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. © 2014 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.     

Rate of oxygen consumption by isolated articular chondrocytes is sensitive to medium glucose concentration

Cartilage tissue engineering typically involves the culture of isolated chondrocytes within a scaffold material. The oxygen tension within the engineered tissue is known to be an essential parameter for implant success. This will be sensitive to the oxygen consumption behavior of the embedded chondrocytes, which remains to be characterized. We report that the oxygen consumption of bovine articular chondrocytes is sensitive to glucose deprivation below 2.7 mM, increasing from a basal level of 9.6x10(-16) to <18.4x10(-16) mol/cell.h in 1.3 mM glucose. Further studies examined the influence of selecting high (18.4 mM) or low (5.1 mM) glucose medium on the oxygen tension in 2 mm thick cellular agarose constructs. A relative upregulation of oxygen consumption was observed in constructs cultured in low glucose medium. This resulted in the near-anoxic oxygen concentration of 5 microM oxygen in constructs seeded with 40x10(6) cells/ml, compared to 57 microM in the corresponding high glucose culture. The upregulation of oxygen consumption generally corresponded to the inhibition of glycolysis, which is consistent with the Crabtree phenomenon. Medium osmolarity (316-600 mOsm) had minimal effects on chondrocyte oxygen consumption rate. In conclusion, glucose availability is a critical parameter that regulates the oxygen tension within tissue engineered constructs.     

Effect of pore architecture on oxygen diffusion in 3D scaffolds for tissue engineering

The aim of this study was to maximize oxygen diffusion within a three-dimensional scaffold in order to improve cell viability and proliferation. To evaluate the effect of pore architecture on oxygen diffusion, we designed a regular channel shape with uniform diameter, referred to as cylinder shaped, and a new channel shape with a channel diameter gradient, referred to as cone shaped. A numerical analysis predicted higher oxygen concentration in the cone-shaped channels than in the cylinder-shaped channels, throughout the scaffold. To confirm these numerical results, we examined cell proliferation and viability in 2D constructs and 3D scaffolds. Cell culture experiments revealed that cell proliferation and viability were superior in the constructs and scaffolds with cone-shaped channels.     

Cell Proliferation and Oxygen Diffusion in a Vascularising Scaffold

The supply of oxygen to proliferating cells within a scaffold is a key factor for the successful building of new tissue in soft tissue engineering applications. A recent in vivo model, where an arteriovenous loop is placed in a scaffold, allows a vascularising network to form within a scaffold, establishing an oxygen source within, rather than external, to the scaffold. A one-dimensional model of oxygen concentration, cell proliferation and cell migration inside such a vascularising scaffold is developed and investigated. In addition, a vascularisation model is presented, which supports a vascularisation front which moves at a constant speed. The effects of vascular growth, homogenous and heterogenous seeding, diffusion of cells and critical hypoxic oxygen concentration are considered. For homogenous seeding, a relationship between the speed of the vascular front and a parameter defining the rate of oxygen diffusion relative to the rate of oxygen consumption determines whether a hypoxic region exists at some time. In particular, an estimate of the length of time that a fixed point in the scaffold will remain under hypoxic conditions is determined. For heterogenous seeding, a Fisher-like travelling wave of cells is established behind the vascular front. These findings provide a fundamental understanding of the important interplay between the parameters and allows for a theoretical assessment of a seeding strategy in a vascularising scaffold.     

Modeling spatial distribution of oxygen in 3d culture of islet beta‐cells

Three‐dimensional (3D) scaffold culture of pancreatic β‐cell has been proven to be able to better mimic physiological conditions in the body. However, one critical issue with culturing pancreatic β‐cells is that β‐cells consume large amounts of oxygen, and hence insufficient oxygen supply in the culture leads to loss of β‐cell mass and functions. This becomes more significant when cells are cultured in a 3D scaffold. In this study, in order to understand the effect of oxygen tension inside a cell‐laden collagen culture on β‐cell proliferation, a culture model with encapsulation of an oxygen‐generator was established. The oxygen‐generator was made by embedding hydrogen peroxide into nontoxic polydimethylsiloxane to avoid the toxicity of a chemical reaction in the β‐cell culture. To examine the effectiveness of the oxygenation enabled 3D culture, the spatial‐temporal distribution of oxygen tension inside a scaffold was evaluated by a mathematical modeling approach. Our simulation results indicated that an oxygenation‐aided 3D culture would augment the oxygen supply required for the β‐cells. Furthermore, we identified that cell seeding density and the capacity of the oxygenator are two critical parameters in the optimization of the culture. Notably, cell‐laden scaffold cultures with an in situ oxygen supply significantly improved the β‐cells' biological function. These β‐cells possess high insulin secretion capacity. The results obtained in this work would provide valuable information for optimizing and encouraging functional β‐cell cultures. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 33:221–228, 2017     

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

     

Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models

We present a combined macro-scale/micro-scale computational approach to quantify oxygen transport and flow-mediated shear stress to human chondrocytes cultured in three-dimensional scaffolds in a perfusion bioreactor system. A macro-scale model was developed to assess the influence of the bioreactor design and to identify the proper boundary conditions for the micro-scale model. The micro-scale model based on a micro-computed tomography (microCT) reconstruction of a poly(ethylene glycol terephthalate)/poly(butylene terephthalate) (PEGT/PBT) foam scaffold, was developed to assess the influence of the scaffold micro-architecture on local shear stress and oxygen levels within the scaffold pores. Experiments were performed to derive specific oxygen consumption rates for constructs perfused under flow rates of 0.3 and 0.03 ml min(-1). While macro-scale and micro-scale models predicted similar average oxygen levels at different depths within the scaffold, microCT models revealed small local oxygen variations within the scaffold micro-architecture. The combined macro-scale/micro-scale approach indicated that 0.3 ml min(-1), which subjected 95% of the cells to less than 6.3 mPa shear, would maintain the oxygen supply throughout the scaffold above anoxic levels (>1%), with 99.5% of the scaffold supplied with 8-2% O(2). Alternatively, at 0.03 ml min(-1), the macro-scale model predicted 6% of the cells would be supplied with 0.5-1% O(2), although this region of cells was confined to the periphery of the scaffold. Together with local variations predicted by the micro-scale model, the simulations underline that in the current model system, reducing the flow below 0.03 ml min(-1) would likely have dire consequences on cell viability to pronounced regions within the engineered construct. The presented approach provides a sensitive tool to aid efficient bioreactor optimization and scaffold design.     

Oxygen gradients correlate with cell density and cell viability in engineered cardiac tissue

For clinical utility, cardiac grafts should be thick and compact, and contain physiologic density of metabolically active, differentiated cells. This involves the need to control the levels of nutrients, and most critically oxygen, throughout the construct volume. Most culture systems involve diffusional transport within the constructs, a situation associated with gradients of oxygen concentration, cell density, cell viability, and function. The goal of our study was to measure diffusional gradients of oxygen in statically cultured cardiac constructs, and to correlate oxygen gradients to the spatial distributions of cell number and cell viability. Using microelectrodes, we measured oxygen distribution in a disc-shaped constructs (3.6 mm diameter, 1.8 mm thickness) based on neonatal rat cardiomyocytes cultured on collagen scaffolds for 16 days in static dishes. To rationalize experimental data, a mathematical model of oxygen distribution was derived as a function of cell density, viability, and spatial position within the construct. Oxygen concentration and cell viability decreased linearly and the live cell density decreased exponentially with the distance from the construct surface. Physiological density of live cells was present only within the first 128 microm of the construct thickness. Medium flow significantly increased oxygen concentration within the construct, correlating with the improved tissue properties observed for constructs cultured in convectively mixed bioreactors.     

Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis

A simplified 2D mathematical model for tissue growth within a cyclically-loaded tissue engineering scaffold is presented and analyzed. Such cyclic loading has the potential to improve yield and functionality of tissue such as bone and cartilage when grown on a scaffold within a perfusion bioreactor. The cyclic compression affects the flow of the perfused nutrient, leading to flow properties that are inherently unsteady, though periodic, on a timescale short compared with that of tissue proliferation. A two-timescale analysis based on these well-separated timescales is exploited to derive a closed model for the tissue growth on the long timescale of proliferation. Some sample numerical results are given for the final model, and discussed.     

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

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

The interplay between tissue growth and scaffold degradation in engineered tissue constructs

In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties of the engineered tissue are appropriate for the in vivo environment. Achieving this goal will require detailed understanding of the interplay between cell proliferation, extracellular matrix (ECM) deposition and scaffold degradation. In this paper, we use a mathematical model (based upon a multiphase continuum framework) to investigate the interplay between tissue growth and scaffold degradation during tissue construct evolution in vitro. Our model accommodates a cell population and culture medium, modelled as viscous fluids, together with a porous scaffold and ECM deposited by the cells, represented as rigid porous materials. We focus on tissue growth within a perfusion bioreactor system, and investigate how the predicted tissue composition is altered under the influence of (1) differential interactions between cells and the supporting scaffold and their associated ECM, (2) scaffold degradation, and (3) mechanotransduction-regulated cell proliferation and ECM deposition. Numerical simulation of the model equations reveals that scaffold heterogeneity typical of that obtained from $\mu $ CT scans of tissue engineering scaffolds can lead to significant variation in the flow-induced mechanical stimuli experienced by cells seeded in the scaffold. This leads to strong heterogeneity in the deposition of ECM. Furthermore, preferential adherence of cells to the ECM in favour of the artificial scaffold appears to have no significant influence on the eventual construct composition; adherence of cells to these supporting structures does, however, lead to cell and ECM distributions which mimic and exaggerate the heterogeneity of the underlying scaffold. Such phenomena have important ramifications for the mechanical integrity of engineered tissue constructs and their suitability for implantation in vivo.     

