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.

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.

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.

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.

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.