Computational study of culture conditions and nutrient supply in cartilage tissue engineering

Optimization of Oxygen Delivery Within Hydrogels

The field of tissue engineering has been continuously evolving since its inception over three decades ago with numerous new advancements in biomaterials and cell sources and widening applications to most tissues in the body. Despite the substantial promise and great opportunities for the advancement of current medical therapies and procedures, the field has yet to capture wide clinical translation due to some remaining challenges, including oxygen availability within constructs, both in vitro and in vivo. While this insufficiency of nutrients, specifically oxygen, is a limitation within the current frameworks of this field, the literature shows promise in new technological advances to efficiently provide adequate delivery of nutrients to cells. This review attempts to capture the most recent advances in the field of oxygen transport in hydrogel-based tissue engineering, including a comparison of current research as it pertains to the modeling, sensing, and optimization of oxygen within hydrogel constructs as well as new technological innovations to overcome traditional diffusion-based limitations. The application of these findings can further the advancement and development of better hydrogel-based tissue engineered constructs for future clinical translation and adoption.

Optimized Media Volumes Enable Homogeneous Growth of Mesenchymal Stem Cell-Based Engineered Cartilage Constructs

Despite marked advances in the field of cartilage tissue engineering, it remains a challenge to engineer cartilage constructs with homogeneous properties. Moreover, for engineered cartilage to make it to the clinic, this homogeneous growth must occur in a time-efficient manner. In this study we investigated the potential of increased media volume to expedite the homogeneous maturation of mesenchymal stem cell (MSC) laden engineered constructs over time in vitro. We assessed the MSC-laden constructs after 4 and 8 weeks of chondrogenic culture using bulk mechanical, histological, and biochemical measures. These assays were performed on both the intact total constructs and the construct cores to elucidate region-dependent differences. In addition, local strain transfer was assessed to quantify depth-dependent mechanical properties throughout the constructs. Our findings suggest that increased media volume enhances matrix deposition early in culture and ameliorates unwanted regional heterogeneities at later time points. Taken together, these data support the use of higher media volumes during in vitro culture to hasten tissue maturation and increase the core strength of tissue constructs. These findings will forward the field of cartilage tissue engineering and the translation of tissue engineered constructs.

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.

Biophysical Stimuli: A Review of Electrical and Mechanical Stimulation in Hyaline Cartilage

OBJECTIVE

Hyaline cartilage degenerative pathologies induce morphologic and biomechanical changes resulting in cartilage tissue damage. In pursuit of therapeutic options, electrical and mechanical stimulation have been proposed for improving tissue engineering approaches for cartilage repair. The purpose of this review was to highlight the effect of electrical stimulation and mechanical stimuli in chondrocyte behavior.

DESIGN

Different information sources and the MEDLINE database were systematically revised to summarize the different contributions for the past 40 years.

RESULTS

It has been shown that electric stimulation may increase cell proliferation and stimulate the synthesis of molecules associated with the extracellular matrix of the articular cartilage, such as collagen type II, aggrecan and glycosaminoglycans, while mechanical loads trigger anabolic and catabolic responses in chondrocytes.

CONCLUSION

The biophysical stimuli can increase cell proliferation and stimulate molecules associated with hyaline cartilage extracellular matrix maintenance.

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.

Computational Modeling and Reverse Engineering to Reveal Dominant Regulatory Interactions Controlling Osteochondral Differentiation: Potential for Regenerative Medicine

The specialization of cartilage cells, or chondrogenic differentiation, is an intricate and meticulously regulated process that plays a vital role in both bone formation and cartilage regeneration. Understanding the molecular regulation of this process might help to identify key regulatory factors that can serve as potential therapeutic targets, or that might improve the development of qualitative and robust skeletal tissue engineering approaches. However, each gene involved in this process is influenced by a myriad of feedback mechanisms that keep its expression in a desirable range, making the prediction of what will happen if one of these genes defaults or is targeted with drugs, challenging. Computer modeling provides a tool to simulate this intricate interplay from a network perspective. This paper aims to give an overview of the current methodologies employed to analyze cell differentiation in the context of skeletal tissue engineering in general and osteochondral differentiation in particular. In network modeling, a network can either be derived from mechanisms and pathways that have been reported in the literature (knowledge-based approach) or it can be inferred directly from the data (data-driven approach). Combinatory approaches allow further optimization of the network. Once a network is established, several modeling technologies are available to interpret dynamically the relationships that have been put forward in the network graph (implication of the activation or inhibition of certain pathways on the evolution of the system over time) and to simulate the possible outcomes of the established network such as a given cell state. This review provides for each of the aforementioned steps (building, optimizing, and modeling the network) a brief theoretical perspective, followed by a concise overview of published works, focusing solely on applications related to cell fate decisions, cartilage differentiation and growth plate biology. Particular attention is paid to an in-house developed example of gene regulatory network modeling of growth plate chondrocyte differentiation as all the aforementioned steps can be illustrated. In summary, this paper discusses and explores a series of tools that form a first step toward a rigorous and systems-level modeling of osteochondral differentiation in the context of regenerative medicine.