Oxygen gradients in tissue-engineered PEGT/PBT cartilaginous constructs: measurement and modeling

The supply of oxygen within three-dimensional tissue-engineered (TE) cartilage polymer constructs is mainly by diffusion. Oxygen consumption by cells results in gradients in the oxygen concentration. The aims of this study were, firstly, to identify the gradients within TE cartilage polymer constructs and, secondly, to predict the profiles during in vitro culture. A glass microelectrode system was adapted and used to penetrate cartilage and TE cartilaginous constructs, yielding reproducible measurements with high spatial resolution. Cartilage polymer constructs were cultured for up to 41 days in vitro. Oxygen concentrations, as low as 2-5%, were measured within the center of these constructs. At the beginning of in vitro culture, the oxygen gradients were steeper in TE constructs in comparison to native tissue. Nevertheless, during the course of culture, oxygen concentrations approached the values measured in native tissue. A mathematical model was developed which yields oxygen profiles within cartilage explants and TE constructs. Model input parameters were assessed, including the diffusion coefficient of cartilage (2.2 x 10(-9)) + (0.4 x 10(-9) m(2) s(-1)), 70% of the diffusion coefficient of water and the diffusion coefficient of constructs (3.8 x 10(-10) m(2) s(-1)). The model confirmed that chondrocytes in polymer constructs cultured for 27 days have low oxygen requirements (0.8 x 10(-19) mol m(-3) s(-1)), even lower than chondrocytes in native cartilage. The ability to measure and predict local oxygen tensions offers new opportunities to obtain more insight in the relation between oxygen tension and chondrogenesis.     

Cartilage tissue engineering: controversy in the effect of oxygen

Articular cartilage lacks the ability to repair itself and consequently defects in this tissue do not heal. Tissue engineering approaches, employing a scaffold material and cartilage producing cells (chondrocytes), hold promise for the treatment of such defects. In these strategies the limitation of nutrients, such as oxygen, during in vitro culture are of major concern and will have implications for proper bioreactor design. We recently demonstrated that oxygen gradients are indeed present within tissue engineered cartilaginous constructs. Interestingly, oxygen, besides being an essential nutrient, is also a controlling agent of developmental processes including cartilage formation. However, the specific role of oxygen in these processes is still obscure despite the recent advances in the field. In particular, the outcome of published investigations is inconsistent regarding the effect of oxygen tension on chondrocytes. Therefore, this article describes the possible roles of oxygen gradients during embryonic cartilage development and reviews the data reported on the effect of oxygen tension on in vitro chondrocyte proliferation and differentiation from a tissue engineering perspective. Furthermore, possible causes for the variance in the data are discussed. Finally, recommendations are included that may reduce the variation, resulting in more reliable and comparable data.     

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.     

Optimization of cardiac cell seeding and distribution in 3D porous alginate scaffolds

Cardiac tissue engineering has evolved as a potential therapeutic approach to assist in cardiac regeneration. We have recently shown that tissue-engineered cardiac graft, constructed from cardiomyocytes seeded within an alginate scaffold, is capable of preventing the deterioration in cardiac function after myocardial infarction in rats. The present article addresses cell seeding within porous alginate scaffolds in an attempt to achieve 3D high-density cardiac constructs with a uniform cell distribution. Due to the hydrophilic nature of the alginate scaffold, its >90% porosity and interconnected pore structure, cell seeding onto the scaffold was efficient and short, up to 30 min. Application of a moderate centrifugal force during cell seeding resulted in a uniform cell distribution throughout the alginate scaffolds, consequently enabling the loading of a large number of cells onto the 3D scaffolds. The percent cell yield in the alginate scaffolds ranged between 60-90%, depending on cell density at seeding; it was 90% at seeding densities of up to 1 x 10(8) cells/cm(3) scaffold and decreased to 60% at higher densities. The highly dense cardiac constructs maintained high metabolic activity in culture. Scanning electron microscopy revealed that the cells aggregated within the scaffold pores. Some of the aggregates were contracting spontaneously within the matrix pores. Throughout the culture there was no indication of cardiomyocyte proliferation within the scaffolds, nor was it found in 3D cultures of cardiofibroblasts. This may enable the development of cardiac cocultures, without domination of cardiofibroblasts with time.     

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. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 452–462, 2013     

Cartilage Tissue Engineering: Controversy in the Effect of Oxygen

Articular cartilage lacks the ability to repair itself and consequently defects in this tissue do not heal. Tissue engineering approaches, employing a scaffold material and cartilage producing cells (chondrocytes), hold promise for the treatment of such defects. In these strategies the limitation of nutrients, such as oxygen, during in vitro culture are of major concern and will have implications for proper bioreactor design. We recently demonstrated that oxygen gradients are indeed present within tissue engineered cartilaginous constructs. Interestingly, oxygen, besides being an essential nutrient, is also a controlling agent of developmental processes including cartilage formation. However, the specific role of oxygen in these processes is still obscure despite the recent advances in the field. In particular, the outcome of published investigations is inconsistent regarding the effect of oxygen tension on chondrocytes. Therefore, this article describes the possible roles of oxygen gradients during embryonic cartilage development and reviews the data reported on the effect of oxygen tension on in vitro chondrocyte proliferation and differentiation from a tissue engineering perspective. Furthermore, possible causes for the variance in the data are discussed. Finally, recommendations are included that may reduce the variation, resulting in more reliable and comparable data.     

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

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

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

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