessed. Our aim was to define the heterogeneous behavior associated with these regional variations, and to establish if different decellularization technologies can modulate transport conditions to improve microenvironmental conditions that enhance cell integration. The effect of three decellularization methods [Triton X-100 (TX100), sodium dodecyl sulfate (SDS), and acetone/ethanol (ACE/EtOH)] on mass transfer, cellular migration, proliferation, and metabolic activity were assessed. Results show that regional variation in tissue structure and composition significantly affects both mass transfer and cell function. ACE/EtOH decellularization was shown to increase albumin mass flux through the intima and proximate-medial region (0-250 μm) when compared with sections decellularized with TX100 or SDS; although, mass flux remained constant over all regions of the full tissue thickness when using TX100. Scaffolds decellularized with TX100 were shown to promote cell migration up to 146% further relative to SDS decellularized samples. These results show that depending on scaffold derivation and expectations for cellular integration, specificities of the decellularization chemistry affect the scaffold molecular architecture resulting in variable effects on mass transfer and cellular response.

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.

Distraction osteogenesis combined with tissue-engineered cartilage in the reconstruction of condylar osteochondral defect

PURPOSE

Surgical rehabilitation of condylar osteochondral defect remains a challenge for surgeons. The aim of this study was to explore the feasibility of combining distraction osteogenesis with tissue-engineered cartilage in the reconstruction of condylar osteochondral defect.

MATERIALS AND METHODS

A condylar defect model was established in 18 goats that were randomly divided into 2 groups: the experimental group and the control group. Mandibular ramus osteotomies were performed and distractors were implanted in all animals. The mixture of chondrocytes and Pluronic F-127 (Sigma-Aldrich, St Louis, MO) was injected on the notched surface of a transport disc in the experimental group, whereas a scaffold without cells was transplanted into the control group. After a 5-day latency period, distraction was activated at a rate of 0.5 mm twice per day for 15 days. The goats were killed at the end of the fourth, eighth, or twelfth week in the consolidation period. Specimens were harvested and macroscopic evaluation, as well as Masson trichrome and immunohistochemical staining, were performed to compare the results between the 2 groups.

RESULTS

Osteogenesis was found in all animals with no evidence of infection. Condyle-like structures were formed at the upper end of the transport segment in all animals. The neocondylar surface was covered with a layer of smooth lustrous fibrocartilage in the experimental group. Collagen was shown in the reparative tissue by Masson trichrome staining. Immunohistochemistry staining indicated that type II collagen was positive, whereas type I collagen was negative on the neocondylar surface in the experimental group. No cartilage-like tissue was seen, but fibrous tissue was identified at the bony surface in the control group. In the experimental group, immunofluorescent semiquantitative analysis showed that the positive rate of type II collagen was 1.62% ± 0.53% after the fourth week of consolidation, and it increased to 12.39% ± 3.27% after the twelfth week. There was a significant difference in the expression of type II collagen between the goats examined after the fourth week, and those examined after the twelfth week.

CONCLUSION

The combination of distraction osteogenesis with tissue-engineered cartilage is an ideal alternative in the reconstruction of condylar osteochondral defect. By use of this method, the simultaneous rehabilitation and regeneration of condylar bone and cartilage were achieved.

Biomimetic three-dimensional microenvironment for controlling stem cell fate

Stem cell therapy is an emerging technique which is being translated into treatment of degenerated tissues. However, the success of translation relies on the stem cell lineage commitment in the degenerated regions of interest. This commitment is precisely controlled by the stem cell microenvironment. Engineering a biomimetic three-dimensional microenvironment enables a thorough understanding of the mechanisms of governing stem cell fate. We review the individual microenvironment components, including soluble factors, extracellular matrix, cell-cell interaction and mechanical stimulation. The perspectives in creating the biomimetic microenvironments are discussed with emerging techniques.