Role of oxygen as a regulator of stem cell fate during the spontaneous repair of osteochondral defects

The complexity of the in vivo environment makes it is difficult to isolate the effects of specific cues on regulating cell fate during regenerative events such as osteochondral defect repair. The objective of this study was to develop a computational model to explore how joint specific environmental factors regulate mesenchymal stem cell (MSC) fate during osteochondral defect repair. To this end, the spontaneous repair process within an osteochondral defect was simulated using a tissue differentiation algorithm which assumed that MSC fate was regulated by local oxygen levels and substrate stiffness. The developed model was able to predict the main stages of tissue formation observed by a number of in vivo studies. Following this, a parametric study was conducted to better understand why interventions that modulate angiogenesis dramatically impact the outcome of osteochondral defect healing. In the simulations where angiogenesis was reduced, by week 12, the subchondral plate was predicted to remain below the native tidemark, although the chondral region was composed entirely of cartilage and fibrous tissue. In the simulations where angiogenesis was increased, more robust cell proliferation and cartilage formation were observed during the first 4 weeks, however, by week 12 the subchondral plate had advanced above the native tidemark although any remaining tissue was either hypertrophic cartilage or fibrous tissue. These results suggest that osteochondral defect repair could be enhanced by interventions where angiogenesis is promoted but confined to within the subchondral region of the defect. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1026-1036, 2016.

Relative Effects of Fluid Oscillations and Nutrient Transport in the In Vitro Growth of Valvular Tissues

Engineered valvular tissues are cultured dynamically, and involve specimen movement. We previously demonstrated that oscillatory shear stresses (OSS) under combined steady flow and specimen cyclic flexure (flex-flow) promote tissue formation. However, localized efficiency of specimen mass transport is also important in the context of cell viability within the growing tissues. Here, we investigated the delivery of two essential species for cell survival, glucose and oxygen, to 3-dimensional (3D) engineered valvular tissues. We applied a convective-diffusive model to characterize glucose and oxygen mass transport with and without valve-like specimen flexural movement. We found the mass transport effects for glucose and oxygen to be negligible for scaffold porosities typically present during in vitro experiments and non-essential unless the porosity was unusually low (<40%). For more typical scaffold porosities (75%) however, we found negligible variation in the specimen mass fraction of glucose and oxygen in both non-moving and moving constructs (p > 0.05). Based on this result, we conducted an experiment using bone marrow stem cell (BMSC)-seeded scaffolds under Pulsatile flow-alone states to permit OSS without any specimen movement. BMSC-seeded specimen collagen from the pulsatile flow and flex-flow environments were subsequently found to be comparable (p > 0.05) and exhibited some gene expression similarities. We conclude that a critical magnitude of fluid-induced, OSS created by either pulsatile flow or flex-flow conditions, particularly when the oscillations are physiologically-relevant, is the direct, principal stimulus that promotes engineered valvular tissues and its phenotype, whereas mass transport benefits derived from specimen movement are minimal.

