Tuning tissue growth with scaffold degradation in enzyme-sensitive hydrogels: a mathematical model.

Despite tremendous advances in the field of tissue engineering, a number of obstacles remain that hinder its successful translation to the clinic. One challenge that relates to the use of cells encapsulated in a hydrogel is identifying a hydrogel design that can provide an appropriate environment for cells to successfully synthesize and deposit new matrix molecules while providing a mechanical support that can resist physiological loads at the early stage of implementation. A solution to this problem has been to balance tissue growth and hydrogel degradation. However, identifying this balance is difficult due to the complexity of coupling diffusion, deposition, and degradation mechanisms. Very little is known about the complex behavior of these mechanisms, emphasizing the need for a rigorous mathematical approach that can assist and guide experimental advances. To address this issue, this paper discusses a model for interstitial growth based on mixture theory, that can capture the coupling between cell-mediated hydrogel degradation (i.e., hydrogels containing enzyme-sensitive crosslinks) and the transport of extracellular matrix (ECM) molecules released by encapsulated cells within a hydrogel. Taking cartilage tissue engineering as an example, the model investigates the role of enzymatic degradation on ECM diffusion and its impact on two important outcomes: the extent of ECM transport (and deposition) and the evolution of the hydrogel's mechanical integrity. Numerical results based on finite element analysis show that if properly tuned, enzymatic degradation yields the appearance of a highly localized degradation front propagating away from the cell, which can be immediately followed by a front of growing neotissue. We show that this situation is key to maintaining mechanical properties (e.g., stiffness) while allowing for deposition of new ECM molecules. Overall, our study suggests a hydrogel design that could enable successful tissue engineering (e.g., of cartilage, bone, etc.) where mechanical integrity is important.

Determination of the Polymer-Solvent Interaction Parameter for PEG Hydrogels in Water: Application of a Self Learning Algorithm.

Concentrating on the case of poly(ethylene glycol) hydrogels, this paper introduces a methodology that enables a natural integration between the development of a so-called mechanistic model and experimental data relating material's processing to response. In a nutshell, we develop a data-driven modeling component that is able to learn and indirectly infer its own parameters and structure by observing experimental data. Using this method, we investigate the relationship between processing conditions, microstructure and chemistry (cross-link density and polymer-solvent interactions) and response (swelling and elasticity) of non-degradable and degradable PEG hydrogels. We show that the method not only enables the determination of the polymer-solvent interaction parameter, but also it predicts that this parameter, among others, varies with processing conditions and degradation. The proposed methodology therefore offers a new approach that accounts for subtle changes in the hydrogel processing.

* Understanding the Spatiotemporal Degradation Behavior of Aggrecanase-Sensitive Poly(ethylene glycol) Hydrogels for Use in Cartilage Tissue Engineering.

Enzyme-sensitive hydrogels are promising cell delivery vehicles for cartilage tissue engineering. However, a better understanding of their spatiotemporal degradation behavior and its impact on tissue growth is needed. The goal of this study was to combine experimental and computational approaches to provide new insights into spatiotemporal changes in hydrogel crosslink density and extracellular matrix (ECM) growth and how these changes influence the evolving macroscopic properties as a function of time. Hydrogels were designed from aggrecanase-sensitive peptide crosslinks using a simple and robust thiol-norbornene photoclick reaction. To study the influence of variations in cellular activity of different donors, chondrocytes were isolated from either juvenile or adult bovine donors. Initial studies were performed to validate and calibrate the model against experiments. Through this process, two key features were identified. These included spatial variations in the hydrogel crosslink density in the immediate vicinity of the cell and the presence of cell clustering within the construct. When these spatial heterogeneities were incorporated into the computational model along with model inputs of initial hydrogel properties and cellular activity (i.e., enzyme and ECM production rates), the model was able to capture the spatial and temporal evolution of ECM growth that was observed experimentally for both donors. In this study, the juvenile chondrocytes produced an interconnected matrix within the cell clusters leading to overall improved ECM growth, while the adult chondrocytes resulted in poor ECM growth. Overall, the computational model was able to capture the spatiotemporal ECM growth of two different donors and provided new insights into the importance of spatial heterogeneities in facilitating ECM growth. Our long-term goal is to use this model to predict optimal hydrogel designs for a wide range of donors and improve cartilage tissue engineering.

