Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion: a continuum model of matrix metabolism and transport

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.

Systems Based Study of the Therapeutic Potential of Small Charged Molecules for the Inhibition of IL-1 Mediated Cartilage Degradation

Inflammatory cytokines are key drivers of cartilage degradation in post-traumatic osteoarthritis. Cartilage degradation mediated by these inflammatory cytokines has been extensively investigated using in vitro experimental systems. Based on one such study, we have developed a computational model to quantitatively assess the impact of charged small molecules intended to inhibit IL-1 mediated cartilage degradation. We primarily focus on the simplest possible computational model of small molecular interaction with the IL-1 system-direct binding of the small molecule to the active site on the IL-1 molecule itself. We first use the model to explore the uptake and release kinetics of the small molecule inhibitor by cartilage tissue. Our results show that negatively charged small molecules are excluded from the negatively charged cartilage tissue and have uptake kinetics in the order of hours. In contrast, the positively charged small molecules are drawn into the cartilage with uptake and release timescales ranging from hours to days. Using our calibrated computational model, we subsequently explore the effect of small molecule charge and binding constant on the rate of cartilage degradation. The results from this analysis indicate that the small molecules are most effective in inhibiting cartilage degradation if they are either positively charged and/or bind strongly to IL-1α, or both. Furthermore, our results showed that the cartilage structural homeostasis can be restored by the small molecule if administered within six days following initial tissue exposure to IL-1α. We finally extended the scope of the computational model by simulating the competitive inhibition of cartilage degradation by the small molecule. Results from this model show that small molecules are more efficient in inhibiting cartilage degradation by binding directly to IL-1α rather than binding to IL-1α receptors. The results from this study can be used as a template for the design and development of more pharmacologically effective osteoarthritis drugs, and to investigate possible therapeutic options.

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

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

Modeling IL-1 induced degradation of articular cartilage

In this study, we develop a computational model to simulate the in vitro biochemical degradation of articular cartilage explants sourced from the femoropatellar grooves of bovine calves. Cartilage explants were incubated in culture medium with and without the inflammatory cytokine IL-1α. The spatio-temporal evolution of the cartilage explant's extracellular matrix components is modelled. Key variables in the model include chondrocytes, aggrecan, collagen, aggrecanase, collagenase and IL-1α. The model is first calibrated for aggrecan homeostasis of cartilage in vivo, then for data on (explant) controls, and finally for data on the IL-1α driven proteolysis of aggrecan and collagen over a 4-week period. The model was found to fit the experimental data best when: (i) chondrocytes continue to synthesize aggrecan during the cytokine challenge, (ii) a one to two day delay is introduced between the addition of IL-1α to the culture medium and subsequent aggrecanolysis, (iii) collagen degradation does not commence until the total concentration of aggrecan (i.e. both intact and degraded aggrecan) at any specific location within the explant becomes ≤ 1.5 mg/ml and (iv) degraded aggrecan formed due to the IL-1α induced proteolysis of intact aggrecan protects the collagen network while collagen degrades in a two-step process which, together, significantly modulate the collagen network degradation. Under simulated in vivo conditions, the model predicts increased aggrecan turnover rates in the presence of synovial IL-1α, consistent with experimental observations. Such models may help to infer the course of events in vivo following traumatic joint injury, and may also prove useful in quantitatively evaluating the efficiency of various therapeutic molecules that could be employed to avoid or modify the course of cartilage disease states.

Trends in biological joint resurfacing

The treatment of osteochondral lesions and osteoarthritis remains an ongoing clinical challenge in orthopaedics. This review examines the current research in the fields of cartilage regeneration, osteochondral defect treatment, and biological joint resurfacing, and reports on the results of clinical and pre-clinical studies. We also report on novel treatment strategies and discuss their potential promise or pitfalls. Current focus involves the use of a scaffold providing mechanical support with the addition of chondrocytes or mesenchymal stem cells (MSCs), or the use of cell homing to differentiate the organism’s own endogenous cell sources into cartilage. This method is usually performed with scaffolds that have been coated with a chemotactic agent or with structures that support the sustained release of growth factors or other chondroinductive agents. We also discuss unique methods and designs for cell homing and scaffold production, and improvements in biological joint resurfacing. There have been a number of exciting new studies and techniques developed that aim to repair or restore osteochondral lesions and to treat larger defects or the entire articular surface. The concept of a biological total joint replacement appears to have much potential.