Glucose gradients influence zonal matrix deposition in 3D cartilage constructs

Reproducing the native collagen structure and glycosaminoglycan (GAG) distribution in tissue-engineered cartilage constructs is still a challenge. Articular cartilage has a specific nutrient supply and mechanical environment due to its location and function in the body. Efforts to simulate this native environment have been reported through the use of bioreactor systems. However, few of these devices take into account the existence of gradients over cartilage as a consequence of the nutrient supply by diffusion. We hypothesized that culturing chondrocytes in an environment, in which gradients of nutrients can be mimicked, would induce zonal differentiation. Indeed, we show that glucose gradients facilitating a concentration distribution as low as physiological glucose levels enhanced a zonal chondrogenic capacity similar to the one found in native cartilage. Furthermore, we found that the glucose consumption rates of cultured chondrocytes were higher under physiological glucose concentrations and that GAG production rates were highest in 5 mM glucose. From these findings, we concluded that this condition is better suited for matrix deposition compared to 20 mM glucose standard used in a chondrocyte culture system. Reconsidering the culture conditions in cartilage tissue engineering strategies can lead to cartilaginous constructs that have better mechanical and structural properties, thus holding the potential of further enhancing integration with the host tissue.

Matrix Production in Large Engineered Cartilage Constructs Is Enhanced by Nutrient Channels and Excess Media Supply

Cartilage tissue engineering is a promising approach to resurfacing osteoarthritic joints. Existing techniques successfully engineer small-sized constructs with native levels of extracellular matrix (glycosaminoglycans [GAG] or collagen). However, a remaining challenge is the growth of large-sized constructs with properties similar to those of small constructs, due to consumption and transport limitations resulting in inadequate nutrient availability within the interior of large constructs. This study employed system-specific computational models for estimating glucose requirements of large constructs, with or without channels, to enhance nutrient availability. Based on glucose requirements for matrix synthesis in cartilage constructs, computational simulations were performed to identify the media volume (MV) and the number of nutrient channels (CH) needed to maintain adequate glucose levels within tissue constructs over the 3-day period between media replenishments. In Study 1, the influence of MV (5, 10, 15 mL/construct) and number of nutrient channels (CH: 0, 3, 7, 12 per construct) on glucose availability was investigated computationally for ∅10 × 2.34 mm cylindrical constructs. Results showed that the conventionally used MV 5 led to deleterious glucose depletion after only 40 h of culture, and that MV 15 was required to maintain sufficient glucose levels for all channel configurations. Study 2 examined experimentally the validity of these predictions, for tissue constructs cultured for 56 days. Matrix elaboration was highest in MV 15/CH 12 constructs (21.6% ± 2.4%/ww GAG, 5.5% ± 0.7%/ww collagen, normalized to wet weight (ww) on day 0), leading to the greatest amount of swelling (3.0 ± 0.3 times day-0 volume), in contrast to the significantly lower matrix elaboration of conventional culture, MV 5/CH 0 (11.8% ± 1.6%/ww GAG and 2.5% ± 0.6%/ww collagen, 1.6 ± 0.1 times day-0 volume). The computational analyses correctly predicted the need to increase the conventional media levels threefold to support matrix synthesis in large channeled engineered constructs. Results also suggested that more elaborate computational models are needed for accurate predictive tissue engineering simulations, which account for a broader set of nutrients, cell proliferation, matrix synthesis, and swelling of the constructs.

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.

Computational modeling of chemical reactions and interstitial growth and remodeling involving charged solutes and solid-bound molecules

Mechanobiological processes are rooted in mechanics and chemistry, and such processes may be modeled in a framework that couples their governing equations starting from fundamental principles. In many biological applications, the reactants and products of chemical reactions may be electrically charged, and these charge effects may produce driving forces and constraints that significantly influence outcomes. In this study, a novel formulation and computational implementation are presented for modeling chemical reactions in biological tissues that involve charged solutes and solid-bound molecules within a deformable porous hydrated solid matrix, coupling mechanics with chemistry while accounting for electric charges. The deposition or removal of solid-bound molecules contributes to the growth and remodeling of the solid matrix; in particular, volumetric growth may be driven by Donnan osmotic swelling, resulting from charged molecular species fixed to the solid matrix. This formulation incorporates the state of strain as a state variable in the production rate of chemical reactions, explicitly tying chemistry with mechanics for the purpose of modeling mechanobiology. To achieve these objectives, this treatment identifies the specific theoretical and computational challenges faced in modeling complex systems of interacting neutral and charged constituents while accommodating any number of simultaneous reactions where reactants and products may be modeled explicitly or implicitly. Several finite element verification problems are shown to agree with closed-form analytical solutions. An illustrative tissue engineering analysis demonstrates tissue growth and swelling resulting from the deposition of chondroitin sulfate, a charged solid-bound molecular species. This implementation is released in the open-source program FEBio ( www.febio.org ). The availability of this framework may be particularly beneficial to optimizing tissue engineering culture systems by examining the influence of nutrient availability on the evolution of inhomogeneous tissue composition and mechanical properties, the evolution of construct dimensions with growth, the influence of solute and solid matrix electric charge on the transport of cytokines, the influence of binding kinetics on transport, the influence of loading on binding kinetics, and the differential growth response to dynamically loaded versus free-swelling culture conditions.