Structural Modeling of Mechanosensitivity in Non-Muscle Cells: Multiscale Approach to Understand Cell Sensing.

The contraction and spreading of nonmuscle cells are important phenomena in a number of cellular processes such as differentiation, morphogenesis, and tissue growth. Recent experimental work has shown that the topology and the mechanical properties of the underlying substrate play a significant role in directing the cell's response. In this work, we introduce a multiscale model to understand the sensing, activation, and contraction of the actin cytoskeleton of nonmuscle cells based on the idea that acto-myosin cross-bridges display a catch-bond response. After investigating the respective roles of bond catchiness and acto-myosin assembly on the mechano-sensitivity of stress fibers, we present full simulations of cells laying on arrays of micropillars. Model predictions show good qualitative agreements with experimental observation, suggesting that acto-myosin catch bonds are a major mechano-sensing element in nonmuscle cells.

Role of catch bonds in actomyosin mechanics and cell mechanosensitivity.

We propose a mechanism of adherent cell mechanosensing, based on the idea that the contractile actomyosin machinery behaves as a catch bond. For this, we construct a simplified model of the actomyosin structure that constitutes the building block of stress fibers and express the stability of cross bridges in terms of the force-dependent bonding energy of the actomyosin bond. Consistent with experimental measurements, we then consider that the energy barrier of the actomyosin bond increases for tension and show that this response is enough to explain the force-induced stabilization of a stress fiber. Further numerical simulations at the cellular level show that the catch-bond hypothesis can help in understanding and predict the sensitivity of adherent cells to substrate stiffness.

Tuning Reaction and Diffusion Mediated Degradation of Enzyme-Sensitive Hydrogels.

Enzyme-sensitive hydrogels are promising for cell encapsulation and tissue engineering, but result in complex spatiotemporal degradation behavior that is characteristic of reaction-diffusion mechanisms. An experimental and theoretical approach is presented to identify dimensionless quantities that serve as a design tool for engineering enzyme-sensitive hydrogels with controlled degradation patterns by tuning the initial hydrogel properties and enzyme kinetics.

On the role of hydrogel structure and degradation in controlling the transport of cell-secreted matrix molecules for engineered cartilage.

Damage to cartilage caused by injury or disease can lead to pain and loss of mobility, diminishing one's quality of life. Because cartilage has a limited capacity for self-repair, tissue engineering strategies, such as cells encapsulated in synthetic hydrogels, are being investigated as a means to restore the damaged cartilage. However, strategies to date are suboptimal in part because designing degradable hydrogels is complicated by structural and temporal complexities of the gel and evolving tissue along multiple length scales. To address this problem, this study proposes a multi-scale mechanical model using a triphasic formulation (solid, fluid, unbound matrix molecules) based on a single chondrocyte releasing extracellular matrix molecules within a degrading hydrogel. This model describes the key players (cells, proteoglycans, collagen) of the biological system within the hydrogel encompassing different length scales. Two mechanisms are included: temporal changes of bulk properties due to hydrogel degradation, and matrix transport. Numerical results demonstrate that the temporal change of bulk properties is a decisive factor in the diffusion of unbound matrix molecules through the hydrogel. Transport of matrix molecules in the hydrogel contributes both to the development of the pericellular matrix and the extracellular matrix and is dependent on the relative size of matrix molecules and the hydrogel mesh. The numerical results also demonstrate that osmotic pressure, which leads to changes in mesh size, is a key parameter for achieving a larger diffusivity for matrix molecules in the hydrogel. The numerical model is confirmed with experimental results of matrix synthesis by chondrocytes in biodegradable poly(ethylene glycol)-based hydrogels. This model may ultimately be used to predict key hydrogel design parameters towards achieving optimal cartilage growth.