Mathematical modeling in wound healing, bone regeneration and tissue engineering

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

Analysis of collagen and glucose modulated cell growth within tissue engineered scaffolds

The strategy of tissue engineering includes seeding cells onto porous scaffolds. The cellular construct is cultured in vitro for a period of time before transplantation for the patient. Because of the intrinsic complexity of biological systems, it is valuable to have models of simulation that can assess the culture conditions and optimize experiments. This work presents a mathematical model to account for the effects of glucose and type II collagen on chondrocyte growth under static culture conditions. Dependence of cell growth on collagen was assumed as a biphasic function of collagen quantity, whereby the cell growth rate increases and then decreases with increasing collagen content. Results from simulation were compared with experimental data in literature. The model was then applied to investigate the effects of cell seeding area, demonstrating the spatiotemporal evolution of cell distribution in scaffolds. Results show that the conventional uniform seeding method may not be a good way of gaining uniform and large cell number densities at the final stage of cultivation. A seeding mode that has cells reside initially in the middle area of scaffold was shown to be able to not only reduce the diffusion limitation of nutrients but also weaken the inhibiting impact of aggregated collagen on cell growth. Therefore the middle seeding mode may result in better cell amounts and uniformities for developing tissue engineered constructs.

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

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

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.

Potential and bottlenecks of bioreactors in 3D cell culture and tissue manufacturing

Over the last decade, we have witnessed an increased recognition of the importance of 3D culture models to study various aspects of cell physiology and pathology, as well as to engineer implantable tissues. As compared to well-established 2D cell-culture systems, cell/tissue culture within 3D porous biomaterials has introduced new scientific and technical challenges associated with complex transport phenomena, physical forces, and cell-microenvironment interactions. While bioreactor-based 3D model systems have begun to play a crucial role in addressing fundamental scientific questions, numerous hurdles currently impede the most efficient utilization of these systems. We describe how computational modeling and innovative sensor technologies, in conjunction with well-defined and controlled bioreactor-based 3D culture systems, will be key to gain further insight into cell behavior and the complexity of tissue development. These model systems will lay a solid foundation to further develop, optimize, and effectively streamline the essential bioprocesses to safely and reproducibly produce appropriately scaled tissue grafts for clinical studies.

Experimental-computational evaluation of human bone marrow stromal cell spreading on trabecular bone structures

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading. Only the first phase of in vitro scaffold colonization was addressed, in which cells migrate and proliferate up to the stage when the surface of the bone is covered as a monolayer, a critical prerequisite for further tissue formation. The results confirm the model's ability to represent experimentally observed cell population spreading. The key advantage of the computational model was that by incorporating complex 3D structure, cell behavior can be characterized quantitatively in terms of intrinsic migration parameters, which could potentially be used for predictions on different macro-porous scaffolds subject to additional experimental validation. This type of modeling will prove useful in predicting cell colonization and improving strategies for skeletal tissue engineering.

A compact computational model for cell construct development in perfusion culture

A problem nowadays tissue engineers encounter in developing sizable tissue implants is the nonuniform spread of cells and/or extracellular matrices. Research shows such a nutrients transport restriction may be improved by employing hydrodynamic culture systems. We propose a compact model for the simulation of cell growth in a porous construct under direct perfusion. Unlike the previous model proposed in the literature, which composes a cellular scaffold sandwiched between two culture media layers, the current model includes only the scaffold layer to simplify the mathematical and computational complex. Results show the present single-layer model can predict cell spreads and the nutrient and metabolic waste distribution as accurately as does the three-layer model. Only if the hydrodynamic aspects such as the pressure and viscous stress are prominent to know, should the more sophisticated analyses with the three-layer model be employed. The compact model provides comparable investigations for the tissue-engineering construct developments.

Computational fluid dynamics for improved bioreactor design and 3D culture

The complex relationship between the hydrodynamic environment and surrounding tissues directly impacts on the design and production of clinically useful grafts and implants. Tissue engineers have generally seen bioreactors as 'black boxes' within which tissue engineering constructs (TECs) are cultured. It is accepted that a more detailed description of fluid mechanics and nutrient transport within process equipment can be achieved by using computational fluid dynamics (CFD) technology. This review discusses applications of CFD for tissue engineering-related bioreactors -- fluid flow processes have direct implications on cellular responses such as attachment, migration and proliferation. We conclude that CFD should be seen as an invaluable tool for analyzing and visualizing the impact of fluidic forces and stresses on cells and TECs.