Mass transfer analysis of growth and substance metabolism of NSCs cultured in collagen-based scaffold in vitro

The aim of this study is to analyze the growth and substance metabolism of neural stem cells (NSCs) cultured in biological collagen-based scaffolds. Mass transfer and metabolism model of glucose, lactic acid, and dissolved oxygen (DO) were established and solved on MATLAB platform to obtain the concentration distributions of DO, glucose, and lactic acid in culture system, respectively. Calculation results showed that the DO influenced their normal growth and metabolism of NSCs mostly in the in vitro culture within collagen-based scaffolds. This study also confirmed that 2-mm thickness of collagen scaffold was capable of in vitro cultivation and growth of NSCs with an inoculating density of 1 × 10(6) cells/mL.

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.

Synthesis rates and binding kinetics of matrix products in engineered cartilage constructs using chondrocyte-seeded agarose gels

Large-sized cartilage constructs suffer from inhomogeneous extracellular matrix deposition due to insufficient nutrient availability. Computational models of nutrient consumption and tissue growth can be utilized as an efficient alternative to experimental trials to optimize the culture of large constructs; models require system-specific growth and consumption parameters. To inform models of the [bovine chondrocyte]-[agarose gel] system, total synthesis rate (matrix accumulation rate+matrix release rate) and matrix retention fractions of glycosaminoglycans (GAG), collagen, and cartilage oligomeric matrix protein (COMP) were measured either in the presence (continuous or transient) or absence of TGF-β3 supplementation. TGF-β3's influences on pyridinoline content and mechanical properties were also measured. Reversible binding kinetic parameters were characterized using computational models. Based on our recent nutrient supplementation work, we measured glucose consumption and critical glucose concentration for tissue growth to computationally simulate the culture of a human patella-sized tissue construct, reproducing the experiment of Hung et al. (2003). Transient TGF-β3 produced the highest GAG synthesis rate, highest GAG retention ratio, and the highest binding affinity; collagen synthesis was elevated in TGF-β3 supplementation groups over control, with the highest binding affinity observed in the transient supplementation group; both COMP synthesis and retention were lower than those for GAG and collagen. These results informed the modeling of GAG deposition within a large patella construct; this computational example was similar to the previous experimental results without further adjustments to modeling parameters. These results suggest that these nutrient consumption and matrix synthesis models are an attractive alternative for optimizing the culture of large-sized constructs.

Computational model for oxygen transport and consumption in human vitreous

PURPOSE

Previous studies that measured liquefaction and oxygen content in human vitreous suggested that exposure of the lens to excess oxygen causes nuclear cataracts. Here, we developed a computational model that reproduced available experimental oxygen distributions for intact and degraded human vitreous in physiologic and environmentally perturbed conditions. After validation, the model was used to estimate how age-related changes in vitreous physiology and structure alter oxygen levels at the lens.

METHODS

A finite-element model for oxygen transport and consumption in the human vitreous was created. Major inputs included ascorbate-mediated oxygen consumption in the vitreous, consumption at the posterior lens surface, and inflow from the retinal vasculature. Concentration-dependent relations were determined from experimental human data or estimated from animal studies, with the impact of all assumptions explored via parameter studies.

RESULTS

The model reproduced experimental data in humans, including oxygen partial pressure (Po2) gradients (≈15 mm Hg) across the anterior-posterior extent of the vitreous body, higher oxygen levels at the pars plana relative to the vitreous core, increases in Po2 near the lens after cataract surgery, and equilibration in the vitreous chamber following vitrectomy. Loss of the antioxidative capacity of ascorbate increases oxygen levels 3-fold at the lens surface. Homogeneous vitreous degeneration (liquefaction), but not partial posterior vitreous detachment, greatly increases oxygen exposure to the lens.

CONCLUSIONS

Ascorbate content and the structure of the vitreous gel are critical determinants of lens oxygen exposure. Minimally invasive surgery and restoration of vitreous structure warrant further attention as strategies for preventing nuclear cataracts.