Cite this article: Bone Joint Res 2013;2:193–9.

Novel strategies to engineering biological tissue in vitro

Tissue engineering creates biological tissues that aim to improve the function of diseased or damaged tissues. In this chapter, we examine the promise and shortcomings of "top-down" and "bottom-up" approaches for creating engineered biological tissues. In top-down approaches, the cells are expected to populate the scaffold and create the appropriate extracellular matrix and microarchitecture often with the aid of a bioreactor that furnish the set of stimuli required for an optimal cellular viability. Specifically, we survey the role of cell material interaction on oxygen metabolism in three-dimensional (3D) in vitro cultures as well as the time and space evolution of the transport and biophysical properties during the development of de novo synthesized tissue-engineered constructs. We show how to monitor and control the evolution of these parameters that is of crucial importance to process biohybrid constructs in vitro as well as to elaborate reliable mathematical model to forecast tissue growth under specific culture conditions. Furthermore, novel strategies such as bottom-up approaches to build tissue constructs in vitro are examined. In this fashion, tissue building blocks with specific microarchitectural features are used as modular units to engineer biological tissues from the bottom up. In particular, the attention will be focused on the use of cell seeded microbeads as functional building blocks to realize 3D complex tissue. Finally, a challenge will be the potential integration of bottom-up techniques with more traditional top-down approaches to create more complex tissues than are currently achievable using either technique alone by optimizing the advantages of each technique.

A systems biology approach to synovial joint lubrication in health, injury, and disease

The synovial joint contains synovial fluid (SF) within a cavity bounded by articular cartilage and synovium. SF is a viscous fluid that has lubrication, metabolic, and regulatory functions within synovial joints. SF contains lubricant molecules, including proteoglycan-4 and hyaluronan. SF is an ultrafiltrate of plasma with secreted contributions from cell populations lining and within the synovial joint space, including chondrocytes and synoviocytes. Maintenance of normal SF lubricant composition and function are important for joint homeostasis. In osteoarthritis, rheumatoid arthritis, and joint injury, changes in lubricant composition and function accompany alterations in the cytokine and growth factor environment and increased fluid and molecular transport through joint tissues. Thus, understanding the synovial joint lubrication system requires a multifaceted study of the various parts of the synovial joint and their interactions. Systems biology approaches at multiple scales are being used to describe the molecular, cellular, and tissue components and their interactions that comprise the functioning synovial joint. Analyses of the transcriptome and proteome of SF, cartilage, and synovium suggest that particular molecules and pathways play important roles in joint homeostasis and disease. Such information may be integrated with physicochemical tissue descriptions to construct integrative models of the synovial joint that ultimately may explain maintenance of health, recovery from injury, or development and progression of arthritis.

Novel Cell Culture Model Using Pure Hydrostatic Pressure and a Semipermeable Membrane Pouch

Cell constructs and culture methods are essential tools in tissue engineering. The cell construct should be equivalent to the native cartilage it is intended to replace. Thus, three-dimensional cell constructs are usually composed of a high density of cells and dense extracellular matrix. However, dense constructs suffer from a lack of passive nutrient supply, gas exchange, and removal of degraded debris. We have developed a novel hydrostatic pressure/perfusion culture system that improves the quality of neo-tissues, providing an automated and affordable system for clinical applications. We have also developed a semipermeable membrane pouch that contains a fragile amorphous cell carrier. Although amorphous material is difficult to handle, it is a useful medium in which to deliver cells to the desired site via injection. We evaluated phenotypes of bovine articular chondrocytes embedded in a collagen type I gel enclosed within membrane pouches permeable to molecules of various sizes. Constant or cyclic hydrostatic pressure was externally applied to the medium phase with a new culture system. Accumulation of cartilage specific matrix was promoted with a 500-kDa cutoff membrane pouch and cyclic hydrostatic pressure at 0.5 MPa, 0.5 Hz. This new method will be useful in the delivery of engineered cells to a desired tissue in regenerative medicine.