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.

Interstitial growth and remodeling of biological tissues: tissue composition as state variables

Growth and remodeling of biological tissues involves mass exchanges between soluble building blocks in the tissue's interstitial fluid and the various constituents of cells and the extracellular matrix. As the content of these various constituents evolves with growth, associated material properties, such as the elastic modulus of the extracellular matrix, may similarly evolve. Therefore, growth theories may be formulated by accounting for the evolution of tissue composition over time in response to various biological and mechanical triggers. This approach has been the foundation of classical bone remodeling theories that successfully describe Wolff's law by establishing a dependence between Young's modulus and bone apparent density and by formulating a constitutive relation between bone mass supply and the state of strain. The goal of this study is to demonstrate that adding tissue composition as state variables in the constitutive relations governing the stress-strain response and the mass supply represents a very general and straightforward method to model interstitial growth and remodeling in a wide variety of biological tissues. The foundation for this approach is rooted in the framework of mixture theory, which models the tissue as a mixture of multiple solid and fluid constituents. A further generalization is to allow each solid constituent in a constrained solid mixture to have its own reference (stress-free) configuration. Several illustrations are provided, ranging from bone remodeling to cartilage tissue engineering and cervical remodeling during pregnancy.

Influence of tissue- and cell-scale extracellular matrix distribution on the mechanical properties of tissue-engineered cartilage

The insufficient load-bearing capacity of today's tissue- engineered (TE) cartilage limits its clinical application. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the load-bearing properties of the cartilage. However, there are apparent inconsistencies in the literature regarding the correlation between ECM content and mechanical properties of TE constructs. In addition to the amount of ECM, the spatial inhomogeneities in ECM distribution at the tissue scale as well as at the cell scale may affect the mechanical properties of TE cartilage. The relative importance of such structural inhomogeneities on mechanical behavior of TE cartilage is unknown. The aim of the present study was, therefore, to theoretically elucidate the influence of these inhomogeneities on the mechanical behavior of chondrocyte-agarose TE constructs. A validated non-linear fiber-reinforced poro-elastic swelling cartilage model that can accommodate for effects of collagen reinforcement and swelling by proteoglycans was used. At the tissue scale, ECM was gradually varied from predominantly localized in the periphery of the TE construct toward an ECM-rich inner core. The effect of these inhomogeneities in relation to the total amount of ECM was also evaluated. At the cell scale, ECM was gradually varied from localized in the pericellular area, toward equally distributed throughout the interterritorial area. Results from the tissue-scale model indicated that localization of ECM in either the construct periphery or in the inner core may reduce construct stiffness compared with that of constructs with homogeneous ECM. Such effects are more significant at high ECM amounts. At the cell scale, localization of ECM around the cells significantly reduced the overall stiffness, even at low ECM amounts. The compressive stiffness gradually increased when ECM distribution became more homogeneous and the osmotic swelling pressure in the interterritorial area increased. We conclude that for the same amount of ECM content in TE cartilage constructs, superior mechanical properties can be achieved with more homogeneous ECM distribution at both tissue and cell scale. Inhomogeneities at the cell scale are more important than those at the tissue scale.

Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Finite element model for nutrient distribution analysis of a hollow fiber membrane bioreactor

Hollow fiber membrane bioreactors (HFMB) are extensively used for the development of tissue substitutes for bones and cartilages. In an HFMB, the nutrient transport is dependent on the material properties of the porous scaffold and fiber membrane and also on the fluid flow through the hollow fiber. The difficulty in obtaining real-time data along with the presence of large number of variables in experimental studies have lead to increased application of computational models for the performance analysis of bioreactors. A major difficulty in the computational analysis of HFMB is the modeling of the interactions at the fluid and porous scaffold interfaces, which has often been neglected or incorporated using specific boundary conditions. In this study, a new FEM is developed to analyze the fluid flow in the fluid-porous region with the interface coupled directly into the FEM. Distribution of nutrients in the bioreactor is studied by coupling mass transport equations to the fluid-porous finite element framework. The new model is implemented to study the influence of permeability, cell density, and flow rate on the nutrient concentration distribution in the HFMB. The developed computational framework is an ideal tool to study fluid flow through porous-open channels and can also be used for the design of bioreactors for optimal tissue growth.

Hypoxic culture and insulin yield improvements to fibrin-based engineered tissue

We examined the effect of insulin supplementation and hypoxic culture (2% vs. 20% oxygen tension) on collagen deposition and mechanical properties of fibrin-based tubular tissue constructs seeded with neonatal human dermal fibroblasts. The results presented here demonstrate that constructs cultured under hypoxic conditions with insulin supplementation increased in collagen density by approximately five-fold and both the ultimate tensile strength (UTS) and modulus by more than three-fold compared with normoxic (20% oxygen tension), noninsulin supplemented controls. In addition, collagen deposited on a per-cell basis increased by approximately four-fold. Interaction was demonstrated for hypoxia and insulin in combination in terms of UTS and collagen production on a per-cell basis. This interaction resulted from two distinct processes involved in collagen fibril formation. Western blot analysis showed that insulin supplementation alone increased Akt phosphorylation and the combined treatment increased collagen prolyl-4-hydroxylase. These molecules are distinct regulators of collagen deposition, having an impact at both the transcriptional and posttranslational modification stages of collagen fibril formation that, in turn, increase collagen density in the tissue constructs. These findings highlight the potential of utilizing insulin supplementation and hypoxic culture in combination to increase the mechanical strength and stiffness of fibrin-based engineered tissues.

Fetal development, mechanobiology and optimal control processes can improve vascular tissue regeneration in bioreactors: an integrative review

Vascular tissue engineering aims to regenerate blood vessels to replace diseased arteries for cardiovascular patients. With the scaffold-based approach, cells are seeded on a scaffold showing specific properties and are expected to proliferate and self-organize into a functional vascular tissue. Bioreactors can significantly contribute to this objective by providing a suitable environment for the maturation of the tissue engineered blood vessel. It is recognized from the mechanotransduction principles that mechanical stimuli can influence the protein synthesis of the extra-cellular matrix thus leading to maturation and organization of the tissues. Up to date, no bioreactor is especially conceived to take advantage of the mechanobiology and optimize the construct maturation through an advanced control strategy. In this review, experimental strategies in the field of vascular tissue engineering are detailed, and a new approach inspired by fetal development, mechanobiology and optimal control paradigms is proposed. In this new approach, the culture conditions (i.e. flow, circumferential strain, pressure frequency, and others) are supposed to dynamically evolve to match the maturity of vascular constructs and maximize the efficiency of the regeneration process. Moreover, this approach allows the investigation of the mechanisms of growth, remodeling and mechanotransduction during the culture.

Tissue engineering of functional articular cartilage: the current status

Osteoarthritis is a degenerative joint disease characterized by pain and disability. It involves all ages and 70% of people aged >65 have some degree of osteoarthritis. Natural cartilage repair is limited because chondrocyte density and metabolism are low and cartilage has no blood supply. The results of joint-preserving treatment protocols such as debridement, mosaicplasty, perichondrium transplantation and autologous chondrocyte implantation vary largely and the average long-term result is unsatisfactory. One reason for limited clinical success is that most treatments require new cartilage to be formed at the site of a defect. However, the mechanical conditions at such sites are unfavorable for repair of the original damaged cartilage. Therefore, it is unlikely that healthy cartilage would form at these locations. The most promising method to circumvent this problem is to engineer mechanically stable cartilage ex vivo and to implant that into the damaged tissue area. This review outlines the issues related to the composition and functionality of tissue-engineered cartilage. In particular, the focus will be on the parameters cell source, signaling molecules, scaffolds and mechanical stimulation. In addition, the current status of tissue engineering of cartilage will be discussed, with the focus on extracellular matrix content, structure and its functionality.

Microplate-reader compatible perfusion microbioreactor array for modular tissue culture and cytotoxicity assays

One important application of tissue engineering is to provide novel in vitro models for cell-based assays. Perfusion microbioreactor array provides a useful tool for microscale tissue culture in parallel. However, high-throughput data generation has been a challenge. In this study, a 4 x 4 array of perfusion microbioreactors was developed for plate-reader compatible, time-series quantification of cell proliferation, and cytotoxicity assays. The device was built through multilayer soft lithography. Low-cost nonwoven polyethylene terephthalate fibrous matrices were integrated as modular tissue culture scaffolds. Human colon cancer HT-29 cells with stable expression of enhanced green fluorescent protein were cultured in the device with continuous perfusion and reached a cell density over 5 x 10(7) cells/mL. The microbioreactor array was used to test a chemotherapeutic drug 5-FU for its effect on HT-29 cells in continuous perfusion 3D culture. Compared with conventional 2D cytotoxicity assay, significant drug resistance was observed in the 3D perfusion culture.