A validated model of GAG deposition, cell distribution, and growth of tissue engineered cartilage cultured in a rotating bioreactor

In this work a new phenomenological model of growth of cartilage tissue cultured in a rotating bioreactor is developed. It represents an advancement of a previously derived model of deposition of glycosaminoglycan (GAG) in engineered cartilage by (i) introduction of physiological mechanisms of proteoglycan accumulation in the extracellular matrix (ECM) as well as by correlating (ii) local cell densities and (iii) tissue growth to the ECM composition. In particular, previously established predictions and correlations of local oxygen concentrations and GAG synthesis rates are extended to distinguish cell secreted proteoglycan monomers free to diffuse in cell surroundings and outside from the engineered construct, from large aggrecan molecules, which are constrained within the ECM and practically immovable. The model includes kinetics of aggregation, that is, transformation of mobile GAG species into immobile aggregates as well as maintenance of the normal ECM composition after the physiological GAG concentration is reached by incorporation of a product inhibition term. The model also includes mechanisms of the temporal evolution of cell density distributions and tissue growth under in vitro conditions. After a short initial proliferation phase the total cell number in the construct remains constant, but the local cell distribution is leveled out by GAG accumulation and repulsion due to negative molecular charges. Furthermore, strong repulsive forces result in expansion of the local tissue elements observed macroscopically as tissue growth (i.e., construct enlargement). The model is validated by comparison with experimental data of (i) GAG distribution and leakage, (ii) spatial-temporal distributions of cells, and (iii) tissue growth reported in previous works. Validation of the model predictive capability--against a selection of measured data that were not used to construct the model--suggests that the model successfully describes the interplay of several simultaneous processes carried out during in vitro cartilage tissue regeneration and indicates that this approach could also be attractive for application in other tissue engineering systems.

Bioengineering cartilage growth, maturation, and form

Cartilage of articular joints grows and matures to achieve characteristic sizes, forms, and functional properties. Through these processes, the tissue not only serves as a template for bone growth but also yields mature articular cartilage providing joints with a low-friction, wear-resistant bearing material. The study of cartilage growth and maturation is a focus of both cartilage biologists and bioengineers with one goal of trying to create biologic tissue substitutes for the repair of damaged joints. Experimental approaches both in vivo and in vitro are being used to better understand the mechanisms and regulation of growth and maturation processes. This knowledge may facilitate the controlled manipulation of cartilage size, shape, and maturity to meet the criteria needed for successful clinical applications. Mathematical models are also useful tools for quantitatively describing the dynamically changing composition, structure and function of cartilage during growth and maturation and may aid the development of tissue engineering solutions. Recent advances in methods of cartilage formation and culture which control the size, shape, and maturity of these tissues are numerous and provide contrast to the physiologic development of cartilage.

Theoretical analysis of engineered cartilage oxygenation: influence of construct thickness and media flow rate

A novel parallel-plate bioreactor has been shown to modulate the mechanical and biochemical properties of engineered cartilage by the application of fluid-induced shear stress. Flow or perfusion bioreactors may improve tissue development via enhanced transport of nutrients or gases as well as the application of mechanical stimuli, or a combination of these factors. The goal of this study was to complement observed experimental responses to flow by simulating oxygen transport within cartilage constructs of different thicknesses (250 microm or 1 mm). Using numerical computation of convection-diffusion equations, the evaluation of the tissue oxygenation is performed. Four culture conditions are defined based on tissue thickness and flow rates ranging from 0 to approximately 25 mL min(-1). Under these experimental conditions results show a mean oxygen concentration within the tissue varying from 0.01 to 0.19 mol m(-3) as a function of the tissue thickness and the magnitude of the applied shear stress. More generally, the influence of shear stress varying (via flow rate modification) from 10(-3) to 10 dynes cm(-2) on the tissue oxygenation is studied. The influence on the results of important physical parameters such as the maximal oxygen consumption rate of cells is discussed. Lastly, the importance of oxygen concentration in the lower chamber and its relevance to tissue oxygenation are highlighted by the model results.