Controlling matrix formation and cross-linking by hypoxia in cardiovascular tissue engineering

In vivo functionality of cardiovascular tissue engineered constructs requires in vitro control of tissue development to obtain a well developed extracellular matrix (ECM). We hypothesize that ECM formation and maturation is stimulated by culturing at low oxygen concentrations. Gene expression levels of monolayers of human vascular-derived myofibroblasts, exposed to 7, 4, 2, 1, and 0.5% O(2) (n = 9 per group) for 24 h, were measured for vascular endothelial growth factor (VEGF), procollagen α1(I) and α1(III), elastin, and cross-link enzymes lysyl oxidase (LOX) and lysyl hydroxylase 2 (LH2). After 4 days of exposure to 7, 2, and 0.5% O(2) (n = 3 per group), protein synthesis was evaluated. All analyses were compared with control cultures at 21% O(2). Human myofibroblasts turned to hypoxia-driven gene expression, indicated by VEGF expression, at oxygen concentrations of 4% and lower. Gene expression levels of procollagen α1(I) and α1(III) increased to 138 ± 26 and 143 ± 19%, respectively, for all oxygen concentrations below 4%. At 2% O(2), LH2 and LOX gene expression levels were higher than control cultures (340 ± 53 and 136 ± 29%, respectively), and these levels increased even further with decreasing oxygen concentrations (611 ± 176 and 228 ± 45%, respectively, at 0.5% O(2)). Elastin gene expression levels remained unaffected. Collagen synthesis and LH2 protein levels increased at oxygen concentrations of 2% and lower. Oxygen concentrations below 4% induce enhanced ECM production by human myofibroblasts. Implementation of these results in cardiovascular tissue engineering approaches enables in vitro control of tissue development.

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.

Windows of operation for bioreactor design for the controlled formation of tissue-engineered arteries

The availability of large numbers of units of artificial arteries would offer significant benefits to the clinical management of bypass surgery. Tissue engineering offers the potential of providing vessels that can mimic the morphology, function, and physiological environment of native vessels. Ideally this would involve culturing stem cells in vitro within a biodegradable tubular scaffold so as to construct tissue for implantation. Essential to establishing a robust process for the production of tissue-engineered arteries is the understanding of the impact of changes in the operating conditions and bioreactor design on the construct formation. In this article, models of transport phenomena were developed to predict the critical flow rates and mass transfer requirements of a prototype bioreactor for the formation of tissue-engineered arteries. The impact of the cell concentration, tube geometry, oxygen effective diffusivity in alginate, substrate and metabolite concentration levels, feed rate, and recycle rate on the design of the bioreactor was visualized using windows of operation and contour plots. The result of this analysis determined the best configuration of the bioreactor that meets the cellular transport requirements as well as being reliable in performance while seeking to reduce the amount of nutrients to be used.

A double-chamber rotating bioreactor for the development of tissue-engineered hollow organs: from concept to clinical trial

Cell and tissue engineering are now being translated into clinical organ replacement, offering alternatives to fight morbidity, organ shortages and ethico-social problems associated with allotransplantation. Central to the recent first successful use of stem cells to create an organ replacement in man was our development of a bioreactor environment. Critical design features were the abilities to drive the growth of two different cell types, to support 3D maturation, to maintain biomechanical and biological properties and to provide appropriate hydrodynamic stimuli and adequate mass transport. An analytical model was developed and applied to predict oxygen profiles in the bioreactor-cultured organ construct and in the culture media, comparing representative culture configurations and operating conditions. Autologous respiratory epithelial cells and mesenchymal stem cells (BMSCs, then differentiated into chondrocytes) were isolated, characterized and expanded. Both cell types were seeded and cultured onto a decellularized human donor tracheal matrix within the bioreactor. One year post-operatively, graft and patient are healthy, and biopsies confirm angiogenesis, viable epithelial cells and chondrocytes. Our rotating double-chamber bioreactor permits the efficient repopulation of a decellularized human matrix, a concept that can be applied clinically, as demonstrated by the successful tracheal transplantation.

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.